Counterion-Induced Swelling of Ionic Microgels

TL;DR

This paper develops a theoretical framework to understand how counterion distribution influences the swelling and deswelling of ionic microgels, combining statistical mechanics, electrostatics, and polymer physics, with validation against experiments.

Contribution

It introduces an exact statistical mechanical theorem for electrostatic osmotic pressure in permeable colloids and applies it to explain counterion-driven microgel swelling behavior.

Findings

Counterion distribution determines internal osmotic pressure.

Deswelling occurs with increasing particle concentration due to counterion redistribution.

The linearized electrostatic pressure approximation is highly accurate and insightful.

Abstract

Ionic microgel particles, when dispersed in a solvent, swell to equilibrium sizes that are governed by a balance between electrostatic and elastic forces. Tuning of particle size by varying external stimuli, such as $p$H, salt concentration, and temperature, has relevance for drug delivery, microfluidics, and filtration. To model swelling of ionic microgels, we derive a statistical mechanical theorem, which proves exact within the cell model, for the electrostatic contribution to the osmotic pressure inside a permeable colloidal macroion. Applying the theorem, we demonstrate how the distribution of counterions within an ionic microgel determines the internal osmotic pressure. By combining the electrostatic pressure, which we compute via both Poisson-Boltzmann theory and molecular dynamics simulation, with the elastic pressure, modeled via the Flory-Rehner theory of swollen polymer networks, we show how deswelling of ionic microgels with increasing concentration of particles can result from a redistribution of counterions that reduces electrostatic pressure. A linearized approximation for the electrostatic pressure, which proves remarkably accurate, provides physical insight and greatly eases numerical calculations for practical applications. Comparing with experiments, we explain why soft particles in deionized suspensions deswell upon increasing concentration and why this effect may be suppressed at higher ionic strength. The failure of the uniform ideal-gas approximation to adequately account for counterion-induced deswelling below close packing of microgels is attributed to neglect of spatial variation of the counterion density profile and the electrostatic pressure of incompletely neutralized macroions.