Characterization of frequency dispersion in the impedance response of a distributed model from the mathematical properties of the distribution function of relaxation times

被引:15
作者
Cordoba-Torres, Pedro [1 ]
机构
[1] UNED, Fac Ciencias, Dept Fis Matemat & Fluidos, Madrid 28040, Spain
关键词
Electrochemical impedance; Frequency dispersion; Constant-phase element; Distribution of relaxation times; Ideally-polarized electrode; GRAIN-SIZE DISTRIBUTIONS; PHASE ELEMENT BEHAVIOR; UNDERLYING DISTRIBUTIONS; CAPACITANCE DISPERSION; FRACTAL INTERFACES; ANION ADSORPTION; SPECTROSCOPY; ELECTRODES; DECONVOLUTION; ELECTROCHEMISTRY;
D O I
10.1016/j.electacta.2015.08.140
中图分类号
O646 [电化学、电解、磁化学];
学科分类号
081704 ;
摘要
Heterogeneity and disorder univocally leads to distortion phenomena in the immittance response of a system. The analysis of this response in terms of a distribution of relaxation times (DRT) has become an important topic of basic and applied research. In this work we theoretically and numerically study the impact of the mathematical properties of a distribution function of relaxation times (DFRT) on the frequency dispersion displayed by the immittance response of a distributed model for an ideal dielectric system such as an ideally-polarized electrode, paying special attention to constant-phase-element (CPE) behavior. The analysis of the problem encompasses both explicit and implicit results reported in the literature, and a number of new findings. It is shown, for instance, that CPE exponent is upper bounded by 1, as found in experiments. Conditions to be fulfilled by the DFRT in order to give frequency dispersion are revealed, and CPE behavior is related to scale invariance. The extent of this capacitance dispersion on the frequency spectrum of the response is also addressed for both infinite and finite systems. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码:591 / 603
页数:13
相关论文
共 60 条
[1]   Anomalous power law dispersions in ac conductivity and permittivity shown to be characteristics of microstructural electrical networks [J].
Almond, DP ;
Bowen, CR .
PHYSICAL REVIEW LETTERS, 2004, 92 (15) :157601-1
[2]  
[Anonymous], 1967, Advances in electrochemistry and electrochemical engineering
[3]  
Barsoukov E, 2005, IMPEDANCE SPECTROSCOPY: THEORY, EXPERIMENT, AND APPLICATIONS, 2ND EDITION, pXII
[4]   Fourier transform distribution function of relaxation times; application and limitations [J].
Boukamp, Bernard A. .
ELECTROCHIMICA ACTA, 2015, 154 :35-46
[5]   THE ANALYSIS OF ELECTRODE IMPEDANCES COMPLICATED BY THE PRESENCE OF A CONSTANT PHASE ELEMENT [J].
BRUG, GJ ;
VANDENEEDEN, ALG ;
SLUYTERSREHBACH, M ;
SLUYTERS, JH .
JOURNAL OF ELECTROANALYTICAL CHEMISTRY, 1984, 176 (1-2) :275-295
[6]   Analysis of Electrochemical Impedance Spectroscopy Data Using the Distribution of Relaxation Times: A Bayesian and Hierarchical Bayesian Approach [J].
Ciucci, Francesco ;
Chen, Chi .
ELECTROCHIMICA ACTA, 2015, 167 :439-454
[7]   Dispersion and absorption in dielectrics I. Alternating current characteristics [J].
Cole, KS ;
Cole, RH .
JOURNAL OF CHEMICAL PHYSICS, 1941, 9 (04) :341-351
[8]   Electrochemical impedance analysis of TiO2 nanotube porous layers based on an alternative representation of impedance data [J].
Cordoba-Torres, P. ;
Oliveira, N. T. C. ;
Bolfarini, C. ;
Roche, V. ;
Nogueira, R. P. .
JOURNAL OF ELECTROANALYTICAL CHEMISTRY, 2015, 737 :54-64
[9]   Toward a better characterization of constant-phase element behavior on disk electrodes from direct impedance analysis: Methodological considerations and mass transport effects [J].
Cordoba-Torres, P. ;
Mesquita, T. J. ;
Nogueira, R. P. .
ELECTROCHIMICA ACTA, 2013, 92 :323-334
[10]   Influence of geometry-induced current and potential distributions on the characterization of constant-phase element behavior [J].
Cordoba-Torres, P. ;
Mesquita, T. J. ;
Nogueira, R. P. .
ELECTROCHIMICA ACTA, 2013, 87 :676-685