Mixtures of interacting particles with well-defined composition field coupling χ parameters

Abstract

This article proposes a systematic, quantitative treatment of the problem of associating a scalar Flory-Huggins-like chi parameter directly with the interaction potentials in a binary mixture of point particles. This work fulfills the need for a general, quantitative way to compare chi values in explicitly simulated ensembles of lattice and off-lattice polymer models with field theoretic calculations. Emphasis is placed on constructing particle models where chi is relatively well defined. In general, chi is defined through pair correlation functions, whose thermal fluctuations are coupled to local average composition and composition gradients. This implies that chi is composition dependent even in the simplest particle models. At the same time, by quantifying this effect, it is found that composition-independent chi may be defined to within a few percent for cases where the range of the potential is large relative to the interparticle distance. An explicit formula for chi in terms of interaction potentials is given.