A lattice model for self- and mutually avoiding semiflexible polymer chains

Abstract

We introduce a spin field theory for many self- and mutually avoiding polymers with arbitrary stiffness on a regular lattice. The model allows for the complete crossover between flexible polymers and rods. The model also includes arbitrary polymer length distributions and arbitrary volume fractions from the highly dilute regime to the melt. The mean field approximation to the full theory reproduces Flory theory, but our model permits a rigorous and systematic evaluation of corrections to the mean field approximation. The corrections are in the form of a double expansion in powers of the volume fraction ψ and, formally, in powers of the inverse lattice coordination number z−1. We present the correction to first order in z−1 and discuss its relevance to the entropic contribution to the Flory χ parameter for semiflexible polymers.