On the evaluation and analysis of the Marcus–Hush–Chidsey integral

► The unfriendly Marcus–Hush–Chidsey integral has been solved. ► A simple and exact, though slow to execute, formula replaces the integral. ► Even simpler formulas are shown to apply in special circumstances. ► The Marcus–Hush theory is contrasted with the Butler–Volmer model. ► Behaviors for extrem...

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Bibliographic Details
Published in:Journal of electroanalytical chemistry (Lausanne, Switzerland) Switzerland), 2011-05, Vol.655 (1), p.65-72
Main Authors: Oldham, Keith B., Myland, Jan C.
Format: Article
Language:English
Subjects:
Butler–Volmer
Chemistry
Electrochemistry
Electrode kinetics
Electrodes: preparations and properties
Exact sciences and technology
General and physical chemistry
Marcus–Hush
Other electrodes
Overvoltage
prediction
Rate constant
Reorganization energy
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Summary:► The unfriendly Marcus–Hush–Chidsey integral has been solved. ► A simple and exact, though slow to execute, formula replaces the integral. ► Even simpler formulas are shown to apply in special circumstances. ► The Marcus–Hush theory is contrasted with the Butler–Volmer model. ► Behaviors for extreme values of the parameters are examined. Chidsey’s implementation of the electron-exchange theories of Marcus and Hush leads to a prediction of the potential-dependence of electrochemical rate constants that is couched in terms of unfriendly integrals. Here we perform the integrations and recast the resulting series into formulas that are more easily enumerated and manipulated. Thereby, several observations are made concerning rate constants that follow the Marcus–Hush–Chidsey theory, and contrasted with the predictions of the Butler–Volmer model.
ISSN:1572-6657
1873-2569
DOI:10.1016/j.jelechem.2011.01.044