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liquid crystalline materials</span> </div> </a> <ul id="toc-Design_of_liquid_crystalline_materials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liquid-crystal_phases" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Liquid-crystal_phases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Liquid-crystal phases</span> </div> </a> <button aria-controls="toc-Liquid-crystal_phases-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Liquid-crystal phases subsection</span> </button> <ul id="toc-Liquid-crystal_phases-sublist" class="vector-toc-list"> <li id="toc-Thermotropic_liquid_crystals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thermotropic_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Thermotropic liquid crystals</span> </div> </a> <ul id="toc-Thermotropic_liquid_crystals-sublist" class="vector-toc-list"> <li id="toc-Nematic_phase" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Nematic_phase"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Nematic phase</span> </div> </a> <ul id="toc-Nematic_phase-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Smectic_phases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Smectic_phases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Smectic phases</span> </div> </a> <ul id="toc-Smectic_phases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chiral_phases_or_twisted_nematics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Chiral_phases_or_twisted_nematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Chiral phases or twisted nematics</span> </div> </a> <ul id="toc-Chiral_phases_or_twisted_nematics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Blue_phases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Blue_phases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.4</span> <span>Blue phases</span> </div> </a> <ul id="toc-Blue_phases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discotic_phases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Discotic_phases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.5</span> <span>Discotic phases</span> </div> </a> <ul id="toc-Discotic_phases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conic_phases" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Conic_phases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.6</span> <span>Conic phases</span> </div> </a> <ul id="toc-Conic_phases-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Lyotropic_liquid_crystals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lyotropic_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Lyotropic liquid crystals</span> </div> </a> <ul id="toc-Lyotropic_liquid_crystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Metallotropic_liquid_crystals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Metallotropic_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Metallotropic liquid crystals</span> </div> </a> <ul id="toc-Metallotropic_liquid_crystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Laboratory_analysis_of_mesophases" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Laboratory_analysis_of_mesophases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Laboratory analysis of mesophases</span> </div> </a> <ul id="toc-Laboratory_analysis_of_mesophases-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Biological_liquid_crystals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Biological_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Biological liquid crystals</span> </div> </a> <ul id="toc-Biological_liquid_crystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mineral_liquid_crystals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Mineral_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Mineral liquid crystals</span> </div> </a> <ul id="toc-Mineral_liquid_crystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pattern_formation_in_liquid_crystals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Pattern_formation_in_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Pattern formation in liquid crystals</span> </div> </a> <ul id="toc-Pattern_formation_in_liquid_crystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theoretical_treatment_of_liquid_crystals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Theoretical_treatment_of_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Theoretical treatment of liquid crystals</span> </div> </a> <button aria-controls="toc-Theoretical_treatment_of_liquid_crystals-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Theoretical treatment of liquid crystals subsection</span> </button> <ul id="toc-Theoretical_treatment_of_liquid_crystals-sublist" class="vector-toc-list"> <li id="toc-Director" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Director"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Director</span> </div> </a> <ul id="toc-Director-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Order_parameter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Order_parameter"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Order parameter</span> </div> </a> <ul id="toc-Order_parameter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Onsager_hard-rod_model" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Onsager_hard-rod_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Onsager hard-rod model</span> </div> </a> <ul id="toc-Onsager_hard-rod_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maier–Saupe_mean_field_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Maier–Saupe_mean_field_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Maier–Saupe mean field theory</span> </div> </a> <ul id="toc-Maier–Saupe_mean_field_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-McMillan's_model" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#McMillan's_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5</span> <span>McMillan's model</span> </div> </a> <ul id="toc-McMillan's_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elastic_continuum_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elastic_continuum_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6</span> <span>Elastic continuum theory</span> </div> </a> <ul id="toc-Elastic_continuum_theory-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_influences_on_liquid_crystals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_influences_on_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External influences on liquid crystals</span> </div> </a> <button aria-controls="toc-External_influences_on_liquid_crystals-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle External influences on liquid crystals subsection</span> </button> <ul id="toc-External_influences_on_liquid_crystals-sublist" class="vector-toc-list"> <li id="toc-Electric_and_magnetic_field_effects" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electric_and_magnetic_field_effects"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Electric and magnetic field effects</span> </div> </a> <ul id="toc-Electric_and_magnetic_field_effects-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface_preparations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surface_preparations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Surface preparations</span> </div> </a> <ul id="toc-Surface_preparations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fréedericksz_transition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fréedericksz_transition"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Fréedericksz transition</span> </div> </a> <ul id="toc-Fréedericksz_transition-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Effect_of_chirality" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Effect_of_chirality"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Effect of chirality</span> </div> </a> <ul id="toc-Effect_of_chirality-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_of_liquid_crystals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications_of_liquid_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Applications of liquid crystals</span> </div> </a> <ul id="toc-Applications_of_liquid_crystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Liquid crystal</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" 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Available in 55 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-55" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">55 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D8%B1%D8%A9_%D8%B3%D8%A7%D8%A6%D9%84%D8%A9" title="بلورة سائلة – Arabic" lang="ar" hreflang="ar" data-title="بلورة سائلة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Maye_kristal" title="Maye kristal – Azerbaijani" lang="az" hreflang="az" data-title="Maye kristal" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%DB%8C%D8%B9_%DA%A9%D8%B1%DB%8C%D8%B3%D8%AA%D8%A7%D9%84" title="مایع کریستال – South Azerbaijani" lang="azb" hreflang="azb" data-title="مایع کریستال" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/E%CC%8Dk-cheng" title="E̍k-cheng – Minnan" lang="nan" hreflang="nan" data-title="E̍k-cheng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D0%B0%D0%B4%D0%BA%D1%96%D1%8F_%D0%BA%D1%80%D1%8B%D1%88%D1%82%D0%B0%D0%BB%D1%96" title="Вадкія крышталі – Belarusian" lang="be" hreflang="be" data-title="Вадкія крышталі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D1%87%D0%B5%D0%BD_%D0%BA%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB" title="Течен кристал – Bulgarian" lang="bg" hreflang="bg" data-title="Течен кристал" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cristall_l%C3%ADquid" title="Cristall líquid – Catalan" lang="ca" hreflang="ca" data-title="Cristall líquid" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kapaln%C3%BD_krystal" title="Kapalný krystal – Czech" lang="cs" hreflang="cs" data-title="Kapalný krystal" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Flydende_krystal" title="Flydende krystal – Danish" lang="da" hreflang="da" data-title="Flydende krystal" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fl%C3%BCssigkristall" title="Flüssigkristall – German" lang="de" hreflang="de" data-title="Flüssigkristall" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Vedelkristall" title="Vedelkristall – Estonian" lang="et" hreflang="et" data-title="Vedelkristall" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CE%B3%CF%81%CF%8C%CF%82_%CE%BA%CF%81%CF%8D%CF%83%CF%84%CE%B1%CE%BB%CE%BB%CE%BF%CF%82" title="Υγρός κρύσταλλος – Greek" lang="el" hreflang="el" data-title="Υγρός κρύσταλλος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cristal_l%C3%ADquido" title="Cristal líquido – Spanish" lang="es" hreflang="es" data-title="Cristal líquido" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Likva_kristalo" title="Likva kristalo – Esperanto" lang="eo" hreflang="eo" data-title="Likva kristalo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kristal_likido" title="Kristal likido – Basque" lang="eu" hreflang="eu" data-title="Kristal likido" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D8%B1%DB%8C%D8%B3%D8%AA%D8%A7%D9%84_%D9%85%D8%A7%DB%8C%D8%B9" title="کریستال مایع – Persian" lang="fa" hreflang="fa" data-title="کریستال مایع" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cristal_liquide" title="Cristal liquide – French" lang="fr" hreflang="fr" data-title="Cristal liquide" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Leachtchriostail" title="Leachtchriostail – Irish" lang="ga" hreflang="ga" data-title="Leachtchriostail" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cristal_l%C3%ADquido" title="Cristal líquido – Galician" lang="gl" hreflang="gl" data-title="Cristal líquido" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Yi%CC%8Dt-ch%C3%AEn" title="Yi̍t-chîn – Hakka Chinese" lang="hak" hreflang="hak" data-title="Yi̍t-chîn" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%A1%EC%A0%95" title="액정 – Korean" lang="ko" hreflang="ko" data-title="액정" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D5%B2%D5%B8%D6%82%D5%AF_%D5%A2%D5%B5%D5%B8%D6%82%D6%80%D5%A5%D5%B2%D5%B6%D5%A5%D6%80" title="Հեղուկ բյուրեղներ – Armenian" lang="hy" hreflang="hy" data-title="Հեղուկ բյուրեղներ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teku%C4%87i_kristali" title="Tekući kristali – Croatian" lang="hr" hreflang="hr" data-title="Tekući kristali" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kristal_cair" title="Kristal cair – Indonesian" lang="id" hreflang="id" data-title="Kristal cair" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Cristalli_liquidi" title="Cristalli liquidi – Italian" lang="it" hreflang="it" data-title="Cristalli liquidi" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%91%D7%99%D7%A9_%D7%A0%D7%95%D7%96%D7%9C%D7%99" title="גביש נוזלי – Hebrew" lang="he" hreflang="he" data-title="גביש נוזלי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D2%B1%D0%B9%D1%8B%D2%9B_%D0%BA%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%B4%D0%B0%D1%80" title="Сұйық кристалдар – Kazakh" lang="kk" hreflang="kk" data-title="Сұйық кристалдар" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Crystallum_liquidum" title="Crystallum liquidum – Latin" lang="la" hreflang="la" data-title="Crystallum liquidum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C5%A0%C4%B7idrais_krist%C4%81ls" title="Šķidrais kristāls – Latvian" lang="lv" hreflang="lv" data-title="Šķidrais kristāls" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hablur_cecair" title="Hablur cecair – Malay" lang="ms" hreflang="ms" data-title="Hablur cecair" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/%C4%ACk-c%C4%ADng" title="Ĭk-cĭng – Mindong" lang="cdo" hreflang="cdo" data-title="Ĭk-cĭng" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vloeibaar_kristal" title="Vloeibaar kristal – Dutch" lang="nl" hreflang="nl" data-title="Vloeibaar kristal" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B6%B2%E6%99%B6" title="液晶 – Japanese" lang="ja" hreflang="ja" data-title="液晶" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Flytende_krystall" title="Flytende krystall – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Flytende krystall" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Cristau_liquid" title="Cristau liquid – Occitan" lang="oc" hreflang="oc" data-title="Cristau liquid" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%BE%D8%A7%D9%86%DB%8C_%D8%B3%D8%A7%D8%B1_%DA%A9%D8%B1%D8%B3%D9%B9%D9%84" title="پانی سار کرسٹل – Western Punjabi" lang="pnb" hreflang="pnb" data-title="پانی سار کرسٹل" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D8%A7%DB%8C%D8%B9_%DA%A9%D8%B1%DB%8C%D8%B3%D9%BC%D8%A7%D9%84" title="مایع کریسټال – Pashto" lang="ps" hreflang="ps" data-title="مایع کریسټال" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ciek%C5%82y_kryszta%C5%82" title="Ciekły kryształ – Polish" lang="pl" hreflang="pl" data-title="Ciekły kryształ" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cristal_l%C3%ADquido" title="Cristal líquido – Portuguese" lang="pt" hreflang="pt" data-title="Cristal líquido" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cristal_lichid" title="Cristal lichid – Romanian" lang="ro" hreflang="ro" data-title="Cristal lichid" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%96%D0%B8%D0%B4%D0%BA%D0%B8%D0%B5_%D0%BA%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BB%D1%8B" title="Жидкие кристаллы – Russian" lang="ru" hreflang="ru" data-title="Жидкие кристаллы" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Liquid_crystal" title="Liquid crystal – Simple English" lang="en-simple" hreflang="en-simple" data-title="Liquid crystal" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvapaln%C3%BD_kry%C5%A1t%C3%A1l" title="Kvapalný kryštál – Slovak" lang="sk" hreflang="sk" data-title="Kvapalný kryštál" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Teko%C4%8Di_kristal" title="Tekoči kristal – Slovenian" lang="sl" hreflang="sl" data-title="Tekoči kristal" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D9%88%D8%B1%DB%8C_%D8%B4%D9%84" title="بلووری شل – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بلووری شل" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D1%87%D0%BD%D0%B8_%D0%BA%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB" title="Течни кристал – Serbian" lang="sr" hreflang="sr" data-title="Течни кристал" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Te%C4%8Dni_kristal" title="Tečni kristal – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Tečni kristal" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Nestekide" title="Nestekide – Finnish" lang="fi" hreflang="fi" data-title="Nestekide" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Flytande_kristall" title="Flytande kristall – Swedish" lang="sv" hreflang="sv" data-title="Flytande kristall" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/S%C4%B1v%C4%B1_kristal" title="Sıvı kristal – Turkish" lang="tr" hreflang="tr" data-title="Sıvı kristal" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D1%96%D0%B4%D0%BA%D1%96_%D0%BA%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%B8" title="Рідкі кристали – Ukrainian" lang="uk" hreflang="uk" data-title="Рідкі кристали" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tinh_th%E1%BB%83_l%E1%BB%8Fng" title="Tinh thể lỏng – Vietnamese" lang="vi" hreflang="vi" data-title="Tinh thể lỏng" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%B6%B2%E6%99%B6" title="液晶 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="液晶" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B6%B2%E6%99%B6%E9%AB%94" title="液晶體 – Cantonese" lang="yue" hreflang="yue" data-title="液晶體" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B6%B2%E6%99%B6" title="液晶 – Chinese" lang="zh" hreflang="zh" data-title="液晶" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q203989#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Liquid_crystal" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">State of matter with properties of both conventional liquids and crystals</div> <p class="mw-empty-elt"> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Nematische_Phase_Schlierentextur.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Nematische_Phase_Schlierentextur.jpg/300px-Nematische_Phase_Schlierentextur.jpg" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Nematische_Phase_Schlierentextur.jpg/450px-Nematische_Phase_Schlierentextur.jpg 1.5x, 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href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">Condensed matter physics</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:QuantumPhaseTransition.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/220px-QuantumPhaseTransition.svg.png" decoding="async" width="220" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/330px-QuantumPhaseTransition.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/440px-QuantumPhaseTransition.svg.png 2x" data-file-width="512" data-file-height="369" /></a></span></td></tr><tr><td class="sidebar-content"> <div class="hlist"><ul><li><a href="/wiki/Phase_(matter)" title="Phase (matter)">Phases</a></li><li><a href="/wiki/Phase_transition" title="Phase transition">Phase transition</a></li><li><a href="/wiki/Quantum_critical_point" title="Quantum critical point">QCP</a></li></ul></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/State_of_matter" title="State of matter">States of matter</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Solid" title="Solid">Solid</a></li><li><a href="/wiki/Liquid" title="Liquid">Liquid</a></li><li><a href="/wiki/Gas" title="Gas">Gas</a></li><li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li><li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li><li><a href="/wiki/Bose_gas" title="Bose gas">Bose gas</a></li><li><a href="/wiki/Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li><li><a href="/wiki/Fermi_gas" title="Fermi gas">Fermi gas</a></li><li><a href="/wiki/Fermi_liquid_theory" title="Fermi liquid theory">Fermi liquid</a></li><li><a href="/wiki/Supersolid" title="Supersolid">Supersolid</a></li><li><a href="/wiki/Superfluidity" title="Superfluidity">Superfluidity</a></li><li><a href="/wiki/Luttinger_liquid" title="Luttinger liquid">Luttinger liquid</a></li><li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Phase phenomena</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Order_parameter" class="mw-redirect" title="Order parameter">Order parameter</a></li><li><a href="/wiki/Phase_transition" title="Phase transition">Phase transition</a></li><li><a href="/wiki/Quantum_critical_point" title="Quantum critical point">QCP</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Electronic phases</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Electronic_band_structure" title="Electronic band structure">Electronic band structure</a></li><li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li><li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li><li><a href="/wiki/Mott_insulator" title="Mott insulator">Mott insulator</a></li><li><a href="/wiki/Semiconductor" title="Semiconductor">Semiconductor</a></li><li><a href="/wiki/Semimetal" title="Semimetal">Semimetal</a></li><li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li><li><a href="/wiki/Superconductivity" title="Superconductivity">Superconductor</a></li><li><a href="/wiki/Thermoelectric_effect" title="Thermoelectric effect">Thermoelectric</a></li><li><a href="/wiki/Piezoelectricity" title="Piezoelectricity">Piezoelectric</a></li><li><a href="/wiki/Ferroelectricity" title="Ferroelectricity">Ferroelectric</a></li><li><a href="/wiki/Topological_insulator" title="Topological insulator">Topological insulator</a></li><li><a href="/wiki/Spin_gapless_semiconductor" title="Spin gapless semiconductor">Spin gapless semiconductor</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Electronic phenomena</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a></li><li><a href="/wiki/Spin_Hall_effect" title="Spin Hall effect">Spin Hall effect</a></li><li><a href="/wiki/Kondo_effect" title="Kondo effect">Kondo effect</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Magnetic phases</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Diamagnetism" title="Diamagnetism">Diamagnet</a></li><li><a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">Superdiamagnet</a><br /> <a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnet</a></li><li><a href="/wiki/Superparamagnetism" title="Superparamagnetism">Superparamagnet</a><br /><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li><li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a><br /><a href="/wiki/Metamagnetism" title="Metamagnetism">Metamagnet</a></li><li><a href="/wiki/Spin_glass" title="Spin glass">Spin glass</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Quasiparticle" title="Quasiparticle">Quasiparticles</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Phonon" title="Phonon">Phonon</a></li><li><a href="/wiki/Exciton" title="Exciton">Exciton</a></li><li><a href="/wiki/Plasmon" title="Plasmon">Plasmon</a><br /><a href="/wiki/Polariton" title="Polariton">Polariton</a></li><li><a href="/wiki/Polaron" title="Polaron">Polaron</a></li><li><a href="/wiki/Magnon" title="Magnon">Magnon</a></li><li><a href="/wiki/Roton" title="Roton">Roton</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Soft_matter" title="Soft matter">Soft matter</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Amorphous_solid" title="Amorphous solid">Amorphous solid</a></li><li><a href="/wiki/Colloid" title="Colloid">Colloid</a></li><li><a href="/wiki/Granular_material" title="Granular material">Granular material</a></li><li><a class="mw-selflink selflink">Liquid crystal</a></li><li><a href="/wiki/Polymer" title="Polymer">Polymer</a></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"><ul><li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">Van der Waals</a></li><li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li><li><a href="/wiki/Max_von_Laue" title="Max von Laue">von Laue</a></li><li><a href="/wiki/William_Henry_Bragg" title="William Henry Bragg">Bragg</a></li><li><a href="/wiki/Peter_Debye" title="Peter Debye">Debye</a></li><li><a href="/wiki/Felix_Bloch" title="Felix Bloch">Bloch</a></li><li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li><li><a href="/wiki/Neville_Mott" class="mw-redirect" title="Neville Mott">Mott</a></li><li><a href="/wiki/Rudolf_Peierls" title="Rudolf Peierls">Peierls</a></li><li><a href="/wiki/Lev_Landau" title="Lev Landau">Landau</a></li><li><a href="/wiki/Luttinger" class="mw-redirect" title="Luttinger">Luttinger</a></li><li><a href="/wiki/Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Anderson</a></li><li><a href="/wiki/John_Hasbrouck_Van_Vleck" title="John Hasbrouck Van Vleck">Van Vleck</a></li><li><a href="/wiki/John_Hubbard_(physicist)" title="John Hubbard (physicist)">Hubbard</a></li><li><a href="/wiki/William_Bradford_Shockley" class="mw-redirect" title="William Bradford Shockley">Shockley</a></li><li><a href="/wiki/John_Bardeen" title="John Bardeen">Bardeen</a></li><li><a href="/wiki/Leon_Cooper" title="Leon Cooper">Cooper</a></li><li><a href="/wiki/John_Robert_Schrieffer" title="John Robert Schrieffer">Schrieffer</a></li><li><a href="/wiki/Brian_Josephson" title="Brian Josephson">Josephson</a></li><li><a href="/wiki/Louis_N%C3%A9el" title="Louis Néel">Louis Néel</a></li><li><a href="/wiki/Leo_Esaki" title="Leo Esaki">Esaki</a></li><li><a href="/wiki/Ivar_Giaever" title="Ivar Giaever">Giaever</a></li><li><a href="/wiki/Walter_Kohn" title="Walter Kohn">Kohn</a></li><li><a href="/wiki/Leo_Kadanoff" title="Leo Kadanoff">Kadanoff</a></li><li><a href="/wiki/Michael_Fisher" title="Michael Fisher">Fisher</a></li><li><a href="/wiki/Kenneth_G._Wilson" title="Kenneth G. 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For example, a liquid crystal can flow like a liquid, but its <a href="/wiki/Molecules" class="mw-redirect" title="Molecules">molecules</a> may be oriented in a common direction as in a solid. There are many types of LC <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a>, which can be distinguished by their <a href="/wiki/Optics" title="Optics">optical</a> properties (such as <a href="/wiki/Texture_(crystalline)" class="mw-redirect" title="Texture (crystalline)">textures</a>). The contrasting textures arise due to molecules within one area of material ("domain") being oriented in the same direction but different areas having different orientations. An LC material may not always be in an LC state of matter (just as water may be ice or water vapor). </p><p>Liquid crystals can be divided into three main types: <a href="/wiki/Thermotropic" class="mw-redirect" title="Thermotropic">thermotropic</a>, <a href="/wiki/Lyotropic" class="mw-redirect" title="Lyotropic">lyotropic</a>, and <a href="#Metallotropic_liquid_crystals">metallotropic</a>. Thermotropic and lyotropic liquid crystals consist mostly of <a href="/wiki/Organic_molecules" class="mw-redirect" title="Organic molecules">organic molecules</a>, although a few minerals are also known. Thermotropic LCs exhibit a <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a> into the LC phase as temperature changes. Lyotropic LCs exhibit phase transitions as a function of both temperature and <a href="/wiki/Concentration" title="Concentration">concentration</a> of molecules in a <a href="/wiki/Solvent" title="Solvent">solvent</a> (typically water). Metallotropic LCs are composed of both organic and inorganic molecules; their LC transition additionally depends on the inorganic-organic composition ratio. </p><p>Examples of LCs exist both in the natural world and in technological applications. Lyotropic LCs abound in living systems; many proteins and cell membranes are LCs, as well as the <a href="/wiki/Tobacco_mosaic_virus" title="Tobacco mosaic virus">tobacco mosaic virus</a> <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="I cannot find a reference to the tobacco mosaic virus being a liquid crystal (July 2024)">citation needed</span></a></i>]</sup>. LCs in the mineral world include solutions of <a href="/wiki/Soap" title="Soap">soap</a> and various related <a href="/wiki/Detergent" title="Detergent">detergents</a>, and some <a href="/wiki/Clays" class="mw-redirect" title="Clays">clays</a>. Widespread <a href="/wiki/Liquid-crystal_display" title="Liquid-crystal display">liquid-crystal displays</a> (LCD) use liquid crystals. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> In 1888, Austrian botanical physiologist <a href="/wiki/Friedrich_Reinitzer" title="Friedrich Reinitzer">Friedrich Reinitzer</a>, working at the <a href="/wiki/Karl-Ferdinands-Universit%C3%A4t" class="mw-redirect" title="Karl-Ferdinands-Universität">Karl-Ferdinands-Universität</a>, examined the physico-chemical properties of various <a href="/wiki/Derivative_(chemistry)" title="Derivative (chemistry)">derivatives</a> of <a href="/wiki/Cholesterol" title="Cholesterol">cholesterol</a> which now belong to the class of materials known as cholesteric liquid crystals. Previously, other researchers had observed distinct color effects when cooling cholesterol derivatives just above the <a href="/wiki/Freezing_point" class="mw-redirect" title="Freezing point">freezing point</a>, but had not associated it with a new phenomenon. Reinitzer perceived that color changes in a derivative <a href="/wiki/Cholesteryl_benzoate" title="Cholesteryl benzoate">cholesteryl benzoate</a> were not the most peculiar feature.</p><figure typeof="mw:File/Thumb"><a href="/wiki/File:Cholesteryl_benzoate.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Cholesteryl_benzoate.png/250px-Cholesteryl_benzoate.png" decoding="async" width="250" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Cholesteryl_benzoate.png/375px-Cholesteryl_benzoate.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Cholesteryl_benzoate.png/500px-Cholesteryl_benzoate.png 2x" data-file-width="4734" data-file-height="2213" /></a><figcaption>Chemical structure of <a href="/wiki/Cholesteryl_benzoate" title="Cholesteryl benzoate">cholesteryl benzoate</a> molecule</figcaption></figure><p> He found that cholesteryl benzoate does not <a href="/wiki/Melting" title="Melting">melt</a> in the same manner as other compounds, but has two <a href="/wiki/Melting_point" title="Melting point">melting points</a>. At 145.5 °C (293.9 °F) it melts into a cloudy liquid, and at 178.5 °C (353.3 °F) it melts again and the cloudy liquid becomes clear. The phenomenon is reversible. Seeking help from a physicist, on March 14, 1888, he wrote to <a href="/wiki/Otto_Lehmann_(physicist)" title="Otto Lehmann (physicist)">Otto Lehmann</a>, at that time a <i><span title="German-language text"><i lang="de"><a href="/wiki/Privatdozent" title="Privatdozent">Privatdozent</a></i></span></i> in <a href="/wiki/Aachen" title="Aachen">Aachen</a>. They exchanged letters and samples. Lehmann examined the intermediate cloudy fluid, and reported seeing <a href="/wiki/Crystallite" title="Crystallite">crystallites</a>. Reinitzer's Viennese colleague von Zepharovich also indicated that the intermediate "fluid" was crystalline. The exchange of letters with Lehmann ended on April 24, with many questions unanswered. Reinitzer presented his results, with credits to Lehmann and von Zepharovich, at a meeting of the Vienna Chemical Society on May 3, 1888.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>By that time, Reinitzer had discovered and described three important features of cholesteric liquid crystals (the name coined by Otto Lehmann in 1904): the existence of two melting points, the reflection of <a href="/wiki/Circular_polarization" title="Circular polarization">circularly polarized light</a>, and the ability to rotate the polarization direction of light. </p><p>After his accidental discovery, Reinitzer did not pursue studying liquid crystals further. The research was continued by Lehmann, who realized that he had encountered a new phenomenon and was in a position to investigate it: In his postdoctoral years he had acquired expertise in <a href="/wiki/Crystallography" title="Crystallography">crystallography</a> and <a href="/wiki/Microscopy" title="Microscopy">microscopy</a>. Lehmann started a systematic study, first of cholesteryl benzoate, and then of related compounds which exhibited the double-melting phenomenon. He was able to make observations in <a href="/wiki/Polarized_light" class="mw-redirect" title="Polarized light">polarized light</a>, and his microscope was equipped with a hot stage (sample holder equipped with a heater) enabling high temperature observations. The intermediate cloudy phase clearly sustained flow, but other features, particularly the signature under a microscope, convinced Lehmann that he was dealing with a solid. By the end of August 1889 he had published his results in the <a href="/wiki/Zeitschrift_f%C3%BCr_Physikalische_Chemie" title="Zeitschrift für Physikalische Chemie">Zeitschrift für Physikalische Chemie</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Otto_Lehmann.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Otto_Lehmann.jpg/180px-Otto_Lehmann.jpg" decoding="async" width="180" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Otto_Lehmann.jpg/270px-Otto_Lehmann.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Otto_Lehmann.jpg/360px-Otto_Lehmann.jpg 2x" data-file-width="1541" data-file-height="2000" /></a><figcaption>Otto Lehmann</figcaption></figure> <p>Lehmann's work was continued and significantly expanded by the German chemist <a href="/wiki/Daniel_Vorl%C3%A4nder" title="Daniel Vorländer">Daniel Vorländer</a>, who from the beginning of the 20th century until he retired in 1935, had synthesized most of the liquid crystals known. However, liquid crystals were not popular among scientists and the material remained a pure scientific curiosity for about 80 years.<sup id="cite_ref-b3_3-0" class="reference"><a href="#cite_note-b3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>After World War II, work on the synthesis of liquid crystals was restarted at university research laboratories in Europe. <a href="/wiki/George_William_Gray" class="mw-redirect" title="George William Gray">George William Gray</a>, a prominent researcher of liquid crystals, began investigating these materials in England in the late 1940s. His group synthesized many new materials that exhibited the liquid crystalline state and developed a better understanding of how to design molecules that exhibit the state. His book <i>Molecular Structure and the Properties of Liquid Crystals</i><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> became a guidebook on the subject. One of the first U.S. chemists to study liquid crystals was Glenn H. Brown, starting in 1953 at the <a href="/wiki/University_of_Cincinnati" title="University of Cincinnati">University of Cincinnati</a> and later at <a href="/wiki/Kent_State_University" title="Kent State University">Kent State University</a>. In 1965, he organized the first international conference on liquid crystals, in Kent, Ohio, with about 100 of the world's top liquid crystal scientists in attendance. This conference marked the beginning of a worldwide effort to perform research in this field, which soon led to the development of practical applications for these unique materials.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Liquid crystal materials became a focus of research in the development of flat panel electronic displays beginning in 1962 at <a href="/wiki/RCA" title="RCA">RCA</a> Laboratories.<sup id="cite_ref-castellano_7-0" class="reference"><a href="#cite_note-castellano-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> When physical chemist Richard Williams applied an electric field to a thin layer of a <a href="#Nematic_phase">nematic</a> liquid crystal at 125 °C, he observed the formation of a regular pattern that he called domains (now known as Williams Domains). This led his colleague <a href="/wiki/George_H._Heilmeier" title="George H. Heilmeier">George H. Heilmeier</a> to perform research on a liquid crystal-based flat panel display to replace the cathode ray vacuum tube used in televisions. But the <a href="/wiki/Para-Azoxyanisole" title="Para-Azoxyanisole">para-azoxyanisole</a> that Williams and Heilmeier used exhibits the nematic liquid crystal state only above 116 °C, which made it impractical to use in a commercial display product. A material that could be operated at room temperature was clearly needed. </p><p>In 1966, Joel E. Goldmacher and Joseph A. Castellano, research chemists in Heilmeier group at RCA, discovered that mixtures made exclusively of nematic compounds that differed only in the number of carbon atoms in the terminal side chains could yield room-temperature nematic liquid crystals. A ternary mixture of <a href="/wiki/Schiff_base" title="Schiff base">Schiff base</a> compounds resulted in a material that had a nematic range of 22–105 °C.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Operation at room temperature enabled the first practical display device to be made.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The team then proceeded to prepare numerous mixtures of nematic compounds many of which had much lower melting points. This technique of mixing nematic compounds to obtain wide <a href="/wiki/Operating_temperature" title="Operating temperature">operating temperature</a> range eventually became the industry standard and is still used to tailor materials to meet specific applications. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MBBA_cleaner.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/MBBA_cleaner.svg/220px-MBBA_cleaner.svg.png" decoding="async" width="220" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/MBBA_cleaner.svg/330px-MBBA_cleaner.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/MBBA_cleaner.svg/440px-MBBA_cleaner.svg.png 2x" data-file-width="334" data-file-height="123" /></a><figcaption>Chemical structure of N-(4-methoxybenzylidene)-4-butylaniline (MBBA) molecule</figcaption></figure> <p>In 1969, Hans Keller succeeded in synthesizing a substance that had a nematic phase at room temperature, <a href="/wiki/MBBA" title="MBBA">N-(4-methoxybenzylidene)-4-butylaniline</a> (MBBA), which is one of the most popular subjects of liquid crystal research.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The next step to commercialization of liquid-crystal displays was the synthesis of further chemically stable substances (cyanobiphenyls) with low melting temperatures by <a href="/wiki/George_William_Gray" class="mw-redirect" title="George William Gray">George Gray</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> That work with Ken Harrison and the UK MOD (<a href="/wiki/Royal_Radar_Establishment" title="Royal Radar Establishment">RRE Malvern</a>), in 1973, led to design of new materials resulting in rapid adoption of small area LCDs within electronic products. </p><p>These molecules are rod-shaped, some created in the laboratory and some appearing spontaneously in nature. Since then, two new types of LC molecules have been synthesized: <a href="/wiki/Columnar_phase" title="Columnar phase">disc-shaped</a> (by <a href="/wiki/Sivaramakrishna_Chandrasekhar" title="Sivaramakrishna Chandrasekhar">Sivaramakrishna Chandrasekhar</a> in India in 1977)<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and cone or bowl shaped (predicted by Lui Lam in China in 1982 and synthesized in Europe in 1985).<sup id="cite_ref-Collyer_13-0" class="reference"><a href="#cite_note-Collyer-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>In 1991, when liquid crystal displays were already well established, <a href="/wiki/Pierre-Gilles_de_Gennes" title="Pierre-Gilles de Gennes">Pierre-Gilles de Gennes</a> working at the <a href="/wiki/Universit%C3%A9_Paris-Sud" class="mw-redirect" title="Université Paris-Sud">Université Paris-Sud</a> received the Nobel Prize in physics "for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers".<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Design_of_liquid_crystalline_materials">Design of liquid crystalline materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=2" title="Edit section: Design of liquid crystalline materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A large number of chemical compounds are known to exhibit one or several liquid crystalline phases. Despite significant differences in chemical composition, these molecules have some common features in chemical and physical properties. There are three types of thermotropic liquid crystals: discotic, conic (bowlic), and rod-shaped molecules. Discotics are disc-like molecules consisting of a flat core of adjacent aromatic rings, whereas the core in a conic LC is not flat, but is shaped like a rice bowl (a three-dimensional object).<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> This allows for two dimensional columnar ordering, for both discotic and conic LCs. Rod-shaped molecules have an elongated, anisotropic geometry which allows for <a href="/wiki/Preferential_alignment" title="Preferential alignment">preferential alignment</a> along one spatial direction. </p> <ul><li>The molecular shape should be relatively thin, flat or conic, especially within rigid molecular frameworks.</li> <li>The molecular length should be at least 1.3 nm, consistent with the presence of long alkyl group on many room-temperature liquid crystals.</li> <li>The structure should not be branched or angular, except for the conic LC.</li> <li>A low melting point is preferable in order to avoid metastable, monotropic liquid crystalline phases. Low-temperature mesomorphic behavior in general is technologically more useful, and alkyl terminal groups promote this.</li></ul> <p>An extended, structurally rigid, highly anisotropic shape seems to be the main criterion for liquid crystalline behavior, and as a result many liquid crystalline materials are based on benzene rings.<sup id="cite_ref-Chemical_Properties_of_Liquid_Crystals_17-0" class="reference"><a href="#cite_note-Chemical_Properties_of_Liquid_Crystals-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Liquid-crystal_phases">Liquid-crystal phases</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=3" title="Edit section: Liquid-crystal phases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The various liquid-crystal phases (called <a href="/wiki/Mesophase" title="Mesophase">mesophases</a> together with <a href="/wiki/Plastic_crystal" title="Plastic crystal">plastic crystal</a> phases) can be characterized by the type of ordering. One can distinguish positional order (whether molecules are arranged in any sort of ordered lattice) and orientational order (whether molecules are mostly pointing in the same direction). Liquid crystals are characterized by orientational order, but only partial or completely absent positional order. In contrast, materials with positional order but no orientational order are known as <a href="/wiki/Plastic_crystal" title="Plastic crystal">plastic crystals</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Most thermotropic LCs will have an <a href="/wiki/Isotropic" class="mw-redirect" title="Isotropic">isotropic</a> phase at high temperature: heating will eventually drive them into a conventional liquid phase characterized by random and isotropic molecular ordering and <a href="/wiki/Fluid" title="Fluid">fluid</a>-like flow behavior. Under other conditions (for instance, lower temperature), a LC might inhabit one or more phases with significant <a href="/wiki/Anisotropic" class="mw-redirect" title="Anisotropic">anisotropic</a> orientational structure and short-range orientational order while still having an ability to flow.<sup id="cite_ref-b2_19-0" class="reference"><a href="#cite_note-b2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b1_20-0" class="reference"><a href="#cite_note-b1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>The ordering of liquid crystals extends up to the entire domain size, which may be on the order of micrometers, but usually not to the macroscopic scale as often occurs in classical <a href="/wiki/Crystal" title="Crystal">crystalline</a> solids. However some techniques, such as the use of boundaries or an applied <a href="/wiki/Electric_field" title="Electric field">electric field</a>, can be used to enforce a single ordered domain in a macroscopic liquid crystal sample. <sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> The orientational ordering in a liquid crystal might extend along only one <a href="/wiki/Dimension" title="Dimension">dimension</a>, with the material being essentially disordered in the other two directions.<sup id="cite_ref-b4_22-0" class="reference"><a href="#cite_note-b4-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b5_23-0" class="reference"><a href="#cite_note-b5-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Thermotropic_liquid_crystals">Thermotropic liquid crystals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=4" title="Edit section: Thermotropic liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Thermotropic_crystal" title="Thermotropic crystal">Thermotropic crystal</a></div> <p>Thermotropic phases are those that occur in a certain temperature range. If the temperature rise is too high, thermal motion will destroy the delicate cooperative ordering of the LC phase, pushing the material into a conventional isotropic liquid phase. At too low temperature, most LC materials will form a conventional crystal.<sup id="cite_ref-b2_19-1" class="reference"><a href="#cite_note-b2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b1_20-1" class="reference"><a href="#cite_note-b1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Many thermotropic LCs exhibit a variety of phases as temperature is changed. For instance, a particular type of LC molecule (called a <a href="/wiki/Mesogen" title="Mesogen">mesogen</a>) may exhibit various smectic phases followed by the nematic phase and finally the isotropic phase as temperature is increased. An example of a compound displaying thermotropic LC behavior is <a href="/wiki/Para-azoxyanisole" class="mw-redirect" title="Para-azoxyanisole">para-azoxyanisole</a>.<sup id="cite_ref-Shao_24-0" class="reference"><a href="#cite_note-Shao-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Nematic_phase">Nematic phase</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=5" title="Edit section: Nematic phase"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Biaxial_nematic" title="Biaxial nematic">Biaxial nematic</a> and <a href="/wiki/Twisted_nematic_field_effect" title="Twisted nematic field effect">Twisted nematic field effect</a></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:LiquidCrystal-MesogenOrder-Nematic.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/LiquidCrystal-MesogenOrder-Nematic.jpg/120px-LiquidCrystal-MesogenOrder-Nematic.jpg" decoding="async" width="120" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/LiquidCrystal-MesogenOrder-Nematic.jpg/180px-LiquidCrystal-MesogenOrder-Nematic.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/LiquidCrystal-MesogenOrder-Nematic.jpg/240px-LiquidCrystal-MesogenOrder-Nematic.jpg 2x" data-file-width="328" data-file-height="513" /></a><figcaption>Alignment in a nematic phase</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Smectic_nematic.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Smectic_nematic.jpg/220px-Smectic_nematic.jpg" decoding="async" width="220" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Smectic_nematic.jpg/330px-Smectic_nematic.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/67/Smectic_nematic.jpg/440px-Smectic_nematic.jpg 2x" data-file-width="600" data-file-height="386" /></a><figcaption>Phase transition between a nematic (left) and smectic A (right) phases observed between crossed <a href="/wiki/Polarizers" class="mw-redirect" title="Polarizers">polarizers</a>. The black color corresponds to isotropic medium.</figcaption></figure> <p>The simplest liquid crystal phase is the nematic. In a nematic phase, <a href="https://en.wiktionary.org/wiki/calamitic" class="extiw" title="wikt:calamitic">calamitic</a> organic molecules lack a crystalline positional order, but do self-align with their long axes roughly parallel. The molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but their orientation is constrained to form a long-range directional order.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>The word <i>nematic</i> comes from the <a href="/wiki/Greek_language" title="Greek language">Greek</a> <span title="Greek-language text"><span lang="el">νήμα</span></span> (<i><a href="/wiki/Greek_language" title="Greek language">Greek</a>: <i lang="el">nema</i></i>), which means "thread". This term originates from the <a href="/wiki/Disclination" title="Disclination">disclinations</a>: thread-like <a href="/wiki/Topological_defect" title="Topological defect">topological defects</a> observed in nematic phases. </p><p>Nematics also exhibit so-called "hedgehog" topological defects. In two dimensions, there are topological defects with topological charges <span class="texhtml">+<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></span> and <span class="texhtml">-<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></span>. Due to hydrodynamics, the <span class="texhtml">+<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></span> defect moves considerably faster than the <span class="texhtml">-<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></span> defect. When placed close to each other, the defects attract; upon collision, they annihilate.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>Most nematic phases are uniaxial: they have one axis (called a directrix) that is longer and preferred, with the other two being equivalent (can be approximated as cylinders or rods). However, some liquid crystals are <a href="/wiki/Biaxial_nematic" title="Biaxial nematic">biaxial nematic</a>, meaning that in addition to orienting their long axis, they also orient along a secondary axis.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Nematic crystals have fluidity similar to that of ordinary (isotropic) liquids but they can be easily aligned by an external magnetic or electric field. Aligned nematics have the optical properties of uniaxial crystals and this makes them extremely useful in <a href="/wiki/Liquid-crystal_display" title="Liquid-crystal display">liquid-crystal displays</a> (LCD).<sup id="cite_ref-castellano_7-1" class="reference"><a href="#cite_note-castellano-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Nematic phases are also known in non-molecular systems: at high magnetic fields, electrons flow in <a href="/wiki/Charge_density_wave" title="Charge density wave">bundles or stripes</a> to create an "electronic nematic" form of matter.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Smectic_phases">Smectic phases</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=6" title="Edit section: Smectic phases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:LiquidCrystal-MesogenOrder-SmecticPhases.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/LiquidCrystal-MesogenOrder-SmecticPhases.jpg/220px-LiquidCrystal-MesogenOrder-SmecticPhases.jpg" decoding="async" width="220" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/LiquidCrystal-MesogenOrder-SmecticPhases.jpg/330px-LiquidCrystal-MesogenOrder-SmecticPhases.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f2/LiquidCrystal-MesogenOrder-SmecticPhases.jpg 2x" data-file-width="400" data-file-height="315" /></a><figcaption>Schematic of alignment in the smectic phases. The smectic A phase (left) has molecules organized into layers. In the smectic C phase (right), the molecules are tilted inside the layers.</figcaption></figure> <p>The smectic phases, which are found at lower temperatures than the nematic, form well-defined layers that can slide over one another in a manner similar to that of soap. The word "smectic" originates from the Latin word "smecticus", meaning cleaning, or having soap-like properties.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> The smectics are thus positionally ordered along one direction. In the Smectic A phase, the molecules are oriented along the layer normal, while in the Smectic C phase they are tilted away from it. These phases are liquid-like within the layers. There are many different smectic phases, all characterized by different types and degrees of positional and orientational order.<sup id="cite_ref-b2_19-2" class="reference"><a href="#cite_note-b2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b1_20-2" class="reference"><a href="#cite_note-b1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Beyond organic molecules, Smectic ordering has also been reported to occur within colloidal suspensions of 2-D materials or nanosheets.<sup id="cite_ref-Swollen_liquid-crystalline_lamellar_32-0" class="reference"><a href="#cite_note-Swollen_liquid-crystalline_lamellar-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> One example of smectic LCs is <a href="/w/index.php?title=P,p-dinonylazobenzene&action=edit&redlink=1" class="new" title="P,p-dinonylazobenzene (page does not exist)"><i>p,p'</i>-dinonylazobenzene</a>.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Chiral_phases_or_twisted_nematics">Chiral phases or twisted nematics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=7" title="Edit section: Chiral phases or twisted nematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:LiquidCrystal-MesogenOrder-ChiralPhases.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/LiquidCrystal-MesogenOrder-ChiralPhases.jpg/220px-LiquidCrystal-MesogenOrder-ChiralPhases.jpg" decoding="async" width="220" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/bf/LiquidCrystal-MesogenOrder-ChiralPhases.jpg 1.5x" data-file-width="250" data-file-height="197" /></a><figcaption>Schematic of ordering in chiral liquid crystal phases. The chiral nematic phase (left), also called the cholesteric phase, and the smectic C* phase (right).</figcaption></figure> <p>The <a href="/wiki/Chirality_(chemistry)" title="Chirality (chemistry)">chiral</a> <a href="/wiki/Nematic" class="mw-redirect" title="Nematic">nematic</a> phase exhibits <a href="/wiki/Chirality_(chemistry)" title="Chirality (chemistry)">chirality</a> (handedness). This phase is often called the <a href="/wiki/Cholesteric_liquid_crystal" title="Cholesteric liquid crystal"><i>cholesteric</i></a> phase because it was first observed for <a href="/wiki/Cholesterol" title="Cholesterol">cholesterol</a> derivatives. Only <a href="/wiki/Chirality_(chemistry)" title="Chirality (chemistry)">chiral molecules</a> can give rise to such a phase. This phase exhibits a twisting of the molecules perpendicular to the director, with the molecular axis parallel to the director. The finite twist angle between adjacent molecules is due to their asymmetric packing, which results in longer-range chiral order. In the smectic C* phase (an asterisk denotes a chiral phase), the molecules have positional ordering in a layered structure (as in the other smectic phases), with the molecules tilted by a finite angle with respect to the layer normal. The chirality induces a finite azimuthal twist from one layer to the next, producing a spiral twisting of the molecular axis along the layer normal, hence they are also called <i>twisted nematics</i>.<sup id="cite_ref-b1_20-3" class="reference"><a href="#cite_note-b1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b4_22-1" class="reference"><a href="#cite_note-b4-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b5_23-1" class="reference"><a href="#cite_note-b5-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cholesterinisch.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d2/Cholesterinisch.png" decoding="async" width="212" height="173" class="mw-file-element" data-file-width="212" data-file-height="173" /></a><figcaption>Chiral nematic phase. The numerator <i>p</i> refers to the chiral pitch (see text).</figcaption></figure> <p>The <i>chiral pitch</i>, p, refers to the distance over which the LC molecules undergo a full 360° twist (but note that the structure of the chiral nematic phase repeats itself every half-pitch, since in this phase directors at 0° and ±180° are equivalent). The pitch, p, typically changes when the temperature is altered or when other molecules are added to the LC host (an achiral LC host material will form a chiral phase if doped with a chiral material), allowing the pitch of a given material to be tuned accordingly. In some liquid crystal systems, the pitch is of the same order as the <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> of <a href="/wiki/Visible_light" class="mw-redirect" title="Visible light">visible light</a>. This causes these systems to exhibit unique optical properties, such as <a href="/wiki/Bragg_reflection" class="mw-redirect" title="Bragg reflection">Bragg reflection</a> and low-threshold <a href="/wiki/Laser" title="Laser">laser</a> emission,<sup id="cite_ref-Kopp1998_35-0" class="reference"><a href="#cite_note-Kopp1998-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> and these properties are exploited in a number of optical applications.<sup id="cite_ref-b3_3-1" class="reference"><a href="#cite_note-b3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b4_22-2" class="reference"><a href="#cite_note-b4-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> For the case of Bragg reflection only the lowest-order reflection is allowed if the light is incident along the helical axis, whereas for oblique incidence higher-order reflections become permitted. Cholesteric liquid crystals also exhibit the unique property that they reflect circularly polarized light when it is incident along the helical axis and <a href="/wiki/Elliptically_polarized" class="mw-redirect" title="Elliptically polarized">elliptically polarized</a> if it comes in obliquely.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Wikipedia_LCD_prototype.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Wikipedia_LCD_prototype.jpg/211px-Wikipedia_LCD_prototype.jpg" decoding="async" width="211" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Wikipedia_LCD_prototype.jpg/317px-Wikipedia_LCD_prototype.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Wikipedia_LCD_prototype.jpg/422px-Wikipedia_LCD_prototype.jpg 2x" data-file-width="1608" data-file-height="1084" /></a><figcaption>A planar cell, filled with achiral LC host doped with an optically active Tröger base analog, placed between a pair of parallel (A) and crossed (B) linear polarizers. This doped mesogenic phase forms self-organized helical superstructures, that allow specific wavelengths of light to pass through the crossed polarizers, and selectively reflects a particular wavelength of light.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup></figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Blue_phases">Blue phases</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=8" title="Edit section: Blue phases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Blue phases are liquid crystal phases that appear in the temperature range between a <a href="/wiki/Chirality_(chemistry)" title="Chirality (chemistry)">chiral</a> <a href="/wiki/Nematic" class="mw-redirect" title="Nematic">nematic</a> phase and an <a href="/wiki/Isotropy" title="Isotropy">isotropic</a> liquid phase. Blue phases have a regular three-dimensional cubic structure of defects with <a href="/wiki/Crystal_structure" title="Crystal structure">lattice</a> periods of several hundred nanometers, and thus they exhibit selective <a href="/wiki/Bragg%27s_law" title="Bragg's law">Bragg reflections</a> in the wavelength range of visible light corresponding to the <a href="/wiki/Cubic_phase" class="mw-redirect" title="Cubic phase">cubic lattice</a>. It was theoretically predicted in 1981 that these phases can possess icosahedral symmetry similar to <a href="/wiki/Quasicrystal" title="Quasicrystal">quasicrystals</a>.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>Although blue phases are of interest for fast light modulators or tunable <a href="/wiki/Photonic_crystal" title="Photonic crystal">photonic crystals</a>, they exist in a very narrow temperature range, usually less than a few <a href="/wiki/Kelvin" title="Kelvin">kelvins</a>. Recently the stabilization of blue phases over a temperature range of more than 60 K including room temperature (260–326 K) has been demonstrated.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Blue phases stabilized at room temperature allow electro-optical switching with response times of the order of 10<sup>−4</sup> s.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> In May 2008, the first <a href="/wiki/Blue_Phase_Mode_LCD" class="mw-redirect" title="Blue Phase Mode LCD">blue phase mode LCD</a> panel had been developed.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>Blue phase crystals, being a periodic cubic structure with a bandgap in the visible wavelength range, can be considered as <a href="/wiki/Photonic_crystal" title="Photonic crystal">3D photonic crystals</a>. Producing ideal blue phase crystals in large volumes is still problematic, since the produced crystals are usually polycrystalline (platelet structure) or the single crystal size is limited (in the micrometer range). Recently, blue phases obtained as ideal 3D photonic crystals in large volumes have been stabilized and produced with different controlled crystal lattice orientations.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Discotic_phases">Discotic phases</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=9" title="Edit section: Discotic phases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Disk-shaped LC molecules can orient themselves in a layer-like fashion known as the discotic nematic phase. If the disks pack into stacks, the phase is called a <a href="/wiki/Columnar_phase" title="Columnar phase">discotic columnar</a>. The columns themselves may be organized into rectangular or hexagonal arrays. Chiral discotic phases, similar to the chiral nematic phase, are also known. </p> <div class="mw-heading mw-heading4"><h4 id="Conic_phases">Conic phases</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=10" title="Edit section: Conic phases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Conic LC molecules, like in discotics, can form columnar phases. Other phases, such as nonpolar nematic, polar nematic, stringbean, donut and onion phases, have been predicted. Conic phases, except nonpolar nematic, are polar phases.<sup id="cite_ref-Bowlics_45-0" class="reference"><a href="#cite_note-Bowlics-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Lyotropic_liquid_crystals">Lyotropic liquid crystals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=11" title="Edit section: Lyotropic liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Lyotropic_liquid_crystal" title="Lyotropic liquid crystal">Lyotropic liquid crystal</a> and <a href="/wiki/Columnar_phase" title="Columnar phase">Columnar phase</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Lipid_bilayer_and_micelle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Lipid_bilayer_and_micelle.svg/250px-Lipid_bilayer_and_micelle.svg.png" decoding="async" width="250" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Lipid_bilayer_and_micelle.svg/375px-Lipid_bilayer_and_micelle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Lipid_bilayer_and_micelle.svg/500px-Lipid_bilayer_and_micelle.svg.png 2x" data-file-width="530" data-file-height="266" /></a><figcaption>Structure of lyotropic liquid crystal. The red heads of surfactant molecules are in contact with water, whereas the blue tails of surfactant molecules are immersed in oil:<a href="/wiki/Bilayer" title="Bilayer">bilayer</a> (left) and <a href="/wiki/Micelle" title="Micelle">micelle</a> (right).</figcaption></figure> <p>A <a href="/wiki/Lyotropic_liquid_crystal" title="Lyotropic liquid crystal">lyotropic liquid crystal</a> consists of two or more components that exhibit liquid-crystalline properties in certain concentration ranges. In the <a href="/wiki/Lyotropic" class="mw-redirect" title="Lyotropic">lyotropic</a> phases, <a href="/wiki/Solvent" title="Solvent">solvent</a> molecules fill the space around the compounds to provide <a href="/wiki/Viscosity" title="Viscosity">fluidity</a> to the system.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> In contrast to thermotropic liquid crystals, these lyotropics have another degree of freedom of concentration that enables them to induce a variety of different phases. </p><p>A compound that has two immiscible <a href="/wiki/Hydrophilic" class="mw-redirect" title="Hydrophilic">hydrophilic</a> and <a href="/wiki/Hydrophobic" class="mw-redirect" title="Hydrophobic">hydrophobic</a> parts within the same molecule is called an <a href="/wiki/Amphiphilic" class="mw-redirect" title="Amphiphilic">amphiphilic</a> molecule. Many amphiphilic molecules show lyotropic liquid-crystalline phase sequences depending on the volume balances between the hydrophilic part and hydrophobic part. These structures are formed through the micro-phase segregation of two incompatible components on a nanometer scale. Soap is an everyday example of a lyotropic liquid crystal. </p><p>The content of water or other solvent molecules changes the self-assembled structures. At very low amphiphile concentration, the molecules will be dispersed randomly without any ordering. At slightly higher (but still low) concentration, amphiphilic molecules will spontaneously assemble into <a href="/wiki/Micelle" title="Micelle">micelles</a> or <a href="/wiki/Vesicle_(biology)" class="mw-redirect" title="Vesicle (biology)">vesicles</a>. This is done so as to 'hide' the hydrophobic tail of the amphiphile inside the micelle core, exposing a hydrophilic (water-soluble) surface to aqueous solution. These spherical objects do not order themselves in solution, however. At higher concentration, the assemblies will become ordered. A typical phase is a hexagonal columnar phase, where the amphiphiles form long cylinders (again with a hydrophilic surface) that arrange themselves into a roughly hexagonal lattice. This is called the middle soap phase. At still higher concentration, a lamellar phase (neat soap phase) may form, wherein extended sheets of amphiphiles are separated by thin layers of water. For some systems, a cubic (also called viscous isotropic) phase may exist between the hexagonal and lamellar phases, wherein spheres are formed that create a dense cubic lattice. These spheres may also be connected to one another, forming a bicontinuous cubic phase. </p><p>The objects created by amphiphiles are usually spherical (as in the case of micelles), but may also be disc-like (bicelles), rod-like, or biaxial (all three micelle axes are distinct). These anisotropic self-assembled nano-structures can then order themselves in much the same way as thermotropic liquid crystals do, forming large-scale versions of all the thermotropic phases (such as a nematic phase of rod-shaped micelles). </p><p>For some systems, at high concentrations, inverse phases are observed. That is, one may generate an inverse hexagonal columnar phase (columns of water encapsulated by amphiphiles) or an inverse micellar phase (a bulk liquid crystal sample with spherical water cavities). </p><p>A generic progression of phases, going from low to high amphiphile concentration, is: </p> <ul><li>Discontinuous cubic phase (<a href="/wiki/Micellar_cubic" title="Micellar cubic">micellar cubic</a> phase)</li> <li><a href="/wiki/Hexagonal_phase" title="Hexagonal phase">Hexagonal phase</a> (hexagonal columnar phase) (middle phase)</li> <li><a href="/wiki/Lamellar_phase" title="Lamellar phase">Lamellar phase</a></li> <li>Bicontinuous <a href="/wiki/Cubic_phase" class="mw-redirect" title="Cubic phase">cubic phase</a></li> <li>Reverse hexagonal columnar phase</li> <li>Inverse cubic phase (Inverse micellar phase)</li></ul> <p>Even within the same phases, their self-assembled structures are tunable by the concentration: for example, in lamellar phases, the layer distances increase with the solvent volume. Since lyotropic liquid crystals rely on a subtle balance of intermolecular interactions, it is more difficult to analyze their structures and properties than those of thermotropic liquid crystals. </p><p>Similar phases and characteristics can be observed in immiscible diblock <a href="/wiki/Copolymer" title="Copolymer">copolymers</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Metallotropic_liquid_crystals">Metallotropic liquid crystals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=12" title="Edit section: Metallotropic liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Liquid crystal phases can also be based on low-melting inorganic phases like <a href="/wiki/Zinc_chloride" title="Zinc chloride">ZnCl<sub>2</sub></a> that have a structure formed of linked tetrahedra and easily form glasses. The addition of long chain soap-like molecules leads to a series of new phases that show a variety of liquid crystalline behavior both as a function of the inorganic-organic composition ratio and of temperature. This class of materials has been named metallotropic.<sup id="cite_ref-martin_47-0" class="reference"><a href="#cite_note-martin-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Laboratory_analysis_of_mesophases">Laboratory analysis of mesophases</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=13" title="Edit section: Laboratory analysis of mesophases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermotropic <a href="/wiki/Mesophase" title="Mesophase">mesophases</a> are detected and characterized by two major methods, the original method was use of thermal optical microscopy,<sup id="cite_ref-Tomczyk2017_48-0" class="reference"><a href="#cite_note-Tomczyk2017-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> in which a small sample of the material was placed between two crossed polarizers; the sample was then heated and cooled. As the isotropic phase would not significantly affect the polarization of the light, it would appear very dark, whereas the crystal and liquid crystal phases will both polarize the light in a uniform way, leading to brightness and color gradients. This method allows for the characterization of the particular phase, as the different phases are defined by their particular order, which must be observed. The second method, <a href="/wiki/Differential_scanning_calorimetry" title="Differential scanning calorimetry">differential scanning calorimetry</a> (DSC),<sup id="cite_ref-Tomczyk2017_48-1" class="reference"><a href="#cite_note-Tomczyk2017-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> allows for more precise determination of phase transitions and transition enthalpies. In DSC, a small sample is heated in a way that generates a very precise change in temperature with respect to time. During phase transitions, the heat flow required to maintain this heating or cooling rate will change. These changes can be observed and attributed to various phase transitions, such as key liquid crystal transitions. </p><p>Lyotropic mesophases are analyzed in a similar fashion, though these experiments are somewhat more complex, as the concentration of mesogen is a key factor. These experiments are run at various concentrations of <a href="/wiki/Mesogen" title="Mesogen">mesogen</a> in order to analyze that impact. </p> <div class="mw-heading mw-heading2"><h2 id="Biological_liquid_crystals">Biological liquid crystals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=14" title="Edit section: Biological liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lyotropic liquid-crystalline phases are abundant in living systems, the study of which is referred to as <a href="/wiki/Lipid_polymorphism" title="Lipid polymorphism">lipid polymorphism</a>. Accordingly, lyotropic liquid crystals attract particular attention in the field of biomimetic chemistry. In particular, <a href="/wiki/Biological_membrane" title="Biological membrane">biological membranes</a> and <a href="/wiki/Cell_membranes" class="mw-redirect" title="Cell membranes">cell membranes</a> are a form of liquid crystal. Their constituent molecules (e.g. <a href="/wiki/Phospholipid" title="Phospholipid">phospholipids</a>) are perpendicular to the membrane surface, yet the membrane is flexible.<sup id="cite_ref-Templer_Seddon_1991_50-0" class="reference"><a href="#cite_note-Templer_Seddon_1991-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> These lipids vary in shape (see page on <a href="/wiki/Lipid_polymorphism" title="Lipid polymorphism">lipid polymorphism</a>). The constituent molecules can inter-mingle easily, but tend not to leave the membrane due to the high energy requirement of this process. Lipid molecules can flip from one side of the membrane to the other, this process being catalyzed by <a href="/wiki/Flippase" title="Flippase">flippases</a> and floppases (depending on the direction of movement). These liquid crystal membrane phases can also host important proteins such as receptors freely "floating" inside, or partly outside, the membrane, e.g. CTP:phosphocholine cytidylyltransferase (CCT). </p><p>Many other biological structures exhibit liquid-crystal behavior. For instance, the concentrated <a href="/wiki/Protein" title="Protein">protein</a> solution that is extruded by a spider to generate <a href="/wiki/Spider_silk" title="Spider silk">silk</a> is, in fact, a liquid crystal phase. The precise ordering of molecules in silk is critical to its renowned strength. <a href="/wiki/DNA" title="DNA">DNA</a> and many <a href="/wiki/Peptide" title="Peptide">polypeptides</a>, including actively-driven cytoskeletal filaments,<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> can also form liquid crystal phases. Monolayers of elongated cells have also been described to exhibit liquid-crystal behavior, and the associated topological defects have been associated with biological consequences, including cell death and extrusion.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Together, these biological applications of liquid crystals form an important part of current academic research. </p> <div class="mw-heading mw-heading2"><h2 id="Mineral_liquid_crystals">Mineral liquid crystals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=15" title="Edit section: Mineral liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Examples of liquid crystals can also be found in the mineral world, most of them being lyotropic. The first discovered was <a href="/wiki/Vanadium(V)_oxide" title="Vanadium(V) oxide">vanadium(V) oxide</a>, by Zocher in 1925.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> Since then, few others have been discovered and studied in detail.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> The existence of a true <a href="/wiki/Nematic" class="mw-redirect" title="Nematic">nematic</a> phase in the case of the smectite <a href="/wiki/Clays" class="mw-redirect" title="Clays">clays</a> family was raised by Langmuir in 1938,<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> but remained an open question for a very long time and was only confirmed recently.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p><p>With the rapid development of nanosciences, and the synthesis of many new anisotropic <a href="/wiki/Nanoparticle" title="Nanoparticle">nanoparticles</a>, the number of such mineral liquid crystals is increasing quickly, with, for example, carbon nanotubes and graphene. A lamellar phase was even discovered, H<sub>3</sub>Sb<sub>3</sub>P<sub>2</sub>O<sub>14</sub>, which exhibits hyperswelling up to ~250 nm for the interlamellar distance.<sup id="cite_ref-Swollen_liquid-crystalline_lamellar_32-1" class="reference"><a href="#cite_note-Swollen_liquid-crystalline_lamellar-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Pattern_formation_in_liquid_crystals">Pattern formation in liquid crystals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=16" title="Edit section: Pattern formation in liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Pattern_formation" title="Pattern formation">Pattern formation</a></div> <p>Anisotropy of liquid crystals is a property not observed in other fluids. This anisotropy makes flows of liquid crystals behave more differentially than those of ordinary fluids. For example, injection of a flux of a liquid crystal between two close parallel plates (<a href="/wiki/Viscous_fingering" class="mw-redirect" title="Viscous fingering">viscous fingering</a>) causes orientation of the molecules to couple with the flow, with the resulting emergence of dendritic patterns.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> This anisotropy is also manifested in the interfacial energy (<a href="/wiki/Surface_tension" title="Surface tension">surface tension</a>) between different liquid crystal phases. This anisotropy determines the equilibrium shape at the coexistence temperature, and is so strong that usually facets appear. When temperature is changed one of the phases grows, forming different morphologies depending on the temperature change.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> Since growth is controlled by heat diffusion, anisotropy in thermal conductivity favors growth in specific directions, which has also an effect on the final shape.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Theoretical_treatment_of_liquid_crystals">Theoretical treatment of liquid crystals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=17" title="Edit section: Theoretical treatment of liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Microscopic theoretical treatment of fluid phases can become quite complicated, owing to the high material density, meaning that strong interactions, hard-core repulsions, and many-body correlations cannot be ignored. In the case of liquid crystals, anisotropy in all of these interactions further complicates analysis. There are a number of fairly simple theories, however, that can at least predict the general behavior of the phase transitions in liquid crystal systems. </p> <div class="mw-heading mw-heading3"><h3 id="Director">Director</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=18" title="Edit section: Director"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As we already saw above, the nematic liquid crystals are composed of rod-like molecules with the long axes of neighboring molecules aligned approximately to one another. To describe this anisotropic structure, a dimensionless unit vector <i><b>n</b></i> called the <i>director</i>, is introduced to represent the direction of preferred orientation of molecules in the neighborhood of any point. Because there is no physical polarity along the director axis, <i><b>n</b></i> and <i><b>-n</b></i> are fully equivalent.<sup id="cite_ref-b1_20-4" class="reference"><a href="#cite_note-b1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Order_parameter">Order parameter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=19" title="Edit section: Order parameter"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Nematic-Director.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Nematic-Director.png/220px-Nematic-Director.png" decoding="async" width="220" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Nematic-Director.png/330px-Nematic-Director.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Nematic-Director.png/440px-Nematic-Director.png 2x" data-file-width="711" data-file-height="810" /></a><figcaption>The <i>local nematic director</i>, which is also the <i>local optical axis</i>, is given by the spatial and temporal average of the long molecular axes.</figcaption></figure> <p>The description of liquid crystals involves an analysis of order. A second rank symmetric traceless tensor order parameter, the <a href="/wiki/Q_tensor" title="Q tensor">Q tensor</a> is used to describe the orientational order of the most general <a href="/wiki/Biaxial_nematic" title="Biaxial nematic">biaxial nematic</a> liquid crystal. However, to describe the more common case of uniaxial nematic liquid crystals, a scalar order parameter is sufficient.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> To make this quantitative, an orientational order parameter is usually defined based on the average of the second <a href="/wiki/Legendre_polynomial" class="mw-redirect" title="Legendre polynomial">Legendre polynomial</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=\langle P_{2}(\cos \theta )\rangle =\left\langle {\frac {3\cos ^{2}(\theta )-1}{2}}\right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow> <mo>⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\langle P_{2}(\cos \theta )\rangle =\left\langle {\frac {3\cos ^{2}(\theta )-1}{2}}\right\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f50bb955d5257ce26ef2e018836f826bec317235" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:35.65ex; height:7.509ex;" alt="{\displaystyle S=\langle P_{2}(\cos \theta )\rangle =\left\langle {\frac {3\cos ^{2}(\theta )-1}{2}}\right\rangle }"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> is the angle between the liquid-crystal molecular axis and the <i>local director</i> (which is the 'preferred direction' in a volume element of a liquid crystal sample, also representing its <i><a href="/wiki/Optical_axis" title="Optical axis">local optical axis</a></i>). The brackets denote both a temporal and spatial average. This definition is convenient, since for a completely random and isotropic sample, <i>S</i> = 0, whereas for a perfectly aligned sample S=1. For a typical liquid crystal sample, <i>S</i> is on the order of 0.3 to 0.8, and generally decreases as the temperature is raised. In particular, a sharp drop of the order parameter to 0 is observed when the system undergoes a phase transition from an LC phase into the isotropic phase.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> The order parameter can be measured experimentally in a number of ways; for instance, <a href="/wiki/Diamagnetism" title="Diamagnetism">diamagnetism</a>, <a href="/wiki/Birefringence" title="Birefringence">birefringence</a>, <a href="/wiki/Raman_scattering" title="Raman scattering">Raman scattering</a>, <a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">NMR</a> and <a href="/wiki/Electron_Paramagnetic_Resonance" class="mw-redirect" title="Electron Paramagnetic Resonance">EPR</a> can be used to determine S.<sup id="cite_ref-b5_23-2" class="reference"><a href="#cite_note-b5-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>The order of a liquid crystal could also be characterized by using other even Legendre polynomials (all the odd polynomials average to zero since the director can point in either of two antiparallel directions). These higher-order averages are more difficult to measure, but can yield additional information about molecular ordering.<sup id="cite_ref-b2_19-3" class="reference"><a href="#cite_note-b2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>A positional order parameter is also used to describe the ordering of a liquid crystal. It is characterized by the variation of the density of the center of mass of the liquid crystal molecules along a given vector. In the case of positional variation along the <i>z</i>-axis the density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho (z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho (z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fd5da7771d83a8b8784e1aebb1092c3f415d0bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.099ex; height:2.843ex;" alt="{\displaystyle \rho (z)}"></span> is often given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho (\mathbf {r} )=\rho (z)=\rho _{0}+\rho _{1}\cos(q_{s}z-\varphi )+\cdots \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mi>z</mi> <mo>−</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo>⋯</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho (\mathbf {r} )=\rho (z)=\rho _{0}+\rho _{1}\cos(q_{s}z-\varphi )+\cdots \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a39368cfd87af08068181154164e876eff78ebbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.51ex; height:2.843ex;" alt="{\displaystyle \rho (\mathbf {r} )=\rho (z)=\rho _{0}+\rho _{1}\cos(q_{s}z-\varphi )+\cdots \,}"></span></dd></dl> <p>The complex positional order parameter is defined as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (\mathbf {r} )=\rho _{1}(\mathbf {r} )e^{i\varphi (\mathbf {r} )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>φ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (\mathbf {r} )=\rho _{1}(\mathbf {r} )e^{i\varphi (\mathbf {r} )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c66421ec81db2581a1aabd0228fc9550313330fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.707ex; height:3.343ex;" alt="{\displaystyle \psi (\mathbf {r} )=\rho _{1}(\mathbf {r} )e^{i\varphi (\mathbf {r} )}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c04a9d26b86af8c6205ba2a6287fd655b6b714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.256ex; height:2.176ex;" alt="{\displaystyle \rho _{0}}"></span> the average density. Typically only the first two terms are kept and higher order terms are ignored since most phases can be described adequately using sinusoidal functions. For a perfect nematic <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7eca9b06e607571768c9b79cb231a9997308c4e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.774ex; height:2.509ex;" alt="{\displaystyle \psi =0}"></span> and for a smectic phase <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> will take on complex values. The complex nature of this order parameter allows for many parallels between nematic to smectic phase transitions and conductor to superconductor transitions.<sup id="cite_ref-b1_20-5" class="reference"><a href="#cite_note-b1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Onsager_hard-rod_model">Onsager hard-rod model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=20" title="Edit section: Onsager hard-rod model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1233989161">.mw-parser-output .unsolved{margin:0.5em 0 1em 1em;border:#ccc solid;padding:0.35em 0.35em 0.35em 2.2em;background-color:var(--background-color-interactive-subtle);background-image:url("https://upload.wikimedia.org/wikipedia/commons/2/26/Question%2C_Web_Fundamentals.svg");background-position:top 50%left 0.35em;background-size:1.5em;background-repeat:no-repeat}@media(min-width:720px){.mw-parser-output .unsolved{clear:right;float:right;max-width:25%}}.mw-parser-output .unsolved-label{font-weight:bold}.mw-parser-output .unsolved-body{margin:0.35em;font-style:italic}.mw-parser-output .unsolved-more{font-size:smaller}</style> <div role="note" aria-labelledby="unsolved-label-physics" class="unsolved"> <div><span class="unsolved-label" id="unsolved-label-physics">Unsolved problem in physics</span>:</div> <div class="unsolved-body">Can the nematic to smectic (A) phase transition in liquid crystal states be characterized as a <a href="/wiki/Background_independence" title="Background independence">universal</a> phase transition?</div> <div class="unsolved-more"><a href="/wiki/List_of_unsolved_problems_in_physics" title="List of unsolved problems in physics">(more unsolved problems in physics)</a></div> </div> <p>A simple model which predicts lyotropic phase transitions is the hard-rod model proposed by <a href="/wiki/Lars_Onsager" title="Lars Onsager">Lars Onsager</a>. This theory considers the volume excluded from the center-of-mass of one idealized cylinder as it approaches another. Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder (it can come quite close to the other cylinder). If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder which the approaching cylinder's center-of-mass cannot enter (due to the hard-rod repulsion between the two idealized objects). Thus, this angular arrangement sees a <i>decrease</i> in the net positional <a href="/wiki/Entropy" title="Entropy">entropy</a> of the approaching cylinder (there are fewer states available to it).<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-vroege_64-0" class="reference"><a href="#cite_note-vroege-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p><p>The fundamental insight here is that, whilst parallel arrangements of anisotropic objects lead to a decrease in orientational entropy, there is an increase in positional entropy. Thus in some case greater positional order will be entropically favorable. This theory thus predicts that a solution of rod-shaped objects will undergo a phase transition, at sufficient concentration, into a nematic phase. Although this model is conceptually helpful, its mathematical formulation makes several assumptions that limit its applicability to real systems.<sup id="cite_ref-vroege_64-1" class="reference"><a href="#cite_note-vroege-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> An extension of Onsager Theory was proposed by Flory to account for non entropic effects. </p> <div class="mw-heading mw-heading3"><h3 id="Maier–Saupe_mean_field_theory"><span id="Maier.E2.80.93Saupe_mean_field_theory"></span>Maier–Saupe mean field theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=21" title="Edit section: Maier–Saupe mean field theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This statistical theory, proposed by <a href="/wiki/Alfred_Saupe" title="Alfred Saupe">Alfred Saupe</a> and Wilhelm Maier, includes contributions from an attractive intermolecular potential from an induced dipole moment between adjacent rod-like liquid crystal molecules. The anisotropic attraction stabilizes parallel alignment of neighboring molecules, and the theory then considers a <a href="/wiki/Mean-field_theory" title="Mean-field theory">mean-field</a> average of the interaction. Solved self-consistently, this theory predicts thermotropic nematic-isotropic phase transitions, consistent with experiment.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> Maier-Saupe mean field theory is extended to high molecular weight liquid crystals by incorporating the <a href="/wiki/Bending_stiffness" title="Bending stiffness">bending stiffness</a> of the molecules and using the method of <a href="/wiki/Path_integrals_in_polymer_science" title="Path integrals in polymer science">path integrals in polymer science</a>.<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="McMillan's_model"><span id="McMillan.27s_model"></span>McMillan's model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=22" title="Edit section: McMillan's model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>McMillan's model, proposed by William McMillan,<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> is an extension of the Maier–Saupe mean field theory used to describe the phase transition of a liquid crystal from a nematic to a smectic A phase. It predicts that the phase transition can be either continuous or discontinuous depending on the strength of the short-range interaction between the molecules. As a result, it allows for a triple critical point where the nematic, isotropic, and smectic A phase meet. Although it predicts the existence of a triple critical point, it does not successfully predict its value. The model utilizes two order parameters that describe the orientational and positional order of the liquid crystal. The first is simply the average of the second <a href="/wiki/Legendre_polynomials" title="Legendre polynomials">Legendre polynomial</a> and the second order parameter is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma =\left\langle \cos \left({\frac {2\pi z_{i}}{d}}\right)\left({\frac {3}{2}}\cos ^{2}\left(\theta _{i}\right)-{\frac {1}{2}}\right)\right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mrow> <mo>⟨</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mi>d</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =\left\langle \cos \left({\frac {2\pi z_{i}}{d}}\right)\left({\frac {3}{2}}\cos ^{2}\left(\theta _{i}\right)-{\frac {1}{2}}\right)\right\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cea98798ed194e3c64c1f9a5651b3f7df06e413" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:38.556ex; height:6.176ex;" alt="{\displaystyle \sigma =\left\langle \cos \left({\frac {2\pi z_{i}}{d}}\right)\left({\frac {3}{2}}\cos ^{2}\left(\theta _{i}\right)-{\frac {1}{2}}\right)\right\rangle }"></span></dd></dl> <p>The values <i>z<sub>i</sub>, θ<sub>i</sub></i>, and <i>d</i> are the position of the molecule, the angle between the molecular axis and director, and the layer spacing. The postulated potential energy of a single molecule is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{i}(\theta _{i},z_{i})=-U_{0}\left(S+\alpha \sigma \cos \left({\frac {2\pi z_{i}}{d}}\right)\right)\left({\frac {3}{2}}\cos ^{2}\left(\theta _{i}\right)-{\frac {1}{2}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mo>+</mo> <mi>α</mi> <mi>σ</mi> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mi>d</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{i}(\theta _{i},z_{i})=-U_{0}\left(S+\alpha \sigma \cos \left({\frac {2\pi z_{i}}{d}}\right)\right)\left({\frac {3}{2}}\cos ^{2}\left(\theta _{i}\right)-{\frac {1}{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/261f3e4b35e31143b6e887f51907b5e1d5b0dfd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:58.543ex; height:6.176ex;" alt="{\displaystyle U_{i}(\theta _{i},z_{i})=-U_{0}\left(S+\alpha \sigma \cos \left({\frac {2\pi z_{i}}{d}}\right)\right)\left({\frac {3}{2}}\cos ^{2}\left(\theta _{i}\right)-{\frac {1}{2}}\right)}"></span></dd></dl> <p>Here constant α quantifies the strength of the interaction between adjacent molecules. The potential is then used to derive the thermodynamic properties of the system assuming thermal equilibrium. It results in two self-consistency equations that must be solved numerically, the solutions of which are the three stable phases of the liquid crystal.<sup id="cite_ref-b5_23-3" class="reference"><a href="#cite_note-b5-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Elastic_continuum_theory">Elastic continuum theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=23" title="Edit section: Elastic continuum theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Distortion_free_energy_density" title="Distortion free energy density">Distortion free energy density</a></div> <p>In this formalism, a liquid crystal material is treated as a continuum; molecular details are entirely ignored. Rather, this theory considers perturbations to a presumed oriented sample. The distortions of the liquid crystal are commonly described by the <a href="/wiki/Frank_free_energy_density" class="mw-redirect" title="Frank free energy density">Frank free energy density</a>. One can identify three types of distortions that could occur in an oriented sample: (1) twists of the material, where neighboring molecules are forced to be angled with respect to one another, rather than aligned; (2) splay of the material, where bending occurs perpendicular to the director; and (3) bend of the material, where the distortion is parallel to the director and molecular axis. All three of these types of distortions incur an energy penalty. They are distortions that are induced by the boundary conditions at domain walls or the enclosing container. The response of the material can then be decomposed into terms based on the elastic constants corresponding to the three types of distortions. Elastic continuum theory is an effective tool for modeling liquid crystal devices and lipid bilayers.<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="External_influences_on_liquid_crystals">External influences on liquid crystals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=24" title="Edit section: External influences on liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Scientists and engineers are able to use liquid crystals in a variety of applications because external perturbation can cause significant changes in the macroscopic properties of the liquid crystal system. Both electric and magnetic fields can be used to induce these changes. The magnitude of the fields, as well as the speed at which the molecules align are important characteristics industry deals with. Special surface treatments can be used in liquid crystal devices to force specific orientations of the director. </p> <div class="mw-heading mw-heading3"><h3 id="Electric_and_magnetic_field_effects">Electric and magnetic field effects</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=25" title="Edit section: Electric and magnetic field effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ability of the director to align along an external field is caused by the electric nature of the molecules. Permanent electric dipoles result when one end of a molecule has a net positive charge while the other end has a net negative charge. When an external electric field is applied to the liquid crystal, the dipole molecules tend to orient themselves along the direction of the field.<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> </p><p>Even if a molecule does not form a permanent dipole, it can still be influenced by an electric field. In some cases, the field produces slight re-arrangement of electrons and protons in molecules such that an induced electric dipole results. While not as strong as permanent dipoles, orientation with the external field still occurs. </p><p>The response of any system to an external electrical field is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{i}=\epsilon _{0}E_{i}+P_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{i}=\epsilon _{0}E_{i}+P_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ede56d6de8e94406fddb1efef7c10257993dd213" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.468ex; height:2.509ex;" alt="{\displaystyle D_{i}=\epsilon _{0}E_{i}+P_{i}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.515ex; height:2.509ex;" alt="{\displaystyle E_{i}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f07b53d3212e08ca316a536c8aac0bbefa79ee1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.724ex; height:2.509ex;" alt="{\displaystyle D_{i}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ba1396129f7be3c7f828a571b6649e6807d10d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.292ex; height:2.509ex;" alt="{\displaystyle P_{i}}"></span> are the components of the electric field, electric displacement field and polarization density. The electric energy per volume stored in the system is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\text{elec}}=-{\frac {1}{2}}D_{i}E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>elec</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\text{elec}}=-{\frac {1}{2}}D_{i}E_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dc3dd2655197e569df6b9d5e7da4b31627e1f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.163ex; height:5.176ex;" alt="{\displaystyle f_{\text{elec}}=-{\frac {1}{2}}D_{i}E_{i}}"></span></dd></dl> <p>(summation over the doubly appearing index <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>). In nematic liquid crystals, the polarization, and electric displacement both depend linearly on the direction of the electric field. The polarization should be even in the director since liquid crystals are invariants under reflexions of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>. The most general form to express <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{i}=\epsilon _{0}\epsilon _{\bot }E_{i}+\left(\epsilon _{\parallel }-\epsilon _{\bot }\right)n_{i}n_{j}E_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{i}=\epsilon _{0}\epsilon _{\bot }E_{i}+\left(\epsilon _{\parallel }-\epsilon _{\bot }\right)n_{i}n_{j}E_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c64f2ad17f15c9774ce5b097cc4a172a9a454cd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:32.565ex; height:3.343ex;" alt="{\displaystyle D_{i}=\epsilon _{0}\epsilon _{\bot }E_{i}+\left(\epsilon _{\parallel }-\epsilon _{\bot }\right)n_{i}n_{j}E_{j}}"></span></dd></dl> <p>(summation over the index <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>) with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{\bot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{\bot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a3e44ddb109637b52e480439bfb3163e4e9a277" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.455ex; height:2.009ex;" alt="{\displaystyle \epsilon _{\bot }}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{\parallel }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{\parallel }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3bd3720aa151b18560be1a3b23e49b1af477a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.998ex; height:2.509ex;" alt="{\displaystyle \epsilon _{\parallel }}"></span> the electric <a href="/wiki/Permittivity" title="Permittivity">permittivity</a> parallel and perpendicular to the director <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>. Then density of energy is (ignoring the constant terms that do not contribute to the dynamics of the system)<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\text{elec}}=-{\frac {1}{2}}\epsilon _{0}\left(\epsilon _{\parallel }-\epsilon _{\bot }\right)\left(E_{i}n_{i}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>elec</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\text{elec}}=-{\frac {1}{2}}\epsilon _{0}\left(\epsilon _{\parallel }-\epsilon _{\bot }\right)\left(E_{i}n_{i}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84537ebb41772c6cced06888a19adc96089c2e75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.693ex; height:5.176ex;" alt="{\displaystyle f_{\text{elec}}=-{\frac {1}{2}}\epsilon _{0}\left(\epsilon _{\parallel }-\epsilon _{\bot }\right)\left(E_{i}n_{i}\right)^{2}}"></span></dd></dl> <p>(summation over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>). If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{\parallel }-\epsilon _{\bot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{\parallel }-\epsilon _{\bot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b3e989cfa1bae187f39f069d171dc246896acc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:7.294ex; height:2.843ex;" alt="{\displaystyle \epsilon _{\parallel }-\epsilon _{\bot }}"></span> is positive, then the minimum of the energy is achieved when <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> are parallel. This means that the system will favor aligning the liquid crystal with the externally applied electric field. If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{\parallel }-\epsilon _{\bot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{\parallel }-\epsilon _{\bot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b3e989cfa1bae187f39f069d171dc246896acc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:7.294ex; height:2.843ex;" alt="{\displaystyle \epsilon _{\parallel }-\epsilon _{\bot }}"></span> is negative, then the minimum of the energy is achieved when <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> are perpendicular (in nematics the perpendicular orientation is degenerated, making possible the emergence of vortices<sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup>). </p><p>The difference <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \epsilon =\epsilon _{\parallel }-\epsilon _{\bot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ϵ</mi> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \epsilon =\epsilon _{\parallel }-\epsilon _{\bot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bed4cbbff7c43ae1b9a5682aee79e833725910b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:13.272ex; height:3.009ex;" alt="{\displaystyle \Delta \epsilon =\epsilon _{\parallel }-\epsilon _{\bot }}"></span> is called dielectrical anisotropy and is an important parameter in liquid crystal applications. There are both <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \epsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ϵ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \epsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a699942f96ac4737531138f227b7b4bd6198461c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.141ex; height:2.176ex;" alt="{\displaystyle \Delta \epsilon >0}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \epsilon <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ϵ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \epsilon <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2694a056822ebea1fb2d403ccd1fda6f37693cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.141ex; height:2.176ex;" alt="{\displaystyle \Delta \epsilon <0}"></span> commercial liquid crystals. <a href="/wiki/5CB" class="mw-redirect" title="5CB">5CB</a> and <a href="/wiki/E7_liquid_crystal_mixture" class="mw-redirect" title="E7 liquid crystal mixture">E7 liquid crystal mixture</a> are two <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \epsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ϵ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \epsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a699942f96ac4737531138f227b7b4bd6198461c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.141ex; height:2.176ex;" alt="{\displaystyle \Delta \epsilon >0}"></span> liquid crystals commonly used. <a href="/wiki/MBBA" title="MBBA">MBBA</a> is a common <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \epsilon <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ϵ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \epsilon <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2694a056822ebea1fb2d403ccd1fda6f37693cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.141ex; height:2.176ex;" alt="{\displaystyle \Delta \epsilon <0}"></span> liquid crystal. </p><p>The effects of magnetic fields on liquid crystal molecules are analogous to electric fields. Because magnetic fields are generated by moving electric charges, permanent magnetic dipoles are produced by electrons moving about atoms. When a magnetic field is applied, the molecules will tend to align with or against the field. Electromagnetic radiation, e.g. UV-Visible light, can influence light-responsive liquid crystals which mainly carry at least a photo-switchable unit.<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Surface_preparations">Surface preparations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=26" title="Edit section: Surface preparations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the absence of an external field, the director of a liquid crystal is free to point in any direction. It is possible, however, to force the director to point in a specific direction by introducing an outside agent to the system. For example, when a thin polymer coating (usually a polyimide) is spread on a glass substrate and rubbed in a single direction with a cloth, it is observed that liquid crystal molecules in contact with that surface align with the rubbing direction. The currently accepted mechanism for this is believed to be an epitaxial growth of the liquid crystal layers on the partially aligned polymer chains in the near surface layers of the polyimide. </p><p>Several liquid crystal chemicals also align to a 'command surface' which is in turn aligned by electric field of polarized light. This process is called <a href="/wiki/Photoalignment" title="Photoalignment">photoalignment</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Fréedericksz_transition"><span id="Fr.C3.A9edericksz_transition"></span>Fréedericksz transition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=27" title="Edit section: Fréedericksz transition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The competition between orientation produced by surface anchoring and by electric field effects is often exploited in liquid crystal devices. Consider the case in which liquid crystal molecules are aligned parallel to the surface and an electric field is applied perpendicular to the cell. At first, as the electric field increases in magnitude, no change in alignment occurs. However at a threshold magnitude of electric field, deformation occurs. Deformation occurs where the director changes its orientation from one molecule to the next. The occurrence of such a change from an aligned to a deformed state is called a <a href="/wiki/Fr%C3%A9edericksz_transition" title="Fréedericksz transition">Fréedericksz transition</a> and can also be produced by the application of a magnetic field of sufficient strength. </p><p>The Fréedericksz transition is fundamental to the operation of many liquid crystal displays because the director orientation (and thus the properties) can be controlled easily by the application of a field. </p> <div class="mw-heading mw-heading2"><h2 id="Effect_of_chirality">Effect of chirality</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=28" title="Edit section: Effect of chirality"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As already described, <a href="/wiki/Chirality_(chemistry)" title="Chirality (chemistry)">chiral</a> liquid-crystal molecules usually give rise to chiral mesophases. This means that the molecule must possess some form of asymmetry, usually a <a href="/wiki/Stereogenic" class="mw-redirect" title="Stereogenic">stereogenic</a> center. An additional requirement is that the system not be <a href="/wiki/Racemic" class="mw-redirect" title="Racemic">racemic</a>: a mixture of right- and left-handed molecules will cancel the chiral effect. Due to the cooperative nature of liquid crystal ordering, however, a small amount of chiral dopant in an otherwise achiral mesophase is often enough to select out one domain handedness, making the system overall chiral. </p><p>Chiral phases usually have a helical twisting of the molecules. If the pitch of this twist is on the order of the wavelength of visible light, then interesting optical interference effects can be observed. The chiral twisting that occurs in chiral LC phases also makes the system respond differently from right- and left-handed circularly polarized light. These materials can thus be used as <a href="/wiki/Polarizer" title="Polarizer">polarization filters</a>.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> </p><p>It is possible for chiral LC molecules to produce essentially achiral mesophases. For instance, in certain ranges of concentration and <a href="/wiki/Molecular_weight" class="mw-redirect" title="Molecular weight">molecular weight</a>, DNA will form an achiral line hexatic phase. An interesting recent observation is of the formation of chiral mesophases from achiral LC molecules. Specifically, bent-core molecules (sometimes called banana liquid crystals) have been shown to form liquid crystal phases that are chiral.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> In any particular sample, various domains will have opposite handedness, but within any given domain, strong chiral ordering will be present. The appearance mechanism of this macroscopic chirality is not yet entirely clear. It appears that the molecules stack in layers and orient themselves in a tilted fashion inside the layers. These liquid crystals phases may be <a href="/wiki/Ferroelectric" class="mw-redirect" title="Ferroelectric">ferroelectric</a> or anti-ferroelectric, both of which are of interest for applications.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> </p><p>Chirality can also be incorporated into a phase by adding a chiral <a href="/wiki/Dopant" title="Dopant">dopant</a>, which may not form LCs itself. <a href="/wiki/Twisted_nematic_field_effect" title="Twisted nematic field effect">Twisted-nematic</a> or <a href="/wiki/Super-twisted_nematic_display" class="mw-redirect" title="Super-twisted nematic display">super-twisted nematic</a> mixtures often contain a small amount of such dopants. </p> <div class="mw-heading mw-heading2"><h2 id="Applications_of_liquid_crystals">Applications of liquid crystals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=29" title="Edit section: Applications of liquid crystals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Liquid-crystal_display" title="Liquid-crystal display">Liquid-crystal display</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:LCD_layers.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/LCD_layers.svg/220px-LCD_layers.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/LCD_layers.svg/330px-LCD_layers.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/LCD_layers.svg/440px-LCD_layers.svg.png 2x" data-file-width="800" data-file-height="600" /></a><figcaption>Structure of liquid crystal display: 1 – vertical polarization filter, 2, 4 – glass with electrodes, 3 – liquid crystals, 5 – horizontal polarization filter, 6 – reflector</figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Wikipedia_Liquid_Crystal_Display_Arduino.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Wikipedia_Liquid_Crystal_Display_Arduino.jpg/220px-Wikipedia_Liquid_Crystal_Display_Arduino.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Wikipedia_Liquid_Crystal_Display_Arduino.jpg/330px-Wikipedia_Liquid_Crystal_Display_Arduino.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Wikipedia_Liquid_Crystal_Display_Arduino.jpg/440px-Wikipedia_Liquid_Crystal_Display_Arduino.jpg 2x" data-file-width="480" data-file-height="360" /></a><figcaption>"Wikipedia" displayed on an LCD</figcaption></figure> <p>Liquid crystals find wide use in liquid crystal displays, which rely on the <a href="/wiki/Optics" title="Optics">optical</a> properties of certain liquid crystalline substances in the presence or absence of an <a href="/wiki/Electric_field" title="Electric field">electric field</a>. In a typical device, a liquid crystal layer (typically 4 μm thick) sits between two <a href="/wiki/Polarizer" title="Polarizer">polarizers</a> that are crossed (oriented at 90° to one another). The liquid crystal alignment is chosen so that its relaxed phase is a twisted one (see <a href="/wiki/Twisted_nematic_field_effect" title="Twisted nematic field effect">Twisted nematic field effect</a>).<sup id="cite_ref-castellano_7-2" class="reference"><a href="#cite_note-castellano-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This twisted phase reorients light that has passed through the first polarizer, allowing its transmission through the second polarizer (and reflected back to the observer if a reflector is provided). The device thus appears transparent. When an electric field is applied to the LC layer, the long molecular axes tend to align parallel to the electric field thus gradually untwisting in the center of the liquid crystal layer. In this state, the LC molecules do not reorient light, so the light polarized at the first polarizer is absorbed at the second polarizer, and the device loses transparency with increasing voltage. In this way, the electric field can be used to make a pixel switch between transparent or opaque on command. Color LCD systems use the same technique, with color filters used to generate red, green, and blue pixels.<sup id="cite_ref-castellano_7-3" class="reference"><a href="#cite_note-castellano-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Chiral smectic liquid crystals are used in ferroelectric LCDs which are fast-switching binary light modulators. Similar principles can be used to make other liquid crystal based optical devices.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Liquid_crystal_tunable_filter" title="Liquid crystal tunable filter">Liquid crystal tunable filters</a> are used as <a href="/wiki/Electrooptical" class="mw-redirect" title="Electrooptical">electro-optical</a> devices,<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> e.g., in <a href="/wiki/Hyperspectral_imaging" title="Hyperspectral imaging">hyperspectral imaging</a>. </p><p><a href="/wiki/Thermochromism" title="Thermochromism">Thermotropic</a> chiral LCs whose pitch varies strongly with temperature can be used as crude <a href="/wiki/Liquid_crystal_thermometer" title="Liquid crystal thermometer">liquid crystal thermometers</a>, since the color of the material will change as the pitch is changed. Liquid crystal color transitions are used on many aquarium and pool thermometers as well as on thermometers for infants or baths.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> Other liquid crystal materials change color when stretched or stressed. Thus, liquid crystal sheets are often used in industry to look for hot spots, map heat flow, measure stress distribution patterns, and so on. Liquid crystal in fluid form is used to detect electrically generated hot spots for <a href="/wiki/Failure_analysis" title="Failure analysis">failure analysis</a> in the <a href="/wiki/Semiconductor" title="Semiconductor">semiconductor</a> industry.<sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> </p><p>Liquid crystal lenses converge or diverge the incident light by adjusting the refractive index of liquid crystal layer with applied voltage or temperature. Generally, the liquid crystal lenses generate a parabolic refractive index distribution by arranging molecular orientations. Therefore, a plane wave is reshaped into a parabolic wavefront by a liquid crystal lens. The <a href="/wiki/Focal_length" title="Focal length">focal length</a> of liquid crystal lenses could be continuously tunable when the external electric field can be properly tuned. Liquid crystal lenses are a kind of <a href="/wiki/Adaptive_optics" title="Adaptive optics">adaptive optics</a>. Imaging systems can benefit from focusing correction, image plane adjustment, or changing the range of <a href="/wiki/Depth-of-field" class="mw-redirect" title="Depth-of-field">depth-of-field</a> or <a href="/wiki/Depth_of_focus" title="Depth of focus">depth of focus</a>. The liquid crystal lense is one of the candidates to develop vision correction devices for <a href="/wiki/Myopia" title="Myopia">myopia</a> and <a href="/wiki/Presbyopia" title="Presbyopia">presbyopia</a> (e.g., tunable eyeglass and smart contact lenses).<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> Being an optical <a href="/wiki/Phase_modulator" class="mw-redirect" title="Phase modulator">phase modulator</a>, a liquid crystal lens feature space-variant <a href="/wiki/Optical_path_length" title="Optical path length">optical path length</a> (i.e., optical path length as the function of its pupil coordinate). In different imaging system, the required function of <a href="/wiki/Optical_path_length" title="Optical path length">optical path length</a> varies from one to another. For example, to converge a plane wave into a diffraction limited spot, for a physically-planar liquid crystal structure, the refractive index of liquid crystal layer should be spherical or paraboloidal under <a href="/wiki/Paraxial_approximation" title="Paraxial approximation">paraxial approximation</a>. As for projecting images or sensing objects, it may be expected to have the liquid crystal lens with aspheric distribution of optical path length across its aperture of interest. Liquid crystal lenses with electrically tunable refractive index (by addressing the different magnitude of electric field on liquid crystal layer) have potentials to achieve arbitrary function of <a href="/wiki/Optical_path_length" title="Optical path length">optical path length</a> for modulating incoming wavefront; current liquid crystal <a href="/wiki/Freeform_surface_machining" title="Freeform surface machining">freeform</a> optical elements were extended from liquid crystal lens with same optical mechanisms.<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup> The applications of liquid crystals lenses includes pico-projectors, prescriptions lenses (eyeglasses or contact lenses), smart phone camera, augmented reality, virtual reality etc. </p><p><a href="/wiki/Liquid_crystal_laser" class="mw-redirect" title="Liquid crystal laser">Liquid crystal lasers</a> use a liquid crystal in the <a href="/wiki/Active_laser_medium" title="Active laser medium">lasing medium</a> as a distributed feedback mechanism instead of external mirrors. Emission at a <a href="/wiki/Photonic_crystal" title="Photonic crystal">photonic bandgap</a> created by the periodic dielectric structure of the liquid crystal gives a low-threshold high-output device with stable monochromatic emission.<sup id="cite_ref-Kopp1998_35-1" class="reference"><a href="#cite_note-Kopp1998-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Dolgaleva2008_88-0" class="reference"><a href="#cite_note-Dolgaleva2008-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Smart_glass#Polymer-dispersed_liquid-crystal_devices" title="Smart glass">Polymer dispersed liquid crystal</a> (PDLC) sheets and rolls are available as adhesive backed <a href="/wiki/Smart_film" class="mw-redirect" title="Smart film">Smart film</a> which can be applied to windows and electrically switched between transparent and opaque to provide privacy. </p><p>Many common fluids, such as <a href="/wiki/Soap" title="Soap">soapy water</a>, are in fact liquid crystals. Soap forms a variety of LC phases depending on its concentration in water.<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup> </p><p>Liquid crystal films have revolutionized the world of technology. Currently they are used in the most diverse devices, such as digital clocks, mobile phones, calculating machines and televisions. The use of liquid crystal films in optical memory devices, with a process similar to the recording and reading of <a href="/wiki/Compact_disc" title="Compact disc">CDs</a> and <a href="/wiki/DVD" title="DVD">DVDs</a> may be possible.<sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p><p>Liquid crystals are also used as basic technology to imitate <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computers</a>, using <a href="/wiki/Electric_field" title="Electric field">electric fields</a> to manipulate the orientation of the liquid crystal <a href="/wiki/Molecule" title="Molecule">molecules</a>, to store data and to encode a different value for every different degree of misalignment with other molecules.<sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=30" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Biaxial_nematic" title="Biaxial nematic">Biaxial nematic</a></li> <li><a href="/wiki/Columnar_phase" title="Columnar phase">Columnar phase</a></li> <li><a href="/wiki/LCD_classification" title="LCD classification">LCD classification</a></li> <li><a href="/wiki/Liquid-crystal_display" title="Liquid-crystal display">Liquid-crystal display</a> – Display that uses the light-modulating properties of liquid crystals</li> <li><a href="/wiki/Liquid_crystal_on_silicon" title="Liquid crystal on silicon">Liquid crystal on silicon</a> – Type of display technology</li> <li><a href="/wiki/Liquid-crystal_polymer" title="Liquid-crystal polymer">Liquid-crystal polymer</a> – Class of extremely unreactive, inert and fire-resistant polymers</li> <li><a href="/wiki/Liquid_crystal_tunable_filter" title="Liquid crystal tunable filter">Liquid crystal tunable filter</a></li> <li><a href="/wiki/Lyotropic_liquid_crystal" title="Lyotropic liquid crystal">Lyotropic liquid crystal</a> – Solution of amphiphilic molecules which has both fluid and crystalline properties</li> <li><a href="/wiki/Pattern_formation" title="Pattern formation">Pattern formation</a> – Study of how patterns form by self-organization in nature</li> <li><a href="/wiki/Plastic_crystal" title="Plastic crystal">Plastic crystal</a> – non-classical state of matter<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Smart_glass" title="Smart glass">Smart glass</a> – Glass with electrically switchable opacity</li> <li><a href="/wiki/Thermochromism" title="Thermochromism">Thermochromism</a> – Property of substances to change colour due to a change in temperature</li> <li><a href="/wiki/Thermotropic_crystal" title="Thermotropic crystal">Thermotropic crystal</a></li> <li><a href="/wiki/Twisted_nematic_field_effect" title="Twisted nematic field effect">Twisted nematic field effect</a> – Type of thin-film-transistor liquid-crystal display technology</li> <li><a href="/wiki/Nematicon" title="Nematicon">Nematicon</a></li> <li><a href="/wiki/Liquid_crystal_thermometer" title="Liquid crystal thermometer">Liquid crystal thermometer</a></li> <li><a href="/wiki/Mood_ring" title="Mood ring">Mood ring</a> – A ring that contains a thermochromic element</li> <li><a href="/wiki/Active_fluid" title="Active fluid">Active fluid</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=31" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFReinitzer1888" class="citation journal cs1">Reinitzer F (1888). <a rel="nofollow" class="external text" href="https://www.biodiversitylibrary.org/part/232475">"Beiträge zur Kenntniss des Cholesterins"</a>. <i>Monatshefte für Chemie</i>. <b>9</b> (1): 421–441. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01516710">10.1007/BF01516710</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:97166902">97166902</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221104084215/https://www.biodiversitylibrary.org/part/232475">Archived</a> from the original on November 4, 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">September 8,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monatshefte+f%C3%BCr+Chemie&rft.atitle=Beitr%C3%A4ge+zur+Kenntniss+des+Cholesterins&rft.volume=9&rft.issue=1&rft.pages=421-441&rft.date=1888&rft_id=info%3Adoi%2F10.1007%2FBF01516710&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A97166902%23id-name%3DS2CID&rft.aulast=Reinitzer&rft.aufirst=Friedrich&rft_id=https%3A%2F%2Fwww.biodiversitylibrary.org%2Fpart%2F232475&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLehmann1889" class="citation journal cs1">Lehmann O (1889). "Über fliessende Krystalle". <i>Zeitschrift für Physikalische Chemie</i>. <b>4</b>: 462–72. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzpch-1889-0434">10.1515/zpch-1889-0434</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:92908969">92908969</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physikalische+Chemie&rft.atitle=%C3%9Cber+fliessende+Krystalle&rft.volume=4&rft.pages=462-72&rft.date=1889&rft_id=info%3Adoi%2F10.1515%2Fzpch-1889-0434&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A92908969%23id-name%3DS2CID&rft.aulast=Lehmann&rft.aufirst=O&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-b3-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-b3_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-b3_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSluckinDunmurStegemeyer2004" class="citation book cs1">Sluckin TJ, Dunmur DA, Stegemeyer H (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iMEMAuxrhFcC"><i>Crystals That Flow – classic papers from the history of liquid crystals</i></a>. London: Taylor & Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-415-25789-3" title="Special:BookSources/978-0-415-25789-3"><bdi>978-0-415-25789-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Crystals+That+Flow+%E2%80%93+classic+papers+from+the+history+of+liquid+crystals&rft.place=London&rft.pub=Taylor+%26+Francis&rft.date=2004&rft.isbn=978-0-415-25789-3&rft.aulast=Sluckin&rft.aufirst=TJ&rft.au=Dunmur%2C+DA&rft.au=Stegemeyer%2C+H&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiMEMAuxrhFcC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGray1962" class="citation book cs1">Gray GW (1962). <i>Molecular Structure and the Properties of Liquid Crystals</i>. Academic Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+Structure+and+the+Properties+of+Liquid+Crystals&rft.pub=Academic+Press&rft.date=1962&rft.aulast=Gray&rft.aufirst=GW&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStegemeyer1994" class="citation journal cs1">Stegemeyer H (1994). <a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F13583149408628630">"Professor Horst Sackmann, 1921 – 1993"</a>. <i>Liquid Crystals Today</i>. <b>4</b>: 1–2. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F13583149408628630">10.1080/13583149408628630</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Liquid+Crystals+Today&rft.atitle=Professor+Horst+Sackmann%2C+1921+%E2%80%93+1993&rft.volume=4&rft.pages=1-2&rft.date=1994&rft_id=info%3Adoi%2F10.1080%2F13583149408628630&rft.aulast=Stegemeyer&rft.aufirst=H&rft_id=https%3A%2F%2Fdoi.org%2F10.1080%252F13583149408628630&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://archive.today/20120805230930/http://www1.kfupm.edu.sa/phys101/docs/Physics%20Success%20Stories%20-%20Physics%20On%20Display.htm">"Liquid Crystals"</a>. <i>King Fahd University of Petroleum & Minerals</i>. Archived from <a rel="nofollow" class="external text" href="http://www1.kfupm.edu.sa/phys101/docs/Physics%20Success%20Stories%20-%20Physics%20On%20Display.htm">the original</a> on August 5, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=King+Fahd+University+of+Petroleum+%26+Minerals&rft.atitle=Liquid+Crystals&rft_id=http%3A%2F%2Fwww1.kfupm.edu.sa%2Fphys101%2Fdocs%2FPhysics%2520Success%2520Stories%2520-%2520Physics%2520On%2520Display.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-castellano-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-castellano_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-castellano_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-castellano_7-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-castellano_7-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCastellano2005" class="citation book cs1">Castellano JA (2005). <i>Liquid Gold: The Story of Liquid Crystal Displays and the Creation of an Industry</i>. World Scientific Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-238-956-5" title="Special:BookSources/978-981-238-956-5"><bdi>978-981-238-956-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liquid+Gold%3A+The+Story+of+Liquid+Crystal+Displays+and+the+Creation+of+an+Industry&rft.pub=World+Scientific+Publishing&rft.date=2005&rft.isbn=978-981-238-956-5&rft.aulast=Castellano&rft.aufirst=Joseph+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent" id="CITEREFGoldmacher_JE,_Castellano_JA1970"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US3540796">US 3540796</a>, Goldmacher JE, Castellano JA, "Electro-optical Compositions and Devices", issued 17 November 1970,  assigned to RCA Corp</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=3540796&rft.cc=US&rft.title=Electro-optical+Compositions+and+Devices&rft.inventor=Goldmacher+JE%2C+Castellano+JA&rft.assignee=RCA+Corp&rft.date=17 November 1970"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeilmeierZanoniBarton1968" class="citation journal cs1">Heilmeier GH, Zanoni LA, Barton LA (1968). "Dynamic Scattering in Nematic Liquid Crystals". <i>Applied Physics Letters</i>. <b>13</b> (1): 46–47. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1968ApPhL..13...46H">1968ApPhL..13...46H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1652453">10.1063/1.1652453</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Physics+Letters&rft.atitle=Dynamic+Scattering+in+Nematic+Liquid+Crystals&rft.volume=13&rft.issue=1&rft.pages=46-47&rft.date=1968&rft_id=info%3Adoi%2F10.1063%2F1.1652453&rft_id=info%3Abibcode%2F1968ApPhL..13...46H&rft.aulast=Heilmeier&rft.aufirst=GH&rft.au=Zanoni%2C+LA&rft.au=Barton%2C+LA&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKelkerScheurle1969" class="citation journal cs1">Kelker H, Scheurle B (1969). "A Liquid-crystalline (Nematic) Phase with a Particularly Low Solidification Point". <i>Angew. Chem. Int. Ed</i>. <b>8</b> (11): 884. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fanie.196908841">10.1002/anie.196908841</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Angew.+Chem.+Int.+Ed.&rft.atitle=A+Liquid-crystalline+%28Nematic%29+Phase+with+a+Particularly+Low+Solidification+Point&rft.volume=8&rft.issue=11&rft.pages=884&rft.date=1969&rft_id=info%3Adoi%2F10.1002%2Fanie.196908841&rft.aulast=Kelker&rft.aufirst=H&rft.au=Scheurle%2C+B&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrayHarrisonNash1973" class="citation journal cs1">Gray GW, Harrison KJ, Nash JA (1973). "New family of nematic liquid crystals for displays". <i>Electronics Letters</i>. <b>9</b> (6): 130. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973ElL.....9..130G">1973ElL.....9..130G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1049%2Fel%3A19730096">10.1049/el:19730096</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Electronics+Letters&rft.atitle=New+family+of+nematic+liquid+crystals+for+displays&rft.volume=9&rft.issue=6&rft.pages=130&rft.date=1973&rft_id=info%3Adoi%2F10.1049%2Fel%3A19730096&rft_id=info%3Abibcode%2F1973ElL.....9..130G&rft.aulast=Gray&rft.aufirst=GW&rft.au=Harrison%2C+KJ&rft.au=Nash%2C+JA&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandrasekharSadashivaSuresh1977" class="citation journal cs1">Chandrasekhar S, Sadashiva BK, Suresh KA (1977). "Liquid crystals of disc-like molecules". <i>Pramana</i>. <b>9</b> (5): 471–480. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1977Prama...9..471C">1977Prama...9..471C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02846252">10.1007/bf02846252</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:98207805">98207805</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pramana&rft.atitle=Liquid+crystals+of+disc-like+molecules&rft.volume=9&rft.issue=5&rft.pages=471-480&rft.date=1977&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A98207805%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fbf02846252&rft_id=info%3Abibcode%2F1977Prama...9..471C&rft.aulast=Chandrasekhar&rft.aufirst=S&rft.au=Sadashiva%2C+BK&rft.au=Suresh%2C+KA&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Collyer-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Collyer_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCollyer2012" class="citation book cs1">Collyer AA (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=p2bxCAAAQBAJ&pg=PA21"><i>Liquid Crystal Polymers: From Structures to Applications</i></a>. Springer Science & Business Media. p. 21. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-94-011-1870-5" title="Special:BookSources/978-94-011-1870-5"><bdi>978-94-011-1870-5</bdi></a>. <q>The names pyramidic or bowlic were proposed, but eventually it was decided to adopt the name conic.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liquid+Crystal+Polymers%3A+From+Structures+to+Applications&rft.pages=21&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012&rft.isbn=978-94-011-1870-5&rft.aulast=Collyer&rft.aufirst=AA&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dp2bxCAAAQBAJ%26pg%3DPA21&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_Gennes1992" class="citation journal cs1">de Gennes PG (1992). "Soft Matter(Nobel Lecture)". <i>Angewandte Chemie International Edition</i>. <b>31</b> (7): 842–845. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fanie.199208421">10.1002/anie.199208421</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Angewandte+Chemie+International+Edition&rft.atitle=Soft+Matter%28Nobel+Lecture%29&rft.volume=31&rft.issue=7&rft.pages=842-845&rft.date=1992&rft_id=info%3Adoi%2F10.1002%2Fanie.199208421&rft.aulast=de+Gennes&rft.aufirst=Pierre-Gilles&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLam1994" class="citation book cs1">Lam L (1994). "Bowlics". In Shibaev VP, Lam L (eds.). <i>Liquid Crystalline and Mesomorphic Polymers</i>. Partially Ordered Systems. New York: Springer. pp. 324–353. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4613-8333-8_10">10.1007/978-1-4613-8333-8_10</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4613-8333-8" title="Special:BookSources/978-1-4613-8333-8"><bdi>978-1-4613-8333-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Bowlics&rft.btitle=Liquid+Crystalline+and+Mesomorphic+Polymers&rft.place=New+York&rft.series=Partially+Ordered+Systems&rft.pages=324-353&rft.pub=Springer&rft.date=1994&rft_id=info%3Adoi%2F10.1007%2F978-1-4613-8333-8_10&rft.isbn=978-1-4613-8333-8&rft.aulast=Lam&rft.aufirst=L&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLei1987" class="citation journal cs1">Lei L (1987). "Bowlic Liquid Crystals". <i>Molecular Crystals and Liquid Crystals</i>. <b>146</b> (1): 41–54. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1987MCLC..146...41L">1987MCLC..146...41L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00268948708071801">10.1080/00268948708071801</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Molecular+Crystals+and+Liquid+Crystals&rft.atitle=Bowlic+Liquid+Crystals&rft.volume=146&rft.issue=1&rft.pages=41-54&rft.date=1987&rft_id=info%3Adoi%2F10.1080%2F00268948708071801&rft_id=info%3Abibcode%2F1987MCLC..146...41L&rft.aulast=Lei&rft.aufirst=Lin&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Chemical_Properties_of_Liquid_Crystals-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chemical_Properties_of_Liquid_Crystals_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20121125091905/http://plc.cwru.edu/tutorial/enhanced/files/lc/chem/chem.htm">"Chemical Properties of Liquid Crystals"</a>. Case Western Reserve University. Archived from <a rel="nofollow" class="external text" href="http://plc.cwru.edu/tutorial/enhanced/files/lc/chem/chem.htm">the original</a> on November 25, 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">June 13,</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Chemical+Properties+of+Liquid+Crystals&rft.pub=Case+Western+Reserve+University&rft_id=http%3A%2F%2Fplc.cwru.edu%2Ftutorial%2Fenhanced%2Ffiles%2Flc%2Fchem%2Fchem.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGennes1974" class="citation book cs1">Gennes, Pierre-Gilles de (1974). <a rel="nofollow" class="external text" href="http://archive.org/details/physicsofliquidc0000genn"><i>The physics of liquid crystals</i></a>. Oxford [Eng.] Clarendon Press. p. 2. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-851285-1" title="Special:BookSources/978-0-19-851285-1"><bdi>978-0-19-851285-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+physics+of+liquid+crystals&rft.pages=2&rft.pub=Oxford+%5BEng.%5D+Clarendon+Press&rft.date=1974&rft.isbn=978-0-19-851285-1&rft.aulast=Gennes&rft.aufirst=Pierre-Gilles+de&rft_id=http%3A%2F%2Farchive.org%2Fdetails%2Fphysicsofliquidc0000genn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-b2-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-b2_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-b2_19-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-b2_19-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-b2_19-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandrasekhar1992" class="citation book cs1"><a href="/wiki/Sivaramakrishna_Chandrasekhar" title="Sivaramakrishna Chandrasekhar">Chandrasekhar S</a> (1992). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=TxvUxFlQsEsC"><i>Liquid Crystals</i></a> (2nd ed.). Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-41747-1" title="Special:BookSources/978-0-521-41747-1"><bdi>978-0-521-41747-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liquid+Crystals&rft.place=Cambridge&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=1992&rft.isbn=978-0-521-41747-1&rft.aulast=Chandrasekhar&rft.aufirst=S&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DTxvUxFlQsEsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged February 2023">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-b1-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-b1_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-b1_20-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-b1_20-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-b1_20-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-b1_20-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-b1_20-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_GennesProst1993" class="citation book cs1"><a href="/wiki/Pierre-Gilles_de_Gennes" title="Pierre-Gilles de Gennes">de Gennes PG</a>, Prost J (1993). <i>The Physics of Liquid Crystals</i>. Oxford: Clarendon Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-852024-5" title="Special:BookSources/978-0-19-852024-5"><bdi>978-0-19-852024-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Physics+of+Liquid+Crystals&rft.place=Oxford&rft.pub=Clarendon+Press&rft.date=1993&rft.isbn=978-0-19-852024-5&rft.aulast=de+Gennes&rft.aufirst=PG&rft.au=Prost%2C+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarrollLeeMcConneyHall2023" class="citation journal cs1">Carroll, Gregory T.; Lee, Kyung Min; McConney, Michael E.; Hall, Harris J. (2023). <a rel="nofollow" class="external text" href="https://pubs.rsc.org/en/content/articlelanding/2023/tc/d2tc04869h">"Optical control of alignment and patterning in an azobenzene liquid crystal photoresist"</a>. <i>Journal of Materials Chemistry C</i>. <b>11</b> (6): 2177–2185. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FD2TC04869H">10.1039/D2TC04869H</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:256151872">256151872</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230420215100/https://pubs.rsc.org/en/content/articlelanding/2023/tc/d2tc04869h">Archived</a> from the original on April 20, 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">April 16,</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Materials+Chemistry+C&rft.atitle=Optical+control+of+alignment+and+patterning+in+an+azobenzene+liquid+crystal+photoresist&rft.volume=11&rft.issue=6&rft.pages=2177-2185&rft.date=2023&rft_id=info%3Adoi%2F10.1039%2FD2TC04869H&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A256151872%23id-name%3DS2CID&rft.aulast=Carroll&rft.aufirst=Gregory+T.&rft.au=Lee%2C+Kyung+Min&rft.au=McConney%2C+Michael+E.&rft.au=Hall%2C+Harris+J.&rft_id=https%3A%2F%2Fpubs.rsc.org%2Fen%2Fcontent%2Farticlelanding%2F2023%2Ftc%2Fd2tc04869h&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-b4-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-b4_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-b4_22-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-b4_22-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDierking2003" class="citation book cs1">Dierking I (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=p-0xdzDRB2kC"><i>Textures of Liquid Crystals</i></a>. Weinheim: Wiley-VCH. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-30725-8" title="Special:BookSources/978-3-527-30725-8"><bdi>978-3-527-30725-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Textures+of+Liquid+Crystals&rft.place=Weinheim&rft.pub=Wiley-VCH&rft.date=2003&rft.isbn=978-3-527-30725-8&rft.aulast=Dierking&rft.aufirst=I&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dp-0xdzDRB2kC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-b5-23"><span class="mw-cite-backlink">^ <a href="#cite_ref-b5_23-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-b5_23-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-b5_23-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-b5_23-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCollingsHird1997" class="citation book cs1">Collings PJ, Hird M (1997). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoli0000coll"><i>Introduction to Liquid Crystals</i></a></span>. Bristol, PA: Taylor & Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7484-0643-2" title="Special:BookSources/978-0-7484-0643-2"><bdi>978-0-7484-0643-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Liquid+Crystals&rft.place=Bristol%2C+PA&rft.pub=Taylor+%26+Francis&rft.date=1997&rft.isbn=978-0-7484-0643-2&rft.aulast=Collings&rft.aufirst=PJ&rft.au=Hird%2C+M&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoli0000coll&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Shao-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-Shao_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShaoZerda1998" class="citation journal cs1">Shao Y, Zerda TW (1998). "Phase Transitions of Liquid Crystal PAA in Confined Geometries". <i>Journal of Physical Chemistry B</i>. <b>102</b> (18): 3387–3394. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjp9734437">10.1021/jp9734437</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physical+Chemistry+B&rft.atitle=Phase+Transitions+of+Liquid+Crystal+PAA+in+Confined+Geometries&rft.volume=102&rft.issue=18&rft.pages=3387-3394&rft.date=1998&rft_id=info%3Adoi%2F10.1021%2Fjp9734437&rft.aulast=Shao&rft.aufirst=Y&rft.au=Zerda%2C+TW&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRegoHarveyMacKinnonGatdula2010" class="citation journal cs1">Rego JA, Harvey JA, MacKinnon AL, Gatdula E (January 2010). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121008152304/http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf">"Asymmetric synthesis of a highly soluble 'trimeric' analogue of the chiral nematic liquid crystal twist agent Merck S1011"</a> <span class="cs1-format">(PDF)</span>. <i>Liquid Crystals</i>. <b>37</b> (1): 37–43. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F02678290903359291">10.1080/02678290903359291</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:95102727">95102727</a>. Archived from <a rel="nofollow" class="external text" href="http://www.csupomona.edu/~jarego/pubs/RD2_LC.pdf">the original</a> <span class="cs1-format">(PDF)</span> on October 8, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Liquid+Crystals&rft.atitle=Asymmetric+synthesis+of+a+highly+soluble+%27trimeric%27+analogue+of+the+chiral+nematic+liquid+crystal+twist+agent+Merck+S1011&rft.volume=37&rft.issue=1&rft.pages=37-43&rft.date=2010-01&rft_id=info%3Adoi%2F10.1080%2F02678290903359291&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A95102727%23id-name%3DS2CID&rft.aulast=Rego&rft.aufirst=JA&rft.au=Harvey%2C+JA&rft.au=MacKinnon%2C+AL&rft.au=Gatdula%2C+E&rft_id=http%3A%2F%2Fwww.csupomona.edu%2F~jarego%2Fpubs%2FRD2_LC.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGézaDennistonYeomans2002" class="citation journal cs1">Géza T, Denniston C, Yeomans JM (February 26, 2002). "Hydrodynamics of Topological Defects in Nematic Liquid Crystals". <i>Physical Review Letters</i>. <b>88</b> (10): 105504. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/0201378">cond-mat/0201378</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002PhRvL..88j5504T">2002PhRvL..88j5504T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.88.105504">10.1103/PhysRevLett.88.105504</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11909370">11909370</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:38594358">38594358</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Hydrodynamics+of+Topological+Defects+in+Nematic+Liquid+Crystals&rft.volume=88&rft.issue=10&rft.pages=105504&rft.date=2002-02-26&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A38594358%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2002PhRvL..88j5504T&rft_id=info%3Aarxiv%2Fcond-mat%2F0201378&rft_id=info%3Apmid%2F11909370&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.88.105504&rft.aulast=G%C3%A9za&rft.aufirst=T&rft.au=Denniston%2C+C&rft.au=Yeomans%2C+JM&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGézaDennistonYeomans2003" class="citation journal cs1">Géza T, Denniston C, Yeomans JM (May 21, 2003). "Hydrodynamics of domain growth in nematic liquid crystals". <i>Physical Review E</i>. <b>67</b> (5): 051705. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/0207322">cond-mat/0207322</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003PhRvE..67e1705T">2003PhRvE..67e1705T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevE.67.051705">10.1103/PhysRevE.67.051705</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/12786162">12786162</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13796254">13796254</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+E&rft.atitle=Hydrodynamics+of+domain+growth+in+nematic+liquid+crystals&rft.volume=67&rft.issue=5&rft.pages=051705&rft.date=2003-05-21&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A13796254%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2003PhRvE..67e1705T&rft_id=info%3Aarxiv%2Fcond-mat%2F0207322&rft_id=info%3Apmid%2F12786162&rft_id=info%3Adoi%2F10.1103%2FPhysRevE.67.051705&rft.aulast=G%C3%A9za&rft.aufirst=T&rft.au=Denniston%2C+C&rft.au=Yeomans%2C+JM&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMadsenDingemansNakataSamulski2004" class="citation journal cs1">Madsen LA, Dingemans TJ, Nakata M, Samulski ET (April 2004). "Thermotropic biaxial nematic liquid crystals". <i>Physical Review Letters</i>. <b>92</b> (14): 145505. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004PhRvL..92n5505M">2004PhRvL..92n5505M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.92.145505">10.1103/PhysRevLett.92.145505</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15089552">15089552</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Thermotropic+biaxial+nematic+liquid+crystals&rft.volume=92&rft.issue=14&rft.pages=145505&rft.date=2004-04&rft_id=info%3Apmid%2F15089552&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.92.145505&rft_id=info%3Abibcode%2F2004PhRvL..92n5505M&rft.aulast=Madsen&rft.aufirst=LA&rft.au=Dingemans%2C+TJ&rft.au=Nakata%2C+M&rft.au=Samulski%2C+ET&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKivelsonFradkinEmery1998" class="citation journal cs1">Kivelson SA, Fradkin E, Emery VJ (June 11, 1998). <a rel="nofollow" class="external text" href="https://www.nature.com/articles/31177.pdf">"Electronic liquid-crystal phases of a doped Mott insulator"</a> <span class="cs1-format">(PDF)</span>. Letters to Nature. <i>Nature</i>. <b>393</b> (6685). Macmillan: 550–553. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/9707327">cond-mat/9707327</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998Natur.393..550K">1998Natur.393..550K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F31177">10.1038/31177</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4392009">4392009</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Electronic+liquid-crystal+phases+of+a+doped+Mott+insulator&rft.volume=393&rft.issue=6685&rft.pages=550-553&rft.date=1998-06-11&rft_id=info%3Aarxiv%2Fcond-mat%2F9707327&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4392009%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F31177&rft_id=info%3Abibcode%2F1998Natur.393..550K&rft.aulast=Kivelson&rft.aufirst=SA&rft.au=Fradkin%2C+E&rft.au=Emery%2C+VJ&rft_id=https%3A%2F%2Fwww.nature.com%2Farticles%2F31177.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFradkinKivelsonLawlerEisenstein2010" class="citation journal cs1">Fradkin E, Kivelson SA, Lawler MJ, Eisenstein JP, Mackenzie AP (May 4, 2010). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200914003558/https://authors.library.caltech.edu/20497/">"Nematic Fermi Fluids in Condensed Matter Physics"</a>. <i>Annual Review of Condensed Matter Physics</i>. <b>1</b>: 153–178. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0910.4166">0910.4166</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010ARCMP...1..153F">2010ARCMP...1..153F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev-conmatphys-070909-103925">10.1146/annurev-conmatphys-070909-103925</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:55917078">55917078</a>. Archived from <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/20497/">the original</a> on September 14, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">August 5,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Condensed+Matter+Physics&rft.atitle=Nematic+Fermi+Fluids+in+Condensed+Matter+Physics&rft.volume=1&rft.pages=153-178&rft.date=2010-05-04&rft_id=info%3Aarxiv%2F0910.4166&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55917078%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1146%2Fannurev-conmatphys-070909-103925&rft_id=info%3Abibcode%2F2010ARCMP...1..153F&rft.aulast=Fradkin&rft.aufirst=Eduardo&rft.au=Kivelson%2C+Steven+A&rft.au=Lawler%2C+Michael+J&rft.au=Eisenstein%2C+James+P&rft.au=Mackenzie%2C+Andrew+P&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F20497%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.merriam-webster.com/dictionary/smectic">"smectic"</a>. Merriam-Webster Dictionary. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130731023631/http://www.merriam-webster.com/dictionary/smectic">Archived</a> from the original on July 31, 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">April 26,</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=smectic&rft.pub=Merriam-Webster+Dictionary&rft_id=http%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2Fsmectic&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Swollen_liquid-crystalline_lamellar-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-Swollen_liquid-crystalline_lamellar_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Swollen_liquid-crystalline_lamellar_32-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGabrielCamerelLemaireDesvaux2001" class="citation journal cs1">Gabriel JC, Camerel F, Lemaire BJ, Desvaux H, Davidson P, Batail P (October 2001). <a rel="nofollow" class="external text" href="https://hal-cea.archives-ouvertes.fr/cea-03194654/file/24-Article.pdf">"Swollen liquid-crystalline lamellar phase based on extended solid-like sheets"</a> <span class="cs1-format">(PDF)</span>. <i>Nature</i>. <b>413</b> (6855): 504–8. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001Natur.413..504G">2001Natur.413..504G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F35097046">10.1038/35097046</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11586355">11586355</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4416985">4416985</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210715065520/https://hal-cea.archives-ouvertes.fr/cea-03194654/file/24-Article.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on July 15, 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">September 8,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Swollen+liquid-crystalline+lamellar+phase+based+on+extended+solid-like+sheets&rft.volume=413&rft.issue=6855&rft.pages=504-8&rft.date=2001-10&rft_id=info%3Adoi%2F10.1038%2F35097046&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4416985%23id-name%3DS2CID&rft_id=info%3Apmid%2F11586355&rft_id=info%3Abibcode%2F2001Natur.413..504G&rft.aulast=Gabriel&rft.aufirst=JC&rft.au=Camerel%2C+F&rft.au=Lemaire%2C+BJ&rft.au=Desvaux%2C+H&rft.au=Davidson%2C+P&rft.au=Batail%2C+P&rft_id=https%3A%2F%2Fhal-cea.archives-ouvertes.fr%2Fcea-03194654%2Ffile%2F24-Article.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavidsonPenissonConstantinGabriel2018" class="citation journal cs1">Davidson P, Penisson C, Constantin D, Gabriel JP (June 2018). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6042086">"Isotropic, nematic, and lamellar phases in colloidal suspensions of nanosheets"</a>. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. <b>115</b> (26): 6662–6667. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018PNAS..115.6662D">2018PNAS..115.6662D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1802692115">10.1073/pnas.1802692115</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6042086">6042086</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/29891691">29891691</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=Isotropic%2C+nematic%2C+and+lamellar+phases+in+colloidal+suspensions+of+nanosheets&rft.volume=115&rft.issue=26&rft.pages=6662-6667&rft.date=2018-06&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6042086%23id-name%3DPMC&rft_id=info%3Apmid%2F29891691&rft_id=info%3Adoi%2F10.1073%2Fpnas.1802692115&rft_id=info%3Abibcode%2F2018PNAS..115.6662D&rft.aulast=Davidson&rft.aufirst=P&rft.au=Penisson%2C+C&rft.au=Constantin%2C+D&rft.au=Gabriel%2C+JP&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6042086&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVertogenJeu2012" class="citation book cs1">Vertogen, Ger; Jeu, Wim H. de (December 6, 2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7SHrCAAAQBAJ&dq=examples+of+smectic+liquid+crystals&pg=PA13"><i>Thermotropic Liquid Crystals, Fundamentals</i></a>. Springer Science & Business Media. p. 13. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783642831331" title="Special:BookSources/9783642831331"><bdi>9783642831331</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/851375789">851375789</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231017052201/https://books.google.com/books?id=7SHrCAAAQBAJ&dq=examples+of+smectic+liquid+crystals&pg=PA13">Archived</a> from the original on October 17, 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">March 21,</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermotropic+Liquid+Crystals%2C+Fundamentals&rft.pages=13&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012-12-06&rft_id=info%3Aoclcnum%2F851375789&rft.isbn=9783642831331&rft.aulast=Vertogen&rft.aufirst=Ger&rft.au=Jeu%2C+Wim+H.+de&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7SHrCAAAQBAJ%26dq%3Dexamples%2Bof%2Bsmectic%2Bliquid%2Bcrystals%26pg%3DPA13&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Kopp1998-35"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kopp1998_35-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kopp1998_35-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoppFanVithanaGenack1998" class="citation journal cs1">Kopp VI, Fan B, Vithana HK, Genack AZ (November 1998). "Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals". <i>Optics Letters</i>. <b>23</b> (21): 1707–9. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998OptL...23.1707K">1998OptL...23.1707K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FOL.23.001707">10.1364/OL.23.001707</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18091891">18091891</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+Letters&rft.atitle=Low-threshold+lasing+at+the+edge+of+a+photonic+stop+band+in+cholesteric+liquid+crystals&rft.volume=23&rft.issue=21&rft.pages=1707-9&rft.date=1998-11&rft_id=info%3Apmid%2F18091891&rft_id=info%3Adoi%2F10.1364%2FOL.23.001707&rft_id=info%3Abibcode%2F1998OptL...23.1707K&rft.aulast=Kopp&rft.aufirst=VI&rft.au=Fan%2C+B&rft.au=Vithana%2C+HK&rft.au=Genack%2C+AZ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPriestleyWojtowiczSheng1974" class="citation book cs1">Priestley EB, Wojtowicz PJ, Sheng P (1974). <i>Introduction to Liquid Crystals</i>. Plenum Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-306-30858-1" title="Special:BookSources/978-0-306-30858-1"><bdi>978-0-306-30858-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Liquid+Crystals&rft.pub=Plenum+Press&rft.date=1974&rft.isbn=978-0-306-30858-1&rft.aulast=Priestley&rft.aufirst=EB&rft.au=Wojtowicz%2C+PJ&rft.au=Sheng%2C+P&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKazem-Rostami2019" class="citation journal cs1">Kazem-Rostami M (2019). "Optically active and photoswitchable Tröger's base analogs". <i>New Journal of Chemistry</i>. <b>43</b> (20): 7751–7755. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC9NJ01372E">10.1039/C9NJ01372E</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:164362391">164362391</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+Journal+of+Chemistry&rft.atitle=Optically+active+and+photoswitchable+Tr%C3%B6ger%27s+base+analogs&rft.volume=43&rft.issue=20&rft.pages=7751-7755&rft.date=2019&rft_id=info%3Adoi%2F10.1039%2FC9NJ01372E&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A164362391%23id-name%3DS2CID&rft.aulast=Kazem-Rostami&rft.aufirst=Masoud&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKleinertMaki1981" class="citation journal cs1"><a href="/wiki/Hagen_Kleinert" title="Hagen Kleinert">Kleinert H</a>, Maki K (1981). <a rel="nofollow" class="external text" href="http://www.physik.fu-berlin.de/~kleinert/75/75.pdf">"Lattice Textures in Cholesteric Liquid Crystals"</a> <span class="cs1-format">(PDF)</span>. <i>Fortschritte der Physik</i>. <b>29</b> (5): 219–259. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981ForPh..29..219K">1981ForPh..29..219K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fprop.19810290503">10.1002/prop.19810290503</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200426005943/http://users.physik.fu-berlin.de/~kleinert/75/75.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on April 26, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">October 7,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Fortschritte+der+Physik&rft.atitle=Lattice+Textures+in+Cholesteric+Liquid+Crystals&rft.volume=29&rft.issue=5&rft.pages=219-259&rft.date=1981&rft_id=info%3Adoi%2F10.1002%2Fprop.19810290503&rft_id=info%3Abibcode%2F1981ForPh..29..219K&rft.aulast=Kleinert&rft.aufirst=H&rft.au=Maki%2C+K&rft_id=http%3A%2F%2Fwww.physik.fu-berlin.de%2F~kleinert%2F75%2F75.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSeideman1990" class="citation journal cs1">Seideman T (1990). <a rel="nofollow" class="external text" href="http://chemgroups.northwestern.edu/seideman/Publications/The%20liquid-crystalline%20blue%20phases.pdf">"The liquid-crystalline blue phases"</a> <span class="cs1-format">(PDF)</span>. <i>Rep. Prog. Phys</i>. <b>53</b> (6): 659–705. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1990RPPh...53..659S">1990RPPh...53..659S</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.397.3141">10.1.1.397.3141</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0034-4885%2F53%2F6%2F001">10.1088/0034-4885/53/6/001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:250776819">250776819</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120330204736/http://chemgroups.northwestern.edu/seideman/Publications/The%20liquid-crystalline%20blue%20phases.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on March 30, 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">October 7,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rep.+Prog.+Phys.&rft.atitle=The+liquid-crystalline+blue+phases&rft.volume=53&rft.issue=6&rft.pages=659-705&rft.date=1990&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.397.3141%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250776819%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0034-4885%2F53%2F6%2F001&rft_id=info%3Abibcode%2F1990RPPh...53..659S&rft.aulast=Seideman&rft.aufirst=T&rft_id=http%3A%2F%2Fchemgroups.northwestern.edu%2Fseideman%2FPublications%2FThe%2520liquid-crystalline%2520blue%2520phases.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColesPivnenko2005" class="citation journal cs1">Coles HJ, Pivnenko MN (August 2005). "Liquid crystal 'blue phases' with a wide temperature range". <i>Nature</i>. <b>436</b> (7053): 997–1000. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005Natur.436..997C">2005Natur.436..997C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature03932">10.1038/nature03932</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16107843">16107843</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4307675">4307675</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Liquid+crystal+%27blue+phases%27+with+a+wide+temperature+range&rft.volume=436&rft.issue=7053&rft.pages=997-1000&rft.date=2005-08&rft_id=info%3Adoi%2F10.1038%2Fnature03932&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4307675%23id-name%3DS2CID&rft_id=info%3Apmid%2F16107843&rft_id=info%3Abibcode%2F2005Natur.436..997C&rft.aulast=Coles&rft.aufirst=HJ&rft.au=Pivnenko%2C+MN&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYamamotoNishiyamaInoueYokoyama2005" class="citation journal cs1">Yamamoto J, Nishiyama I, Inoue M, Yokoyama H (September 2005). "Optical isotropy and iridescence in a smectic 'blue phase'<span class="cs1-kern-right"></span>". <i>Nature</i>. <b>437</b> (7058): 525–8. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005Natur.437..525Y">2005Natur.437..525Y</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature04034">10.1038/nature04034</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16177785">16177785</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4432184">4432184</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Optical+isotropy+and+iridescence+in+a+smectic+%27blue+phase%27&rft.volume=437&rft.issue=7058&rft.pages=525-8&rft.date=2005-09&rft_id=info%3Adoi%2F10.1038%2Fnature04034&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4432184%23id-name%3DS2CID&rft_id=info%3Apmid%2F16177785&rft_id=info%3Abibcode%2F2005Natur.437..525Y&rft.aulast=Yamamoto&rft.aufirst=J&rft.au=Nishiyama%2C+I&rft.au=Inoue%2C+M&rft.au=Yokoyama%2C+H&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKikuchiYokotaHisakadoYang2002" class="citation journal cs1">Kikuchi H, Yokota M, Hisakado Y, Yang H, Kajiyama T (September 2002). "Polymer-stabilized liquid crystal blue phases". <i>Nature Materials</i>. <b>1</b> (1): 64–8. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002NatMa...1...64K">2002NatMa...1...64K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnmat712">10.1038/nmat712</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/12618852">12618852</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:31419926">31419926</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Materials&rft.atitle=Polymer-stabilized+liquid+crystal+blue+phases&rft.volume=1&rft.issue=1&rft.pages=64-8&rft.date=2002-09&rft_id=info%3Adoi%2F10.1038%2Fnmat712&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A31419926%23id-name%3DS2CID&rft_id=info%3Apmid%2F12618852&rft_id=info%3Abibcode%2F2002NatMa...1...64K&rft.aulast=Kikuchi&rft.aufirst=H&rft.au=Yokota%2C+M&rft.au=Hisakado%2C+Y&rft.au=Yang%2C+H&rft.au=Kajiyama%2C+T&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.physorg.com/news129997960.html">"Samsung Develops World's First 'Blue Phase' Technology to Achieve 240 Hz Driving Speed for High-Speed Video"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120315124810/http://www.physorg.com/news129997960.html">Archived</a> from the original on March 15, 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">April 23,</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Samsung+Develops+World%27s+First+%27Blue+Phase%27+Technology+to+Achieve+240+Hz+Driving+Speed+for+High-Speed+Video&rft_id=http%3A%2F%2Fwww.physorg.com%2Fnews129997960.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOtónYoshidaMorawiakStrzeżysz2020" class="citation journal cs1">Otón E, Yoshida H, Morawiak P, Strzeżysz O, Kula P, Ozaki M, Piecek W (June 2020). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7311397">"Orientation control of ideal blue phase photonic crystals"</a>. <i>Scientific Reports</i>. <b>10</b> (1): 10148. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020NatSR..1010148O">2020NatSR..1010148O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41598-020-67083-6">10.1038/s41598-020-67083-6</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7311397">7311397</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/32576875">32576875</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+Reports&rft.atitle=Orientation+control+of+ideal+blue+phase+photonic+crystals&rft.volume=10&rft.issue=1&rft.pages=10148&rft.date=2020-06&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7311397%23id-name%3DPMC&rft_id=info%3Apmid%2F32576875&rft_id=info%3Adoi%2F10.1038%2Fs41598-020-67083-6&rft_id=info%3Abibcode%2F2020NatSR..1010148O&rft.aulast=Ot%C3%B3n&rft.aufirst=E&rft.au=Yoshida%2C+H&rft.au=Morawiak%2C+P&rft.au=Strze%C5%BCysz%2C+O&rft.au=Kula%2C+P&rft.au=Ozaki%2C+M&rft.au=Piecek%2C+W&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7311397&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Bowlics-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bowlics_45-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangHuangLamCheng2017" class="citation journal cs1">Wang L, Huang D, Lam L, Cheng Z (2017). <a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F1358314X.2017.1398307">"Bowlics: history, advances and applications"</a>. <i>Liquid Crystals Today</i>. <b>26</b> (4): 85–111. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F1358314X.2017.1398307">10.1080/1358314X.2017.1398307</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:126256863">126256863</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Liquid+Crystals+Today&rft.atitle=Bowlics%3A+history%2C+advances+and+applications&rft.volume=26&rft.issue=4&rft.pages=85-111&rft.date=2017&rft_id=info%3Adoi%2F10.1080%2F1358314X.2017.1398307&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A126256863%23id-name%3DS2CID&rft.aulast=Wang&rft.aufirst=L&rft.au=Huang%2C+D&rft.au=Lam%2C+L&rft.au=Cheng%2C+Z&rft_id=https%3A%2F%2Fdoi.org%2F10.1080%252F1358314X.2017.1398307&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiangLiuLiuJian2005" class="citation journal cs1">Liang Q, Liu P, Liu C, Jian X, Hong D, Li Y (2005). "Synthesis and Properties of Lyotropic Liquid Crystalline Copolyamides Containing Phthalazinone Moieties and Ether Linkages". <i>Polymer</i>. <b>46</b> (16): 6258–6265. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.polymer.2005.05.059">10.1016/j.polymer.2005.05.059</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Polymer&rft.atitle=Synthesis+and+Properties+of+Lyotropic+Liquid+Crystalline+Copolyamides+Containing+Phthalazinone+Moieties+and+Ether+Linkages&rft.volume=46&rft.issue=16&rft.pages=6258-6265&rft.date=2005&rft_id=info%3Adoi%2F10.1016%2Fj.polymer.2005.05.059&rft.aulast=Liang&rft.aufirst=Qizhen&rft.au=Liu%2C+Pengtao&rft.au=Liu%2C+Cheng&rft.au=Jian%2C+Xigao&rft.au=Hong%2C+Dingyi&rft.au=Li%2C+Yang&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-martin-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-martin_47-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMartinKearyThorntonNovotnak2006" class="citation journal cs1">Martin JD, Keary CL, Thornton TA, Novotnak MP, Knutson JW, Folmer JC (April 2006). "Metallotropic liquid crystals formed by surfactant templating of molten metal halides". <i>Nature Materials</i>. <b>5</b> (4): 271–5. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006NatMa...5..271M">2006NatMa...5..271M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnmat1610">10.1038/nmat1610</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16547520">16547520</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:35833273">35833273</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Materials&rft.atitle=Metallotropic+liquid+crystals+formed+by+surfactant+templating+of+molten+metal+halides&rft.volume=5&rft.issue=4&rft.pages=271-5&rft.date=2006-04&rft_id=info%3Adoi%2F10.1038%2Fnmat1610&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A35833273%23id-name%3DS2CID&rft_id=info%3Apmid%2F16547520&rft_id=info%3Abibcode%2F2006NatMa...5..271M&rft.aulast=Martin&rft.aufirst=JD&rft.au=Keary%2C+CL&rft.au=Thornton%2C+TA&rft.au=Novotnak%2C+MP&rft.au=Knutson%2C+JW&rft.au=Folmer%2C+JC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Tomczyk2017-48"><span class="mw-cite-backlink">^ <a href="#cite_ref-Tomczyk2017_48-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Tomczyk2017_48-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTomczykMarzecJuszyńska-GałązkaWęgłowska2017" class="citation journal cs1">Tomczyk W, Marzec M, Juszyńska-Gałązka E, Węgłowska D (2017). "Mesomorphic and physicochemical properties of liquid crystal mixture composed of chiral molecules with perfluorinated terminal chains". <i>Journal of Molecular Structure</i>. <b>1130</b>: 503–510. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017JMoSt1130..503T">2017JMoSt1130..503T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.molstruc.2016.10.039">10.1016/j.molstruc.2016.10.039</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Molecular+Structure&rft.atitle=Mesomorphic+and+physicochemical+properties+of+liquid+crystal+mixture+composed+of+chiral+molecules+with+perfluorinated+terminal+chains&rft.volume=1130&rft.pages=503-510&rft.date=2017&rft_id=info%3Adoi%2F10.1016%2Fj.molstruc.2016.10.039&rft_id=info%3Abibcode%2F2017JMoSt1130..503T&rft.aulast=Tomczyk&rft.aufirst=W&rft.au=Marzec%2C+M&rft.au=Juszy%C5%84ska-Ga%C5%82%C4%85zka%2C+E&rft.au=W%C4%99g%C5%82owska%2C+D&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJuszyńska-GałązkaGałązkaMassalska-ArodźBąk2014" class="citation journal cs1">Juszyńska-Gałązka E, Gałązka M, Massalska-Arodź M, Bąk A, Chłędowska K, Tomczyk W (December 2014). "Phase Behavior and Dynamics of the Liquid Crystal 4'-butyl-4-(2-methylbutoxy)azoxybenzene (4ABO5*)". <i>The Journal of Physical Chemistry B</i>. <b>118</b> (51): 14982–9. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjp510584w">10.1021/jp510584w</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/25429851">25429851</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Physical+Chemistry+B&rft.atitle=Phase+Behavior+and+Dynamics+of+the+Liquid+Crystal+4%27-butyl-4-%282-methylbutoxy%29azoxybenzene+%284ABO5%2A%29&rft.volume=118&rft.issue=51&rft.pages=14982-9&rft.date=2014-12&rft_id=info%3Adoi%2F10.1021%2Fjp510584w&rft_id=info%3Apmid%2F25429851&rft.aulast=Juszy%C5%84ska-Ga%C5%82%C4%85zka&rft.aufirst=E&rft.au=Ga%C5%82%C4%85zka%2C+M&rft.au=Massalska-Arod%C5%BA%2C+M&rft.au=B%C4%85k%2C+A&rft.au=Ch%C5%82%C4%99dowska%2C+K&rft.au=Tomczyk%2C+W&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Templer_Seddon_1991-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-Templer_Seddon_1991_50-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTemplerSeddon1991" class="citation news cs1">Templer, Richard; Seddon, John (May 18, 1991). <a rel="nofollow" class="external text" href="https://www.newscientist.com/article/mg13017695-400-the-world-of-liquid-crystals/">"The World of Liquid Crystals"</a>. <i><a href="/wiki/New_Scientist" title="New Scientist">New Scientist</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231215151806/https://www.newscientist.com/article/mg13017695-400-the-world-of-liquid-crystals/">Archived</a> from the original on December 15, 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">December 15,</span> 2023</span>. <q>You might be surprised to find out that cell membranes are liquid crystals. In fact, the first recorded observations of the liquid crystalline phase were of myelin, the material that coats nerve fibres.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+Scientist&rft.atitle=The+World+of+Liquid+Crystals&rft.date=1991-05-18&rft.aulast=Templer&rft.aufirst=Richard&rft.au=Seddon%2C+John&rft_id=https%3A%2F%2Fwww.newscientist.com%2Farticle%2Fmg13017695-400-the-world-of-liquid-crystals%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWensinkDunkelHeidenreichDrescher2012" class="citation journal cs1">Wensink HH, Dunkel J, Heidenreich S, Drescher K, Goldstein RE, <a href="/wiki/Hartmut_L%C3%B6wen" title="Hartmut Löwen">Löwen H</a>, Yeomans JM (September 2012). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3607014">"Meso-scale turbulence in living fluids"</a>. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. <b>109</b> (36): 14308–13. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PNAS..110.4488S">2013PNAS..110.4488S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1215368110">10.1073/pnas.1215368110</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3607014">3607014</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22908244">22908244</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=Meso-scale+turbulence+in+living+fluids&rft.volume=109&rft.issue=36&rft.pages=14308-13&rft.date=2012-09&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3607014%23id-name%3DPMC&rft_id=info%3Apmid%2F22908244&rft_id=info%3Adoi%2F10.1073%2Fpnas.1215368110&rft_id=info%3Abibcode%2F2013PNAS..110.4488S&rft.aulast=Wensink&rft.aufirst=HH&rft.au=Dunkel%2C+J&rft.au=Heidenreich%2C+S&rft.au=Drescher%2C+K&rft.au=Goldstein%2C+RE&rft.au=L%C3%B6wen%2C+H&rft.au=Yeomans%2C+JM&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3607014&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSawDoostmohammadiNierKocgozlu2017" class="citation journal cs1">Saw TB, Doostmohammadi A, Nier V, Kocgozlu L, Thampi S, Toyama Y, et al. (April 2017). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5439518">"Topological defects in epithelia govern cell death and extrusion"</a>. <i>Nature</i>. <b>544</b> (7649): 212–216. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017Natur.544..212S">2017Natur.544..212S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature21718">10.1038/nature21718</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5439518">5439518</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28406198">28406198</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Topological+defects+in+epithelia+govern+cell+death+and+extrusion&rft.volume=544&rft.issue=7649&rft.pages=212-216&rft.date=2017-04&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5439518%23id-name%3DPMC&rft_id=info%3Apmid%2F28406198&rft_id=info%3Adoi%2F10.1038%2Fnature21718&rft_id=info%3Abibcode%2F2017Natur.544..212S&rft.aulast=Saw&rft.aufirst=TB&rft.au=Doostmohammadi%2C+A&rft.au=Nier%2C+V&rft.au=Kocgozlu%2C+L&rft.au=Thampi%2C+S&rft.au=Toyama%2C+Y&rft.au=Marcq%2C+P&rft.au=Lim%2C+CT&rft.au=Yeomans%2C+JM&rft.au=Ladoux%2C+B&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5439518&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZocher1925" class="citation journal cs1">Zocher H (1925). "Uber freiwillige Strukturbildung in Solen. (Eine neue Art anisotrop flqssiger Medien)". <i>Z. Anorg. Allg. Chem</i>. <b>147</b>: 91. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fzaac.19251470111">10.1002/zaac.19251470111</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Anorg.+Allg.+Chem.&rft.atitle=Uber+freiwillige+Strukturbildung+in+Solen.+%28Eine+neue+Art+anisotrop+flqssiger+Medien%29&rft.volume=147&rft.pages=91&rft.date=1925&rft_id=info%3Adoi%2F10.1002%2Fzaac.19251470111&rft.aulast=Zocher&rft.aufirst=H&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavidsonGabriel2003" class="citation journal cs1">Davidson P, Gabriel JC (2003). "Mineral Liquid Crystals from Self-Assembly of Anisotropic Nanosystems". <i>Top Curr Chem</i>. <b>226</b>: 119. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fb10827">10.1007/b10827</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Top+Curr+Chem&rft.atitle=Mineral+Liquid+Crystals+from+Self-Assembly+of+Anisotropic+Nanosystems&rft.volume=226&rft.pages=119&rft.date=2003&rft_id=info%3Adoi%2F10.1007%2Fb10827&rft.aulast=Davidson&rft.aufirst=Patrick&rft.au=Gabriel%2C+Jean-Christophe+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLangmuir1938" class="citation journal cs1">Langmuir I (1938). "The role of attractive and repulsive forces in the formation of tactoids, thixotropic gels, protein crystals and coacervates". <i>J Chem Phys</i>. <b>6</b> (12): 873. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1938JChPh...6..873L">1938JChPh...6..873L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1750183">10.1063/1.1750183</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J+Chem+Phys&rft.atitle=The+role+of+attractive+and+repulsive+forces+in+the+formation+of+tactoids%2C+thixotropic+gels%2C+protein+crystals+and+coacervates&rft.volume=6&rft.issue=12&rft.pages=873&rft.date=1938&rft_id=info%3Adoi%2F10.1063%2F1.1750183&rft_id=info%3Abibcode%2F1938JChPh...6..873L&rft.aulast=Langmuir&rft.aufirst=I&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGabrielSanchezDavidson1996" class="citation journal cs1">Gabriel JC, Sanchez C, Davidson P (1996). "Observation of Nematic Liquid-Crystal Textures in Aqueous Gels of Smectite Clays". <i>J. Phys. Chem</i>. <b>100</b> (26): 11139. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjp961088z">10.1021/jp961088z</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Phys.+Chem.&rft.atitle=Observation+of+Nematic+Liquid-Crystal+Textures+in+Aqueous+Gels+of+Smectite+Clays&rft.volume=100&rft.issue=26&rft.pages=11139&rft.date=1996&rft_id=info%3Adoi%2F10.1021%2Fjp961088z&rft.aulast=Gabriel&rft.aufirst=Jean+Christophe+P.&rft.au=Sanchez%2C+Cl%C3%A9ment&rft.au=Davidson%2C+Patrick&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPaineauPhilippeAntonovaBihannic2013" class="citation journal cs1">Paineau E, Philippe AM, Antonova K, Bihannic I, Davidson P, Dozov I, et al. (2013). "Liquid–crystalline properties of aqueous suspensions of natural clay nanosheets". <i>Liquid Crystals Reviews</i>. <b>1</b> (2): 110. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F21680396.2013.842130">10.1080/21680396.2013.842130</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:136533412">136533412</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Liquid+Crystals+Reviews&rft.atitle=Liquid%E2%80%93crystalline+properties+of+aqueous+suspensions+of+natural+clay+nanosheets&rft.volume=1&rft.issue=2&rft.pages=110&rft.date=2013&rft_id=info%3Adoi%2F10.1080%2F21680396.2013.842130&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A136533412%23id-name%3DS2CID&rft.aulast=Paineau&rft.aufirst=E&rft.au=Philippe%2C+AM&rft.au=Antonova%2C+K&rft.au=Bihannic%2C+I&rft.au=Davidson%2C+P&rft.au=Dozov%2C+I&rft.au=Gabriel%2C+JC&rft.au=Imp%C3%A9ror-Clerc%2C+M&rft.au=Levitz%2C+P&rft.au=Meneau%2C+F&rft.au=Michot%2C+LJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBukaPalffy-MuhorayRácz1987" class="citation journal cs1">Buka A, Palffy-Muhoray P, Rácz Z (October 1987). "Viscous fingering in liquid crystals". <i>Physical Review A</i>. <b>36</b> (8): 3984–3989. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1987PhRvA..36.3984B">1987PhRvA..36.3984B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.36.3984">10.1103/PhysRevA.36.3984</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9899337">9899337</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Viscous+fingering+in+liquid+crystals&rft.volume=36&rft.issue=8&rft.pages=3984-3989&rft.date=1987-10&rft_id=info%3Apmid%2F9899337&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.36.3984&rft_id=info%3Abibcode%2F1987PhRvA..36.3984B&rft.aulast=Buka&rft.aufirst=A&rft.au=Palffy-Muhoray%2C+P&rft.au=R%C3%A1cz%2C+Z&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGonzález-CincaRamirez-PiscinaCasademuntHernández-Machado1996" class="citation journal cs1">González-Cinca R, Ramirez-Piscina L, Casademunt J, Hernández-Machado A, Kramer L, Katona TT, et al. (1996). "Phase-field simulations and experiments of faceted growth in liquid crystal". <i>Physica D</i>. <b>99</b> (2–3): 359. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996PhyD...99..359G">1996PhyD...99..359G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0167-2789%2896%2900162-5">10.1016/S0167-2789(96)00162-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physica+D&rft.atitle=Phase-field+simulations+and+experiments+of+faceted+growth+in+liquid+crystal&rft.volume=99&rft.issue=2%E2%80%933&rft.pages=359&rft.date=1996&rft_id=info%3Adoi%2F10.1016%2FS0167-2789%2896%2900162-5&rft_id=info%3Abibcode%2F1996PhyD...99..359G&rft.aulast=Gonz%C3%A1lez-Cinca&rft.aufirst=R&rft.au=Ramirez-Piscina%2C+L&rft.au=Casademunt%2C+J&rft.au=Hern%C3%A1ndez-Machado%2C+A&rft.au=Kramer%2C+L&rft.au=Katona%2C+TT&rft.au=B%C3%B6rzs%C3%B6nyi%2C+T&rft.au=Buka%2C+A&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGonzález-CincaRamırez-PiscinaCasademuntHernández-Machado1998" class="citation journal cs1">González-Cinca R, Ramırez-Piscina L, Casademunt J, Hernández-Machado A, Tóth-Katona T, Börzsönyi T, Buka Á (1998). "Heat diffusion anisotropy in dendritic growth: phase field simulations and experiments in liquid crystals". <i>Journal of Crystal Growth</i>. <b>193</b> (4): 712. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998JCrGr.193..712G">1998JCrGr.193..712G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0022-0248%2898%2900505-3">10.1016/S0022-0248(98)00505-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Crystal+Growth&rft.atitle=Heat+diffusion+anisotropy+in+dendritic+growth%3A+phase+field+simulations+and+experiments+in+liquid+crystals&rft.volume=193&rft.issue=4&rft.pages=712&rft.date=1998&rft_id=info%3Adoi%2F10.1016%2FS0022-0248%2898%2900505-3&rft_id=info%3Abibcode%2F1998JCrGr.193..712G&rft.aulast=Gonz%C3%A1lez-Cinca&rft.aufirst=R&rft.au=Ram%C4%B1rez-Piscina%2C+L&rft.au=Casademunt%2C+J&rft.au=Hern%C3%A1ndez-Machado%2C+A&rft.au=T%C3%B3th-Katona%2C+T&rft.au=B%C3%B6rzs%C3%B6nyi%2C+T&rft.au=Buka%2C+%C3%81&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChaikinLubensky1995" class="citation book cs1">Chaikin, P. M.; Lubensky, T. C. (1995). <i>Principles of condensed matter physics</i>. Cambridge: Cambridge University Press. p. 168. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521794503" title="Special:BookSources/9780521794503"><bdi>9780521794503</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+condensed+matter+physics&rft.place=Cambridge&rft.pages=168&rft.pub=Cambridge+University+Press&rft.date=1995&rft.isbn=9780521794503&rft.aulast=Chaikin&rft.aufirst=P.+M.&rft.au=Lubensky%2C+T.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGhosh1984" class="citation journal cs1">Ghosh SK (1984). "A model for the orientational order in liquid crystals". <i>Il Nuovo Cimento D</i>. <b>4</b> (3): 229. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1984NCimD...4..229G">1984NCimD...4..229G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF02453342">10.1007/BF02453342</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121078315">121078315</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Il+Nuovo+Cimento+D&rft.atitle=A+model+for+the+orientational+order+in+liquid+crystals&rft.volume=4&rft.issue=3&rft.pages=229&rft.date=1984&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121078315%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF02453342&rft_id=info%3Abibcode%2F1984NCimD...4..229G&rft.aulast=Ghosh&rft.aufirst=SK&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOnsager1949" class="citation journal cs1">Onsager L (1949). "The effects of shape on the interaction of colloidal particles". <i>Annals of the New York Academy of Sciences</i>. <b>51</b> (4): 627. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1949NYASA..51..627O">1949NYASA..51..627O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1749-6632.1949.tb27296.x">10.1111/j.1749-6632.1949.tb27296.x</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:84562683">84562683</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+the+New+York+Academy+of+Sciences&rft.atitle=The+effects+of+shape+on+the+interaction+of+colloidal+particles&rft.volume=51&rft.issue=4&rft.pages=627&rft.date=1949&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A84562683%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1111%2Fj.1749-6632.1949.tb27296.x&rft_id=info%3Abibcode%2F1949NYASA..51..627O&rft.aulast=Onsager&rft.aufirst=Lars&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-vroege-64"><span class="mw-cite-backlink">^ <a href="#cite_ref-vroege_64-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-vroege_64-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVroegeLekkerkerker1992" class="citation journal cs1">Vroege GJ, Lekkerkerker HN (1992). <a rel="nofollow" class="external text" href="https://dspace.library.uu.nl/bitstream/1874/22348/1/lekkerkerker_92_phase_transition_lyotropic_colloidal.pdf">"Phase transitions in lyotropic colloidal and polymer liquid crystals"</a> <span class="cs1-format">(PDF)</span>. <i>Rep. Prog. Phys</i>. <b>55</b> (8): 1241. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1992RPPh...55.1241V">1992RPPh...55.1241V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0034-4885%2F55%2F8%2F003">10.1088/0034-4885/55/8/003</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1874%2F22348">1874/22348</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:250865818">250865818</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rep.+Prog.+Phys.&rft.atitle=Phase+transitions+in+lyotropic+colloidal+and+polymer+liquid+crystals&rft.volume=55&rft.issue=8&rft.pages=1241&rft.date=1992&rft_id=info%3Ahdl%2F1874%2F22348&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250865818%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0034-4885%2F55%2F8%2F003&rft_id=info%3Abibcode%2F1992RPPh...55.1241V&rft.aulast=Vroege&rft.aufirst=GJ&rft.au=Lekkerkerker%2C+HN&rft_id=https%3A%2F%2Fdspace.library.uu.nl%2Fbitstream%2F1874%2F22348%2F1%2Flekkerkerker_92_phase_transition_lyotropic_colloidal.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaierSaupe1958" class="citation journal cs1 cs1-prop-foreign-lang-source">Maier W, Saupe A (1958). <a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzna-1958-0716">"Eine einfache molekulare theorie des nematischen kristallinflussigen zustandes"</a>. <i>Z. Naturforsch. A</i> (in German). <b>13</b> (7): 564. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1958ZNatA..13..564M">1958ZNatA..13..564M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzna-1958-0716">10.1515/zna-1958-0716</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:93402217">93402217</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Naturforsch.+A&rft.atitle=Eine+einfache+molekulare+theorie+des+nematischen+kristallinflussigen+zustandes&rft.volume=13&rft.issue=7&rft.pages=564&rft.date=1958&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A93402217%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1515%2Fzna-1958-0716&rft_id=info%3Abibcode%2F1958ZNatA..13..564M&rft.aulast=Maier&rft.aufirst=W&rft.au=Saupe%2C+A&rft_id=https%3A%2F%2Fdoi.org%2F10.1515%252Fzna-1958-0716&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaierSaupe1959" class="citation journal cs1 cs1-prop-foreign-lang-source">Maier W, Saupe A (1959). <a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzna-1959-1005">"Eine einfache molekular-statistische theorie der nematischen kristallinflussigen phase .1"</a>. <i>Z. Naturforsch. A</i> (in German). <b>14</b> (10): 882. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1959ZNatA..14..882M">1959ZNatA..14..882M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzna-1959-1005">10.1515/zna-1959-1005</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:201840526">201840526</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Naturforsch.+A&rft.atitle=Eine+einfache+molekular-statistische+theorie+der+nematischen+kristallinflussigen+phase+.1&rft.volume=14&rft.issue=10&rft.pages=882&rft.date=1959&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A201840526%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1515%2Fzna-1959-1005&rft_id=info%3Abibcode%2F1959ZNatA..14..882M&rft.aulast=Maier&rft.aufirst=W&rft.au=Saupe%2C+A&rft_id=https%3A%2F%2Fdoi.org%2F10.1515%252Fzna-1959-1005&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaierSaupe1960" class="citation journal cs1 cs1-prop-foreign-lang-source">Maier W, Saupe A (1960). <a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzna-1960-0401">"Eine einfache molekular-statistische theorie der nematischen kristallinflussigen phase .2"</a>. <i>Z. Naturforsch. A</i> (in German). <b>15</b> (4): 287. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960ZNatA..15..287M">1960ZNatA..15..287M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fzna-1960-0401">10.1515/zna-1960-0401</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:97407506">97407506</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Naturforsch.+A&rft.atitle=Eine+einfache+molekular-statistische+theorie+der+nematischen+kristallinflussigen+phase+.2&rft.volume=15&rft.issue=4&rft.pages=287&rft.date=1960&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A97407506%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1515%2Fzna-1960-0401&rft_id=info%3Abibcode%2F1960ZNatA..15..287M&rft.aulast=Maier&rft.aufirst=W&rft.au=Saupe%2C+A&rft_id=https%3A%2F%2Fdoi.org%2F10.1515%252Fzna-1960-0401&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-68">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCiferri1991" class="citation book cs1">Ciferri A (1991). <i>Liquid crystallinity in polymers : principles and fundamental properties</i>. Weinheim: VCH Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-527-27922-9" title="Special:BookSources/3-527-27922-9"><bdi>3-527-27922-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liquid+crystallinity+in+polymers+%3A+principles+and+fundamental+properties&rft.place=Weinheim&rft.pub=VCH+Publishers&rft.date=1991&rft.isbn=3-527-27922-9&rft.aulast=Ciferri&rft.aufirst=Alberto&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-69">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcMillan1971" class="citation journal cs1">McMillan W (1971). "Simple Molecular Model for the Smectic A Phase of Liquid Crystals". <i>Phys. Rev. A</i>. <b>4</b> (3): 1238. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1971PhRvA...4.1238M">1971PhRvA...4.1238M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.4.1238">10.1103/PhysRevA.4.1238</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+A&rft.atitle=Simple+Molecular+Model+for+the+Smectic+A+Phase+of+Liquid+Crystals&rft.volume=4&rft.issue=3&rft.pages=1238&rft.date=1971&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.4.1238&rft_id=info%3Abibcode%2F1971PhRvA...4.1238M&rft.aulast=McMillan&rft.aufirst=W&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-70"><span class="mw-cite-backlink"><b><a href="#cite_ref-70">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeslie1992" class="citation journal cs1">Leslie FM (1992). "Continuum theory for nematic liquid crystals". <i>Continuum Mechanics and Thermodynamics</i>. <b>4</b> (3): 167. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1992CMT.....4..167L">1992CMT.....4..167L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01130288">10.1007/BF01130288</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120908851">120908851</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Continuum+Mechanics+and+Thermodynamics&rft.atitle=Continuum+theory+for+nematic+liquid+crystals&rft.volume=4&rft.issue=3&rft.pages=167&rft.date=1992&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120908851%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01130288&rft_id=info%3Abibcode%2F1992CMT.....4..167L&rft.aulast=Leslie&rft.aufirst=FM&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-71"><span class="mw-cite-backlink"><b><a href="#cite_ref-71">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWatsonBrandtWelchBrown2012" class="citation journal cs1">Watson MC, Brandt EG, Welch PM, Brown FL (July 2012). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.109.028102">"Determining biomembrane bending rigidities from simulations of modest size"</a>. <i>Physical Review Letters</i>. <b>109</b> (2): 028102. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012PhRvL.109b8102W">2012PhRvL.109b8102W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.109.028102">10.1103/PhysRevLett.109.028102</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23030207">23030207</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Determining+biomembrane+bending+rigidities+from+simulations+of+modest+size&rft.volume=109&rft.issue=2&rft.pages=028102&rft.date=2012-07&rft_id=info%3Apmid%2F23030207&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.109.028102&rft_id=info%3Abibcode%2F2012PhRvL.109b8102W&rft.aulast=Watson&rft.aufirst=MC&rft.au=Brandt%2C+EG&rft.au=Welch%2C+PM&rft.au=Brown%2C+FL&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRevLett.109.028102&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-72"><span class="mw-cite-backlink"><b><a href="#cite_ref-72">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTakezoe2014" class="citation journal cs1">Takezoe H (2014). "Historical Overview of Polar Liquid Crystals". <i>Ferroelectrics</i>. <b>468</b> (1): 1–17. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014Fer...468....1T">2014Fer...468....1T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00150193.2014.932653">10.1080/00150193.2014.932653</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120165343">120165343</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ferroelectrics&rft.atitle=Historical+Overview+of+Polar+Liquid+Crystals&rft.volume=468&rft.issue=1&rft.pages=1-17&rft.date=2014&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120165343%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1080%2F00150193.2014.932653&rft_id=info%3Abibcode%2F2014Fer...468....1T&rft.aulast=Takezoe&rft.aufirst=Hideo&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-73"><span class="mw-cite-backlink"><b><a href="#cite_ref-73">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOswaldPieranski2005" class="citation book cs1">Oswald P, Pieranski P (2005). <a rel="nofollow" class="external text" href="https://www.crcpress.com/Nematic-and-Cholesteric-Liquid-Crystals-Concepts-and-Physical-Properties/Oswald-Pieranski/p/book/9780415321402"><i>Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780415321402" title="Special:BookSources/9780415321402"><bdi>9780415321402</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190515040953/https://www.crcpress.com/Nematic-and-Cholesteric-Liquid-Crystals-Concepts-and-Physical-Properties/Oswald-Pieranski/p/book/9780415321402">Archived</a> from the original on May 15, 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">May 15,</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nematic+and+Cholesteric+Liquid+Crystals%3A+Concepts+and+Physical+Properties+Illustrated+by+Experiments&rft.pub=CRC+Press&rft.date=2005&rft.isbn=9780415321402&rft.aulast=Oswald&rft.aufirst=Patrick&rft.au=Pieranski%2C+Pavel&rft_id=https%3A%2F%2Fwww.crcpress.com%2FNematic-and-Cholesteric-Liquid-Crystals-Concepts-and-Physical-Properties%2FOswald-Pieranski%2Fp%2Fbook%2F9780415321402&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-74">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarbozaBortolozzoAssantoVidal-Henriquez2012" class="citation journal cs1">Barboza R, Bortolozzo U, Assanto G, Vidal-Henriquez E, Clerc MG, <a href="/wiki/Stefania_Residori" title="Stefania Residori">Residori S</a> (October 2012). "Vortex induction via anisotropy stabilized light-matter interaction". <i>Physical Review Letters</i>. <b>109</b> (14): 143901. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012PhRvL.109n3901B">2012PhRvL.109n3901B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.109.143901">10.1103/PhysRevLett.109.143901</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10533%2F136047">10533/136047</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23083241">23083241</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Vortex+induction+via+anisotropy+stabilized+light-matter+interaction&rft.volume=109&rft.issue=14&rft.pages=143901&rft.date=2012-10&rft_id=info%3Ahdl%2F10533%2F136047&rft_id=info%3Apmid%2F23083241&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.109.143901&rft_id=info%3Abibcode%2F2012PhRvL.109n3901B&rft.aulast=Barboza&rft.aufirst=R&rft.au=Bortolozzo%2C+U&rft.au=Assanto%2C+G&rft.au=Vidal-Henriquez%2C+E&rft.au=Clerc%2C+MG&rft.au=Residori%2C+S&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-75"><span class="mw-cite-backlink"><b><a href="#cite_ref-75">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKazem-Rostami2017" class="citation journal cs1">Kazem-Rostami M (2017). "photoswitchable liquid crystal design". <i>Synthesis</i>. <b>49</b> (6): 1214–1222. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1055%2Fs-0036-1588913">10.1055/s-0036-1588913</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:99913657">99913657</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Synthesis&rft.atitle=photoswitchable+liquid+crystal+design&rft.volume=49&rft.issue=6&rft.pages=1214-1222&rft.date=2017&rft_id=info%3Adoi%2F10.1055%2Fs-0036-1588913&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A99913657%23id-name%3DS2CID&rft.aulast=Kazem-Rostami&rft.aufirst=Masoud&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-76"><span class="mw-cite-backlink"><b><a href="#cite_ref-76">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFujikakeTakizawaAidaNegishi1998" class="citation journal cs1">Fujikake H, Takizawa K, Aida T, Negishi T, Kobayashi M (1998). "Video camera system using liquid-crystal polarizing filter toreduce reflected light". <i>IEEE Transactions on Broadcasting</i>. <b>44</b> (4): 419. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F11.735903">10.1109/11.735903</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Broadcasting&rft.atitle=Video+camera+system+using+liquid-crystal+polarizing+filter+toreduce+reflected+light&rft.volume=44&rft.issue=4&rft.pages=419&rft.date=1998&rft_id=info%3Adoi%2F10.1109%2F11.735903&rft.aulast=Fujikake&rft.aufirst=H&rft.au=Takizawa%2C+K&rft.au=Aida%2C+T&rft.au=Negishi%2C+T&rft.au=Kobayashi%2C+M&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-77">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAchardBedelMarcerouNguyen2003" class="citation journal cs1">Achard MF, Bedel JP, Marcerou JP, Nguyen HT, Rouillon JC (February 2003). "Switching of banana liquid crystal mesophases under field". <i>The European Physical Journal E</i>. <b>10</b> (2): 129–34. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003EPJE...10..129A">2003EPJE...10..129A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1140%2Fepje%2Fe2003-00016-y">10.1140/epje/e2003-00016-y</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15011066">15011066</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:35942754">35942754</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+European+Physical+Journal+E&rft.atitle=Switching+of+banana+liquid+crystal+mesophases+under+field&rft.volume=10&rft.issue=2&rft.pages=129-34&rft.date=2003-02&rft_id=info%3Adoi%2F10.1140%2Fepje%2Fe2003-00016-y&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A35942754%23id-name%3DS2CID&rft_id=info%3Apmid%2F15011066&rft_id=info%3Abibcode%2F2003EPJE...10..129A&rft.aulast=Achard&rft.aufirst=MF&rft.au=Bedel%2C+JP&rft.au=Marcerou%2C+JP&rft.au=Nguyen%2C+HT&rft.au=Rouillon%2C+JC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-78"><span class="mw-cite-backlink"><b><a href="#cite_ref-78">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBausColot1989" class="citation journal cs1">Baus M, Colot JL (November 1989). <a rel="nofollow" class="external text" href="https://dipot.ulb.ac.be/dspace/bitstream/2013/39767/4/02137fa4-0709-490a-b691-101e483af30c.txt">"Ferroelectric nematic liquid-crystal phases of dipolar hard ellipsoids"</a>. <i>Physical Review A</i>. <b>40</b> (9): 5444–5446. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989PhRvA..40.5444B">1989PhRvA..40.5444B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.40.5444">10.1103/PhysRevA.40.5444</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9902823">9902823</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210427211925/https://dipot.ulb.ac.be/dspace/bitstream/2013/39767/4/02137fa4-0709-490a-b691-101e483af30c.txt">Archived</a> from the original on April 27, 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">March 4,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Ferroelectric+nematic+liquid-crystal+phases+of+dipolar+hard+ellipsoids&rft.volume=40&rft.issue=9&rft.pages=5444-5446&rft.date=1989-11&rft_id=info%3Apmid%2F9902823&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.40.5444&rft_id=info%3Abibcode%2F1989PhRvA..40.5444B&rft.aulast=Baus&rft.aufirst=M&rft.au=Colot%2C+JL&rft_id=https%3A%2F%2Fdipot.ulb.ac.be%2Fdspace%2Fbitstream%2F2013%2F39767%2F4%2F02137fa4-0709-490a-b691-101e483af30c.txt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-79"><span class="mw-cite-backlink"><b><a href="#cite_ref-79">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUeharaHatano2002" class="citation journal cs1">Uehara H, Hatano J (2002). "Pressure-Temperature Phase Diagrams of Ferroelectric Liquid Crystals". <i>J. Phys. Soc. Jpn</i>. <b>71</b> (2): 509. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002JPSJ...71..509U">2002JPSJ...71..509U</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1143%2FJPSJ.71.509">10.1143/JPSJ.71.509</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Phys.+Soc.+Jpn.&rft.atitle=Pressure-Temperature+Phase+Diagrams+of+Ferroelectric+Liquid+Crystals&rft.volume=71&rft.issue=2&rft.pages=509&rft.date=2002&rft_id=info%3Adoi%2F10.1143%2FJPSJ.71.509&rft_id=info%3Abibcode%2F2002JPSJ...71..509U&rft.aulast=Uehara&rft.aufirst=Hiroyuki&rft.au=Hatano%2C+Jun&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-80"><span class="mw-cite-backlink"><b><a href="#cite_ref-80">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlkeskjoldScolariNoordegraafLægsgaard2007" class="citation journal cs1">Alkeskjold TT, Scolari L, Noordegraaf D, Lægsgaard J, Weirich J, Wei L, Tartarini G, Bassi P, Gauza S, Wu ST, Bjarklev A (2007). "Integrating liquid crystal based optical devices in photonic crystal". <i>Optical and Quantum Electronics</i>. <b>39</b> (12–13): 1009. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs11082-007-9139-8">10.1007/s11082-007-9139-8</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:54208691">54208691</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optical+and+Quantum+Electronics&rft.atitle=Integrating+liquid+crystal+based+optical+devices+in+photonic+crystal&rft.volume=39&rft.issue=12%E2%80%9313&rft.pages=1009&rft.date=2007&rft_id=info%3Adoi%2F10.1007%2Fs11082-007-9139-8&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A54208691%23id-name%3DS2CID&rft.aulast=Alkeskjold&rft.aufirst=Thomas+Tanggaard&rft.au=Scolari%2C+Lara&rft.au=Noordegraaf%2C+Danny&rft.au=L%C3%A6gsgaard%2C+Jesper&rft.au=Weirich%2C+Johannes&rft.au=Wei%2C+Lei&rft.au=Tartarini%2C+Giovanni&rft.au=Bassi%2C+Paolo&rft.au=Gauza%2C+Sebastian&rft.au=Wu%2C+Shin-Tson&rft.au=Bjarklev%2C+Anders&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-81"><span class="mw-cite-backlink"><b><a href="#cite_ref-81">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCiofaniMenciassi2012" class="citation book cs1">Ciofani G, Menciassi A (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PKwlrW-CrxUC&pg=PA16"><i>Piezoelectric Nanomaterials for Biomedical Applications</i></a>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783642280443" title="Special:BookSources/9783642280443"><bdi>9783642280443</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Piezoelectric+Nanomaterials+for+Biomedical+Applications&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012&rft.isbn=9783642280443&rft.aulast=Ciofani&rft.aufirst=Gianni&rft.au=Menciassi%2C+Arianna&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPKwlrW-CrxUC%26pg%3DPA16&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-82"><span class="mw-cite-backlink"><b><a href="#cite_ref-82">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA.D._Chandra_&_A._Banerjee2020" class="citation journal cs1">A.D. Chandra & A. Banerjee (2020). <a rel="nofollow" class="external text" href="https://www.tandfonline.com/doi/abs/10.1080/09500340.2020.1760954">"Rapid phase calibration of a spatial light modulator using novel phase masks and optimization of its efficiency using an iterative algorithm"</a>. <i>Journal of Modern Optics</i>. <b>67</b> (7). Journal of Modern Optics, Volume 67, Issue 7, 18 May 2020: 628–637. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1811.03297">1811.03297</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020JMOp...67..628C">2020JMOp...67..628C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F09500340.2020.1760954">10.1080/09500340.2020.1760954</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:219646821">219646821</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220410015422/https://www.tandfonline.com/doi/abs/10.1080/09500340.2020.1760954">Archived</a> from the original on April 10, 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">January 7,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Modern+Optics&rft.atitle=Rapid+phase+calibration+of+a+spatial+light+modulator+using+novel+phase+masks+and+optimization+of+its+efficiency+using+an+iterative+algorithm&rft.volume=67&rft.issue=7&rft.pages=628-637&rft.date=2020&rft_id=info%3Aarxiv%2F1811.03297&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A219646821%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1080%2F09500340.2020.1760954&rft_id=info%3Abibcode%2F2020JMOp...67..628C&rft.au=A.D.+Chandra+%26+A.+Banerjee&rft_id=https%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Fabs%2F10.1080%2F09500340.2020.1760954&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-83"><span class="mw-cite-backlink"><b><a href="#cite_ref-83">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><span class="citation patent" id="CITEREFPlimpton_RG1988"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US4738549">US 4738549</a>, Plimpton RG, "Pool thermometer", issued 1988-04-19</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=4738549&rft.cc=US&rft.title=Pool+thermometer&rft.inventor=Plimpton+RG&rft.date=1988-04-19"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-84"><span class="mw-cite-backlink"><b><a href="#cite_ref-84">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090211050934/http://www.acceleratedanalysis.com/LC_hotspotdetection_procedure.html">"Hot-spot detection techniques for ICs"</a>. <i>acceleratedanalysis.com</i>. Archived from <a rel="nofollow" class="external text" href="http://www.acceleratedanalysis.com/LC_hotspotdetection_procedure.html">the original</a> on February 11, 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">May 5,</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=acceleratedanalysis.com&rft.atitle=Hot-spot+detection+techniques+for+ICs&rft_id=http%3A%2F%2Fwww.acceleratedanalysis.com%2FLC_hotspotdetection_procedure.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-85"><span class="mw-cite-backlink"><b><a href="#cite_ref-85">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSato1979" class="citation journal cs1">Sato S (1979). "Liquid-Crystal Lens-Cells with Variable Focal Length". <i>Japanese Journal of Applied Physics</i>. <b>18</b> (9): 1679–1684. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1979JaJAP..18.1679S">1979JaJAP..18.1679S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1143%2FJJAP.18.1679">10.1143/JJAP.18.1679</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119784753">119784753</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Japanese+Journal+of+Applied+Physics&rft.atitle=Liquid-Crystal+Lens-Cells+with+Variable+Focal+Length&rft.volume=18&rft.issue=9&rft.pages=1679-1684&rft.date=1979&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119784753%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1143%2FJJAP.18.1679&rft_id=info%3Abibcode%2F1979JaJAP..18.1679S&rft.aulast=Sato&rft.aufirst=S&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-86"><span class="mw-cite-backlink"><b><a href="#cite_ref-86">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLinWangReshetnyak2017" class="citation journal cs1">Lin YH, Wang YJ, Reshetnyak V (2017). "Liquid crystal lenses with tunable focal length". <i>Liquid Crystals Reviews</i>. <b>5</b> (2): 111–143. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F21680396.2018.1440256">10.1080/21680396.2018.1440256</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:139938136">139938136</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Liquid+Crystals+Reviews&rft.atitle=Liquid+crystal+lenses+with+tunable+focal+length&rft.volume=5&rft.issue=2&rft.pages=111-143&rft.date=2017&rft_id=info%3Adoi%2F10.1080%2F21680396.2018.1440256&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A139938136%23id-name%3DS2CID&rft.aulast=Lin&rft.aufirst=YH&rft.au=Wang%2C+YJ&rft.au=Reshetnyak%2C+V&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-87"><span class="mw-cite-backlink"><b><a href="#cite_ref-87">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangLinCakmakciReshetnyak2020" class="citation journal cs1">Wang, Yu-Jen; Lin, Yi-Hsin; Cakmakci, Ozan; Reshetnyak, Victor (2020). <a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FOE.389647">"Phase modulators with tunability in wavefronts and optical axes originating from anisotropic molecular tilts under symmetric electric field II: Experiments"</a>. <i>Optics Express</i>. <b>28</b> (6): 8985–9001. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020OExpr..28.8985W">2020OExpr..28.8985W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FOE.389647">10.1364/OE.389647</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/32225513">32225513</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:214734642">214734642</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+Express&rft.atitle=Phase+modulators+with+tunability+in+wavefronts+and+optical+axes+originating+from+anisotropic+molecular+tilts+under+symmetric+electric+field+II%3A+Experiments&rft.volume=28&rft.issue=6&rft.pages=8985-9001&rft.date=2020&rft_id=info%3Adoi%2F10.1364%2FOE.389647&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A214734642%23id-name%3DS2CID&rft_id=info%3Apmid%2F32225513&rft_id=info%3Abibcode%2F2020OExpr..28.8985W&rft.aulast=Wang&rft.aufirst=Yu-Jen&rft.au=Lin%2C+Yi-Hsin&rft.au=Cakmakci%2C+Ozan&rft.au=Reshetnyak%2C+Victor&rft_id=https%3A%2F%2Fdoi.org%2F10.1364%252FOE.389647&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-Dolgaleva2008-88"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dolgaleva2008_88-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDolgalevaWeiLukishovaChen2008" class="citation journal cs1">Dolgaleva K, Wei SK, Lukishova SG, Chen SH, Schwertz K, Boyd RW (2008). "Enhanced laser performance of cholesteric liquid crystals doped with oligofluorene dye". <i>Journal of the Optical Society of America</i>. <b>25</b> (9): 1496–1504. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008JOSAB..25.1496D">2008JOSAB..25.1496D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FJOSAB.25.001496">10.1364/JOSAB.25.001496</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Optical+Society+of+America&rft.atitle=Enhanced+laser+performance+of+cholesteric+liquid+crystals+doped+with+oligofluorene+dye&rft.volume=25&rft.issue=9&rft.pages=1496-1504&rft.date=2008&rft_id=info%3Adoi%2F10.1364%2FJOSAB.25.001496&rft_id=info%3Abibcode%2F2008JOSAB..25.1496D&rft.aulast=Dolgaleva&rft.aufirst=K&rft.au=Wei%2C+SK&rft.au=Lukishova%2C+SG&rft.au=Chen%2C+SH&rft.au=Schwertz%2C+K&rft.au=Boyd%2C+RW&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-89"><span class="mw-cite-backlink"><b><a href="#cite_ref-89">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLuzzatiMustacchiSkoulios1957" class="citation journal cs1">Luzzati V, Mustacchi H, Skoulios A (1957). "Structure of the Liquid-Crystal Phases of the Soap–water System: Middle Soap and Neat Soap". <i>Nature</i>. <b>180</b> (4586): 600. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1957Natur.180..600L">1957Natur.180..600L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F180600a0">10.1038/180600a0</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4163714">4163714</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Structure+of+the+Liquid-Crystal+Phases+of+the+Soap%E2%80%93water+System%3A+Middle+Soap+and+Neat+Soap&rft.volume=180&rft.issue=4586&rft.pages=600&rft.date=1957&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4163714%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F180600a0&rft_id=info%3Abibcode%2F1957Natur.180..600L&rft.aulast=Luzzati&rft.aufirst=V&rft.au=Mustacchi%2C+H&rft.au=Skoulios%2C+A&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-90"><span class="mw-cite-backlink"><b><a href="#cite_ref-90">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilvaSotomayorFigueirinhas2015" class="citation journal cs1">Silva MC, Sotomayor J, Figueirinhas J (September 2015). "Effect of an additive on the permanent memory effect of polymer dispersed liquid crystal films". <i>Journal of Chemical Technology & Biotechnology</i>. <b>90</b> (9): 1565–9. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015JCTB...90.1565S">2015JCTB...90.1565S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fjctb.4677">10.1002/jctb.4677</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Technology+%26+Biotechnology&rft.atitle=Effect+of+an+additive+on+the+permanent+memory+effect+of+polymer+dispersed+liquid+crystal+films.&rft.volume=90&rft.issue=9&rft.pages=1565-9&rft.date=2015-09&rft_id=info%3Adoi%2F10.1002%2Fjctb.4677&rft_id=info%3Abibcode%2F2015JCTB...90.1565S&rft.aulast=Silva&rft.aufirst=MC&rft.au=Sotomayor%2C+J&rft.au=Figueirinhas%2C+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-91"><span class="mw-cite-backlink"><b><a href="#cite_ref-91">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFda_SilvaFigueirinhasSotomayor2016" class="citation journal cs1">da Silva MC, Figueirinhas JL, Sotomayor JC (January 2016). "Improvement of permanent memory effect in PDLC films using TX-100 as an additive". <i>Liquid Crystals</i>. <b>43</b> (1): 124–30. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F02678292.2015.1061713">10.1080/02678292.2015.1061713</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:101996816">101996816</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Liquid+Crystals&rft.atitle=Improvement+of+permanent+memory+effect+in+PDLC+films+using+TX-100+as+an+additive.&rft.volume=43&rft.issue=1&rft.pages=124-30&rft.date=2016-01&rft_id=info%3Adoi%2F10.1080%2F02678292.2015.1061713&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A101996816%23id-name%3DS2CID&rft.aulast=da+Silva&rft.aufirst=MC&rft.au=Figueirinhas%2C+JL&rft.au=Sotomayor%2C+JC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-92"><span class="mw-cite-backlink"><b><a href="#cite_ref-92">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPadavic-Callaghan2022" class="citation journal cs1">Padavic-Callaghan, Karmela (August 19, 2022). <a rel="nofollow" class="external text" href="https://www.newscientist.com/article/2334577-computer-made-from-liquid-crystals-would-ripple-with-calculations/">"Computer made from liquid crystals would ripple with calculations"</a>. <i>Science Advances</i>. <b>8</b> (33). <a href="/wiki/New_Scientist" title="New Scientist">New Scientist</a>: eabp8371. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fsciadv.abp8371">10.1126/sciadv.abp8371</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F145669">1721.1/145669</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9390992">9390992</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/35984880">35984880</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220824200410/https://www.newscientist.com/article/2334577-computer-made-from-liquid-crystals-would-ripple-with-calculations/">Archived</a> from the original on August 24, 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">August 24,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science+Advances&rft.atitle=Computer+made+from+liquid+crystals+would+ripple+with+calculations&rft.volume=8&rft.issue=33&rft.pages=eabp8371&rft.date=2022-08-19&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9390992%23id-name%3DPMC&rft_id=info%3Apmid%2F35984880&rft_id=info%3Ahdl%2F1721.1%2F145669&rft_id=info%3Adoi%2F10.1126%2Fsciadv.abp8371&rft.aulast=Padavic-Callaghan&rft.aufirst=Karmela&rft_id=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2334577-computer-made-from-liquid-crystals-would-ripple-with-calculations%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> <li id="cite_note-93"><span class="mw-cite-backlink"><b><a href="#cite_ref-93">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://eandt.theiet.org/content/articles/2022/08/liquid-crystals-could-be-used-to-make-computers-mit-study-says">"Researchers claim that ripples and imperfections in liquid crystals like those found in LCD TVs could be used to build a new type of computer"</a>. <a href="/wiki/Engineering_and_Technology" class="mw-redirect" title="Engineering and Technology">Engineering and Technology</a>. August 22, 2022. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220826104728/https://eandt.theiet.org/content/articles/2022/08/liquid-crystals-could-be-used-to-make-computers-mit-study-says/">Archived</a> from the original on August 26, 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">August 24,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Researchers+claim+that+ripples+and+imperfections+in+liquid+crystals+like+those+found+in+LCD+TVs+could+be+used+to+build+a+new+type+of+computer&rft.pub=Engineering+and+Technology&rft.date=2022-08-22&rft_id=https%3A%2F%2Feandt.theiet.org%2Fcontent%2Farticles%2F2022%2F08%2Fliquid-crystals-could-be-used-to-make-computers-mit-study-says&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquid_crystal&action=edit&section=32" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Liquid_crystal" class="extiw" title="commons:Liquid crystal"><span style="font-style:italic; font-weight:bold;">Liquid crystal</span></a>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://nobelprize.org/educational_games/physics/liquid_crystals/history/">"History and Properties of Liquid Crystals"</a>. Nobelprize.org. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090830015819/http://nobelprize.org/educational_games/physics/liquid_crystals/history/">Archived</a> from the original on August 30, 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">June 6,</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=History+and+Properties+of+Liquid+Crystals&rft_id=http%3A%2F%2Fnobelprize.org%2Feducational_games%2Fphysics%2Fliquid_crystals%2Fhistory%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid+crystal" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.iupac.org/publications/pac/2001/7305/7305x0845.html">Definitions of basic terms relating to low-molar-mass and polymer liquid crystals (IUPAC Recommendations 2001)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091003181404/http://www.iupac.org/publications/pac/2001/7305/7305x0845.html">Archived</a> October 3, 2009, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070813190453/http://plc.cwru.edu/tutorial/enhanced/files/textbook.htm">An intelligible introduction to liquid crystals</a> from Case Western Reserve University</li> <li><a rel="nofollow" class="external text" href="http://bly.colorado.edu/lcphysics.html">Liquid Crystal Physics tutorial</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070805214934/http://bly.colorado.edu/lcphysics.html">Archived</a> August 5, 2007, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> from the Liquid Crystals Group, University of Colorado</li> <li><a rel="nofollow" class="external text" href="http://www.elis.ugent.be/ELISgroups/lcd/lc/lc.php">Liquid Crystals & Photonics Group – Ghent University (Belgium)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070613163026/http://www.elis.ugent.be/ELISgroups/lcd/lc/lc.php">Archived</a> June 13, 2007, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, good tutorial</li> <li><a rel="nofollow" class="external text" href="http://www.elis.ugent.be/ELISgroups/lcd/research/bpm.php">Simulation of light propagation in liquid crystals</a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged October 2022">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup>, free program</li> <li><a rel="nofollow" class="external text" href="http://liqcryst.chemie.uni-hamburg.de/">Liquid Crystals Interactive Online</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210318132425/http://liqcryst.chemie.uni-hamburg.de/">Archived</a> March 18, 2021, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.lci.kent.edu">Liquid Crystal Institute</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170920233330/http://www.lci.kent.edu/">Archived</a> September 20, 2017, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Kent State University</li> <li><a rel="nofollow" class="external text" href="http://www.tandf.co.uk/journals/titles/02678292.asp">Liquid Crystals</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040122033847/http://www.tandf.co.uk/journals/titles/02678292.asp">Archived</a> January 22, 2004, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> a journal by Taylor&Francis</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070820013456/http://www.tandf.co.uk/journals/titles/15421406.asp">Molecular Crystals and Liquid Crystals</a> a journal by Taylor & Francis</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090211050934/http://www.acceleratedanalysis.com/LC_hotspotdetection_procedure.html">Hot-spot detection techniques for ICs</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060216155202/http://www.mc2.chalmers.se/mc2/pl/lc/engelska/frame.html">What are liquid crystals?</a> from Chalmers University of Technology, Sweden</li> <li><a rel="nofollow" class="external text" href="http://www.beilstein-journals.org/bjoc/browse/singleSeries.htm?sn=5">Progress in liquid crystal chemistry</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100616001843/http://www.beilstein-journals.org/bjoc/browse/singleSeries.htm?sn=5">Archived</a> June 16, 2010, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Thematic series in the Open Access Beilstein Journal of Organic Chemistry</li> <li><a rel="nofollow" class="external text" href="http://www.doitpoms.ac.uk/tlplib/liquid_crystals/index.php">DoITPoMS Teaching and Learning Package- "Liquid Crystals"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100804045318/http://www.doitpoms.ac.uk/tlplib/liquid_crystals/index.php">Archived</a> August 4, 2010, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.sjsu.edu/people/lui.lam/bowlic/">Bowlic liquid crystal</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150518102025/http://www.sjsu.edu/people/lui.lam/bowlic/">Archived</a> May 18, 2015, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> from San Jose State University</li> <li><a rel="nofollow" class="external text" href="https://www.tandfonline.com/doi/full/10.1080/09500340.2020.1760954">Phase calibration of a Spatial Light Modulator</a> <a rel="nofollow" class="external 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title="Solid">Solid</a></li> <li><a href="/wiki/Liquid" title="Liquid">Liquid</a></li> <li><a href="/wiki/Gas" title="Gas">Gas</a> / <a href="/wiki/Vapor" title="Vapor">Vapor</a></li> <li><a href="/wiki/Supercritical_fluid" title="Supercritical fluid">Supercritical fluid</a></li> <li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="7" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Phase_change_-_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/150px-Phase_change_-_en.svg.png" decoding="async" width="150" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/225px-Phase_change_-_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/300px-Phase_change_-_en.svg.png 2x" data-file-width="493" data-file-height="524" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Low energy</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li> <li><a href="/wiki/Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li> <li><a href="/wiki/Degenerate_matter" title="Degenerate matter">Degenerate matter</a></li> <li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall</a></li> <li><a href="/wiki/Rydberg_matter" title="Rydberg matter">Rydberg matter</a></li> <li><a href="/wiki/Strange_matter" title="Strange matter">Strange matter</a></li> <li><a href="/wiki/Superfluidity" title="Superfluidity">Superfluid</a></li> <li><a href="/wiki/Supersolid" title="Supersolid">Supersolid</a></li> <li><a href="/wiki/Photonic_molecule" title="Photonic molecule">Photonic molecule</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">High energy</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/QCD_matter" title="QCD matter">QCD matter</a></li> <li><a href="/wiki/Quark%E2%80%93gluon_plasma" title="Quark–gluon plasma">Quark–gluon plasma</a></li> <li><a href="/wiki/Color-glass_condensate" title="Color-glass condensate">Color-glass condensate</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other states</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Colloid" title="Colloid">Colloid</a></li> <li><a href="/wiki/Crystal" title="Crystal">Crystal</a></li> <li><a class="mw-selflink selflink">Liquid crystal</a></li> <li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li> <li><a href="/wiki/Quantum_spin_liquid" title="Quantum spin liquid">Quantum spin liquid</a></li> <li><a href="/wiki/Exotic_matter" title="Exotic matter">Exotic matter</a></li> <li><a href="/wiki/Programmable_matter" title="Programmable matter">Programmable matter</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Antimatter" title="Antimatter">Antimatter</a></li> <li>Magnetically ordered <ul><li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a></li> <li><a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">Ferrimagnet</a></li> <li><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li></ul></li> <li><a href="/wiki/String-net_liquid" title="String-net liquid">String-net liquid</a></li> <li><a href="/wiki/Superglass" title="Superglass">Superglass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Phase_transitions" class="mw-redirect" title="Phase transitions">Phase transitions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boiling" title="Boiling">Boiling</a></li> <li><a href="/wiki/Boiling_point" title="Boiling point">Boiling point</a></li> <li><a href="/wiki/Condensation" title="Condensation">Condensation</a></li> <li><a href="/wiki/Critical_line_(thermodynamics)" title="Critical line (thermodynamics)">Critical line</a></li> <li><a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">Critical point</a></li> <li><a href="/wiki/Crystallization" title="Crystallization">Crystallization</a></li> <li><a href="/wiki/Deposition_(phase_transition)" title="Deposition (phase transition)">Deposition</a></li> <li><a href="/wiki/Evaporation" title="Evaporation">Evaporation</a></li> <li><a href="/wiki/Flash_evaporation" title="Flash evaporation">Flash evaporation</a></li> <li><a href="/wiki/Freezing" title="Freezing">Freezing</a></li> <li><a href="/wiki/Chemical_ionization" title="Chemical ionization">Chemical ionization</a></li> <li><a href="/wiki/Ionization" title="Ionization">Ionization</a></li> <li><a href="/wiki/Lambda_point" title="Lambda point">Lambda point</a></li> <li><a href="/wiki/Melting" title="Melting">Melting</a></li> <li><a href="/wiki/Melting_point" title="Melting point">Melting point</a></li> <li><a href="/wiki/Plasma_recombination" title="Plasma recombination">Recombination</a></li> <li><a href="/wiki/Regelation" title="Regelation">Regelation</a></li> <li><a href="/wiki/Vapor%E2%80%93liquid_equilibrium" title="Vapor–liquid equilibrium">Saturated fluid</a></li> <li><a href="/wiki/Sublimation_(phase_transition)" title="Sublimation (phase transition)">Sublimation</a></li> <li><a href="/wiki/Supercooling" title="Supercooling">Supercooling</a></li> <li><a href="/wiki/Triple_point" title="Triple point">Triple point</a></li> <li><a href="/wiki/Vaporization" title="Vaporization">Vaporization</a></li> <li><a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantities</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Enthalpy_of_fusion" title="Enthalpy of fusion">Enthalpy of fusion</a></li> <li><a href="/wiki/Enthalpy_of_sublimation" title="Enthalpy of sublimation">Enthalpy of sublimation</a></li> <li><a href="/wiki/Enthalpy_of_vaporization" title="Enthalpy of vaporization">Enthalpy of vaporization</a></li> <li><a href="/wiki/Latent_heat" title="Latent heat">Latent heat</a></li> <li><a href="/wiki/Latent_internal_energy" title="Latent internal energy">Latent internal energy</a></li> <li><a href="/wiki/Trouton%27s_rule" title="Trouton's rule">Trouton's rule</a></li> <li><a href="/wiki/Volatility_(chemistry)" title="Volatility (chemistry)">Volatility</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Baryonic_matter" class="mw-redirect" title="Baryonic matter">Baryonic matter</a></li> <li><a href="/wiki/Binodal" title="Binodal">Binodal</a></li> <li><a href="/wiki/Compressed_fluid" title="Compressed fluid">Compressed fluid</a></li> <li><a href="/wiki/Cooling_curve" title="Cooling curve">Cooling curve</a></li> <li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Leidenfrost_effect" title="Leidenfrost effect">Leidenfrost effect</a></li> <li><a href="/wiki/Macroscopic_quantum_phenomena" title="Macroscopic quantum phenomena">Macroscopic quantum phenomena</a></li> <li><a href="/wiki/Mpemba_effect" title="Mpemba effect">Mpemba effect</a></li> <li><a href="/wiki/Order_and_disorder_(physics)" class="mw-redirect" title="Order and disorder (physics)">Order and disorder (physics)</a></li> <li><a href="/wiki/Spinodal" title="Spinodal">Spinodal</a></li> <li><a href="/wiki/Superconductivity" title="Superconductivity">Superconductivity</a></li> <li><a href="/wiki/Superheated_water" title="Superheated water">Superheated vapor</a></li> <li><a href="/wiki/Superheating" title="Superheating">Superheating</a></li> <li><a href="/wiki/Thermo-dielectric_effect" title="Thermo-dielectric effect">Thermo-dielectric effect</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link 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srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85077357">United States</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Cristaux liquides"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11981189m">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Cristaux liquides"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11981189m">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00561894">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="kapalné krystaly"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph126495&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007531570605171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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