Drift-Diffusion in Electrochemistry: Thresholds for Boundary Flux and Discontinuous Optical Generation

By: Siegfried Carl and Joseph W. Jerome

We consider an extension of the classical drift-diffusion model, which incorporates thermodynamic switching rules for generation and boundary flux. The motivation is the important case of the splitting of water molecules upon photonic irradiation of a semiconductor electrode located in an electrochemical cell. The solid state electrode forms the spatial domain of the model. The rules are motivated by the fact that the valence band of the semiconductor, which supplies positive charge to solution, has to be located at a lower energy level than the electrochemical potential of oxygen evolution in solution, and the conduction band, which supplies electrons to solution, has to be positioned at a higher energy level than the electrochemical potential of hydrogen evolution. This defines thresholds in terms of electrochemical potentials before boundary flux is activated. The optical generation rate is affected, due to increased carrier relaxation time, when these thresholds are crossed, and may be discontinuous. We thus consider a self-consistent model, in which `switching' occurs only in principal variables. The steady-state model is considered, and trapping regions are derived for the solutions.
This paper has appeared in Applicable Analysis 83 (2004) 915--931, and can be viewed in the following format: