# Mathematical modelling of dye-sensitised solar cells

Penny, Melissa
(2006)
*Mathematical modelling of dye-sensitised solar cells.*
PhD
thesis,
Queensland University of Technology.

## Abstract

This thesis presents a mathematical model of the nanoporous anode within a dyesensitised solar cell (DSC). The main purpose of this work is to investigate interfacial charge transfer and charge transport within the porous anode of the DSC under both illuminated and non-illuminated conditions. Within the porous anode we consider many of the charge transfer reactions associated with the electrolyte species, adsorbed dye molecules and semiconductor electrons at the semiconductor-dye- electrolyte interface. Each reaction at this interface is modelled explicitly via an electrochemical equation, resulting in an interfacial model that consists of a coupled system of non-linear algebraic equations. We develop a general model framework for charge transfer at the semiconductor-dye-electrolyte interface and simplify this framework to produce a model based on the available interfacial kinetic data. We account for the charge transport mechanisms within the porous semiconductor and the electrolyte filled pores that constitute the anode of the DSC, through a one- dimensional model developed under steady-state conditions. The governing transport equations account for the diffusion and migration of charge species within the porous anode. The transport model consists of a coupled system of non-linear differential equations, and is coupled to the interfacial model via reaction terms within the mass-flux balance equations. An equivalent circuit model is developed to account for those components of the DSC not explicitly included in the mathematical

model of the anode. To obtain solutions for our DSC mathematical model we develop code in FORTRAN for the numerical simulation of the governing equations. We additionally employ regular perturbation analysis to obtain analytic approximations to the solutions of the interfacial charge transfer model. These approximations facilitate a reduction in computation time for the coupled mathematical model with no significant loss of accuracy. To obtain predictions of the current generated by the cell we source kinetic and transport parameter values from the literature and from experimental measurements associated with the DSC commissioned for this study. The model solutions we obtain with these values correspond very favourably with experimental data measured from standard DSC configurations consisting of titanium dioxide porous films with iodide/triiodide redox couples within the electrolyte. The mathematical model within this thesis enables thorough investigation of the interfacial reactions and charge transport within the DSC.We investigate the effects of modified cell configurations on the efficiency of the cell by varying associated parameter values in our model. We find, given our model and the DSC configuration investigated, that the efficiency of the DSC is improved with increasing electron diffusion, decreasing internal resistances and with decreasing dark current. We conclude that transport within the electrolyte, as described by the model, appears to have no limiting effect on the current predicted by the model until large positive voltages. Additionally, we observe that the ultrafast injection from the excited dye molecules limits the interfacial reactions that affect the DSC current.

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ID Code: | 16270 |
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Item Type: | QUT Thesis (PhD) |

Supervisor: | Farrell, Troy, Bell, John, & Will, Geoffrey |

Keywords: | anode, asymptotic analysis, charge injection, charge transfer, charge transport, differential equations, diffusion, dyesensitised solar cell, electrochemistry, electrolyte, electron injection, equivalent circuit, interfacial charge transfer, interfacial kinetics, iodide, lithium, mathematical modelling, migration, model, nanoporous, nonlinear equations, perturbation analysis, porous, porous film, reaction, recombination, semiconductor, semiconductordyeelectrolyte interface, semiconductorelectrolyte interface, sensitised, titanium dioxide, triiodide |

Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Schools > Mathematical Sciences |

Department: | Faculty of Science |

Institution: | Queensland University of Technology |

Copyright Owner: | Copyright Melissa Penny |

Deposited On: | 03 Dec 2008 03:59 |

Last Modified: | 28 Oct 2011 19:45 |

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