Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
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 cuboida...
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todo:paper_00219606_v133_n10_p_Urrutia2023-10-03T14:24:17Z 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00219606_v133_n10_p_Urrutia |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| 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 |
| spellingShingle |
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 Urrutia, I. Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities |
| topic_facet |
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 |
| 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. |
| format |
JOUR |
| author |
Urrutia, I. |
| author_facet |
Urrutia, I. |
| author_sort |
Urrutia, I. |
| title |
Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00219606_v133_n10_p_Urrutia |
| work_keys_str_mv |
AT urrutiai twohardspheresinaporeexactstatisticalmechanicsfordifferentshapedcavities |
| _version_ |
1807320576518258688 |