Fractional Diffusion Equations and Equivalent Circuits Applied to Ionic Solutions

Silva, F.R.G.B.; Ribeiro, Haroldo V.; Lenzi, Marcelo Kaminski; Petrucci, Thiago; Michels, Flávio S.; Lenzi, E. K.

doi:10.1016/s1452-3981(23)07899-9

Cited by 7 publications

(1 citation statement)

References 24 publications

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“…18,19, the role of the displacement current has been analyzed and brought new aspects for the developments performed in terms of the fractional approach for the PNP -model and the possibility of analyzing different scenarios, particularly some experimental results obtained for the electrolytic cells with liquid crystals. Besides fractional approaches, the conduction in dielectric materials can be explained by equivalent circuits approaches, 20,21 Debye and Non-Debye models. 22,23 Since the classical PNP model is not suitable in the low-frequency limit, and owing to the fact that biological materials and complex fluids in general, 14,[24][25][26][27][28] liquid crystals included, typically present anomalous diffusion, here we analyze the electrical impedance obtained from an extension of the PNP model with a suitable displacement current and impedance spectroscopy measurements of nematic liquid crystal cells.…”

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confidence: 99%

Electrical Impedance Response of Liquid Crystals and Anomalous Diffusion: A Fractional Approach

Rosseto,

Ribeiro de Almeida,

Zola

et al. 2023

J. Electrochem. Soc.

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We analyze the electrical impedance response established in terms of the time-fractional approach formulation of the Poisson-Nernst-Planck model by considering a general boundary condition. The total current across the sample is solenoidal, as the Maxwell equations require, and the boundary conditions can be related to different scenarios. We also study the behavior of the electrical conductivity and its connection with the ionic spreading in the sample to establish the diffusion regime present in the system in the low-frequency limit. Furthermore, we investigate impedance spectroscopy measurements of a nematic liquid crystal cell and observe a good agreement between the experimental data and the model.

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