An analytical solution for charge carrier densities in dye-sensitized solar cells

Maldon, Benjamin; Thamwattana, Ngamta

doi:10.1016/j.jphotochem.2018.10.018

Cited by 9 publications

(7 citation statements)

References 27 publications

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“…We propose a new mathematical model for evaluating the efficiency of dye-sensitized solar cells by using fractional diffusion to incorporate the fractal geometry of the

semiconductor. Our results show that lower values of the mean square exponent

lead to lower efficiencies, a result that is consistent with the literature [ 11 , 27 ]. In particular, Figure 11 of Ni et al [ 27 ] shows that efficiency decreases when porosity increases above

or decreases below

, which suggests the relationship between porosity and efficiency is nonlinear.…”

Section: Discussionsupporting

confidence: 93%

“…Future consideration includes incorporating the role of the electrolyte couple by a pair of standard diffusion equations as seen in Maldon and Thamwattana [11].…”

Section: Discussionmentioning

confidence: 99%

“…Anta et al [7] considered a fully nonlinear diffusion equation for DSSCs and investigated the effect of different power-law diffusivities, which was analysed using Lie symmetry by Maldon et al 2020 [8]. Andrade et al 2011 [9] and Gacemi et al 2013 [10] proposed diffusion equations for modelling the electrolyte concentrations, which were solved analytically by Maldon and Thamwattana in 2019 [11].…”

Section: Introductionmentioning

confidence: 99%

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A Fractional Diffusion Model for Dye-Sensitized Solar Cells

Maldon

Thamwattana

2020

Molecules

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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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“…We propose a new mathematical model for evaluating the efficiency of dye-sensitized solar cells by using fractional diffusion to incorporate the fractal geometry of the

semiconductor. Our results show that lower values of the mean square exponent

lead to lower efficiencies, a result that is consistent with the literature [ 11 , 27 ]. In particular, Figure 11 of Ni et al [ 27 ] shows that efficiency decreases when porosity increases above

or decreases below

, which suggests the relationship between porosity and efficiency is nonlinear.…”

Section: Discussionsupporting

confidence: 93%

“…Future consideration includes incorporating the role of the electrolyte couple by a pair of standard diffusion equations as seen in Maldon and Thamwattana [11].…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Fractional Diffusion Model for Dye-Sensitized Solar Cells

Maldon

Thamwattana

2020

Molecules

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“…This special case readily admits an analytical solution, using a standard technique as shown in [19].…”

Section: Analytical Solution For the Linear Electron Diffusion Equationmentioning

confidence: 99%

Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells

Maldon

Thamwattana

Edwards

2020

Entropy

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Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion equations of electron density in the conduction band of the nano-porous semiconductor in dye-sensitized solar cells. Under linear diffusion and recombination, this paper provides analytical solutions to the diffusion equation. Further, Lie symmetry analysis is adopted in order to explore analytical solutions to physically relevant special cases of the nonlinear diffusion equations. While analytical solutions may not be possible, we provide numerical solutions, which are in good agreement with the results given in the literature.

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“…However, most aforementioned continuum works do not consider the ion-host and ion-ion interactions. They simply take the electrostatic interactions and ion concentration effects into account [8,15,16]. However, as suggested by Gomulkiewicz et al [17], when the size of ions is approximately equal to that of biological channels, ionchannel and ion-ion interactions become significant.…”

mentioning

confidence: 99%

A continuum study of ionic layer analysis for single species ion transport in coaxial carbon nanotubes

Chan¹

2020

EPL

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In this letter, we employ the Poisson-Nernst-Planck equation and the continuum molecular model to investigate the ionic layers formation in coaxial carbon nanotubes, which are crucial for understanding the ion transport in nanomaterials, as well as modern solar cells and batteries. Owing to the curvature of nanotubes and the strong ion-nanotubes interactions, our simulations show that stable ionic multi-layers can always be formed inside nanotubes under a wide range of external electric fields and operating temperatures. Approximate solutions have also been deduced to support our numerical results. Most importantly, our hybrid model enjoys rapid and efficient computational times and hence fluid flow, conductivity and VI curve can be extracted almost instantaneously, which opens up a new research direction for the ion transport in nanomaterials.

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An analytical solution for charge carrier densities in dye-sensitized solar cells

Cited by 9 publications

References 27 publications

A Fractional Diffusion Model for Dye-Sensitized Solar Cells

A Fractional Diffusion Model for Dye-Sensitized Solar Cells

Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells

A continuum study of ionic layer analysis for single species ion transport in coaxial carbon nanotubes

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