Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell

Sibatov, Renat T.; Светухин, В. В.; Kitsyuk, E. P.; Павлов, А. А.

doi:10.3390/electronics8060650

Cited by 9 publications

(12 citation statements)

References 42 publications

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“…Note that representations ( 12), (28), and (30) are quite general and they can be used to solve other fractional generalizations of the diffusion-advection equation. In addition to disordered semiconductors, electrode materials and electrolytes of supercapacitors [32] and lithium-ion batteries [33] can be considered as possible applications of the proposed generalizations of Fick's law and solutions of FFP equations.…”

Section: Discussionmentioning

confidence: 99%

Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators

Sibatov

Sun

2020

Fractal Fract

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The approach based on fractional advection–diffusion equations provides an effective and meaningful tool to describe the dispersive transport of charge carriers in disordered semiconductors. A fractional generalization of Fick’s law containing the Riemann–Liouville fractional derivative is related to the well-known fractional Fokker–Planck equation, and it is consistent with the universal characteristics of dispersive transport observed in the time-of-flight experiment (ToF). In the present paper, we consider the generalized Fick laws containing other forms of fractional time operators with singular and non-singular kernels and find out features of ToF transient currents that can indicate the presence of such fractional dynamics. Solutions of the corresponding fractional Fokker–Planck equations are expressed through solutions of integer-order equation in terms of an integral with the subordinating function. This representation is used to calculate the ToF transient current curves. The physical reasons leading to the considered fractional generalizations are elucidated and discussed.

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Section: Discussionmentioning

confidence: 99%

Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators

Sibatov

Sun

2020

Fractal Fract

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“…Based on fractional Equations ( 5) and ( 6), different generalizations of diffusion impedances can be obtained for different geometries and boundary conditions (see in [30,[41][42][43][44] and references therein). In recent paper [45], effects produced by ion subdiffusion in lithium-ion cell are described within the fractional-order generalization of the single-particle model.…”

Section: Cahn-hilliard Equation For Ionic Transport and Its Fractional Generalizationmentioning

confidence: 99%

Time-Fractional Phase Field Model of Electrochemical Impedance

et al. 2021

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In this paper, electrochemical impedance responses of subdiffusive phase transition materials are calculated and analyzed for one-dimensional cell with reflecting and absorbing boundary conditions. The description is based on the generalization of the diffusive Warburg impedance within the fractional phase field approach utilizing the time-fractional Cahn–Hilliard equation. The driving force in the model is the chemical potential of ions, that is described in terms of the phase field allowing us to avoid additional calculation of the activity coefficient. The derived impedance spectra are applied to describe the response of supercapacitors with polyaniline/carbon nanotube electrodes.

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“…Based on fractional Equations 3and 4, different generalizations of diffusion impedances can be obtained for different geometries and boundary conditions (see [32,[40][41][42] and references therein). In our recent paper [43], effects produced by ion subdiffusion in lithium-ion cell are described within the fractional-order generalization of the single-particle model. Here, we use relation of fractional-order impedance to anomalous ion diffusion to interpret the behavior of PMSC.…”

Section: Of 14mentioning

confidence: 99%

Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays

2020

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The development of portable electronic devices has greatly stimulated the need for miniaturized power sources. Planar supercapacitors are micro-scale electrochemical energy storage devices that can be integrated with other microelectronic devices on a chip. In this paper, we study the behavior of microsupercapacitors with in-plane interdigital electrodes of carbon nanotube array under sinusoidal excitation, step voltage input and sawlike voltage input. Considering the anomalous diffusion of ions in the array and interelectrode space, we propose a fractional-order equivalent circuit model that successfully describes the measured impedance spectra. We demonstrate that the response of the investigated micro-supercapacitors is linear and the system is time-invariant. The numerical inversion of the Laplace transforms for electric current response in an equivalent circuit with a given impedance leads to results consistent with potentiostatic measurements and cyclic voltammograms. The use of electrodes based on an ordered array of nanotubes reduces the role of nonlinear effects in the behavior of a supercapacitor. The effect of the disordering of nanotubes with increasing array height on supercapacitor impedance is considered in the framework of a distributed-order subdiffusion model.

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Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell

Cited by 9 publications

References 42 publications

Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators

Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators

Time-Fractional Phase Field Model of Electrochemical Impedance

Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays

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