A stochastic approach to the theory of intramicellar kinetics. I. Master equation for irreversible reactions

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Abstract
We develop in this paper a stochastic master equation to describe the dynamics of a certain class of micellar kinetic processes—those in which the reactants are confined to the interior (or, perhaps, the immediate vicinity) of the micellar assembly. At the outset, the problem is formulated in some detail in order to display the theoretical factors involved in accounting both for chemical reaction and physical diffusion (exit/re‐entry of solubilized reactants). Then, for definiteness, we confine our attention to the study of irreversible intramicellar reactions where complete compartmentalization of reactants is assumed. For this case, chemical processes of molecularity 1, 2, and 3 are considered, and a solution to the resulting master equation for each process is obtained. Our theoretical predictions are compared with experimental results reported by the groups of Grätzel and Singer and nearly exact, quantitative agreement with the data is found.