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Unformatted text preview: III. Reaction Kinetics Lecture 12: Faradaic Reactions in Dilute Solutions As we begin to study electrochemical energy systems out of equilibrium, we are first concerned with the kinetics of Faradaic (charge-transfer) reactions . 1 Stochastic Theory of Reaction Rates Here we model a particle diffusing through a potential energy landscape on the molecular scale. We need U TS- U 1 , 2 k B T to ensure that transitions are rare events and thAT particles are most of the time in well-defined states corresponding to local energy minima. See 2009 notes for analysis of the first passage time for a particle to escape from state 1 to state 2. Here we just quote the result: < 1 2 > = mean first passage time U TS- U 1 = e k B T Or the mean escape rate per particle: 1 MIT Student Lecture 12: Faradaic reactions in dilute solutions 10.626 (2011) Bazant U TS k B T r 1 2 = r e- Where R D with: L min L max D = a microscopic diffusivity (measuring thermal noise)....
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