Statistical mechanical theory of local compositions

The concept of local composition has received much attention during the past few years, much of which has been devoted to justifying the empirical model proposed by Wilson in 1964. In this report the concept of local composition is defined on statiscal mechanical grounds and expressions relating these compositions to thermodynamic properties of equilibrium fluid mixtures are derived. In particular, different local composition approximations are presented and new approximations based on molecular theories of mixtures are derived. Sets of mixing rules consistent with these different local composition approximations result, some of which are density and temperature dependent. Also, relations for partial molar properties in terms of local compositions are derived from the Kirkwood-Buff solution theory. Finally the radius of the sphere of influence of local compositions is formulated on statistical mechanical grounds.