Strongly nonlinear dynamics of electrolytes in large ac voltages

TL;DR

This paper investigates the nonlinear electrochemical dynamics in micro-electrochemical cells under large AC voltages, revealing salt depletion, double layer breakdown, and the effects of finite ion sizes, with implications for electrokinetic phenomena.

Contribution

It extends previous models into the strongly nonlinear regime, introducing new phenomena like ac capacitive desalination and space-charge layer formation, with a mathematical framework for complex electrokinetic responses.

Findings

Salt depletion near electrodes under large AC voltages

Breakdown of quasi-equilibrium double layer structure at high voltages

Steric effects suppress nonlinear regimes in concentrated electrolytes

Abstract

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.