Legendre polynomial expansions of thermodynamic properties of binary solutions

Abstract

The advantages of orthogonal Legendre polynomials for representing the excess thermodynamic properties of binary solutions are presented. It is shown by means of examples that, in searching for empirical correlations among the coefficients of series expansions of several solutions, it is essential to start with a set of coefficients of an orthogonal series. Simple relationships are derived which permit the partial excess properties of each component to be expressed in terms of the same set of Legendre coefficients used for expressing the corresponding integral excess property. The Legendre polynomials are reformulated and the most accurate and convenient means of calculating themvia a simple recursion relationship is described. Explicit conversion formulae from the coefficients of simple power series or Redlich-Kister polynomials to Legendre coefficients are given.