Chemical instabilities as critical phenomena

Abstract

The analogy between equilibrium phase transitions and chemical instabilities is studied in detail in the vicinity of the critical point of a nonequilibrium reacting diffusing system characterized by multiple homogeneous steady states. The critical point of such a system is defined and its mathematical properties are discussed. These properties are shown to be essential in the subsequent reduction of the equations of motion near the critical point. The order parameter characterizing the transition is defined, and its equation of motion near the critical point is obtained in the form of a time-dependent Ginzburg-Landau equation. Fluctuations are taken into account phenomenologically using a Langevin-equation approach. Fluctuations originating from diffusion processes are shown not to be important near the critical point. The size of the critical region for chemical instabilities is estimated using an equivalent of the Ginzburg criterion of equilibrium critical phenomena. The reduction method fails within this region. It is concluded that critical points of chemical instabilities can in principle exhibit "nonclassical" criticàl behavior. Systems involving the photothermochemical instability and computer simulations of model systems seem currently to be the best candidates for studying the critical properties of chemical instabilities, and for experimental or numerical tests of the predictions of the present theory.