Steady-State Operation of Porous Photoelectrochemical Cells Under the Conditions of Mixed Diffusional and Migrational Mass Transport: Theory

Abstract

The model of mixed diffusional–migrational transport in photoelectrochemical cells, including a mesoporous semiconductor that operates under steady-state conditions, is developed. The dye-sensitized nanocrystalline solar cell (DSSC) served as a reference system. The model takes into account the presence of the bulk solution layer in contact with the mesoporous semiconductor anode, illumination from either side of the cell, and the attenuation of light due to its absorption by sensitizing molecules. The expressions derived allow one to calculate concentration profiles of each species present in the electrolyte solution, electrostatic potential profiles, and current density–concentration overpotential curves for any level of ionic support and various schemes of the electron exchange reaction. Limitations due to the mass transport arise when DSSC operates under significant light intensities, e.g., at solar illumination levels. The calculation scheme allowing determination of the limiting current density is also included in the model. The impact of changes in various parameters on the steady-state transport-limited current density of dye-sensitized semiconductor-based photoelectrochemical cells has been evaluated for the three classes of redox systems, , , and . The analytical expressions derived have been implemented for the redox mediator, the most widely used in dye-sensitized solar cells. In the calculations the following parameters were varied: the supporting electrolyte concentration, initial concentrations of the redox species, their diffusion coefficients, the porous layer absorbance, the bulk liquid layer thickness, and the photoanode porosity. The effect of migration is altered by these parameters only for the redox mediators involving both charged forms. For the redox couples involving one uncharged species, only varying content of supporting ions affects the migrational transport. The present study also provides definitive answers to certain questions related to the role of migration in the transport-limited operation of the cell, including under what conditions the migrational effects become negligible and how we might take advantage of migration to improve the cell performance.