A new equation of state of a flexible-chain polyelectrolyte solution: Phase equilibria and osmotic pressure in the salt-free case

TL;DR

This paper presents a first-principle equation of state for salt-free flexible-chain polyelectrolyte solutions, predicting phase separation and osmotic pressure with good agreement to simulations, beyond traditional Debye-Hueckel theory.

Contribution

It introduces a novel theoretical framework combining field theory and modified RPA to accurately describe phase behavior of polyelectrolyte solutions.

Findings

Predicts liquid-liquid phase separation induced by correlation attraction.

Accurately calculates osmotic pressure across monomer concentrations.

Shows strong agreement with Monte Carlo and MD simulation results.

Abstract

We develop a first-principle equation of state of salt-free polyelectrolyte solution in the limit of infinitely long flexible polymer chains in the framework of a field-theoretical formalism beyond the linear Debye-Hueckel theory and predict a liquid-liquid phase separation induced by a strong correlation attraction. As a reference system we choose a set of two subsystems - charged macromolecules immersed in a structureless oppositely charged background created by counterions (polymer one component plasma) and counterions immersed in oppositely charged background created by polymer chains (hard-core one component plasma). We calculate the excess free energy of polymer one component plasma in the framework of Modified Random Phase Approximation, whereas a contribution of charge densities fluctuations of neutralizing backgrounds we evaluate at the level of Gaussian approximation. We show that our theory is in a very good agreement with the results of Monte-Carlo and MD simulations for critical parameters of liquid-liquid phase separation and osmotic pressure in a wide range of monomer concentration above the critical point, respectively.