# A mathematical model for the anodic half cell of a dye-sensitised solar cell

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## Abstract

We present a mathematical model of the steady-state current produced by the anodic half cell of a dye-sensitised solar cell (DSC) under both illuminated and non-illuminated conditions. A one-dimensional transport model that describes the transport of charged species via migration and diffusion within the electrolyte filled pores and the porous semiconductor that constitutes the porous anode of the DSC is given. This model is coupled to an interfacial model, developed previously by the authors, that describes charge transfer across the semiconductor–dye–electrolyte interface by explicitly accounting for each reaction at the interface involving dye molecules, electrolyte species, and semiconductor electrons. An equivalent circuit extension to the anode model (in the form of a boundary condition) is developed in order to validate some of the simulation results of the anode model with experimental results obtained from a full DSC specifically commissioned for the study. Parameter values associated with the model are obtained from the literature or experimentally from the specifically commissioned cell. A comparison of the numerical simulation results with experimental results shows a favourable correspondence without the need to fit parameter values.

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