The theory of liquids at equilibrium

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Abstract
No rigorous calculation of the properties of a liquid has yet been made from a knowledge of the forces between its molecules. This review describes the method by which most solutions have been sought and the progress that has been made in the last five years. The equilibrium properties of a simple liquid can be expressed in terms of the pair distribution function g(r), which measures the probability of finding a second molecule at distance r from a first. Kirkwood, and Born and Green showed that an approximate calculation of g(r) can be made by solving an integral equation. This equation, its solutions and their imperfections are described briefly. More recently it has been found convenient to write the correlation function, h(r)=g(r) -1, as the sum of two terms, a direct term, c(r), and an indirect term. Four recent approximations can be described and compared by the form they assume for the direct correlation function, c(r). The most promising of these is the approximation of Percus and Yevick and its quantitative predictions are discussed in some detail.