Non-linear Osmotic Brush Regime: Simulations and mean-field theory

TL;DR

This study combines simulations and mean-field theory to explore the non-linear osmotic regime of polyelectrolyte brushes, revealing complex behaviors like non-monotonic height variation due to electrostatic effects and chain elasticity.

Contribution

It introduces a comprehensive analysis considering lateral electrostatics and chain elasticity, explaining deviations from classical scaling laws in polyelectrolyte brush behavior.

Findings

Brush height varies weakly with grafting density at moderate Bjerrum length.

Non-monotonic brush height behavior as a function of grafting density.

Chain re-stretching at low grafting densities due to electrostatic effects.

Abstract

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and the counterion-condensation process at polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.