Effects of counterion fluctuations in a polyelectrolyte brush

TL;DR

This paper studies how counterion fluctuations influence the behavior of polyelectrolyte brushes, revealing a collapse transition influenced by charge density and counterion valency, with implications for brush structure.

Contribution

It introduces a systematic expansion of counterion free energy beyond mean field theory, uncovering a collapse transition and its dependence on counterion valency and grafting density.

Findings

Strongly charged brushes can undergo a collapse transition.

Transition type depends on counterion valency and solvent conditions.

Collapsed brush height scales linearly with grafting density.

Abstract

We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that for monovalent counterions the transition is discontinuous in theta solvent, while for multivalent counterions the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.