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Drift-diffusion in electrochemistry: thresholds for boundary flux and discontinuous optical generation. (English) Zbl 1066.35012

Summary: 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 \(O_2\) 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 \(H_2\) evolution. This defines thresholds in terms of electrochemical potentials before boundary flux is activated. The optical generation rate is affected, due to the 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.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35R05 PDEs with low regular coefficients and/or low regular data
49J40 Variational inequalities
82D37 Statistical mechanics of semiconductors
92E99 Chemistry
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