Drift-Diffusion in Electrochemistry:
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
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 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
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