Dynamics of Counterion Condensation

TL;DR

This paper investigates the dynamic behavior of counterion condensation around a charged plate, revealing diffusive approach to equilibrium and a velocity-induced transition with nonlinear force-velocity relations.

Contribution

It introduces a generalized Poisson-Boltzmann framework to analyze dynamic counterion condensation and uncovers a velocity-driven transition and nonlinear force-velocity behavior.

Findings

Counterion condensation approaches equilibrium diffusively.

A dynamical transition occurs at a critical velocity.

Nonlinear force-velocity relation for moving charged plates.

Abstract

Using a generalization of the Poisson-Boltzmann equation, dynamics of counterion condensation is studied. For a single charged plate in the presence of counterions, it is shown that the approach to equilibrium is diffusive. In the far from equilibrium case of a moving charged plate, a dynamical counterion condensation transition occurs at a critical velocity. The complex dynamic behavior of the counterion cloud is shown to lead to a novel nonlinear force-velocity relation for the moving plate.