Fluids with Internal Degrees of Freedom

Abstract

The essential core of the modern integral equation approach to liquid state theory was arrived at nearly simultaneously in 1960 by a remarkable number of authors working independently [1], They found that the density expansion of the pair distribution function g(r) of a simple fluid with interatomic potential ϕ(r) could be grouped into infinite subsets of diagrams such that

$$ g(r){e^{{\beta \phi (r)}}} = 1 + S(r) + P(r) + B(r) $$

((1))

where, in the pictorial electrical language of M. S. Green [2], the diagrams of the series set S(r) resemble series circuits and those of the parallel set P(r) resemble parallel circuits; the remaining bridge set B(r) begins with a diagram that looks like a Wheatstone bridge. Further, the diagrams of P(r) could be summed in direct space to give P(r) = g(r) exp(βϕ(r)) - 1 - ln[g(r) exp(βϕ(r))], while those of S(r) could be summed in Fourier space to yield S(k) = č²(k)/[l-pc(k)], which is the Ornstein-Zernike (OZ) equation in Fourier transform representation. Here, c(r) = h(r) - S(r) is the sum of non-nodal graphs, or direct correlation function, while h(r) = g(r) - 1 is the total correlation function.