Invariance of density correlations with charge density in polyelectrolyte solutions

TL;DR

This paper introduces a new optimization-based theory for polyelectrolyte solutions that accurately models their structure and explains the invariance of density correlations with charge density without relying solely on counterion condensation.

Contribution

A novel optimization scheme enabling RPA-based theories to handle strong repulsive forces in polyelectrolyte solutions, providing a better understanding of density correlation invariance.

Findings

The theory matches neutron scattering data across various charge densities.

Polymer-counterion correlations at Debye-Huckel level suffice to explain invariance.

Proper treatment of polymer-polymer correlations is crucial for accurate modeling.

Abstract

We present a theory for the equilibrium structure of polyelectrolyte solutions. The main element is a simple, new optimization scheme that allows theories such as the random phase approximation (RPA) to handle the harsh repulsive forces present in such systems. Comparison is made with data from recent neutron scattering experiments of randomly charged, hydrophilic polymers in salt-free, semi-dilute solution at various charge densities. Models with varying degrees of realism are examined. The usual explanation of the invariance observed at high charge density has been counterion condensation. However, when polymer-polymer correlations are treated properly, we find that modeling polymer-counterion correlations at the level of Debye-Huckel theory is sufficient.