On a remark of de Gennes concerning three-dimensional polyelectrolytes

TL;DR

This paper investigates the size scaling of three-dimensional polyelectrolytes modeled as charged Brownian paths, showing the radius of gyration grows linearly with polymer length, with minor logarithmic corrections.

Contribution

It provides a mathematical analysis of polyelectrolyte size scaling, connecting Coulomb interactions with the linear growth of the radius of gyration in three dimensions.

Findings

Radius of gyration grows linearly with polymer length T.

Growth includes logarithmic corrections.

Model based on Coulomb potential for charged polymers.

Abstract

This work is inspired by a remark of de Gennes about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For polyelectrolytes, the repelling potential is the Coulomb potential arising from pairs of charged particles. We show that in the continuous case of Brownian motion in three dimensions, the radius of gyration of a polyelectrolyte of length T grows linearly with T, up to logarithmic corrections.