Density functional methods for polymers: a coil-globule transition case study

TL;DR

This paper develops a density functional approach to study the coil-globule transition in polymers, deriving an analytical solution that reproduces classical theory and discussing applications to polymer dynamics.

Contribution

It introduces a free energy functional based on monomer density, explicitly deriving entropic and energetic contributions, and applies it to analytically model the coil-globule transition.

Findings

Reproduces de Gennes' classical coil-globule theory

Derives entropic contribution as Kullback-Leibler distance

Proposes application to polymer dynamics

Abstract

We consider a free energy functional on the monomer density function that is suitable for the study of coil-globule transition. We demonstrate, with explicitly stated assumptions, why the entropic contribution is in the form of the Kullback-Leibler distance, and that the energy contribution is given by two-body and three-body terms. We then solve for the free energy analytically on a set of trial density functions, and reproduce de Gennes' classical theory on polymer coil-globule transition. We then discuss how our formalism can be applied to study polymer dynamics from the perspective of dynamical density function theory.