On the modeling of the dye-sensitized solar cell

Abstract

A simplified electric model of the dye-sensitized electrochemical solar cell (DSC) is presented. It permits the calculation of internal steady-state cell characteristics like particle density distributions or the electric field as a function of the (measured) external current Iext. The cell is modeled as an one-dimensional pseudo-homogeneous medium of thickness L, where all the electroactive particles involved in the current supporting process move according to different effective transport coefficients (i.e. effective diffusivities D and effective mobilities μ). The electroactive particles are the electrons e− injected into the nanoporous TiO2 layer after light absorption by the dye, the reduced and the oxidized counterpart of the redox electrolyte ElRed and ElOx, and the positively charged cation Kat+ being brought into the cell together with the electrolyte. By applying the continuity equation, the transport-equation and Poisson's equation to all the electroactive species involved (e−, ElRed, ElOx and Kat+) and by assuming a linear Boltzmann relaxation approximation for the back reaction, a system of differential equations is derived, describing particle densities, particle currents and the electric field within the cell. The underlying simplifying assumptions as well as the resulting limits of the model are stated, and some possible extensions are given. This paper aims to outline the general ideas and limitations of the proposed electric modeling, numerical calculations have been successfully implemented, but will be presented in a future paper.