Reactions in microemulsions: Effect of thermal fluctuations on reaction kinetics

In this paper we address the generic effects arising from the interplay of thermal fluctuations and reactions. This is accomplished by considering specifically the kinetics of reactions effected in microemulsion media. In the first part of this paper we consider the kinetics of the reaction A + B --> empty set in bicontinuous microemulsion media, wherein the solutes A and B are assumed to be preferentially attracted to water and oil, respectively, and O constitutes an inert product. We formulate the diffusion and reaction of these solutes in a field-theoretical framework within which the fluctuations of the background microemulsion are embedded. We then employ mean-field arguments and a perturbative Wilson-type renormalization group (RG) approach to discern the relevance, at long length scales, of the background fluctuations. Our analysis indicates that the dynamic fluctuations of the microemulsion prove irrelevant in impacting the asymptotic kinetics of the reaction. In view of the fact that our field-theoretic approach enables us to probe only the long time characteristics, moreover, only in the weak-coupling limit, in the second part of this paper we analyze similar issues in the context of the droplet phase of microemulsions. This enables us to surmount some of the restrictions placed upon the results of the first part of this paper. In the second part, our analysis focuses upon a simpler reaction, viz., A --> empty set, wherein the solute A which is present only in the water phase is anhiliated upon contact with the fluctuating interfaces of the droplets. We employ a standard diffusion equation framework to formulate the transport and reaction of A. The fluctuations of the microemulsion are manifest in the boundary condition positing the vanishing concentration of A. We then employ a perturbation scheme to the solution of the diffusion equation, and thereby discern the explicit effects of the fluctuations of the sinks. Our formulation enables, in a sequentially improvable asymptotic manner, the explicit computation of the time-dependent and the steady state fluctuation contributions to the reaction rate. (C) 2000 American Institute of Physics. [S0021-9606(00)51731-0].