Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions |
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| Authors: | Ignacio Urrutia |
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| Institution: | (1) Consejo Nacional de Investigaciones Científicas y Técnicas y Departamento de Física, Comisión Nacional de Energía Atómica, Av. Gral. Paz 1499 (RA-1650) San Martín, Buenos Aires, Argentina |
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| 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. |
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| Keywords: | Hard spheres Configuration integral Exact results Confined fluids Small systems Inhomogeneous fluids Spherical interfaces Spherical wall |
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