Random Polyelectrolytes and Polyampholytes in Solution

TL;DR

This paper presents a theoretical investigation of polyelectrolytes and polyampholytes in semi-dilute solutions, analyzing various charge distributions and their effects on electrostatic screening and phase behavior.

Contribution

It introduces a comprehensive theoretical framework using path integral and mean field approaches to model different charge distributions and their impact on solution properties.

Findings

Fluctuations in monomer charges influence electrostatic screening.

Variance in charge distribution affects polyampholyte behavior.

Enhanced mesophase separation occurs in bad solvent conditions.

Abstract

The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions is investigated theoretically. Various statistical charge distributions along the polyelectrolyte chains are considered: smeared, annealed, permuted and quenched. Annealed polyampholytes are also considered. Path integral formulation was used to derive mean field free energies for the different models. Self-consistent field equation is obtained for the polymer order parameter and a Poisson-Boltzmann like equation for the electrostatic potential. The random phase approximation is used to calculate the monomer-monomer structure factor S(q) for the different statistical charge distribution models. We show that in the annealed model, fluctuations of the the monomer charges contribute to the electrostatic screening in addition to the free ions in the solution. The strength of this screening depends on the variance of the monomer charge distribution and is especially important for polyampholytes in bad solvent conditions where the mesophase separation is enhanced. The ratio between the variance and the net average charge determines whether polyampholytes behave as polyelectrolytes or as neutral chains.