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class="vector-toc-list"> <li id="toc-Force_Contributions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Force_Contributions"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Force Contributions</span> </div> </a> <ul id="toc-Force_Contributions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-London_dispersion_force" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#London_dispersion_force"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>London dispersion force</span> </div> </a> <ul id="toc-London_dispersion_force-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Van_der_Waals_forces_between_macroscopic_objects" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Van_der_Waals_forces_between_macroscopic_objects"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Van der Waals forces between macroscopic objects</span> </div> </a> <ul id="toc-Van_der_Waals_forces_between_macroscopic_objects-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Use_by_geckos_and_arthropods" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Use_by_geckos_and_arthropods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Use by geckos and arthropods</span> </div> </a> <ul id="toc-Use_by_geckos_and_arthropods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</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">Van der Waals force</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" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 56 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-56" 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">56 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Van_der_Waals_se_krag" title="Van der Waals se krag – Afrikaans" lang="af" hreflang="af" data-title="Van der Waals se krag" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D9%88%D9%89_%D9%81%D8%A7%D9%86_%D8%AF%D9%8A%D8%B1_%D9%81%D8%A7%D9%84%D8%B3" title="قوى فان دير فالس – Arabic" lang="ar" hreflang="ar" data-title="قوى فان دير فالس" 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/Van-der-Vaals_q%C3%BCvv%C9%99l%C9%99ri" title="Van-der-Vaals qüvvələri – Azerbaijani" lang="az" hreflang="az" data-title="Van-der-Vaals qüvvələri" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AD%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A8%E0%A6%A1%E0%A6%BE%E0%A6%B0_%E0%A6%93%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%B2%E0%A6%B8_%E0%A6%AC%E0%A6%A8%E0%A7%8D%E0%A6%A7%E0%A6%A8" title="ভ্যানডার ওয়ালস বন্ধন – Bangla" lang="bn" hreflang="bn" data-title="ভ্যানডার ওয়ালস বন্ধন" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%96%D0%BB%D1%8B_%D0%92%D0%B0%D0%BD-%D0%B4%D1%8D%D1%80-%D0%92%D0%B0%D0%B0%D0%BB%D1%8C%D1%81%D0%B0" title="Сілы Ван-дэр-Ваальса – Belarusian" lang="be" hreflang="be" data-title="Сілы Ван-дэр-Ваальса" 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%A1%D0%B8%D0%BB%D0%B8_%D0%BD%D0%B0_%D0%92%D0%B0%D0%BD_%D0%B4%D0%B5%D1%80_%D0%92%D0%B0%D0%B0%D0%BB%D1%81" title="Сили на Ван дер Ваалс – Bulgarian" lang="bg" hreflang="bg" data-title="Сили на Ван дер Ваалс" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Van_der_Waalsove_sile" title="Van der Waalsove sile – Bosnian" lang="bs" hreflang="bs" data-title="Van der Waalsove sile" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Forces_de_van_der_Waals" title="Forces de van der Waals – Catalan" lang="ca" hreflang="ca" data-title="Forces de van der Waals" 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/Van_der_Waalsovy_s%C3%ADly" title="Van der Waalsovy síly – Czech" lang="cs" hreflang="cs" data-title="Van der Waalsovy síly" 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/Van_der_Waals-kr%C3%A6fter" title="Van der Waals-kræfter – Danish" lang="da" hreflang="da" data-title="Van der Waals-kræfter" 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/Van-der-Waals-Kr%C3%A4fte" title="Van-der-Waals-Kräfte – German" lang="de" hreflang="de" data-title="Van-der-Waals-Kräfte" 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/Van_der_Waalsi_j%C3%B5ud" title="Van der Waalsi jõud – Estonian" lang="et" hreflang="et" data-title="Van der Waalsi jõud" 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%94%CF%85%CE%BD%CE%AC%CE%BC%CE%B5%CE%B9%CF%82_%CF%86%CE%B1%CE%BD_%CE%BD%CF%84%CE%B5%CF%81_%CE%92%CE%AC%CE%B1%CE%BB%CF%82" title="Δυνάμεις φαν ντερ Βάαλς – Greek" lang="el" hreflang="el" data-title="Δυνάμεις φαν ντερ Βάαλς" 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/Fuerzas_de_Van_der_Waals" title="Fuerzas de Van der Waals – Spanish" lang="es" hreflang="es" data-title="Fuerzas de Van der Waals" 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/Forto_de_Van-der-Waals" title="Forto de Van-der-Waals – Esperanto" lang="eo" hreflang="eo" data-title="Forto de Van-der-Waals" 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/Van_der_Waalsen_indar" title="Van der Waalsen indar – Basque" lang="eu" hreflang="eu" data-title="Van der Waalsen indar" 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/%D9%86%DB%8C%D8%B1%D9%88%DB%8C_%D9%88%D8%A7%D9%86%D8%AF%D8%B1%D9%88%D8%A7%D9%84%D8%B3%DB%8C" title="نیروی واندروالسی – Persian" lang="fa" hreflang="fa" data-title="نیروی واندروالسی" 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/Force_de_van_der_Waals" title="Force de van der Waals – French" lang="fr" hreflang="fr" data-title="Force de van der Waals" 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/F%C3%B3rsa_van_der_Waals" title="Fórsa van der Waals – Irish" lang="ga" hreflang="ga" data-title="Fórsa van der Waals" 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/Forzas_de_van_der_Waals" title="Forzas de van der Waals – Galician" lang="gl" hreflang="gl" data-title="Forzas de van der Waals" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EB%8D%B0%EB%A5%B4%EB%B0%9C%EC%8A%A4_%ED%9E%98" title="반데르발스 힘 – Korean" lang="ko" hreflang="ko" data-title="반데르발스 힘" 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%8E%D5%A1%D5%B6-%D4%B4%D5%A5%D6%80-%D5%8E%D5%A1%D5%AC%D5%BD%D5%B5%D5%A1%D5%B6_%D5%B8%D6%82%D5%AA%D5%A5%D6%80" title="Վան-Դեր-Վալսյան ուժեր – Armenian" lang="hy" hreflang="hy" data-title="Վան-Դեր-Վալսյան ուժեր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BE%E0%A4%A8_%E0%A4%A1%E0%A4%B0_%E0%A4%B5%E0%A4%BE%E0%A4%B2%E0%A5%8D%E0%A4%B8_%E0%A4%AC%E0%A4%B2" title="वान डर वाल्स बल – Hindi" lang="hi" hreflang="hi" data-title="वान डर वाल्स बल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Van_der_Waalsove_sile" title="Van der Waalsove sile – Croatian" lang="hr" hreflang="hr" data-title="Van der Waalsove sile" 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/Gaya_van_der_Waals" title="Gaya van der Waals – Indonesian" lang="id" hreflang="id" data-title="Gaya van der Waals" 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/Forza_di_van_der_Waals" title="Forza di van der Waals – Italian" lang="it" hreflang="it" data-title="Forza di van der Waals" 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%9B%D7%95%D7%97_%D7%95%D7%90%D7%9F_%D7%93%D7%A8_%D7%95%D7%90%D7%9C%D7%A1" title="כוח ואן דר ואלס – Hebrew" lang="he" hreflang="he" data-title="כוח ואן דר ואלס" 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%92%D0%B0%D0%BD-%D0%B4%D0%B5%D1%80-%D0%92%D0%B0%D0%B0%D0%BB%D1%8C%D1%81_%D0%BA%D2%AF%D1%88%D1%82%D0%B5%D1%80%D1%96" title="Ван-дер-Ваальс күштері – Kazakh" lang="kk" hreflang="kk" data-title="Ван-дер-Ваальс күштері" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Van_der_Waals-er%C5%91k" title="Van der Waals-erők – Hungarian" lang="hu" hreflang="hu" data-title="Van der Waals-erők" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Daya_van_der_Waals" title="Daya van der Waals – Malay" lang="ms" hreflang="ms" data-title="Daya van der Waals" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vanderwaalskrachten" title="Vanderwaalskrachten – Dutch" lang="nl" hreflang="nl" data-title="Vanderwaalskrachten" 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/%E3%83%95%E3%82%A1%E3%83%B3%E3%83%87%E3%83%AB%E3%83%AF%E3%83%BC%E3%83%AB%E3%82%B9%E5%8A%9B" title="ファンデルワールス力 – Japanese" lang="ja" hreflang="ja" data-title="ファンデルワールス力" 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/Van_der_Waalske_krefter" title="Van der Waalske krefter – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Van der Waalske krefter" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Van_der_Waals-kraft" title="Van der Waals-kraft – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Van der Waals-kraft" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/F%C3%B2r%C3%A7a_de_van_der_Waals" title="Fòrça de van der Waals – Occitan" lang="oc" hreflang="oc" data-title="Fòrça de van der Waals" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Van-der-vaals_kuchlari" title="Van-der-vaals kuchlari – Uzbek" lang="uz" hreflang="uz" data-title="Van-der-vaals kuchlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/For%C3%A7as_de_Van_der_Waals" title="Forças de Van der Waals – Portuguese" lang="pt" hreflang="pt" data-title="Forças de Van der Waals" 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/For%C8%9B%C4%83_van_der_Waals" title="Forță van der Waals – Romanian" lang="ro" hreflang="ro" data-title="Forță van der Waals" 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%A1%D0%B8%D0%BB%D1%8B_%D0%92%D0%B0%D0%BD-%D0%B4%D0%B5%D1%80-%D0%92%D0%B0%D0%B0%D0%BB%D1%8C%D1%81%D0%B0" title="Силы Ван-дер-Ваальса – Russian" lang="ru" hreflang="ru" data-title="Силы Ван-дер-Ваальса" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Forca_e_Van_der_Waals" title="Forca e Van der Waals – Albanian" lang="sq" hreflang="sq" data-title="Forca e Van der Waals" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%90%E0%B6%B1%E0%B7%8A_%E0%B6%A9%27_%E0%B7%80%E0%B7%8F%E0%B6%BD%E0%B7%8A%E0%B7%83%E0%B7%8A_%E0%B6%85%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B6%BB%E0%B7%8A%E0%B6%9A%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%BA%E0%B7%8F" title="වැන් ඩ' වාල්ස් අන්තර්ක්‍රියා – Sinhala" lang="si" hreflang="si" data-title="වැන් ඩ' වාල්ස් අන්තර්ක්‍රියා" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Van_der_Waals_force" title="Van der Waals force – Simple English" lang="en-simple" hreflang="en-simple" data-title="Van der Waals force" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Van_der_Waalsova_sila" title="Van der Waalsova sila – Slovenian" lang="sl" hreflang="sl" data-title="Van der Waalsova sila" 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%DB%95%D9%86%D8%AF%DB%8C_%DA%A4%D8%A7%D9%86_%D8%AF%DB%95%D8%B1_%DA%A4%DB%86%D9%84%D8%B3" title="بەندی ڤان دەر ڤۆلس – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بەندی ڤان دەر ڤۆلس" 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%92%D0%B0%D0%BD_%D0%B4%D0%B5%D1%80_%D0%92%D0%B0%D0%BB%D1%81%D0%BE%D0%B2%D0%B0_%D0%B2%D0%B5%D0%B7%D0%B0" title="Ван дер Валсова веза – Serbian" lang="sr" hreflang="sr" data-title="Ван дер Валсова веза" 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/Van_der_Waalsova_veza" title="Van der Waalsova veza – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Van der Waalsova veza" 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/Van_der_Waalsin_voima" title="Van der Waalsin voima – Finnish" lang="fi" hreflang="fi" data-title="Van der Waalsin voima" 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/Van_der_Waals-kraft" title="Van der Waals-kraft – Swedish" lang="sv" hreflang="sv" data-title="Van der Waals-kraft" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BE%E0%AE%A9%E0%AF%8D_%E0%AE%9F%E0%AF%86%E0%AE%B0%E0%AF%8D_%E0%AE%B5%E0%AE%BE%E0%AE%B2%E0%AF%8D%E0%AE%B8%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%9A%E0%AF%88" title="வான் டெர் வால்ஸ் விசை – Tamil" lang="ta" hreflang="ta" data-title="வான் டெர் வால்ஸ் விசை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%A3%E0%B8%87%E0%B9%81%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%94%E0%B8%AD%E0%B8%A3%E0%B9%8C%E0%B8%A7%E0%B8%B2%E0%B8%A5%E0%B8%AA%E0%B9%8C" title="แรงแวนเดอร์วาลส์ – Thai" lang="th" hreflang="th" data-title="แรงแวนเดอร์วาลส์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Van_der_Waals_kuvveti" title="Van der Waals kuvveti – Turkish" lang="tr" hreflang="tr" data-title="Van der Waals kuvveti" 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%A1%D0%B8%D0%BB%D0%B8_%D0%92%D0%B0%D0%BD_%D0%B4%D0%B5%D1%80_%D0%92%D0%B0%D0%B0%D0%BB%D1%8C%D1%81%D0%B0" title="Сили Ван дер Ваальса – Ukrainian" lang="uk" hreflang="uk" 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width="280" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/RainDrops1.jpg/420px-RainDrops1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/RainDrops1.jpg/560px-RainDrops1.jpg 2x" data-file-width="5472" data-file-height="3648" /></a><figcaption>Rainwater flux from a canopy. Among the forces that govern drop formation: Van der Waals force, <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a>, <a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">cohesion</a>, <a href="/wiki/Plateau%E2%80%93Rayleigh_instability" title="Plateau–Rayleigh instability">Plateau–Rayleigh instability</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Brillenputzt%C3%BCcher-trocken.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Brillenputzt%C3%BCcher-trocken.jpg/220px-Brillenputzt%C3%BCcher-trocken.jpg" decoding="async" width="220" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Brillenputzt%C3%BCcher-trocken.jpg/330px-Brillenputzt%C3%BCcher-trocken.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Brillenputzt%C3%BCcher-trocken.jpg/440px-Brillenputzt%C3%BCcher-trocken.jpg 2x" data-file-width="1119" data-file-height="926" /></a><figcaption><a href="/wiki/Microfiber" title="Microfiber">Microfiber</a> cloth makes use of van der Waals force to remove dirt without scratches.<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></figcaption></figure> <p>In <a href="/wiki/Molecular_physics" title="Molecular physics">molecular physics</a> and <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, the <b>van der Waals force</b> (sometimes <b>van de Waals' force</b>) is a distance-dependent interaction between <a href="/wiki/Atom" title="Atom">atoms</a> or <a href="/wiki/Molecule" title="Molecule">molecules</a>. Unlike <a href="/wiki/Ionic_bond" class="mw-redirect" title="Ionic bond">ionic</a> or <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bonds</a>, these attractions do not result from a <a href="/wiki/Chemical_bond" title="Chemical bond">chemical electronic bond</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> they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanishes at longer distances between interacting molecules. </p><p>Named after Dutch physicist <a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">Johannes Diderik van der Waals</a>, the van der Waals force plays a fundamental role in fields as diverse as <a href="/wiki/Supramolecular_chemistry" title="Supramolecular chemistry">supramolecular chemistry</a>, <a href="/wiki/Structural_biology" title="Structural biology">structural biology</a>, <a href="/wiki/Polymer_science" title="Polymer science">polymer science</a>, <a href="/wiki/Nanotechnology" title="Nanotechnology">nanotechnology</a>, <a href="/wiki/Surface_science" title="Surface science">surface science</a>, and <a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a>. It also underlies many properties of <a href="/wiki/Organic_chemistry" title="Organic chemistry">organic compounds</a> and <a href="/wiki/Molecular_solid" title="Molecular solid">molecular solids</a>, including their <a href="/wiki/Solubility" title="Solubility">solubility</a> in <a href="/wiki/Chemical_polarity" title="Chemical polarity">polar and non-polar</a> media. </p><p>If no other <a href="/wiki/Force" title="Force">force</a> is present, the distance between atoms at which the force becomes repulsive rather than attractive as the atoms approach one another is called the <b>van der Waals contact distance</b>; this phenomenon results from the mutual repulsion between the atoms' <a href="/wiki/Atomic_orbital" title="Atomic orbital">electron clouds</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The van der Waals forces<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> are usually described as a combination of the <a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion forces</a> between "instantaneously induced <a href="/wiki/Dipole" title="Dipole">dipoles</a>",<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> <a href="/wiki/Debye_force" class="mw-redirect" title="Debye force">Debye forces</a> between permanent dipoles and induced dipoles, and the <a href="/wiki/Keesom_force" class="mw-redirect" title="Keesom force">Keesom force</a> between permanent <a href="/wiki/Molecular_dipole_moment" class="mw-redirect" title="Molecular dipole moment">molecular dipoles</a> whose rotational orientations are dynamically averaged over time. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_force&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Van der Waals forces include attraction and repulsions between <a href="/wiki/Atom" title="Atom">atoms</a>, <a href="/wiki/Molecule" title="Molecule">molecules</a>, as well as other <a href="/wiki/Intermolecular_force" title="Intermolecular force">intermolecular forces</a>. They differ from <a href="/wiki/Covalent_bond" title="Covalent bond">covalent</a> and <a href="/wiki/Ionic_bond" class="mw-redirect" title="Ionic bond">ionic</a> bonding in that they are caused by correlations in the fluctuating <a href="/wiki/Polarizability" title="Polarizability">polarizations</a> of nearby particles (a consequence of <a href="/wiki/Quantum_dynamics" title="Quantum dynamics">quantum dynamics</a><sup id="cite_ref-Abrikosov_6-0" class="reference"><a href="#cite_note-Abrikosov-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>). </p><p>The force results from a transient shift in <a href="/wiki/Electron_density" title="Electron density">electron density</a>. Specifically, the electron density may temporarily shift to be greater on one side of the nucleus. This shift generates a transient charge which a nearby atom can be attracted to or repelled by. The force is repulsive at very short distances, reaches zero at an equilibrium distance characteristic for each atom, or molecule, and becomes attractive for distances larger than the equilibrium distance. For individual atoms, the equilibrium distance is between 0.3 <a href="/wiki/Nanometre" title="Nanometre">nm</a> and 0.5 nm, depending on the atomic-specific diameter.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> When the interatomic distance is greater than 1.0 nm the force is not strong enough to be easily observed as it decreases as a function of distance <i>r</i> approximately with the 7th power (~<i>r</i><sup>−7</sup>).<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> </p><p>Van der Waals forces are often among the weakest chemical forces. For example, the pairwise attractive van der Waals interaction energy between H (<a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a>) atoms in different H<sub>2</sub> molecules equals 0.06 kJ/mol (0.6 meV) and the pairwise attractive interaction energy between O (<a href="/wiki/Oxygen" title="Oxygen">oxygen</a>) atoms in different O<sub>2</sub> molecules equals 0.44 kJ/mol (4.6 meV).<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 corresponding vaporization energies of H<sub>2</sub> and O<sub>2</sub> molecular liquids, which result as a sum of all van der Waals interactions per molecule in the molecular liquids, amount to 0.90 kJ/mol (9.3 meV) and 6.82 kJ/mol (70.7 meV), respectively, and thus approximately 15 times the value of the individual pairwise interatomic interactions (excluding <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bonds</a>). </p><p>The strength of van der Waals bonds increases with higher <a href="/wiki/Polarizability" title="Polarizability">polarizability</a> of the participating atoms.<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> For example, the pairwise van der Waals interaction energy for more polarizable atoms such as S (<a href="/wiki/Sulfur" title="Sulfur">sulfur</a>) atoms in H<sub>2</sub>S and <a href="/wiki/Sulfide" title="Sulfide">sulfides</a> exceeds 1 kJ/mol (10 meV), and the pairwise interaction energy between even larger, more polarizable Xe (<a href="/wiki/Xenon" title="Xenon">xenon</a>) atoms is 2.35 kJ/mol (24.3 meV).<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> These van der Waals interactions are up to 40 times stronger than in H<sub>2</sub>, which has only one valence electron, and they are still not strong enough to achieve an aggregate state other than gas for Xe under standard conditions. The interactions between atoms in metals can also be effectively described as van der Waals interactions and account for the observed solid aggregate state with bonding strengths comparable to covalent and ionic interactions. The strength of pairwise van der Waals type interactions is on the order of 12 kJ/mol (120 meV) for low-melting Pb (<a href="/wiki/Lead" title="Lead">lead</a>) and on the order of 32 kJ/mol (330 meV) for high-melting Pt (<a href="/wiki/Platinum" title="Platinum">platinum</a>), which is about one order of magnitude stronger than in Xe due to the presence of a highly polarizable <a href="/wiki/Fermi_gas" title="Fermi gas">free electron gas</a>.<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> Accordingly, van der Waals forces can range from weak to strong interactions, and support integral structural loads when multitudes of such interactions are present. </p> <div class="mw-heading mw-heading3"><h3 id="Force_Contributions">Force Contributions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_force&action=edit&section=2" title="Edit section: Force Contributions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>More broadly, <a href="/wiki/Intermolecular_forces" class="mw-redirect" title="Intermolecular forces">intermolecular forces</a> have several possible contributions. They are ordered from strongest to weakest: </p> <ol><li>A repulsive component resulting from the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> that prevents close contact of atoms, or the collapse of molecules.</li> <li>Attractive or repulsive <a href="/wiki/Electrostatic" class="mw-redirect" title="Electrostatic">electrostatic</a> interactions between permanent charges (in the case of molecular ions), dipoles (in the case of molecules without inversion centre), <a href="/wiki/Quadrupole" title="Quadrupole">quadrupoles</a> (all molecules with symmetry lower than cubic), and in general between permanent <a href="/wiki/Multipole" class="mw-redirect" title="Multipole">multipoles</a>. These interactions also include <a href="/wiki/Hydrogen_bond" title="Hydrogen bond">hydrogen bonds</a>, <a href="/wiki/Cation%E2%80%93%CF%80_interaction" title="Cation–π interaction">cation-pi</a>, and <a href="/wiki/Pi-Stacking_(chemistry)" class="mw-redirect" title="Pi-Stacking (chemistry)">pi-stacking</a> interactions. Orientation-averaged contributions from electrostatic interactions are sometimes called the <a href="/wiki/Keesom_force" class="mw-redirect" title="Keesom force">Keesom interaction</a> or Keesom force after <a href="/wiki/Willem_Hendrik_Keesom" title="Willem Hendrik Keesom">Willem Hendrik Keesom</a>.</li> <li>Induction (also known as <a href="/wiki/Polarizability" title="Polarizability">polarization</a>), which is the attractive interaction between a permanent multipole on one molecule with an induced multipole on another. This interaction is sometimes called <a href="/wiki/Debye" title="Debye">Debye</a> force after <a href="/wiki/Peter_J._W._Debye" class="mw-redirect" title="Peter J. W. Debye">Peter J. W. Debye</a>. The interactions (2) and (3) are labelled polar Interactions.</li> <li>Dispersion (usually named <a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion interactions</a> after <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a>), which is the attractive interaction between any pair of molecules, including non-polar atoms, arising from the interactions of instantaneous multipoles.</li></ol> <p>When to apply the term "van der Waals" force depends on the text. The broadest definitions include all intermolecular forces which are electrostatic in origin, namely (2), (3) and (4).<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Some authors, whether or not they consider other forces to be of van der Waals type, focus on (3) and (4) as these are the components which act over the longest range.<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><p>All intermolecular/van der Waals forces are <a href="/wiki/Anisotropic" class="mw-redirect" title="Anisotropic">anisotropic</a> (except those between two <a href="/wiki/Noble_gas" title="Noble gas">noble gas</a> atoms), which means that they depend on the relative orientation of the molecules. The induction and dispersion interactions are always attractive, irrespective of orientation, but the electrostatic interaction changes sign upon rotation of the molecules. That is, the electrostatic force can be attractive or repulsive, depending on the mutual orientation of the molecules. When molecules are in thermal motion, as they are in the gas and liquid phase, the electrostatic force is averaged out to a large extent because the molecules thermally rotate and thus probe both repulsive and attractive parts of the electrostatic force. Random thermal motion can disrupt or overcome the electrostatic component of the van der Waals force but the averaging effect is much less pronounced for the attractive induction and dispersion forces. </p><p>The <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a> is often used as an approximate model for the isotropic part of a total (repulsion plus attraction) van der Waals force as a function of distance. </p><p>Van der Waals forces are responsible for certain cases of pressure broadening (<a href="/wiki/Van_der_Waals_broadening" class="mw-redirect" title="Van der Waals broadening">van der Waals broadening</a>) of spectral lines and the formation of <a href="/wiki/Van_der_Waals_molecule" title="Van der Waals molecule">van der Waals molecules</a>. The London–van der Waals forces are related to the <a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a> for dielectric media, the former being the microscopic description of the latter bulk property. The first detailed calculations of this were done in 1955 by <a href="/wiki/Evgeny_Mikhailovich_Lifshitz" class="mw-redirect" title="Evgeny Mikhailovich Lifshitz">E. M. Lifshitz</a>.<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> A more general theory of van der Waals forces has also been developed.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><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> </p><p>The main characteristics of van der Waals forces are:<sup id="cite_ref-Sethi_1992_19-0" class="reference"><a href="#cite_note-Sethi_1992-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <ul><li>They are weaker than normal covalent and ionic bonds.</li> <li>The van der Waals forces are additive in nature, consisting of several individual interactions, and cannot be saturated.</li> <li>They have no directional characteristic.</li> <li>They are all short-range forces and hence only interactions between the nearest particles need to be considered (instead of all the particles). Van der Waals attraction is greater if the molecules are closer.</li> <li>Van der Waals forces are independent of temperature except for dipole-dipole interactions.</li></ul> <p>In low molecular weight alcohols, the hydrogen-bonding properties of their polar <a href="/wiki/Hydroxyl_group" class="mw-redirect" title="Hydroxyl group">hydroxyl group</a> dominate other weaker van der Waals interactions. In higher molecular weight alcohols, the properties of the nonpolar hydrocarbon chain(s) dominate and determine their solubility. </p><p>Van der Waals forces are also responsible for the weak <a href="/wiki/Hydrogen_bond" title="Hydrogen bond">hydrogen bond</a> interactions between unpolarized dipoles particularly in acid-base aqueous solution and between <a href="/wiki/Biomolecule" title="Biomolecule">biological molecules</a>. </p> <div class="mw-heading mw-heading2"><h2 id="London_dispersion_force">London dispersion force</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_force&action=edit&section=3" title="Edit section: London dispersion force"><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">Main article: <a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion force</a></div> <p><a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion forces</a>, named after the German-American physicist <a href="/wiki/Fritz_London" title="Fritz London">Fritz London</a>, are weak <a href="/wiki/Intermolecular_force" title="Intermolecular force">intermolecular forces</a> that arise from the interactive forces between instantaneous multipoles in molecules without permanent <a href="/wiki/Multipole_expansion" title="Multipole expansion">multipole moments</a>. In and between organic molecules the multitude of contacts can lead to larger contribution of dispersive attraction, particularly in the presence of heteroatoms. London dispersion forces are also known as '<a href="/wiki/London_dispersion_force" title="London dispersion force">dispersion</a> forces', 'London forces', or 'instantaneous dipole–induced dipole forces'. The strength of London dispersion forces is proportional to the polarizability of the molecule, which in turn depends on the total number of electrons and the area over which they are spread. Hydrocarbons display small dispersive contributions, the presence of heteroatoms lead to increased LD forces as function of their polarizability, e.g. in the sequence RI>RBr>RCl>RF.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In absence of solvents weakly polarizable hydrocarbons form crystals due to dispersive forces; their <a href="/wiki/Sublimation_(chemistry)" class="mw-redirect" title="Sublimation (chemistry)">sublimation heat</a> is a measure of the dispersive interaction. </p> <div class="mw-heading mw-heading2"><h2 id="Van_der_Waals_forces_between_macroscopic_objects">Van der Waals forces between macroscopic objects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_force&action=edit&section=4" title="Edit section: Van der Waals forces between macroscopic objects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For <a href="/wiki/Macroscopic_scale" title="Macroscopic scale">macroscopic</a> bodies with known volumes and numbers of atoms or molecules per unit volume, the total van der Waals force is often computed based on the "microscopic theory" as the sum over all interacting pairs. It is necessary to integrate over the total volume of the object, which makes the calculation dependent on the objects' shapes. For example, the van der Waals interaction energy between spherical bodies of radii R<sub>1</sub> and R<sub>2</sub> and with smooth surfaces was approximated in 1937 by <a href="/wiki/H._C._Hamaker" class="mw-redirect" title="H. C. Hamaker">Hamaker</a><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><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2024)">full citation needed</span></a></i>]</sup> (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2024)">full citation needed</span></a></i>]</sup> as the starting point) by: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><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 {\begin{aligned}&U(z;R_{1},R_{2})=-{\frac {A}{6}}\left({\frac {2R_{1}R_{2}}{z^{2}-(R_{1}+R_{2})^{2}}}+{\frac {2R_{1}R_{2}}{z^{2}-(R_{1}-R_{2})^{2}}}+\ln \left[{\frac {z^{2}-(R_{1}+R_{2})^{2}}{z^{2}-(R_{1}-R_{2})^{2}}}\right]\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mi>U</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>;</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mn>6</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&U(z;R_{1},R_{2})=-{\frac {A}{6}}\left({\frac {2R_{1}R_{2}}{z^{2}-(R_{1}+R_{2})^{2}}}+{\frac {2R_{1}R_{2}}{z^{2}-(R_{1}-R_{2})^{2}}}+\ln \left[{\frac {z^{2}-(R_{1}+R_{2})^{2}}{z^{2}-(R_{1}-R_{2})^{2}}}\right]\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d41abc4a7fe57ece5e37f9354e44862a67bf5f19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:86.505ex; height:7.509ex;" alt="{\displaystyle {\begin{aligned}&U(z;R_{1},R_{2})=-{\frac {A}{6}}\left({\frac {2R_{1}R_{2}}{z^{2}-(R_{1}+R_{2})^{2}}}+{\frac {2R_{1}R_{2}}{z^{2}-(R_{1}-R_{2})^{2}}}+\ln \left[{\frac {z^{2}-(R_{1}+R_{2})^{2}}{z^{2}-(R_{1}-R_{2})^{2}}}\right]\right)\end{aligned}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_1" class="reference nourlexpansion" style="font-weight:bold;">1</span>)</b></td></tr></tbody></table> <p>where A is the <a href="/wiki/Hamaker_constant" title="Hamaker constant">Hamaker coefficient</a>, which is a constant (~10<sup>−19</sup> − 10<sup>−20</sup> J) that depends on the material properties (it can be positive or negative in sign depending on the intervening medium), and <i>z</i> is the center-to-center distance; i.e., the sum of <i>R</i><sub>1</sub>, <i>R</i><sub>2</sub>, and <i>r</i> (the distance between the surfaces): <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 \ z=R_{1}+R_{2}+r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>z</mi> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ z=R_{1}+R_{2}+r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c85b945d0252feb8f6bdb70e3fb903bf1df8c89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.133ex; height:2.509ex;" alt="{\displaystyle \ z=R_{1}+R_{2}+r}"></span>. </p><p>The van der Waals <i><a href="/wiki/Force" title="Force">force</a></i> between two spheres of constant radii (<i>R</i><sub>1</sub> and <i>R</i><sub>2</sub> are treated as parameters) is then a function of separation since the force on an object is the negative of the derivative of the potential energy function,<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_{\rm {VdW}}(z)=-{\frac {d}{dz}}U(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">W</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mi>U</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F_{\rm {VdW}}(z)=-{\frac {d}{dz}}U(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/daa808bd196f4c845a6614b378360f6a17ef747e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.767ex; height:5.509ex;" alt="{\displaystyle \ F_{\rm {VdW}}(z)=-{\frac {d}{dz}}U(z)}"></span>. This yields: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><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_{\rm {VdW}}(z)=-{\frac {A}{6}}{\frac {64R_{1}^{3}R_{2}^{3}z}{[z^{2}-(R_{1}+R_{2})^{2}]^{2}[z^{2}-(R_{1}-R_{2})^{2}]^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">W</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mn>6</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>64</mn> <msubsup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <msubsup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <mi>z</mi> </mrow> <mrow> <mo stretchy="false">[</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">[</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F_{\rm {VdW}}(z)=-{\frac {A}{6}}{\frac {64R_{1}^{3}R_{2}^{3}z}{[z^{2}-(R_{1}+R_{2})^{2}]^{2}[z^{2}-(R_{1}-R_{2})^{2}]^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21c5a757baeefcb38bc6dfe2d47d2b4e2ffa6427" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:54.709ex; height:6.843ex;" alt="{\displaystyle \ F_{\rm {VdW}}(z)=-{\frac {A}{6}}{\frac {64R_{1}^{3}R_{2}^{3}z}{[z^{2}-(R_{1}+R_{2})^{2}]^{2}[z^{2}-(R_{1}-R_{2})^{2}]^{2}}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_2" class="reference nourlexpansion" style="font-weight:bold;">2</span>)</b></td></tr></tbody></table> <p>In the limit of close-approach, the spheres are sufficiently large compared to the distance between them; i.e., <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 \ r\ll R_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>r</mi> <mo>≪</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ r\ll R_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73deae975771dbc30f17c6c3c22e50ca3e022669" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.062ex; height:2.509ex;" alt="{\displaystyle \ r\ll R_{1}}"></span> or <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 R_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35f571121c264178676d1df8ab899f238a39bc2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle R_{2}}"></span>, so that equation (1) for the potential energy function simplifies to: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><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(r;R_{1},R_{2})=-{\frac {AR_{1}R_{2}}{(R_{1}+R_{2})6r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>U</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>;</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mn>6</mn> <mi>r</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ U(r;R_{1},R_{2})=-{\frac {AR_{1}R_{2}}{(R_{1}+R_{2})6r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa09cb412a15b35976d291ade52788a921f27554" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:31.166ex; height:6.176ex;" alt="{\displaystyle \ U(r;R_{1},R_{2})=-{\frac {AR_{1}R_{2}}{(R_{1}+R_{2})6r}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_3" class="reference nourlexpansion" style="font-weight:bold;">3</span>)</b></td></tr></tbody></table> <p>with the force: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><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_{\rm {VdW}}(r)=-{\frac {AR_{1}R_{2}}{(R_{1}+R_{2})6r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">W</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mn>6</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F_{\rm {VdW}}(r)=-{\frac {AR_{1}R_{2}}{(R_{1}+R_{2})6r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84fa5d3de156df4b90f32cb4ee74cddfbeb0250b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.295ex; height:6.176ex;" alt="{\displaystyle \ F_{\rm {VdW}}(r)=-{\frac {AR_{1}R_{2}}{(R_{1}+R_{2})6r^{2}}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_4" class="reference nourlexpansion" style="font-weight:bold;">4</span>)</b></td></tr></tbody></table> <p>The van der Waals forces between objects with other geometries using the Hamaker model have been published in the literature.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><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>From the expression above, it is seen that the van der Waals force decreases with decreasing size of bodies (R). Nevertheless, the strength of inertial forces, such as gravity and drag/lift, decrease to a greater extent. Consequently, the van der Waals forces become dominant for collections of very small particles such as very fine-grained dry powders (where there are no capillary forces present) even though the force of attraction is smaller in magnitude than it is for larger particles of the same substance. Such powders are said to be cohesive, meaning they are not as easily fluidized or pneumatically conveyed as their more coarse-grained counterparts. Generally, free-flow occurs with particles greater than about 250 μm. </p><p>The van der Waals force of adhesion is also dependent on the surface topography. If there are surface asperities, or protuberances, that result in a greater total area of contact between two particles or between a particle and a wall, this increases the van der Waals force of attraction as well as the tendency for mechanical interlocking. </p><p>The microscopic theory assumes pairwise additivity. It neglects <a href="/wiki/Many-body_problem" title="Many-body problem">many-body interactions</a> and <a href="/wiki/Retarded_potential" title="Retarded potential">retardation</a>. A more rigorous approach accounting for these effects, called the "<a href="/w/index.php?title=Lifshitz_Theory_of_van_der_Waals_Force&action=edit&redlink=1" class="new" title="Lifshitz Theory of van der Waals Force (page does not exist)">macroscopic theory</a>", was developed by <a href="/wiki/Evgeny_Lifshitz" title="Evgeny Lifshitz">Lifshitz</a> in 1956.<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 class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2024)">full citation needed</span></a></i>]</sup> <a href="/wiki/D._Langbein" class="mw-redirect" title="D. Langbein">Langbein</a> derived a much more cumbersome "exact" expression in 1970 for spherical bodies within the framework of the Lifshitz theory<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><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2024)">full citation needed</span></a></i>]</sup> while a simpler macroscopic model approximation had been made by <a href="/wiki/Boris_Derjaguin" title="Boris Derjaguin">Derjaguin</a> as early as 1934.<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><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2024)">full citation needed</span></a></i>]</sup> Expressions for the van der Waals forces for many different geometries using the Lifshitz theory have likewise been published. </p> <div class="mw-heading mw-heading2"><h2 id="Use_by_geckos_and_arthropods">Use by geckos and arthropods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_force&action=edit&section=5" title="Edit section: Use by geckos and arthropods"><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">Further information: <a href="/wiki/Arthropod_adhesion" title="Arthropod adhesion">Arthropod adhesion</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gecko_Leaftail_1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Gecko_Leaftail_1.jpg/220px-Gecko_Leaftail_1.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Gecko_Leaftail_1.jpg/330px-Gecko_Leaftail_1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/Gecko_Leaftail_1.jpg/440px-Gecko_Leaftail_1.jpg 2x" data-file-width="1632" data-file-height="1224" /></a><figcaption><a href="/wiki/Gecko" title="Gecko">Gecko</a> climbing a glass surface</figcaption></figure> <p>The ability of <a href="/wiki/Gecko" title="Gecko">geckos</a> – which can hang on a glass surface using only one toe – to climb on sheer surfaces has been for many years mainly attributed to the van der Waals forces between these surfaces and the <a href="/wiki/Spatulae_(biology)" class="mw-redirect" title="Spatulae (biology)">spatulae</a>, or microscopic projections, which cover the hair-like <a href="/wiki/Seta" title="Seta">setae</a> found on their footpads.<sup id="cite_ref-RussellHigham2009_29-0" class="reference"><a href="#cite_note-RussellHigham2009-29"><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><p>There were efforts in 2008 to create a <a href="/wiki/Dry_glue" title="Dry glue">dry glue</a> that exploits the effect,<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> and success was achieved in 2011 to create an adhesive tape on similar grounds<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> (i.e. based on van der Waals forces). In 2011, a paper was published relating the effect to both velcro-like hairs and the presence of lipids in gecko footprints.<sup id="cite_ref-HsuGe20112_33-0" class="reference"><a href="#cite_note-HsuGe20112-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>A later study suggested that capillary adhesion might play a role,<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> but that hypothesis has been rejected by more recent studies.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><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><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> </p><p>A 2014 study has shown that gecko adhesion to smooth Teflon and <a href="/wiki/Polydimethylsiloxane" title="Polydimethylsiloxane">polydimethylsiloxane</a> surfaces is mainly determined by electrostatic interaction (caused by <a href="/wiki/Contact_electrification" class="mw-redirect" title="Contact electrification">contact electrification</a>), not van der Waals or capillary forces.<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> </p><p>Among the <a href="/wiki/Arthropod" title="Arthropod">arthropods</a>, some spiders have similar setae on their <a href="/wiki/Scopulae" title="Scopulae">scopulae</a> or scopula pads, enabling them to climb or hang upside-down from extremely smooth surfaces such as glass or porcelain.<sup id="cite_ref-KeselMartin2004_39-0" class="reference"><a href="#cite_note-KeselMartin2004-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><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> </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=Van_der_Waals_force&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Papapishu-Lab-icon-6.svg/42px-Papapishu-Lab-icon-6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Papapishu-Lab-icon-6.svg/56px-Papapishu-Lab-icon-6.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Chemistry" title="Portal:Chemistry">Chemistry portal</a></span></li><li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Issoria_lathonia.jpg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Issoria_lathonia.jpg/32px-Issoria_lathonia.jpg" decoding="async" width="32" height="23" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Issoria_lathonia.jpg/48px-Issoria_lathonia.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Issoria_lathonia.jpg/64px-Issoria_lathonia.jpg 2x" data-file-width="629" data-file-height="445" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Biology" title="Portal:Biology">Biology portal</a></span></li></ul> <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/Arthropod_adhesion" title="Arthropod adhesion">Arthropod adhesion</a></li> <li><a href="/wiki/Cold_welding" title="Cold welding">Cold welding</a></li> <li><a href="/wiki/Dispersion_(chemistry)" title="Dispersion (chemistry)">Dispersion (chemistry)</a></li> <li><a href="/wiki/Gecko_feet" title="Gecko feet">Gecko feet</a></li> <li><a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a></li> <li><a href="/wiki/Noncovalent_interactions" class="mw-redirect" title="Noncovalent interactions">Noncovalent interactions</a></li> <li><a href="/wiki/Synthetic_setae" title="Synthetic setae">Synthetic setae</a></li> <li><a href="/wiki/Van_der_Waals_molecule" title="Van der Waals molecule">Van der Waals molecule</a></li> <li><a href="/wiki/Van_der_Waals_radius" title="Van der Waals radius">Van der Waals radius</a></li> <li><a href="/wiki/Van_der_Waals_strain" title="Van der Waals strain">Van der Waals strain</a></li> <li><a href="/wiki/Van_der_Waals_surface" title="Van der Waals surface">Van der Waals surface</a></li> <li><a href="/wiki/Wringing_(gauge_blocks)" class="mw-redirect" title="Wringing (gauge blocks)">Wringing of gauge blocks</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=Van_der_Waals_force&action=edit&section=7" 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 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href="http://www.explainthatstuff.com/microfibercloths.html">"How do microfiber cloths work? | The science of cleaning"</a>. <i>Explain that Stuff</i><span class="reference-accessdate">. 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Online corrected version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/V06597.html">van der Waals forces</a>". <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.V06597">10.1351/goldbook.V06597</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGarrettGrisham2016" class="citation book cs1">Garrett, Reginald H.; Grisham, Charles M. (2016). <i>Biochemistry</i> (6th ed.). 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(9 July 2014). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4233685">"Role of contact electrification and electrostatic interactions in gecko adhesion"</a>. <i>Journal of the Royal Society Interface</i>. <b>11</b> (98): 20140371. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsif.2014.0371">10.1098/rsif.2014.0371</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/PMC4233685">4233685</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/25008078">25008078</a>. <q>We have demonstrated that it is the CE-driven electrostatic interactions which dictate the strength of gecko adhesion, and not the van der Waals or capillary forces which are conventionally considered as the main source of gecko adhesion.</q></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+Royal+Society+Interface&rft.atitle=Role+of+contact+electrification+and+electrostatic+interactions+in+gecko+adhesion&rft.volume=11&rft.issue=98&rft.pages=20140371&rft.date=2014-07-09&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4233685%23id-name%3DPMC&rft_id=info%3Apmid%2F25008078&rft_id=info%3Adoi%2F10.1098%2Frsif.2014.0371&rft.aulast=Izadi&rft.aufirst=H.&rft.au=Stewart%2C+K.+M.+E.&rft.au=Penlidis%2C+A.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4233685&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></span> </li> <li id="cite_note-KeselMartin2004-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-KeselMartin2004_39-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKeselMartinSeidl2004" class="citation journal cs1">Kesel, Antonia B.; Martin, Andrew; Seidl, Tobias (19 April 2004). "Getting a grip on spider attachment: an AFM approach to microstructure adhesion in arthropods". <i><a href="/wiki/Smart_Materials_and_Structures" title="Smart Materials and Structures">Smart Materials and Structures</a></i>. <b>13</b> (3): 512–518. <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/2004SMaS...13..512K">2004SMaS...13..512K</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%2F0964-1726%2F13%2F3%2F009">10.1088/0964-1726/13/3/009</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0964-1726">0964-1726</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:250841250">250841250</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Smart+Materials+and+Structures&rft.atitle=Getting+a+grip+on+spider+attachment%3A+an+AFM+approach+to+microstructure+adhesion+in+arthropods&rft.volume=13&rft.issue=3&rft.pages=512-518&rft.date=2004-04-19&rft_id=info%3Adoi%2F10.1088%2F0964-1726%2F13%2F3%2F009&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250841250%23id-name%3DS2CID&rft.issn=0964-1726&rft_id=info%3Abibcode%2F2004SMaS...13..512K&rft.aulast=Kesel&rft.aufirst=Antonia+B.&rft.au=Martin%2C+Andrew&rft.au=Seidl%2C+Tobias&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" 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="CITEREFWolffGorb2012" class="citation journal cs1">Wolff, Jonas O.; Gorb, Stanislav N. (7 January 2012). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3223641">"The influence of humidity on the attachment ability of the spider <i>Philodromus dispar</i> (Araneae, Philodromidae)"</a>. <i><a href="/wiki/Proceedings_of_the_Royal_Society_B" class="mw-redirect" title="Proceedings of the Royal Society B">Proceedings of the Royal Society B</a></i>. <b>279</b> (1726): 139–143. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspb.2011.0505">10.1098/rspb.2011.0505</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/PMC3223641">3223641</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/21593034">21593034</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+Royal+Society+B&rft.atitle=The+influence+of+humidity+on+the+attachment+ability+of+the+spider+Philodromus+dispar+%28Araneae%2C+Philodromidae%29&rft.volume=279&rft.issue=1726&rft.pages=139-143&rft.date=2012-01-07&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3223641%23id-name%3DPMC&rft_id=info%3Apmid%2F21593034&rft_id=info%3Adoi%2F10.1098%2Frspb.2011.0505&rft.aulast=Wolff&rft.aufirst=Jonas+O.&rft.au=Gorb%2C+Stanislav+N.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3223641&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_force&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrevikMarachevskyMilton1999" class="citation journal cs1">Brevik, Iver; Marachevsky, V. N.; Milton, Kimball A. (1999). "Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of These Phenomena to Sonoluminescence". <i>Physical Review Letters</i>. <b>82</b> (20): 3948–3951. <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/hep-th/9810062">hep-th/9810062</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/1999PhRvL..82.3948B">1999PhRvL..82.3948B</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.82.3948">10.1103/PhysRevLett.82.3948</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:14762105">14762105</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=Identity+of+the+van+der+Waals+Force+and+the+Casimir+Effect+and+the+Irrelevance+of+These+Phenomena+to+Sonoluminescence&rft.volume=82&rft.issue=20&rft.pages=3948-3951&rft.date=1999&rft_id=info%3Aarxiv%2Fhep-th%2F9810062&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14762105%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.82.3948&rft_id=info%3Abibcode%2F1999PhRvL..82.3948B&rft.aulast=Brevik&rft.aufirst=Iver&rft.au=Marachevsky%2C+V.+N.&rft.au=Milton%2C+Kimball+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDzyaloshinskiiLifshitzPitaevskii1961" class="citation journal cs1 cs1-prop-foreign-lang-source">Dzyaloshinskii, I. D.; Lifshitz, E. M.; Pitaevskii, Lev P. (1961). <a rel="nofollow" class="external text" href="http://ufn.ru/ufn61/ufn61_3/Russian/r613b.pdf">"Общая теория ван-дер-ваальсовых сил"</a> [General theory of van der Waals forces] <span class="cs1-format">(PDF)</span>. <i>Uspekhi Fizicheskikh Nauk</i> (in Russian). <b>73</b> (381).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Uspekhi+Fizicheskikh+Nauk&rft.atitle=%D0%9E%D0%B1%D1%89%D0%B0%D1%8F+%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F+%D0%B2%D0%B0%D0%BD-%D0%B4%D0%B5%D1%80-%D0%B2%D0%B0%D0%B0%D0%BB%D1%8C%D1%81%D0%BE%D0%B2%D1%8B%D1%85+%D1%81%D0%B8%D0%BB&rft.volume=73&rft.issue=381&rft.date=1961&rft.aulast=Dzyaloshinskii&rft.aufirst=I.+D.&rft.au=Lifshitz%2C+E.+M.&rft.au=Pitaevskii%2C+Lev+P.&rft_id=http%3A%2F%2Fufn.ru%2Fufn61%2Fufn61_3%2FRussian%2Fr613b.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span> <ul><li>English translation: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDzyaloshinskiiLifshitzPitaevskii1961" class="citation journal cs1">Dzyaloshinskii, I. D.; Lifshitz, E. M.; Pitaevskii, L. P. (1961). "General theory of van der Waalsforces". <i><a href="/wiki/Soviet_Physics_Uspekhi" class="mw-redirect" title="Soviet Physics Uspekhi">Soviet Physics Uspekhi</a></i>. <b>4</b> (2): 153. <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/1961SvPhU...4..153D">1961SvPhU...4..153D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1070%2FPU1961v004n02ABEH003330">10.1070/PU1961v004n02ABEH003330</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Soviet+Physics+Uspekhi&rft.atitle=General+theory+of+van+der+Waalsforces&rft.volume=4&rft.issue=2&rft.pages=153&rft.date=1961&rft_id=info%3Adoi%2F10.1070%2FPU1961v004n02ABEH003330&rft_id=info%3Abibcode%2F1961SvPhU...4..153D&rft.aulast=Dzyaloshinskii&rft.aufirst=I.+D.&rft.au=Lifshitz%2C+E.+M.&rft.au=Pitaevskii%2C+L.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauLifshitz1960" class="citation book cs1">Landau, L. D.; Lifshitz, E. M. (1960). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/electrodynamicso00land"><i>Electrodynamics of Continuous Media</i></a></span>. Oxford: Pergamon. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/electrodynamicso00land/page/368">368–376</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrodynamics+of+Continuous+Media&rft.place=Oxford&rft.pages=368-376&rft.pub=Pergamon&rft.date=1960&rft.aulast=Landau&rft.aufirst=L.+D.&rft.au=Lifshitz%2C+E.+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectrodynamicso00land&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLangbein1974" class="citation book cs1"><a href="/wiki/Dieter_Langbein" title="Dieter Langbein">Langbein, Dieter</a> (1974). <i>Theory of Van der Waals Attraction</i>. Springer Tracts in Modern Physics. Vol. 72. New York, Heidelberg: Springer-Verlag.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Van+der+Waals+Attraction&rft.place=New+York%2C+Heidelberg&rft.series=Springer+Tracts+in+Modern+Physics&rft.pub=Springer-Verlag&rft.date=1974&rft.aulast=Langbein&rft.aufirst=Dieter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLefers" class="citation web cs1">Lefers, Mark. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190724044455/http://groups.molbiosci.northwestern.edu/holmgren/Glossary/Definitions/Def-V/Van_der_Waals_force.html">"Van der Waals dispersion force"</a>. <i>Life Science Glossary</i>. Holmgren Lab. Archived from <a rel="nofollow" class="external text" href="http://groups.molbiosci.northwestern.edu/holmgren/Glossary/Definitions/Def-V/van_der_Waals_force.html">the original</a> on 24 July 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">2 October</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Life+Science+Glossary&rft.atitle=Van+der+Waals+dispersion+force&rft.aulast=Lefers&rft.aufirst=Mark&rft_id=http%3A%2F%2Fgroups.molbiosci.northwestern.edu%2Fholmgren%2FGlossary%2FDefinitions%2FDef-V%2Fvan_der_Waals_force.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLifshitz1955" class="citation journal cs1 cs1-prop-foreign-lang-source">Lifshitz, E. M. (1955). "Russian title is missing" [The Theory of Molecular Attractive Forces between Solids]. <i>Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki</i> (in Russian). <b>29</b> (1): 94.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zhurnal+%C3%89ksperimental%27no%C4%AD+i+Teoretichesko%C4%AD+Fiziki&rft.atitle=Russian+title+is+missing&rft.volume=29&rft.issue=1&rft.pages=94&rft.date=1955&rft.aulast=Lifshitz&rft.aufirst=E.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span> <ul><li>English translation: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLifshitz1956" class="citation journal cs1">Lifshitz, E. M. (January 1956). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190713075237/http://www.jetp.ac.ru/cgi-bin/dn/e_002_01_0073.pdf">"The Theory of Molecular Attractive Forces between Solids"</a> <span class="cs1-format">(PDF)</span>. <i>Soviet Physics</i>. <b>2</b> (1): 73. Archived from <a rel="nofollow" class="external text" href="http://www.jetp.ac.ru/cgi-bin/dn/e_002_01_0073.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 13 July 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">8 August</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Soviet+Physics&rft.atitle=The+Theory+of+Molecular+Attractive+Forces+between+Solids&rft.volume=2&rft.issue=1&rft.pages=73&rft.date=1956-01&rft.aulast=Lifshitz&rft.aufirst=E.+M.&rft_id=http%3A%2F%2Fwww.jetp.ac.ru%2Fcgi-bin%2Fdn%2Fe_002_01_0073.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li></ul></li> <li><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.wou.edu/las/physci/ch334/lecture/intermol/london.htm">"London force animation"</a>. <i>Intermolecular Forces</i>. Western Oregon University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Intermolecular+Forces&rft.atitle=London+force+animation&rft_id=http%3A%2F%2Fwww.wou.edu%2Flas%2Fphysci%2Fch334%2Flecture%2Fintermol%2Flondon.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLyklema" class="citation book cs1">Lyklema, J. <i>Fundamentals of Interface and Colloid Science</i>. p. 4.43.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Interface+and+Colloid+Science&rft.pages=4.43&rft.aulast=Lyklema&rft.aufirst=J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIsraelachvili1992" class="citation book cs1">Israelachvili, Jacob N. (1992). <i>Intermolecular and Surface Forces</i>. <a href="/wiki/Academic_Press" title="Academic Press">Academic Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780123751812" title="Special:BookSources/9780123751812"><bdi>9780123751812</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Intermolecular+and+Surface+Forces&rft.pub=Academic+Press&rft.date=1992&rft.isbn=9780123751812&rft.aulast=Israelachvili&rft.aufirst=Jacob+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span></li></ul> <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=Van_der_Waals_force&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSenese1999" class="citation web cs1">Senese, Fred (1999). <a rel="nofollow" class="external text" href="http://antoine.frostburg.edu/chem/senese/101/liquids/faq/h-bonding-vs-london-forces.shtml">"What are van der Waals forces?"</a>. Frostburg State University<span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+are+van+der+Waals+forces%3F&rft.pub=Frostburg+State+University&rft.date=1999&rft.aulast=Senese&rft.aufirst=Fred&rft_id=http%3A%2F%2Fantoine.frostburg.edu%2Fchem%2Fsenese%2F101%2Fliquids%2Ffaq%2Fh-bonding-vs-london-forces.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span> An introductory description of the van der Waals force (as a sum of attractive components only)</li> <li><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.ted.com/talks/robert_full_learning_from_the_gecko_s_tail?language=en">"Robert Full: Learning from the gecko's tail"</a>. <a href="/wiki/TED_(conference)" title="TED (conference)">TED</a>. 1 February 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">5 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Robert+Full%3A+Learning+from+the+gecko%27s+tail&rft.pub=TED&rft.date=2009-02-01&rft_id=http%3A%2F%2Fwww.ted.com%2Ftalks%2Frobert_full_learning_from_the_gecko_s_tail%3Flanguage%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+force" class="Z3988"></span> TED Talk on biomimicry, including applications of van der Waals force.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWolffGorb2011" class="citation journal cs1">Wolff, J. O.; Gorb, S. N. (18 May 2011). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3223641">"The influence of humidity on the attachment ability of the spider <i>Philodromus dispar</i> (Araneae, Philodromidae)"</a>. <i>Proceedings of the Royal Society B: Biological Sciences</i>. <b>279</b> (1726): 139–143. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspb.2011.0505">10.1098/rspb.2011.0505</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/PMC3223641">3223641</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/21593034">21593034</a>.</cite><span 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class="navbox-group" style="width:1%"><a href="/wiki/Covalent_bond" title="Covalent bond">Covalent</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/Electron_deficiency" title="Electron deficiency">Electron deficiency</a> <ul><li><a href="/wiki/Three-center_two-electron_bond" title="Three-center two-electron bond">3c–2e</a></li> <li><a href="/wiki/Four-center_two-electron_bond" title="Four-center two-electron bond">4c–2e</a></li> <li><a href="/wiki/Eight-center_two-electron_bond" class="mw-redirect" title="Eight-center two-electron bond">8c–2e</a></li></ul></li> <li><a href="/wiki/Hypervalent_molecule" title="Hypervalent molecule">Hypervalence</a> <ul><li><a href="/wiki/Three-center_four-electron_bond" title="Three-center four-electron bond">3c–4e</a></li></ul></li> <li><a href="/wiki/Agostic_interaction" title="Agostic interaction">Agostic</a></li> <li><a href="/wiki/Bent_bond" title="Bent bond">Bent</a></li> <li><a href="/wiki/Coordinate_covalent_bond" title="Coordinate covalent bond">Coordinate (dipolar)</a></li> <li><a href="/wiki/Pi_backbonding" title="Pi backbonding">Pi backbond</a></li> <li><a href="/wiki/Metal%E2%80%93ligand_multiple_bond" title="Metal–ligand multiple bond">Metal–ligand multiple bond</a></li> <li><a href="/wiki/Charge-shift_bond" title="Charge-shift bond">Charge-shift</a></li> <li><a href="/wiki/Hapticity" title="Hapticity">Hapticity</a></li> <li><a href="/wiki/Conjugated_system" title="Conjugated system">Conjugation</a></li> <li><a href="/wiki/Hyperconjugation" title="Hyperconjugation">Hyperconjugation</a></li> <li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a> <ul><li><a href="/wiki/Homoaromaticity" title="Homoaromaticity">homo</a></li> <li><a href="/wiki/Bicycloaromaticity" title="Bicycloaromaticity">bicyclo</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Metallic_bonding" title="Metallic bonding">Metallic</a></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/Metal_aromaticity" title="Metal aromaticity">Metal aromaticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ionic_bonding" title="Ionic bonding">Ionic</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 class="mw-empty-elt"></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Ligatio-covalens.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Ligatio-covalens.svg/200px-Ligatio-covalens.svg.png" decoding="async" width="200" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Ligatio-covalens.svg/300px-Ligatio-covalens.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Ligatio-covalens.svg/400px-Ligatio-covalens.svg.png 2x" data-file-width="597" data-file-height="265" /></a></span><br /><span typeof="mw:File"><a href="/wiki/File:Chemfm_carbon_monoxide_3_1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Chemfm_carbon_monoxide_3_1.svg/200px-Chemfm_carbon_monoxide_3_1.svg.png" decoding="async" width="200" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Chemfm_carbon_monoxide_3_1.svg/300px-Chemfm_carbon_monoxide_3_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Chemfm_carbon_monoxide_3_1.svg/400px-Chemfm_carbon_monoxide_3_1.svg.png 2x" data-file-width="99" data-file-height="56" /></a></span><br /><span typeof="mw:File"><a href="/wiki/File:Pi-Bond.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pi-Bond.svg/200px-Pi-Bond.svg.png" decoding="async" width="200" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pi-Bond.svg/300px-Pi-Bond.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pi-Bond.svg/400px-Pi-Bond.svg.png 2x" data-file-width="1920" data-file-height="1080" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Intermolecular_force" title="Intermolecular force">Intermolecular</a><br />(weak)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Van der Waals<br />forces</a></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/London_dispersion_force" title="London dispersion force">London dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen</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/Low-barrier_hydrogen_bond" title="Low-barrier hydrogen bond">Low-barrier</a></li> <li><a href="/wiki/Resonance-assisted_hydrogen_bond" class="mw-redirect" title="Resonance-assisted hydrogen bond">Resonance-assisted</a></li> <li><a href="/wiki/Symmetric_hydrogen_bond" title="Symmetric hydrogen bond">Symmetric</a></li> <li><a href="/wiki/Dihydrogen_bond" title="Dihydrogen bond">Dihydrogen bonds</a></li> <li><a href="/wiki/C%E2%80%93H%C2%B7%C2%B7%C2%B7O_interaction" title="C–H···O interaction">C–H···O interaction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Non-covalent_interactions" class="mw-redirect" title="Non-covalent interactions">Noncovalent</a><br />other</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/Mechanically_interlocked_molecular_architectures" title="Mechanically interlocked molecular architectures">Mechanical</a></li> <li><a href="/wiki/Halogen_bond" title="Halogen bond">Halogen</a></li> <li><a href="/wiki/Chalcogen_bond" title="Chalcogen bond">Chalcogen</a></li> <li><a href="/wiki/Metallophilic_interaction" title="Metallophilic interaction">Metallophilic</a> (<a href="/wiki/Aurophilicity" title="Aurophilicity">aurophilic</a>)</li> <li><a href="/wiki/Intercalation_(chemistry)" title="Intercalation (chemistry)">Intercalation</a></li> <li><a href="/wiki/Stacking_(chemistry)" title="Stacking (chemistry)">Stacking</a></li> <li><a href="/wiki/Cation%E2%80%93pi_interaction" class="mw-redirect" title="Cation–pi interaction">Cation–pi</a></li> <li><a href="/wiki/Cation%E2%80%93pi_interaction#Anion–π_interaction" class="mw-redirect" title="Cation–pi interaction">Anion–pi</a></li> <li><a href="/wiki/Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridge</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bond_cleavage" title="Bond cleavage">Bond cleavage</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heterolysis_(chemistry)" title="Heterolysis (chemistry)">Heterolysis</a></li> <li><a href="/wiki/Homolysis_(chemistry)" title="Homolysis (chemistry)">Homolysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electron_counting" title="Electron counting">Electron counting</a> rules</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a> <ul><li><a href="/wiki/H%C3%BCckel%27s_rule" title="Hückel's rule">Hückel's rule</a></li> <li><a href="/wiki/Baird%27s_rule" title="Baird's rule">Baird's rule</a></li> <li><a href="/wiki/M%C3%B6bius_aromaticity" title="Möbius aromaticity">Möbius</a></li> <li><a href="/wiki/Spherical_aromaticity" title="Spherical aromaticity">spherical</a></li></ul></li> <li><a href="/wiki/Polyhedral_skeletal_electron_pair_theory" title="Polyhedral skeletal electron pair theory">Polyhedral skeletal electron pair theory</a></li> <li><a href="/wiki/Jemmis_mno_rules" title="Jemmis mno rules">Jemmis mno rules</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" 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