Negative capacitance and related instabilities in theoretical models of the electric double layer and membrane capacitors

TL;DR

This paper reviews models predicting negative capacitance in electric double layers and membrane capacitors, highlighting the conditions under which negative capacitance arises and discussing instabilities related to charge control methods.

Contribution

It clarifies the conditions leading to negative capacitance in theoretical models and introduces an exactly solvable membrane capacitor model illustrating instabilities and phase transitions.

Findings

Negative capacitance can occur under S-control with uniform charge distribution.

Transition to q-control can cause instability and non-uniform phases.

The membrane capacitor model demonstrates the onset of instability and phase transition features.

Abstract

Various models leading to predictions of negative capacitance, C, are briefly reviewed. Their relation to the nature of electric control is discussed. We reconfirm that the calculated double layer capacitance can be negative under S-control - an artificial construct that requires uniform distribution of the electrode surface charge density, S. It is shown that the combined relaxation of the ionic and electronic contributions can result in C<0 even for the local statistical ionic models with strictly positive diffuse layer capacitance. In reality, however, only the total charge q (or the average surface charge density S) can be experimentally fixed in isolated cell studies (q-control). For those S where C becomes negative under S-control, the transition to q-control (i.e. relaxing the lateral charge density distribution, fixing its mean value to S) leads to instability of the uniform distribution and a transition to a non-uniform phase. As an illustration, a "membrane capacitor" model is discussed. This exactly solvable model, allowing for both uniform and inhomogeneous relaxation of the electrical double layer, helps to demonstrate both the onset and some important features of the instability. Perspectives for further development are discussed briefly.