Mean Field and the Single Homopolymer

TL;DR

This paper introduces a mean field statistical model for a confined homopolymer chain, deriving analytical principles and numerical methods to analyze monomer density profiles under various potentials.

Contribution

It develops a novel mean field approach using Gaussian variables for confined polymers, enabling analytical and numerical analysis of density profiles.

Findings

Derived a minimum principle for physical quantities

Numerical implementation of density profiles in 3D

Validated the model's limits of applicability

Abstract

We develop a statistical model for a confined chain molecule based on a monomer grand canonical ensemble. The molecule is subject to an external chemical potential, a backbone interaction, and an attractive interaction between all monomers. Using a Gaussian variable formalism and a mean field approximation, we analytically derive a minimum principle from which we can obtain relevant physical quantities, such as the monomer density, and we explore the limit in which the chain is subject to a tight confinement. Through a numerical implementation of the minimization process we show how we can obtain density profiles in three dimensions for arbitraty potentials, and we test the limits of validity of the theory.