Hyperbolic subdiffusive impedance

Kosztołowicz, Tadeusz; Lewandowska, Katarzyna D.

doi:10.1088/1751-8113/42/5/055004

Cited by 37 publications

(32 citation statements)

References 25 publications

(46 reference statements)

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“…Here we interpret the impedance spectra of PEDOT:PSS using the anomalous diffusion theory, which may explain the deviations from ideal diffusion behavior due to the particular porous structure of the polymer, as occurs in other porous media, gels, amorphous semiconductors or materials with fractal geometries [9][10][11][12][13]. We hypothesised that ion diffusion is significantly slowed in PED-OT:PSS films due to their highly tortuous, porous nanostructure ( Fig.…”

Section: Resultsmentioning

confidence: 96%

“…However, non-Fickian diffusions can also occur in practical situations [17]. More complex expressions for diffusion impedance are obtained using heuristic descriptions [18,19] or anomalous diffusion models [9,12,13].…”

Section: Resultsmentioning

confidence: 99%

“…(1) can be derived from the continuous time random walk theory [9,12,13]. Solutions of this equation yield concentration profiles c(x, t), i.e.…”

Section: Resultsmentioning

confidence: 99%

“…Physical interpretation of the subdiffusion process suggests that ion movement is obstructed by the nanostructured polymer. Experimental impedance data interpreted by anomalous diffusion theory have been barely reported in the scientific literature [9][10][11]. Although the subdiffusion has been extensively studied from a theoretical point of view [9,12,13], to our knowledge, experimental applications of a subdiffusion impedance model derived from the continuous time random walk theory do not exist.…”

Section: Introductionmentioning

confidence: 99%

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Subdiffusion behavior in poly(3,4-ethylenedioxythiophene): Polystyrene sulfonate (PEDOT:PSS) evidenced by electrochemical impedance spectroscopy

Hernández-Labrado¹,

Contreras-Donayre²,

Collazos‐Castro³

et al. 2011

Journal of Electroanalytical Chemistry

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Section: Resultsmentioning

confidence: 96%

Section: Resultsmentioning

confidence: 99%

“…(1) can be derived from the continuous time random walk theory [9,12,13]. Solutions of this equation yield concentration profiles c(x, t), i.e.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Subdiffusion behavior in poly(3,4-ethylenedioxythiophene): Polystyrene sulfonate (PEDOT:PSS) evidenced by electrochemical impedance spectroscopy

Hernández-Labrado¹,

Contreras-Donayre²,

Collazos‐Castro³

et al. 2011

Journal of Electroanalytical Chemistry

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“…18 charges move in a fractal geometry; [20][21][22] the systems have some particular distribution of relaxation times.…”

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confidence: 99%

A Unifying View of the Constant-Phase-Element and Its Role as an Aging Indicator for Li-Ion Batteries

Cuervo‐Reyes

Scheller

Held

et al. 2015

J. Electrochem. Soc.

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Various materials display a constant phase impedance, Z ∝ [iω] −u , over a wide frequency range. In this paper, we show that this behavior is a natural consequence of charge transport in the macroscopic limit, and that in contrast to the common belief, no assumptions on the "relaxation functions" are required. Our unifying view of the constant-phase-element (CPE) is then employed for analyzing impedance spectra that were recorded during the aging of Li x FePO 4 cells. We find and explain a significant correlation between their capacity loss and changes in the exponent (u) Electrochemical impedance spectroscopy (EIS) is a widely employed method for the characterization of Li-ion batteries (LIBs), and their aging mechanisms.1-11 Its usefulness, however, relies on an adequate selection of an equivalent circuit with a physically sound interpretation. Model-circuits are mainly composed of constant-phaseelements (CPE).12-24 The CPE name comes from the fact that the impedance has the form 25and therefore its phase, θ = −uπ/2, is independent of frequency ω.Resistors, capacitors, and inductors are CPEs with u = 0, 1, and −1, respectively. A case with special relevance in electrochemistry is the Warburg element. It has u = 1 2 and originates, for instance, from charge-transport in the cathode 26 of Li-ion batteries being limited by Li-ion diffusion. CPEs with other u values are sometimes required to obtain a good fit to measured impedance data. However, there is not a complete agreement on the origin of such a behavior. 15 The current understanding is divided into different points of view: the chargetransport is sub-diffusive;18 charges move in a fractal geometry; [20][21][22] the systems have some particular distribution of relaxation times. 15,17The theory of sub-diffusive transport stems from the works of Scher & Montroll.27 They observed a slow electric relaxation in amorphous Selenium with a power-law time dependence.28 They found that this could be explained by a continuous-time random-walk (CTRW) of the electrons, in which the time steps between jumps adhere to a probability distribution function (PDF) with a certain power-law tail. Power-law relaxation functions have then been used in the modeling of electrochemical processes as they lead to a CPE-impedance. 15 Yet, this has faced certain criticism, because of apparent shortcomings of the power-laws. For example, a cutoff in the time domain must be introduced for the distribution to be normalizable. There seem to be no fundamental reasons (besides fitting the experiments) why the relaxation must have this form. On this same line, there is experimental evidence showing deviations from the CPE behavior which cannot be related to finite-size effects.15 Several phenomenological modifications of the diffusion equation have been proposed, all of which add to a more complicated picture of the subject. 12-14The transport in fractal geometries is, in a way, mathematically equivalent to the strange-diffusion. 29 The impedance is also of CPE type. However, it is not clear ...

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A block‐centered finite difference method for fractional Cattaneo equation

Rui

Liu

2017

Numerical Methods Partial

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In this article, a block-centered finite difference method for fractional Cattaneo equation is introduced and analyzed.The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete L 2 norm with optimal order of convergenceboth for pressure and velocity are established on nonuniform rectangular grids. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

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Hyperbolic subdiffusive impedance

Cited by 37 publications

References 25 publications

Subdiffusion behavior in poly(3,4-ethylenedioxythiophene): Polystyrene sulfonate (PEDOT:PSS) evidenced by electrochemical impedance spectroscopy

Subdiffusion behavior in poly(3,4-ethylenedioxythiophene): Polystyrene sulfonate (PEDOT:PSS) evidenced by electrochemical impedance spectroscopy

A Unifying View of the Constant-Phase-Element and Its Role as an Aging Indicator for Li-Ion Batteries

A block‐centered finite difference method for fractional Cattaneo equation

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