Test-charge theory for the electric double layer

TL;DR

This paper introduces a test-charge based model for ion distribution near charged surfaces, accurately capturing behavior in various coupling regimes and predicting a crossover in decay behavior at large distances.

Contribution

The paper develops a test-charge theory that provides exact and approximate ion density profiles across coupling regimes, including a novel prediction of decay crossover.

Findings

Exact density profile in weak and strong coupling limits.

Qualitative agreement with Monte-Carlo simulations at intermediate coupling.

Prediction of exponential to algebraic decay crossover at large distances.

Abstract

We present a model for the ion distribution near a charged surface, based on the response of the ions to the presence of a single test particle. Near an infinite planar surface this model produces the exact density profile in the limits of weak and strong coupling, which correspond to zero and infinite values of the dimensionless coupling parameter. At intermediate values of the coupling parameter our approach leads to approximate density profiles that agree qualitatively with Monte-Carlo simulation. For large values of the coupling parameter our model predicts a crossover from exponential to algebraic decay at large distance from the charged plate. Based on the test charge approach we argue that the exact density profile is described, in this regime, by a modified mean field equation, which takes into account the interaction of an ion with the ions close to the charged plate.