Current Density versus Potential Characteristics of Dye-Sensitized Nanostructured Semiconductor Photoelectrodes. 1. Analytical Expressions

A closed-form analytical model is developed to describe the steady-state current density−potential (J−E) characteristics of dye-sensitized nanostructured semiconductor photoelectrodes. The basic components of the model are a set of differential equations that describe the generation, recombination, and transport of charge carriers in mesoporous semiconductor electrode systems. Charge-carrier transport is treated as a diffusion process, and semiclassical Marcus theory is used to describe the kinetics at the interfaces between the semiconductor and the contacting phase as well as the kinetics at the interfaces with adsorbed dye. The model relates explicitly, within a single formalism, the rate constants for charge transfer of the mesoporous membrane electrode system to conventional intramolecular and intermolecular electron-transfer rate constant expressions and to interfacial electron-transfer processes at planar metal or semiconductor electrodes. The near-equilibrium situation is considered by including the reverse electron-transfer pathways for each rate process of interest. The underlying physical and chemical factors that form the basis of the model are completely parameterized to facilitate input into a numerical simulation algorithm, thereby allowing facile generation of simulated J−E curves for a wide range of experimental conditions