  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.
