Numerical solutions to a fractional diffusion equation used in modelling dye-sensitized solar cells

Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement. doi:10.1017/S1446181121000353

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NUMERICAL SOLUTIONS TO A FRACTIONAL DIFFUSION EQUATION USED IN MODELLING DYE-SENSITIZED SOLAR CELLS

The ANZIAM Journal ◽

10.1017/s1446181121000353 ◽

2021 ◽

pp. 1-14

Author(s):

BENJAMIN MALDON ◽

BISHNU PRASAD LAMICHHANE ◽

NGAMTA THAMWATTANA

Keyword(s):

Solar Cells ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Numerical Solutions ◽

Dye Sensitized Solar Cells ◽

Fractional Diffusion ◽

Operating Efficiency ◽

Dye Sensitized ◽

Sensitized Solar Cells

Abstract Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement.

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Numerical solutions for nonlinear partial differential equations arising from modelling dye-sensitized solar cells

ANZIAM Journal ◽

10.21914/anziamj.v60i0.14053 ◽

2019 ◽

Vol 60 ◽

pp. C231-C246 ◽

Cited By ~ 2

Author(s):

Benjamin James Maldon ◽

Bishnu Prasad Lamichhane ◽

Natalie Thamwattana

Keyword(s):

Solar Cells ◽

Finite Difference ◽

Finite Difference Method ◽

Charge Transport ◽

Difference Method ◽

Numerical Solutions ◽

Dye Sensitized Solar Cells ◽

Photoelectrochemical Cells ◽

Dye Sensitized ◽

Sensitized Solar Cells

Dye-sensitized solar cells have generated diverse research directions, which include a mathematical model based on the diffusion of electrons in the conduction band of a nano-porous semiconductor (traditionally TiO\(_2\)). We solve the nonlinear diffusion equation under its boundary conditions, as stated by Anta et al. [J. Phys. Chem. B 110 (2006) pp 5372--5378]. We employ a standard finite difference method, a fourth order finite difference method scheme and a Runge--Kutta scheme. We calculate errors and evaluate the utility of each scheme as it applies to this boundary value problem. References J. A. Anta, F. Casanueva, and G. Oskam. A numerical model for charge transport and recombination in dye-sensitized solar cells. J. Phys. Chem. B, 110(11):5372–5378, 2006. doi:10.1021/jp056493h. F. Cao, G. Oskam, G. J. Meyer, and P. C. Searson. Electron transport in porous nanocrystalline TiO\(_2\) photoelectrochemical cells. J. Phys. Chem., 100(42):17021–17027, 1996. doi:10.1021/jp9616573. A. J. Frank, N. Kopidakis, and J. van de Lagemaat. Electrons in nanostructured TiO\(_2\) solar cells: transport, recombination and photovoltaic properties. Coordin. Chem. Rev., 248:1165–1179, 2004. doi:10.1016/j.ccr.2004.03.015. Y. Gacemi, A. Cheknane, and H. S. Hilal. Simulation and modelling of charge transport in dye-sensitized solar cells based on carbon nano-tube electrodes. Phys. Scripta, 87(3):035703–035714, 2013. doi:10.1088/0031-8949/87/03/035703. B. O'Regan and M. Gratzel. A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO\(_2\) films. Nature, 353:737–740, 1991. doi:10.1038/353737a0. S. Sodergren, A. Hagfeldt, J. Olsson, and S. Lindquist. 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. doi:10.1021/j100072a023.

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A Fractional Diffusion Model for Dye-Sensitized Solar Cells

Molecules ◽

10.3390/molecules25132966 ◽

2020 ◽

Vol 25 (13) ◽

pp. 2966

Author(s):

B. Maldon ◽

N. Thamwattana

Keyword(s):

Solar Cells ◽

Charge Transfer ◽

Diffusion Model ◽

Numerical Solutions ◽

Short Circuit ◽

Dye Sensitized Solar Cells ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Dye Sensitized ◽

Sensitized Solar Cells

Dye-sensitized solar cells have continued to receive much attention since their introduction by O’Regan and Grätzel in 1991. Modelling charge transfer during the sensitization process is one of several active research areas for the development of dye-sensitized solar cells in order to control and improve their performance and efficiency. Mathematical models for transport of electron density inside nanoporous semiconductors based on diffusion equations have been shown to give good agreement with results observed experimentally. However, the process of charge transfer in dye-sensitized solar cells is complicated and many issues are in need of further investigation, such as the effect of the porous structure of the semiconductor and the recombination of electrons at the interfaces between the semiconductor and electrolyte couple. This paper proposes a new model for electron transport inside the conduction band of a dye-sensitized solar cell comprising of TiO 2 as its nanoporous semiconductor. This model is based on fractional diffusion equations, taking into consideration the random walk network of TiO 2 . Finally, the paper presents numerical solutions of the fractional diffusion model to demonstrate the effect of the fractal geometry of TiO 2 on the fundamental performance parameters of dye-sensitized solar cells, such as the short-circuit current density, open-circuit voltage and efficiency.

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