It has long been known how simple Marcus theory predicts electron transfer rates for donor and acceptor couples as a function of the difference in the free energy of the reaction and experimentation1 has confirmed the predicted parabolic form of transfer rates and the “inverted region,” where rates slow down. Variations in the outer sphere reorganization energies of donor-acceptor couples also result in changes of charge transfer rates predicted by this theory and also indicate this decrease in transfer rates.2 Recently, it has been demonstrated how the temperature dependence of electron transfer rates for a specific donor-acceptor couples also describes this parabolic behavior according to theory.3 This presentation on nanostructures and outer sphere electron transfer explores how the dielectric permittivity within Marcus theory may be an additional variable to control rates of electron transfer reactions.
Geometric configurations will be examined in this work in the limits where the radius of the nanocavity of the solid varies from large compared to that of the redox ion within it to where it approaches the size of the redox ion. The electron transfer will be calculated as a self-exchange rate for reduced and oxidized forms of a redox couple to avoid considerations of electron exchange with the solid. To illustrate the principles involved, the solution will be taken as acetonitrile and the solid as ZnO. Spherical nanoshells will also be considered to illustrate how the same redox ion can have an accelerated electron transfer rate within the cavity while its rate for ions outside the shell slows down.4
1. Closs, G.L.; Miller, J.R. Science 1988, 240, 440-447.
2. Kuss-Petermann, M.; Wenger, O.S. J. Am. Chem. Soc. 2016, 138, 1349-1358.
3. Waskasi, M. M. et al., J. Am. Chem. Soc., 2016, 138, 9251-9257.
4. Spitler, M.T. Electrochim. Acta, 2007, 52, 2294-2301.