Thermodynamic Stability of Driven Open Systems and Control of Phase Separation by Electroautocatalysis
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 Cahn-Hilliard and Allen-Cahn equations. The Glansdorff-Prigogine stability criterion is extended for driving chemical work, based on nonequilibrium Gibbs free energy. Linear stability is 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 resistance (Marcus kinetics). The theory shows how spinodal decomposition can be controlled by autocatalytic charge transfer, or ``electro-autocatalysis", 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, solution electrochemistry, and biological pattern formation.