# Accession Number:

## AD0292937

# Title:

## STATISTICAL THERMODYNAMICS OF NONUNIFORM FLUIDS

# Descriptive Note:

# Corporate Author:

## YESHIVA UNIV NEW YORK

# Personal Author(s):

# Report Date:

## 1962-12-01

# Pagination or Media Count:

## 1.0

# 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 Ur. The method consists of transforming from an initial uniform density n sub o to the final desired density nr via a functional Taylor expansion. When n sub o is chosen to be the density in the neighborhood of the rs 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 Ur as the variable for the n sub q. The transition from Ur to nr 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