Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities

Autores
Urrutia, I.
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The partition function of two hard spheres in a hard-wall pore is studied, appealing to a graph representation. The exact evaluation of the canonical partition function and the one-body distribution function in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical, and ellipsoidal cavities. Results have been compared with two previously studied geometries; the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length, and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based on the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained, which expresses the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two hard spheres in a hard-wall pore for the analyzed different geometries. We obtain analytically the external reversible work, the pressure on the wall, the pressure in the homogeneous region, the wall-fluid surface tension, the line tension, and other similar properties. © 2010 American Institute of Physics.
Fil:Urrutia, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J Chem Phys 2010;133(10)
Materia
Adopted measures
Canonical partition function
Common features
Different geometry
Ellipsoidal cavity
Energy dependence
Extended systems
Graph representation
Hard cores
Hard spheres
Homogeneous regions
Intensive variables
Line tension
Partition functions
Reversible work
Simple geometries
Spherical pores
Surface area
Thermo dynamic analysis
Thermodynamic behaviors
Thermodynamic description
Vapor interface
Distribution functions
Geometry
Laplace equation
Statistical mechanics
Surface tension
Thermoanalysis
Thermodynamics
Spheres
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00219606_v133_n10_p_Urrutia

id BDUBAFCEN_846a4421312aa5538985560ae78f9c62
oai_identifier_str paperaa:paper_00219606_v133_n10_p_Urrutia
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Two hard spheres in a pore: Exact statistical mechanics for different shaped cavitiesUrrutia, I.Adopted measuresCanonical partition functionCommon featuresDifferent geometryEllipsoidal cavityEnergy dependenceExtended systemsGraph representationHard coresHard spheresHomogeneous regionsIntensive variablesLine tensionPartition functionsReversible workSimple geometriesSpherical poresSurface areaThermo dynamic analysisThermodynamic behaviorsThermodynamic descriptionVapor interfaceDistribution functionsGeometryLaplace equationStatistical mechanicsSurface tensionThermoanalysisThermodynamicsSpheresThe partition function of two hard spheres in a hard-wall pore is studied, appealing to a graph representation. The exact evaluation of the canonical partition function and the one-body distribution function in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical, and ellipsoidal cavities. Results have been compared with two previously studied geometries; the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length, and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based on the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained, which expresses the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two hard spheres in a hard-wall pore for the analyzed different geometries. We obtain analytically the external reversible work, the pressure on the wall, the pressure in the homogeneous region, the wall-fluid surface tension, the line tension, and other similar properties. © 2010 American Institute of Physics.Fil:Urrutia, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00219606_v133_n10_p_UrrutiaJ Chem Phys 2010;133(10)reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:42:52Zpaperaa:paper_00219606_v133_n10_p_UrrutiaInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:42:53.546Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
title Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
spellingShingle Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
Urrutia, I.
Adopted measures
Canonical partition function
Common features
Different geometry
Ellipsoidal cavity
Energy dependence
Extended systems
Graph representation
Hard cores
Hard spheres
Homogeneous regions
Intensive variables
Line tension
Partition functions
Reversible work
Simple geometries
Spherical pores
Surface area
Thermo dynamic analysis
Thermodynamic behaviors
Thermodynamic description
Vapor interface
Distribution functions
Geometry
Laplace equation
Statistical mechanics
Surface tension
Thermoanalysis
Thermodynamics
Spheres
title_short Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
title_full Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
title_fullStr Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
title_full_unstemmed Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
title_sort Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
dc.creator.none.fl_str_mv Urrutia, I.
author Urrutia, I.
author_facet Urrutia, I.
author_role author
dc.subject.none.fl_str_mv Adopted measures
Canonical partition function
Common features
Different geometry
Ellipsoidal cavity
Energy dependence
Extended systems
Graph representation
Hard cores
Hard spheres
Homogeneous regions
Intensive variables
Line tension
Partition functions
Reversible work
Simple geometries
Spherical pores
Surface area
Thermo dynamic analysis
Thermodynamic behaviors
Thermodynamic description
Vapor interface
Distribution functions
Geometry
Laplace equation
Statistical mechanics
Surface tension
Thermoanalysis
Thermodynamics
Spheres
topic Adopted measures
Canonical partition function
Common features
Different geometry
Ellipsoidal cavity
Energy dependence
Extended systems
Graph representation
Hard cores
Hard spheres
Homogeneous regions
Intensive variables
Line tension
Partition functions
Reversible work
Simple geometries
Spherical pores
Surface area
Thermo dynamic analysis
Thermodynamic behaviors
Thermodynamic description
Vapor interface
Distribution functions
Geometry
Laplace equation
Statistical mechanics
Surface tension
Thermoanalysis
Thermodynamics
Spheres
dc.description.none.fl_txt_mv The partition function of two hard spheres in a hard-wall pore is studied, appealing to a graph representation. The exact evaluation of the canonical partition function and the one-body distribution function in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical, and ellipsoidal cavities. Results have been compared with two previously studied geometries; the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length, and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based on the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained, which expresses the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two hard spheres in a hard-wall pore for the analyzed different geometries. We obtain analytically the external reversible work, the pressure on the wall, the pressure in the homogeneous region, the wall-fluid surface tension, the line tension, and other similar properties. © 2010 American Institute of Physics.
Fil:Urrutia, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description The partition function of two hard spheres in a hard-wall pore is studied, appealing to a graph representation. The exact evaluation of the canonical partition function and the one-body distribution function in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical, and ellipsoidal cavities. Results have been compared with two previously studied geometries; the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length, and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based on the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained, which expresses the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two hard spheres in a hard-wall pore for the analyzed different geometries. We obtain analytically the external reversible work, the pressure on the wall, the pressure in the homogeneous region, the wall-fluid surface tension, the line tension, and other similar properties. © 2010 American Institute of Physics.
publishDate 2010
dc.date.none.fl_str_mv 2010
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/20.500.12110/paper_00219606_v133_n10_p_Urrutia
url http://hdl.handle.net/20.500.12110/paper_00219606_v133_n10_p_Urrutia
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J Chem Phys 2010;133(10)
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
_version_ 1844618734182858752
score 13.070432