Electrode kinetics Marcus-Hush model

When electron transfer is forced to take place at a large distance from the electrode by means of an appropriate spacer, the reaction quickly falls within the nonadiabatic limit. H is then a strongly decreasing function of distance. Several models predict an exponential decrease of H with distance with a coefficient on the order of 1 A-1.39 The version of the Marcus-Hush model presented so far is simplified in the sense that it assumed that only the electronic states of the electrode of energy close or equal to the Fermi level are involved in the reaction.31 What are the changes in the model predictions brought about by taking into account that all electrode electronic states are actually involved is the question that is examined now. The kinetics... 

The differences between BV and MH also have implications in the concentration profiles of the electro-active species. Thus, whereas the BV model predicts a zero surface concentration of the oxidized species at the electrode surface, in the Marcus-Hush model the surface concentration of species O also depends on the electrode kinetics such that for small values of the heterogeneous... 

Henstridge MC, Rees NV, Compton RG (2012) A comparison of the Butler-Volmer tmd asymmetric Marcus-Hush models of electrode kinetics at the channel electrode. J Electroaneil Chem 687 79 3... 

In Fig. 3.14a, the dimensionless limiting current 7j ne(t)/7j ne(tp) (where lp is the total duration of the potential step) at a planar electrode is plotted versus 1 / ft under the Butler-Volmer (solid line) and Marcus-Hush (dashed lines) treatments for a fully irreversible process with k° = 10 4 cm s 1, where the differences between both models are more apparent according to the above discussion. Regarding the BV model, a unique curve is predicted independently of the electrode kinetics with a slope unity and a null intercept. With respect to the MH model, for typical values of the reorganization energy (X = 0.5 — 1 eV, A 20 — 40 [4]), the variation of the limiting current with time compares well with that predicted by Butler-Volmer kinetics. On the other hand, for small X values (A < 20) and short times, differences between the BV and MH results are observed such that the current expected with the MH model is smaller. In addition, a nonlinear dependence of 7 1 e(fp) with 1 / /l i s predicted, and any attempt at linearization would result in poor correlation coefficient and a slope smaller than unity and non-null intercept. 

In North America the theory is associated with the name of Marcus and referred to as the Marcus theory. However, Hush in Australia and Levitch and Dogonadze in the U.S.S.R. have made original contributions. Marcus started from the transition-state theory for ionic reactions. Hush from solid-state electron-transfer theory and Levitch from a consideration of reactions at electrodes. All arrived at essentially the same result, although using different terminologies. More recently, Tachiya and co-workers have developed a model based on the electrostatic interaction of the reactants with a polar solvent which also reduces to the same result under certain conditions. The version of the theory developed by Marcus has remained predominant for kinetic studies because it is framed in more familiar terminology and yields relationships that appear simple to test by experiment. 

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