Theory of Anomalous Diffusion Impedance of Realistic Fractal Electrode

Kant, Rama; Kumar, Rajesh; Yadav, Vivek

doi:10.1021/jp712066k

Cited by 51 publications

(67 citation statements)

References 37 publications

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“…This correlation function contains experimental observable quantities about the surface morphological characteristics such as area, mean square height, slope, curvature, and correlation length. Now, in Fourier domain we have (22) This is defined as ( r ) = 1…”

Section: Admittance For a Stochastic Roughness Modelmentioning

confidence: 99%

“…These surface disorders of an electrode [19] have resulted in many anomalous behaviors, viz. constant phase element (CPE) [20], anomalous Warburg [21][22][23] and anomalous Gerischer [25,24] behavior. On the other hand various processes like diffusion [1,26,27], adsorption [3][4][5], heterogeneous catalysis [28,29], NMR relaxation [30], fluorescence quenching [31], enzyme kinetics [31], diffusion limited adsorption/aggregation [27,32] and electrochemistry of disordered system [19] are affected by the transport of ion from the bulk and across the interface making the problem investigated here useful for the wide range of the applications.…”

Section: Introductionmentioning

confidence: 99%

“…An elegant formalism based on the diffusion adopting ab initio methodology has been successfully developed to understand the influence of roughness on the electrochemical response. Recently, theories for diffusion limited charge transfer process on rough electrode are developed to generalize various fundamental equations for smooth electrodes: Warburg [22], Gerischer [25], Anson [62,66], quasi-reversible charge transfer admittance has been developed for finite fractal electrodes [63,65]. Similarly, theories for the anomalous Cottrell [64,68,67] and anomalous Warburg admittance [61,22] with ohmic effects [23,69] in rough electrode modeled as finite fractals have also been developed.…”

Section: Introductionmentioning

confidence: 99%

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Generalization of Randles-Ershler admittance for an arbitrary topography electrode: application to random finite fractal roughness

Kant

Singh

2015

Electrochimica Acta

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Section: Admittance For a Stochastic Roughness Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalization of Randles-Ershler admittance for an arbitrary topography electrode: application to random finite fractal roughness

Kant

Singh

2015

Electrochimica Acta

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“…For systems with gold-platinum electrodes and water the value of β is around 0.8 or 0.9 [40,41]. The alleged reason for this power-law behavior is a nonsmooth and fractal surface topology of the electrode material [42][43][44]. With a model of the cell-sensor interface ( Fig.…”

Section: Sensor Impedancementioning

confidence: 99%

Frequency-dependent signal transfer at the interface between electrogenic cells and nanocavity electrodes

et al. 2012

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We present a model to describe the response of chip-based nanocavity sensors during extracellular recording of action potentials. These sensors feature microelectrodes which are embedded in liquid-filled cavities. They can be used for the highly localized detection of electrical signals on a chip. We calculate the sensor's impedance and simulate the propagation of action potentials. Subsequently we apply our findings to analyze cell-chip coupling properties. The results are compared to experimental data obtained from cardiomyocyte-like cells. We show that both the impedance and the modeled action potentials fit the experimental data well. Furthermore, we find evidence for a large seal resistance of cardiomyocytes on nanocavity sensors compared to conventional planar recording systems.

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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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Theory of Anomalous Diffusion Impedance of Realistic Fractal Electrode

Cited by 51 publications

References 37 publications

Generalization of Randles-Ershler admittance for an arbitrary topography electrode: application to random finite fractal roughness

Generalization of Randles-Ershler admittance for an arbitrary topography electrode: application to random finite fractal roughness

Frequency-dependent signal transfer at the interface between electrogenic cells and nanocavity electrodes

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

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