STATISTICAL THERMODYNAMICS OF NONUNIFORM FLUIDS
Abstract
A general formalism is developed for obtaining the low order distribution functions n sub q (r sub 1,...,r sub q) and the thermodynamic parameters of nonuniform equilibrium systems where the nonuniformity is caused by a potential U(r). The method consists of transforming from an initial (uniform) density n sub o to the final desired density n(r) via a functional Taylor expansion. When n sub o is chosen to be the density in the neighborhood of the r's we obtain n sub q as an expansion in the gradients of the density. The expansion parameter is essentially the ratio of the microscopic correlation length to the scale of the inhomogeneities. The analysis is most conveniently done in the grand ensemble formalism where the corresponding thermodynamic potential serves as the generating functional (with the U(r) as the variable) for the n sub q. The transition from U(r) to n(r) as the relevant variable is accomplished via the direct correlation function which enters very naturally relating the change in U at r sub 2 due to a change in n at r sub 1. It is thus essentially the matrix inverse of the two-particle Ursell function. The analysis is applied to obtain the asymptotic behavior of the radial distribution function in a uniform system. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1962
- Accession Number
- AD0292937
Entities
People
- J.k. Percus
- J.l. Lebowitz
Organizations
- Yeshiva University