Systematic corrections to Flory–Huggins theory: Polymer–solvent–void systems and binary blend–void systems

Abstract

A field theory, presented earlier by us, which is formally an exact mathematical solution of the Flory–Huggins lattice model, is used to evaluate corrections to Flory–Huggins mean field theory in a systematic series expansion in the inverse of the lattice coordination number and in the nearest-neighbor interaction energies. We explicitly determine the first few corrections to the free energy of mixing for polymer–solvent–void systems and for systems containing two kinds of polymers and voids (binary blend–void systems). Applications of the theory to the calculation of equations of state and effective Flory χ parameters are discussed. We compare the result of our theory with the lattice Monte Carlo data of Dickman and Hall for the chain insertion probability and for the pressure in a system of athermal chains and voids. Good quantitative agreement is found. We discuss shortcomings of the lattice model in representing real polymers as well as possible extensions of the model to remedy these deficiencies.