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Depending upon the underlying lattice and space dimensionality, phase diagrams that exhibit many different universality domains of critical behavior are found. We discuss these phase diagrams and the values of the critical exponents found from different theoretical methods.","publication_date":"1993,,","publication_name":"Physical Review E","grobid_abstract_attachment_id":"48866911"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Surface adsorption and the collapse transition of a linear polymer chain: Some exact results on fractal lattices","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [10178912]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":48866911,"attachmentType":"pdf"}"><img alt="First page of “Surface adsorption and the collapse transition of a linear polymer chain: Some exact results on fractal lattices”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/48866911/mini_magick20190202-682-1g10igd.png?1549117602" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Surface adsorption and the collapse transition of a linear polymer chain: Some exact results on fractal lattices</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="10178912" href="https://independent.academia.edu/YashwantSingh2"><img alt="Profile image of Yashwant Singh" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Yashwant Singh</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1993, Physical Review E</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">15 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 6443739; 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Members of the SG family are enumerated by an integer $b$ ($2\le b\le\infty$), and it is assumed that one side of each SG fractal is impenetrable adsorbing boundary. We calculate the critical exponents $\gamma_1, \gamma_{11}$, and $\gamma_s$ which, within the self--avoiding walk model (SAW) of polymer chain, are associated with the numbers of all possible SAWs with one, both, and no ends grafted on the adsorbing impenetrable boundary, respectively. By applying the exact renormalization group (RG) method, for $2\le b\le 4$, we have obtained specific values for these exponents, for various type of polymer conformations. We discuss their mutual relations and their relations with other critical exponents pertinent to SAWs on the SG fractals.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Exact study of surface critical exponents of polymer chains grafted to adsorbing boundary of fractal lattices embedded in three-dimensional space","attachmentId":69484120,"attachmentType":"pdf","work_url":"https://www.academia.edu/52032363/Exact_study_of_surface_critical_exponents_of_polymer_chains_grafted_to_adsorbing_boundary_of_fractal_lattices_embedded_in_three_dimensional_space","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/52032363/Exact_study_of_surface_critical_exponents_of_polymer_chains_grafted_to_adsorbing_boundary_of_fractal_lattices_embedded_in_three_dimensional_space"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="26912297" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/26912297/Adsorption_and_collapse_transitions_of_a_linear_polymer_chain_interacting_with_a_surface_adsorbed_polymer_chain">Adsorption and collapse transitions of a linear polymer chain interacting with a surface adsorbed polymer chain</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33109943" href="https://srmscet.academia.edu/SanjayKumar">Sanjay Kumar</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Adsorption and collapse transitions of a linear polymer chain interacting with a surface adsorbed polymer chain","attachmentId":47177050,"attachmentType":"pdf","work_url":"https://www.academia.edu/26912297/Adsorption_and_collapse_transitions_of_a_linear_polymer_chain_interacting_with_a_surface_adsorbed_polymer_chain","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/26912297/Adsorption_and_collapse_transitions_of_a_linear_polymer_chain_interacting_with_a_surface_adsorbed_polymer_chain"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="8051723" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8051723/Exact_and_Monte_Carlo_study_of_adsorption_of_a_self_interacting_polymer_chain_for_a_family_of_three_dimensional_fractals">Exact and Monte Carlo study of adsorption of a self-interacting polymer chain for a family of three-dimensional fractals</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15510184" href="https://bg.academia.edu/SuncicaElezovicHadzic">Suncica Elezovic-Hadzic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A-mathematical and General, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the problem of adsorption of self-interacting linear polymers situated in fractal containers that belong to the three-dimensional (3d) Sierpinski gasket (SG) family of fractals. 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Vannimenus</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica D: Nonlinear Phenomena, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Phase transitions for polymers on fractal lattices","attachmentId":93446415,"attachmentType":"pdf","work_url":"https://www.academia.edu/89696369/Phase_transitions_for_polymers_on_fractal_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/89696369/Phase_transitions_for_polymers_on_fractal_lattices"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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href="https://www.academia.edu/68283085/Effect_of_geometrical_constraint_on_conformational_properties_and_adsorption_transition_of_a_semiflexible_polymer_chain">Effect of geometrical constraint on conformational properties and adsorption transition of a semiflexible polymer chain</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="144738901" href="https://bhu-in.academia.edu/DrPramodKumarMishra">Dr. Pramod K U M A R Mishra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Arxiv preprint arXiv:1006.0560, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Effect of geometrical constraint on conformational properties and adsorption transition of a semiflexible polymer 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href="https://www.academia.edu/68283090/Exact_results_for_the_adsorption_of_a_semiflexible_copolymer_chain_in_three_dimensions">Exact results for the adsorption of a semiflexible copolymer chain in three dimensions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="144738901" href="https://bhu-in.academia.edu/DrPramodKumarMishra">Dr. Pramod K U M A R Mishra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Arxiv preprint arXiv:0909.4653, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Exact results for the adsorption of a semiflexible copolymer chain in three 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ds2-5-body-link" href="https://www.academia.edu/23844310/Fractal_Aspects_in_Polymer_Science">Fractal Aspects in Polymer Science</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46093219" href="https://independent.academia.edu/HelmutSchiessel">Helmut Schiessel</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Fractals, 1995</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fractal Aspects in Polymer Science","attachmentId":44240791,"attachmentType":"pdf","work_url":"https://www.academia.edu/23844310/Fractal_Aspects_in_Polymer_Science","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link 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Owczarek</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Universality of crossover scaling for the adsorption transition of lattice polymers","attachmentId":75923589,"attachmentType":"pdf","work_url":"https://www.academia.edu/63518040/Universality_of_crossover_scaling_for_the_adsorption_transition_of_lattice_polymers","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/63518040/Universality_of_crossover_scaling_for_the_adsorption_transition_of_lattice_polymers"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="14" data-entity-id="86238243" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/86238243/Forced_Induced_Desorption_of_a_Polymer_Chain_Adsorbed_on_an_Attractive_Surface_Theory_and_Computer_Experiment">Forced-Induced Desorption of a Polymer Chain Adsorbed on an Attractive Surface: Theory and Computer Experiment</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35870218" href="https://independent.academia.edu/AndreyMilchev">Andrey Milchev</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Macromolecules, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Forced-Induced Desorption of a Polymer Chain Adsorbed on an Attractive Surface: Theory and Computer Experiment","attachmentId":90737046,"attachmentType":"pdf","work_url":"https://www.academia.edu/86238243/Forced_Induced_Desorption_of_a_Polymer_Chain_Adsorbed_on_an_Attractive_Surface_Theory_and_Computer_Experiment","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/86238243/Forced_Induced_Desorption_of_a_Polymer_Chain_Adsorbed_on_an_Attractive_Surface_Theory_and_Computer_Experiment"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="15" data-entity-id="18688204" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18688204/Exactly_solvable_model_with_stable_and_metastable_states_for_a_polymer_chain_near_an_adsorbing_surface">Exactly solvable model with stable and metastable states for a polymer chain near an adsorbing surface</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38757218" href="https://independent.academia.edu/AlexanderSkvortsov">Alexander Skvortsov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review. E, Statistical, nonlinear, and soft matter physics, 2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Exactly solvable model with stable and metastable states for a polymer chain near an adsorbing surface","attachmentId":40200946,"attachmentType":"pdf","work_url":"https://www.academia.edu/18688204/Exactly_solvable_model_with_stable_and_metastable_states_for_a_polymer_chain_near_an_adsorbing_surface","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/18688204/Exactly_solvable_model_with_stable_and_metastable_states_for_a_polymer_chain_near_an_adsorbing_surface"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="16" data-entity-id="16977921" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16977921/Polymer_Chain_Adsorption_on_a_Solid_Surface_Scaling_Arguments_and_Computer_Simulations">Polymer Chain Adsorption on a Solid Surface: Scaling Arguments and Computer Simulations</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="36497652" href="https://independent.academia.edu/TVilgis">T. Vilgis</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Springer Series in Surface Sciences, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Polymer Chain Adsorption on a Solid Surface: Scaling Arguments and Computer Simulations","attachmentId":39288791,"attachmentType":"pdf","work_url":"https://www.academia.edu/16977921/Polymer_Chain_Adsorption_on_a_Solid_Surface_Scaling_Arguments_and_Computer_Simulations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/16977921/Polymer_Chain_Adsorption_on_a_Solid_Surface_Scaling_Arguments_and_Computer_Simulations"><span 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