Abstract
Dye-sensitized solar cells (DSSCs) are an alternative low-cost solution to the renewable energy problem due to the use of TiO2 as a semiconductor. Electricity generation is achieved through a series of chemical reactions designed to transport excited electrons from photosensitive dyes as a means of creating a circuit. Current modelling approach is based on the diffusion of the density of electrons in the conduction band of a DSSC’s nanoporous semiconductor. In this paper, we review current models for DSSCs based on diffusion equations combining the generation and the loss of the electron density as a result of dye excitation due to sunlight and electron recombination, respectively. Further, we consider another model based on fractional diffusion equation, taking into consideration random porous network of the semiconductor TiO2.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
O’Regan, B., Grätzel, M.: A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO2 films. Nature 353, 737–740 (1991)
Södergren, S., Hagfeldt, A., Olsson, J., Lindquist, S.: Theoretical models for the action spectrum and the current-voltage characteristics of microporous semiconductor films in photoelectrochemical cells. J. Phys. Chem. 98, 5552–5556 (1994)
Maldon B, Thamwattana, N., Edwards, M.: Exploring nonlinear diffusion equations for modelling dye-sensitized solar cells. Entropy 22, 248 (2020)
Maldon, B., Thamwattana, N.: Review of diffusion models for charge-carrier densities in dye-sensitized solar cells. J. Phys. Commun. 4, 1–18 (2020)
Gregg, B.A.: Comment on “Diffusion impedance and space charge capacitance in the nanoporous dye-sensitized electrochemical solar cell” and “Electronic transport in dye-sensitized nanoporous TiO2 solar cells - comparison of electrolyte and solid-state devices”. J. Phys. Chem. B 107, 13540 (2003)
Anta, J.A., Casanueva, F., Oskam, G.A.: Numerical model for charge transport and recombination in dye-sensitized solar cells. J. Phys. Chem. B 110, 5372–53788 (2006)
Andrade, L., Sousa, J., Ribeiro, H.A., Mendes, A.: Phenomenological modeling of dye-sensitized solar cells under transient conditions. Sol. Energy 85, 781–793 (2011)
Papageorgiou, N., Grätzel, M., Infelta, P.P.: On the relevance of mass transport in thin layer nanocrystalline photoelectrochemical solar cells. Sol. Energy Mater. Sol. Cells 44, 405–438 (1996)
Maldon, B., Thamwattana, N.: An analytical solution for charge carrier densities in dye-sensitized solar cells. J. Photochem. Photobiol. A 370, 41–50 (2019)
Maldon, B., Thamwattana, N.: A Fractional Diffusion Model for Dye-Sensitized Solar Cells. Molecules 25, 2966 (2020)
Cao, F., Oskam, G., Meyer, G.J., Searson, P.C.: Electron transport in porous nanocrystalline TiO2 photoelectrochemical cells. J. Phys. Chem. 100, 17021–17027 (1996)
Le Bahers, T., Pauporté, T., Lainé, P.P., Labat, F., Adamo, C., Ciofini, I.: Modeling dye-sensitized solar cells: From theory to experiment. J. Phys. Chem. Lett. 4, 1044–1050 (2013)
Benkstein, K.D., Kopidakis, N., van de Lagemaat, J., Frank, A.J.: Influence of the percolation network geometry on electron transport in dye-sensitized titanium dioxide solar cells. J. Phys. Chem. B 107, 7759–7767 (2003)
O’Shaughnessy, B., Procaccia, I.: Analytical solutions for diffusion on fractal objects. Phys. Rev. Lett. 54, 455–458 (1985)
Nigmatullin, R.: The realization of the generalised transfer equation in a medium with fractal geometry. Phys. Status Solidi B 133, 425–430 (1986)
Henry, B.I., Wearne. S.L.: Fractional reaction-diffusion. Phys. A 276, 448–455 (2000)
Mittal, R.C., Jain, R.K.: Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 17, 4616–4625 (2012)
Oldham, K., Spanier, J.: The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Elsevier (1974)
Acknowledgements
The authors are grateful to the Australian Research Council for the funding of Discovery Project DP170102705. The authors are also grateful to Prof. Phil Broadbridge from La Trobe University, Australia, for many helpful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Thamwattana, N., Maldon, B. (2022). Diffusion of Electron Density in Dye-Sensitized Solar Cells. In: Ehrhardt, M., Günther, M. (eds) Progress in Industrial Mathematics at ECMI 2021. ECMI 2021. Mathematics in Industry(), vol 39. Springer, Cham. https://doi.org/10.1007/978-3-031-11818-0_34
Download citation
DOI: https://doi.org/10.1007/978-3-031-11818-0_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-11817-3
Online ISBN: 978-3-031-11818-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)