It will be shown how the morphology and dimension of inorganic nanostructures in a solution should affect the rates of outer sphere electron transfer for nearby redox ions much differently than is predicted for a macroscopic planar interface. Simple Marcus theory and electrostatic evaluations of the self-energy of the ions near these nanostructures are used to calculate this effect, which is controlled by the degree to which the environment about the ion is the high dielectric permittivity of the solid rather than solution. A higher degree results in a lower reorganization energy for the ion and a smaller activation energy for electron transfer. The extreme of interest to this discussion is that of a redox ion within a spherical or cylindrical nanocavity of an inorganic solid.

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

References:

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.