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Journal of Statistical Physics

, Volume 131, Issue 4, pp 597–611 | Cite as

Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

  • Ignacio UrrutiaEmail author
Article

Abstract

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b 2(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.

Keywords

Hard spheres Configuration integral Exact results Confined fluids Small systems Inhomogeneous fluids Spherical interfaces Spherical wall 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Consejo Nacional de Investigaciones Científicas y Técnicas y Departamento de FísicaComisión Nacional de Energía AtómicaBuenos AiresArgentina

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