Generalized flory equation of state for hard chain—hard monomer mixtures of unequal segment diameter

Abstract

A generalized Flory equation of state is derived for hard chain—hard monomer mixtures, where the monomer diameter is different from the chain segment diameters. An alternate derivation of the osmotic equation of state for binary mixtures is also presented; the equation is derived by inserting both species simultaneously into the fluid. The alternative osmotic equation of state, combined with the generalized Flory theory, predicts the conformal solution mixing rule when the monomer and chain segments are of the same diameter. Chain insertion probabilities, required in the osmotic equation of state in order to predict thermodynamic properties, are estimated using monomer mixture insertion probabilities based on the equation of state of Mansoori and the generalized Flory theory. An extensive set of hard 4-mer—monomer and hard 8-mer—monomer Monte Carlo simulations have also been performed. Simulation compressibility factors are compared to the new equation of state's predictions; agreement is quite good.