Kinetics of self-replicating micelles

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Abstract
Recent experiments which achieved the autopoiesis of caprylate micelles by aqueous alkaline hydrolysis of ethyl caprylate have shown that the kinetics of this process are highly non-linear. There is an extended induction period during which the concentration of micelles remains small; at the end of this period, ethyl caprylate is consumed and micelles form rapidly via an autocatalytic reaction. In this paper, we investigate two macroscopic kinetic models for this process. In the first, we specifically include the equilibrium critical micellar concentration for caprylate anions and require that self-replication of micelles only occurs beyond this point. In the second, we study the properties of a non-linear model which is capable of accounting for the very sharp growth in total caprylate concentration as a function of time, without making any assumptions concerning equilibrium. Although both of these models have limitations, they provide insight into what features a more realistic model must have. We conclude by formulating a mesoscopic model that provides a much more detailed description of the microscopic processes of micelle formation, and which we believe will provide a quantitative description of the observed reaction kinetics.

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