On a remark of de Gennes concerning three-dimensional polyelectrolytes

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.