Onsager's Wien Effect on a Lattice

TL;DR

This paper uses lattice Coulomb gas simulations to analyze Onsager's Wien effect, confirming analytical theories and revealing microscopic dynamics influences, thus providing a new computational approach to study this non-linear electrochemical phenomenon.

Contribution

The study introduces lattice Coulomb gas simulations to investigate the Wien effect, offering detailed characterization and uncovering microscopic corrections beyond existing analytical models.

Findings

Simulation confirms analytical predictions of free charge density evolution.

Microscopic dynamics influence field-dependent conductivity.

Simulations reveal corrections to Onsager's theory.

Abstract

The Second Wien Effect describes the non-linear, non-equilibrium response of a weak electrolyte in moderate to high electric fields. Onsager's 1934 electrodiffusion theory along with various extensions has been invoked for systems and phenomena as diverse as solar cells, surfactant solutions, water splitting reactions, dielectric liquids, electrohydrodynamic flow, water and ice physics, electrical double layers, non-Ohmic conduction in semiconductors and oxide glasses, biochemical nerve response and magnetic monopoles in spin ice. In view of this technological importance and the experimental ubiquity of such phenomena, it is surprising that Onsager's Wien effect has never been studied by numerical simulation. Here we present simulations of a lattice Coulomb gas, treating the widely applicable case of a double equilibrium for free charge generation. We obtain detailed characterisation of the Wien effect and confirm the accuracy of the analytical theories as regards the field evolution of the free charge density and correlations. We also demonstrate that simulations can uncover further corrections, such as how the field-dependent conductivity may be influenced by details of microscopic dynamics. We conclude that lattice simulation offers a powerful means by which to investigate system-specific corrections to the Onsager theory, and thus constitutes a valuable tool for detailed theoretical studies of the numerous practical applications of the Second Wien Effect.