A Modified Random Phase Approximation of Polyelectrolyte Solutions

TL;DR

This paper develops a modified Random Phase Approximation to accurately predict the phase diagram of salt-free polyelectrolyte solutions by incorporating short-range electrostatic effects and chain connectivity.

Contribution

It introduces a novel modification to the RPA that accounts for electrostatic attraction limits and a wave number cut-off, improving phase diagram predictions for long-chain polyelectrolytes.

Findings

Modified electrostatic potential acts as a hard core.

Cut-off on wave modes is essential for accurate phase diagrams.

The approach successfully predicts phase behavior of long-chain solutions.

Abstract

We compute the phase diagram of salt-free polyelectrolyte solutions using a modified Debye-Huckel Approach. We introduce the chain connectivity via the Random Phase Approximation with two important modifications. We modify the electrostatic potential at short distances to include a bound on the electrostatic attractions at the distance of closest approach between charges. This modification is shown to act as a hard core in the phase diagram of electrolyte solutions. We also introduce a cut-off on the integration of the modes of wave length smaller than the size over which the chains are strongly perturbed by the electrostatic interactions. This cut-off is shown to be essential to predict physical phase diagram in long chain solutions.