A stochastic approach to the theory of intramicellar kinetics. III. The homogeneous system limit

Photoinduced reactions when confined to the interior (or perhaps the immediate vicinity) of a micellar assembly are known to exhibit remarkable kinetic effects (e.g., drastically modified reaction rates, transition to pseudo-first-order behavior for reactions of any molecularity) which have been well documented over the last decade. In earlier papers in this series we have shown how a stochastic approach can be mobilized to describe the dynamics of reactions in compartmentalized, distributed systems. A master equation was derived and solved both for the case of irreversible and reversible photoinduced reactions. In this contribution we study the asymptotic properties of the stochastic master equation for (irreversible and reversible) intramicellar reactions and show how the correct homogeneous-system (macroscopic) kinetic description is reached in the limit of large micellar volume and attendant molecular occupancy. We display numerically the kinetic behavior at intermediate stages in the taking of this limit and, for reversible reactions, show how the ’’apparent’’ equilibrium constant Q for a reaction carried out in a compartmentalized, distributed system relaxes to the ’’canonical’’ equilibrium constant K when the homogeneous system limit is reached. The simulations reported have considerable relevance to recent work on microemulsions and in the concluding section we discuss, from the vantage point of the theory presented in this paper, the possible kinetic effects observable experimentally in these systems.