# Thermodynamic Stability of Driven Open Systems and Control of Phase Separation by Electro-autocatalysis

## TL;DR

This paper develops a thermodynamic stability theory for driven reactive mixtures, enabling control of phase separation in electrochemical systems through autocatalysis and kinetic effects, with applications in batteries and other fields.

## Contribution

It introduces a nonlinear variational framework extending classical stability criteria to driven electrochemical systems, highlighting how autocatalysis can control phase separation.

## Key findings

- Electro-autocatalysis can suppress or induce phase separation.
- The theory explains stability in systems with complex electrochemical kinetics.
- Experimental evidence supports the control of phase behavior in batteries.

## Abstract

Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn equations. The Glansdorff-Prigogine stability criterion is extended for driving chemical work, based on variations of nonequilibrium Gibbs free energy. Linear stability is generally determined by the competition of chemical diffusion and driven autocatalysis. Novel features arise for electrochemical systems, related to controlled total current (galvanostatic operation), concentration-dependent exchange current (Butler-Volmer kinetics), and negative differential reaction resistance (Marcus kinetics). The theory shows how spinodal decomposition can be controlled by solo-autocatalytic charge transfer, with only a single Faradaic reaction. Experimental evidence is presented for intercalation and electrodeposition in rechargeable batteries, and further applications are discussed in solid state ionics, electrovariable optics, electrochemical precipitation, and biological pattern formation.