Maximum cumulant method for studying condensation-evaporation phase transitions

Autores
Dos Santos Mendez, Gonzalo Joaquín; Linares, Daniel Humberto; Ramirez Pastor, Antonio Jose
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 07321110.1088/1742-5468/aa7df2] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates (k-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions g1(θ) and g2(θ) with zero overlap and mean values θ1 and θ2, respectively; and (ii) g1(θ) and g2(θ) are unimodal distributions that are symmetric with respect to the middle point (θ1+θ2)/2. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear k-mers on square and triangular lattices, S-shaped k-mers on square lattices and k2-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.
Fil: Dos Santos Mendez, Gonzalo Joaquín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Linares, Daniel Humberto. Universidad Nacional de San Luis. Facultad de Ciencias Físico- Matemáticas y Naturales; Argentina
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Materia
CONDENSATION-EVAPORATION
PHASE TRANSITIONS
MONTE CARLO METHODS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/86514
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/86514
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Maximum cumulant method for studying condensation-evaporation phase transitionsDos Santos Mendez, Gonzalo JoaquínLinares, Daniel HumbertoRamirez Pastor, Antonio JoseCONDENSATION-EVAPORATIONPHASE TRANSITIONSMONTE CARLO METHODShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 07321110.1088/1742-5468/aa7df2] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates (k-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions g1(θ) and g2(θ) with zero overlap and mean values θ1 and θ2, respectively; and (ii) g1(θ) and g2(θ) are unimodal distributions that are symmetric with respect to the middle point (θ1+θ2)/2. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear k-mers on square and triangular lattices, S-shaped k-mers on square lattices and k2-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.Fil: Dos Santos Mendez, Gonzalo Joaquín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Linares, Daniel Humberto. Universidad Nacional de San Luis. Facultad de Ciencias Físico- Matemáticas y Naturales; ArgentinaFil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaAmerican Physical Society2018-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/86514Dos Santos Mendez, Gonzalo Joaquín; Linares, Daniel Humberto; Ramirez Pastor, Antonio Jose; Maximum cumulant method for studying condensation-evaporation phase transitions; American Physical Society; Physical Review E; 98; 3; 9-2018; 1-92470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.98.032134info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.032134info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:34:01Zoai:ri.conicet.gov.ar:11336/86514instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:34:01.557CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Maximum cumulant method for studying condensation-evaporation phase transitions
title Maximum cumulant method for studying condensation-evaporation phase transitions
spellingShingle Maximum cumulant method for studying condensation-evaporation phase transitions
Dos Santos Mendez, Gonzalo Joaquín
CONDENSATION-EVAPORATION
PHASE TRANSITIONS
MONTE CARLO METHODS
title_short Maximum cumulant method for studying condensation-evaporation phase transitions
title_full Maximum cumulant method for studying condensation-evaporation phase transitions
title_fullStr Maximum cumulant method for studying condensation-evaporation phase transitions
title_full_unstemmed Maximum cumulant method for studying condensation-evaporation phase transitions
title_sort Maximum cumulant method for studying condensation-evaporation phase transitions
dc.creator.none.fl_str_mv Dos Santos Mendez, Gonzalo Joaquín
Linares, Daniel Humberto
Ramirez Pastor, Antonio Jose
author Dos Santos Mendez, Gonzalo Joaquín
author_facet Dos Santos Mendez, Gonzalo Joaquín
Linares, Daniel Humberto
Ramirez Pastor, Antonio Jose
author_role author
author2 Linares, Daniel Humberto
Ramirez Pastor, Antonio Jose
author2_role author
author
dc.subject.none.fl_str_mv CONDENSATION-EVAPORATION
PHASE TRANSITIONS
MONTE CARLO METHODS
topic CONDENSATION-EVAPORATION
PHASE TRANSITIONS
MONTE CARLO METHODS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 07321110.1088/1742-5468/aa7df2] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates (k-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions g1(θ) and g2(θ) with zero overlap and mean values θ1 and θ2, respectively; and (ii) g1(θ) and g2(θ) are unimodal distributions that are symmetric with respect to the middle point (θ1+θ2)/2. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear k-mers on square and triangular lattices, S-shaped k-mers on square lattices and k2-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.
Fil: Dos Santos Mendez, Gonzalo Joaquín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Linares, Daniel Humberto. Universidad Nacional de San Luis. Facultad de Ciencias Físico- Matemáticas y Naturales; Argentina
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
description In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 07321110.1088/1742-5468/aa7df2] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates (k-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions g1(θ) and g2(θ) with zero overlap and mean values θ1 and θ2, respectively; and (ii) g1(θ) and g2(θ) are unimodal distributions that are symmetric with respect to the middle point (θ1+θ2)/2. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear k-mers on square and triangular lattices, S-shaped k-mers on square lattices and k2-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.
publishDate 2018
dc.date.none.fl_str_mv 2018-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/86514
Dos Santos Mendez, Gonzalo Joaquín; Linares, Daniel Humberto; Ramirez Pastor, Antonio Jose; Maximum cumulant method for studying condensation-evaporation phase transitions; American Physical Society; Physical Review E; 98; 3; 9-2018; 1-9
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/86514
identifier_str_mv Dos Santos Mendez, Gonzalo Joaquín; Linares, Daniel Humberto; Ramirez Pastor, Antonio Jose; Maximum cumulant method for studying condensation-evaporation phase transitions; American Physical Society; Physical Review E; 98; 3; 9-2018; 1-9
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.98.032134
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.032134
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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