Electrostatics and aggregation: how charge can turn a crystal into a gel

TL;DR

This paper investigates how electrostatic interactions influence the formation of gels versus crystals in protein and colloid systems, revealing that charge and counterion entropy play key roles in determining the resulting structure.

Contribution

It introduces an analytic model showing the impact of electrostatics and counterion entropy on gel and crystal formation, highlighting effects beyond pairwise interactions.

Findings

Electrostatic free energy cost is mainly due to counterion entropy loss.

Gels are favored over crystals due to greater accessible volume for counterions.

Increasing sphere charge promotes gel formation, but high counterion concentration can suppress it.

Abstract

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.