A lattice model for self-avoiding polymers with controlled length distributions. II. Corrections to Flory–Huggins mean field

Abstract

We continue the analysis of the lattice spin-field theory which is introduced in paper I and which formally gives the exact entropy for a set of completely flexible self-avoiding polymers on a lattice. The model allows for arbitrary chain length distributions and arbitrary polymer volume fractions. Use of random fields produces a field theory from which Flory–Huggins results are recovered in the mean field limit. Here we recast the mean field formulation to allow for the rigorous and systematic evaluation of corrections by means of a cluster expansion. We then calculate corrections to the mean field directly up to fourth order and provide a systematic diagrammatic method for evaluating general order corrections. Our results illustrate the polymer concentration dependence of the corrections to the Flory–Huggins mean field results as well as provide the origins for the entropic contribution to the Flory χ parameter and its concentration dependence. Generalizations to treat rods and semiflexible polymers will be given elsewhere.