Quenched Charge Disorder and Coulomb Interactions

TL;DR

This paper develops a formalism to analyze how quenched charge disorder influences electrostatic interactions between charged surfaces in Coulomb fluids, revealing that disorder induces a long-range attraction and potential collapse in strong-coupling regimes.

Contribution

It introduces a comprehensive formalism for studying quenched charge disorder effects on electrostatic interactions, covering both mean-field and strong-coupling limits.

Findings

Disorder has no effect at the mean-field level, maintaining repulsion.

In the strong-coupling limit, disorder enhances attraction between surfaces.

Increased disorder strength reduces the equilibrium separation, leading to collapse.

Abstract

We develop a general formalism to investigate the effect of quenched fixed charge disorder on effective electrostatic interactions between charged surfaces in a one-component (counterion-only) Coulomb fluid. Analytical results are explicitly derived for two asymptotic and complementary cases: i) mean-field or Poisson-Boltzmann limit (including Gaussian-fluctuations correction), which is valid for small electrostatic coupling, and ii) strong-coupling limit, where electrostatic correlations mediated by counterions become significantly large as, for instance, realized in systems with high-valency counterions. In the particular case of two apposed and ideally polarizable planar surfaces with equal mean surface charge, we find that the effect of the disorder is nil on the mean-field level and thus the plates repel. In the strong-coupling limit, however, the effect of charge disorder turns out to be additive in the free energy and leads to an enhanced long-range attraction between the two surfaces. We show that the equilibrium inter-plate distance between the surfaces decreases for elevated disorder strength (i.e. for increasing mean-square deviation around the mean surface charge), and eventually tends to zero, suggesting a disorder-driven collapse transition.