Navegar

Colección

Datos Estadísticas

Artículo

El editor permite incluir el artículo en su versión final en nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

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.

Registro:

Documento: Artículo
Título:Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
Autor:Urrutia, I.
Filiación:Comisión Nacional de Energía Atómica, Universidad de Buenos Aires, Consejo Nacional de Investigaciones Científicas y T́cnicas, Av. Rivadavia 1917, RA-1033 Buenos Aires, Argentina
Departamento de Física, Av. Gral. Paz 1499, RA-1650 San Martín, Buenos Aires, Argentina
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, RA-1428 Buenos Aires, Argentina
Palabras clave: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
Año:2010
Volumen:133
Número:10
DOI: http://dx.doi.org/10.1063/1.3469773
Título revista:Journal of Chemical Physics
Título revista abreviado:J Chem Phys
ISSN:00219606
CODEN:JCPSA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00219606_v133_n10_p_Urrutia.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v133_n10_p_Urrutia

Referencias:

  • Löwen, H., (2000) Statistical Physics and Spatial Statistics, 554, pp. 295-331. , www.springerlink.com/content/w14613phu4254522, Lecture Notes in Physics Vol., edited by K. R. Mecke and D. Stoyan (Springer, Berlin)
  • Nairn, J.H., Kilpatrick, J.E., (1972) Am. J. Phys., 40, p. 503. , AJPIAS 0002-9505,. 10.1119/1.1986605
  • Blaak, R., (1998) Mol. Phys., 95, p. 695. , MOPHAM 0026-8976
  • Carnahan, N.F., Starling, K.E., (1969) J. Chem. Phys., 51, p. 635. , JCPSA6 0021-9606,. 10.1063/1.1672048
  • Alder, B.J., Wainwright, T.E., (1957) J. Chem. Phys., 27, p. 1208. , JCPSA6 0021-9606,. 10.1063/1.1743957
  • Lowen, H., Density functional theory of inhomogeneous classical fluids: Recent developments and new perspectives (2002) Journal of Physics Condensed Matter, 14 (46), pp. 11897-11905. , DOI 10.1088/0953-8984/14/46/301, PII S0953898402527910
  • Roth, R., (2010) J. Phys.: Condens. Matter, 22, p. 063102. , JCOMEL 0953-8984,. 10.1088/0953-8984/22/6/063102
  • Neimark, A.V., Ravikovitch, P.I., Vishnyakov, A., (2003) J. Phys.: Condens. Matter, 15, p. 347. , JCOMEL 0953-8984,. 10.1088/0953-8984/15/3/303
  • Neimark, A.V., Vishnyakov, A., Phase transitions and criticality in small systems: Vapor-liquid transition in nanoscale spherical cavities (2006) Journal of Physical Chemistry B, 110 (19), pp. 9403-9412. , DOI 10.1021/jp056407d
  • Neimark, A.V., Lin, Y., Ravikovitch, P.I., Thommes, M., (2009) Carbon, 47, p. 1617. , CRBNAH 0008-6223,. 10.1016/j.carbon.2009.01.050
  • Kegel, W.K., Reiss, H., Lekkerkerker, H.N.W., (1999) Phys. Rev. Lett., 83, p. 5298. , PRLTAO 0031-9007,. 10.1103/PhysRevLett.83.5298
  • Kruglov, T., Bouwman, W.G., Plomp, J., Rekveldt, M.T., Vroege, G.J., Petukhov, A.V., Thies-Weesie, D.M., (2005) Physica B, 357, p. 452. , PHYBE3 0921-4526
  • Pusey, P.N., Poon, W.C.K., Ilett, S.M., Bartlett, P., (1994) J. Phys.: Condens. Matter, 6, p. 29. , JCOMEL 0953-8984,. 10.1088/0953-8984/6/23A/004
  • Pusey, P.N., Van Megen, W., (1986) Nature (London), 320, p. 340. , NATUAS 0028-0836,. 10.1038/320340a0
  • Urrutia, I., (2008) J. Stat. Phys., 131, p. 597. , JSTPBS 0022-4715, (); 10.1007/s10955-008-9513-3 e-print arXiv:cond-mat/0609608
  • Urrutia, I., Szybisz, L., (2010) J. Math. Phys., 51, p. 033303. , JMAPAQ 0022-2488, (); 10.1063/1.3319560 e-print arXiv:0909.0246
  • Uranagase, M., Munakata, T., Statistical mechanics of two hard spheres in a box (2006) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 74 (6), p. 066101. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevE.74.066101&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevE.74.066101
  • Hill, T.L., (1956) Statistical Mechanics, , (Dover, New York)
  • Abramowitz, M., Stegun, I.A., (1972) Handbook of Mathematical Functions, , (Dover, New York)
  • Wolfram, S., http://functions.wolfram.com; Lamarche Francois, Leroy Claude, Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals (1990) Computer Physics Communications, 59 (2), pp. 359-369. , DOI 10.1016/0010-4655(90)90184-3
  • Irving, J.H., Kirkwood, J.G., (1950) J. Chem. Phys., 18, p. 817. , JCPSA6 0021-9606,. 10.1063/1.1747782
  • Buff, F.P., (1955) J. Chem. Phys., 23, p. 419. , JCPSA6 0021-9606,. 10.1063/1.1742005
  • Schofield, P., Henderson, J.R., (1982) Proc. R. Soc. London, Ser. A, 379, p. 231. , PRLAAZ 1364-5021,. 10.1098/rspa.1982.0015
  • Blokhuis, E.M., Kuipers, J., (2007) J. Chem. Phys., 126, p. 054702. , JCPSA6 0021-9606,. 10.1063/1.2434161
  • Bellemans, A., (1962) Physica (Amsterdam), 28, p. 493. , PHYSAG 0031-8914,. 10.1016/0031-8914(62)90037-X
  • Bellemans, A., (1962) Physica (Amsterdam), 28, p. 617. , PHYSAG 0031-8914,. 10.1016/0031-8914(62)90117-9
  • Bellemans, A., (1963) Physica (Amsterdam), 29, p. 548. , PHYSAG 0031-8914,. 10.1016/S0031-8914(63)80167-6
  • Sokoowski, S., (1977) Czech. J. Phys., 27, p. 850. , CZLIA6 0011-4626,. 10.1007/BF01588931
  • Stecki, J., Sokoowski, S., (1978) Phys. Rev. A, 18, p. 2361. , PLRAAN 1050-2947,. 10.1103/PhysRevA.18.2361
  • Munakata, T., Hu, G., Statistical mechanics of two hard disks in a rectangular box (2002) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 65 (6), pp. 066104/1-066104/4. , http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype= pdf&id=PLEEE8000065000006066104000001&idtype=cvips, DOI 10.1103/PhysRevE.65.066104, 066104
  • Hill, T.L., (1994) Thermodynamics of Small Systems, , (Dover, New York)
  • Callen, H.B., (1985) Thermodynamics and An Introduction to Thermostatistics, , (Wiley, New York)
  • Young, T., (1805) Philos. Trans. R. Soc. London, 95, p. 65. , PTRSAV 0370-2316,. 10.1098/rstl.1805.0005
  • Laplace, P.S., (1806) Ḿcanique Ćleste, , (Duprat, Paris)
  • Gibbs, J.W., (1906) The Scientific Papers of J. W. Gibbs, 1. , (Ox Bow, Connecticut), Vol.
  • Boruvka, L., Neumann, A.W., (1977) J. Chem. Phys., 66, p. 5464. , JCPSA6 0021-9606,. 10.1063/1.433866
  • Sokoowski, S., Stecki, J., (1979) Acta Phys. Pol. A, 55, p. 611. , ATPLB6 0587-4246
  • Henderson, J.R., (1983) Mol. Phys., 50, p. 741. , MOPHAM 0026-8976,. 10.1080/00268978300102661
  • Henderson, J.R., Solvation of a wedge (2002) Physica A: Statistical Mechanics and its Applications, 305 (3-4), pp. 381-386. , DOI 10.1016/S0378-4371(01)00616-1, PII S0378437101006161
  • Henderson, J.R., (2004) J. Chem. Phys., 120, p. 1535. , JCPSA6 0021-9606,. 10.1063/1.1634253
  • Bryk, P., Roth, R., Mecke, K.R., Dietrich, S., (2003) Phys. Rev. e, 68, p. 031602. , PLEEE8 1063-651X,. 10.1103/PhysRevE.68.031602
  • Sokoowski, S., (1978) J. Chem. Phys., 69, p. 941. , JCPSA6 0021-9606,. 10.1063/1.436615
  • Sokoowski, S., Stecki, J., (1981) J. Chem. Phys., 85, p. 1741. , JCPSA6 0021-9606,. 10.1021/j150612a029
  • Rowlinson, J.S., (1985) Proc. R. Soc. London, Ser. A, 402, p. 67. , PRLAAZ 1364-5021,. 10.1098/rspa.1985.0108
  • Urrutia, I., (unpublished); Poniewierski, A., Stecki, J., (1997) J. Chem. Phys., 106, p. 3358. , JCPSA6 0021-9606,. 10.1063/1.473084
  • Henderson, J.R., (1986) Fluid Interfacial Phenomena, pp. 555-605. , edited by C. A. Croxton (Wiley, New York)
  • He, Y., Mi, J., Zhong, C., (2008) J. Phys. Chem. B, 112, p. 7251. , JPCBFK 1089-5647,. 10.1021/jp711692j

Citas:

---------- APA ----------
(2010) . Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities. Journal of Chemical Physics, 133(10).
http://dx.doi.org/10.1063/1.3469773
---------- CHICAGO ----------
Urrutia, I. "Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities" . Journal of Chemical Physics 133, no. 10 (2010).
http://dx.doi.org/10.1063/1.3469773
---------- MLA ----------
Urrutia, I. "Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities" . Journal of Chemical Physics, vol. 133, no. 10, 2010.
http://dx.doi.org/10.1063/1.3469773
---------- VANCOUVER ----------
Urrutia, I. Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities. J Chem Phys. 2010;133(10).
http://dx.doi.org/10.1063/1.3469773