Spectral dependencies of the quantum yield of photochemical processes on the surface of nano/micro-particulates of wide-band-gap metal oxides. IV. Theoretical modeling of the activity and selectivity of semiconductor photocatalysts with inclusion of a subsurface electric field in the space charge region

In an earlier study (Emeline, A. V.; Ryabchuk, V. K.; Serpone, N. J. Phys. Chem. B 1999, 103, 1316) we reported the solution to the continuity equation in which we neglected electric field effects and obtained expressions for the concentrations of the charge carriers at the surface (n(s)), for the quantum yield (Phi) of a photochemical surface redox reaction, together with an expression for the selectivity of the photocatalyst. Various considerations led us to infer and predict wavelength-dependent phenomena (quantum yields and selectivity), which were later confirmed by experimental results (Emeline, A. V.; Serpone, N. J. Phys. Chem. B 2002, 106, 12221). In this article we revisit the continuity equation but include a subsurface electric field (E) in the space charge region of the semiconductor (or dielectric) photocatalyst to assess the effect that the electric field has on the activity and selectivity of the photocatalyst. The solution to the continuity equation yields very complex expressions for n(s) and for Phi. Nonetheless, several cases are considered which simplify the expressions. Taking E = 0, the expression for the quantum yield transforms into the identical equation obtained earlier. Some of the predictions from the expressions obtained herein also find experimental verification from considerations, for example, of the quantum yields of photoadsorption of dioxygen and dihydrogen on TiO2 particles. The agreement between the predicted spectral behavior of the ratio gamma = [e(s)]/[h(s)] against wavelength with the spectral dependence of Phi(O2)/Phi(H2) is remarkable. Another no less significant conclusion from the theoretical modeling results is that a mismatch between the experimental spectral dependence of the quantum yield and the corresponding absorption band may be an indicator of the existence of a space charge region in the solid photocatalyst.