Persistence Length of Flexible Polyelectrolyte Chains

TL;DR

This paper develops a self-consistent variational theory to analyze how the electrostatic persistence length of weakly charged flexible polyelectrolyte chains varies with ionic screening, revealing multiple regimes depending on charge and interaction parameters.

Contribution

It introduces a novel theoretical framework that predicts different scaling regimes for the electrostatic persistence length based on key physical parameters.

Findings

Recover classical l_e rom rac{1}{\u03ba^2} when l_0 l_B /A^2 \u2208C2

Identify intermediate regime with l_e rom rac{1}{rac{1}{2}}

Show l_e rom rac{1}{rac{1}{}} with variable exponent depending on Coulomb strength

Abstract

We calculate the dependence of the electrostatic persistence length, l_e, of weakly charged flexible polyelectrolyte chains using a self-consistent variational theory. The variation of l_e with \kappa, the inverse Debye screening length, is controlled by the parameter l_0 l_B/A^2, where l_0 is the bare persistence length, l_B is the Bjerrum length, and A is the mean distance between charges along the chain. Several distinct regimes for the dependence of l_e on \kappa emerge depending on the value of l_0 l_B/A^2. We show that when l_0 l_B /A^2 << 1 we recover the classical result, l_e \propto \kappa^{-2}. For intermediate values of l_0 l_B /A^2, l_e \propto \kappa^{-1}. In this regime one can also get l_e \propto \kappa^{-y} with y < 1 depending on the strength of the Coulomb interaction. Qualitative comparisons between our theory and simulations as well as other theories are presented.