Analytical behavior of the fourth and fifth virial coefficients of a hard-sphere mixture

Abstract

This paper focus on the study of the composition-dependent fourth and fifth virial coefficient of a hard-sphere binary mixture, namely, B 4(s) and B 5(s). On one side, the analytical expression of B 4(s) is revised. In particular, I analyzed the composition-independent term B4[1](s) included in B 4(s) and found a simplified form of its exact expression, which has the advantage over that previously published of highlighting the geometric properties of this term. On the other side, using a geometrical approach, I found a set of nonanalytic points of B 4(s) and B 5(s) as functions of s by analyzing each of their composition-independent terms.