Rod-like Polyelectrolytes in Presence of Monovalent Salt

TL;DR

This study models rigid polyelectrolyte solutions with monovalent salt using DHBj theory, revealing cluster formation and osmotic behavior consistent with experiments.

Contribution

It introduces a free energy framework for polyelectrolyte solutions accounting for cluster formation and salt effects, aligning theoretical predictions with experimental data.

Findings

Polyelectrolyte solutions form clusters of one polyion with counterions.

Osmotic pressure depends on Manning parameter $\xi$.

Theoretical results agree well with experimental observations.

Abstract

We investigate the properties of rigid polyelectrolyte solutions in presence of monovalent salt. The free energy within the Debye-H\"uckel-Bjerrum (DHBj) theory [M. E. Fisher and Y. Levin, {\it Phys. Rev. Lett.} 71, 3826 (1993)] is constructed. It is found that at thermodynamic equilibrium the polyelectrolyte solution consists of clusters composed of one polyion and various counterions. The distribution of the cluster densities is determined by finding the minimum of the Helmholtz free energy. The osmotic pressure and the average charge of the cluster are found and their dependence on Manning parameter $\xi$ is elucidated. A good agreement with the experimental results is obtained.