Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels

TL;DR

This paper develops a theoretical model to analyze counterion distributions and electrostatic interactions in solutions of polyelectrolyte macroions, revealing differences in counterion penetration and interaction potentials for star-branched and microgel macroions.

Contribution

It provides analytical expressions for counterion profiles and effective interactions, incorporating macroion permeability and deriving implications for screening and macroion overlap.

Findings

Counterions penetrate stars more easily than microgels.

Effective interactions are Yukawa-like for separated macroions.

Overlapping macroions experience softly repulsive, bounded interactions.

Abstract

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.