Comparison of Parametric and Nonparametric Methods for the Analysis and Inversion of Immittance Data: Critique of Earlier Work

Macdonald, J. Ross

doi:10.1006/jcph.1999.6378

Cited by 66 publications

(38 citation statements)

References 29 publications

(147 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (3) is a very similar expression to the distribution of relaxation times (DRT) representation of a broad dielectric dispersion (relaxation) [21,76,82,83,84,85,,86,87,88,89]

\begin{matrix} true \\ right ε (ı ω) = ε_{\infty} + sans-serifΔ ε \int_{0}^{\infty} \frac{sans-serifG (τ) normald τ}{1 + ı ω τ} \end{matrix}

where ε ,

ε_{\infty}

and

Δ ε

are the complex permittivity, permittivity at optical frequencies and dielectric strength, respectively; and

ı \equiv \sqrt{- 1}

. The quantities ω and τ are the angular frequency and relaxation time, respectively.…”

Section: Spectral Density Representationmentioning

confidence: 99%

Geometrical Description in Binary Composites and Spectral Density Representation

Tuncer

2010

Materials

View full text Add to dashboard Cite

In this review, the dielectric permittivity of dielectric mixtures is discussed in view of the spectral density representation method. A distinct representation is derived for predicting the dielectric properties, permittivities ε, of mixtures. The presentation of the dielectric properties is based on a scaled permittivity approach, ξ=(εe-εm)(εsans-serifi-εsans-serifm)-1, where the subscripts e, m and i denote the dielectric permittivities of the effective, matrix and inclusion media, respectively [Tuncer, E. J. Phys.: Condens. Matter 2005, 17, L125]. This novel representation transforms the spectral density formalism to a form similar to the distribution of relaxation times method of dielectric relaxation. Consequently, I propose that any dielectric relaxation formula, i.e., the Havriliak-Negami empirical dielectric relaxation expression, can be adopted as a scaled permittivity. The presented scaled permittivity representation has potential to be improved and implemented into the existing data analyzing routines for dielectric relaxation; however, the information to extract would be the topological/morphological description in mixtures. To arrive at the description, one needs to know the dielectric properties of the constituents and the composite prior to the spectral analysis. To illustrate the strength of the representation and confirm the proposed hypothesis, the Landau-Lifshitz/Looyenga (LLL) [Looyenga, H. Physica 1965, 31, 401] expression is selected. The structural information of a mixture obeying LLL is extracted for different volume fractions of phases. Both an in-house computational tool based on the Monte Carlo method to solve inverse integral transforms and the proposed empirical scaled permittivity expression are employed to estimate the spectral density function of the LLL expression. The estimated spectral functions for mixtures with different inclusion concentration compositions show similarities; they are composed of a couple of bell-shaped distributions, with coinciding peak locations but different heights. It is speculated that the coincidence in the peak locations is an absolute illustration of the self-similar fractal nature of the mixture topology (structure) created with the LLL expression. Consequently, the spectra are not altered significantly with increased filler concentration level—they exhibit a self-similar spectral density function for different concentration levels. Last but not least, the estimated percolation strengths also confirm the fractal nature of the systems characterized by the LLL mixture expression. It is concluded that the LLL expression is suitable for complex composite systems that have hierarchical order in their structure. These observations confirm the finding in the literature.

show abstract

“…Equation (3) is a very similar expression to the distribution of relaxation times (DRT) representation of a broad dielectric dispersion (relaxation) [21,76,82,83,84,85,,86,87,88,89]

\begin{matrix} true \\ right ε (ı ω) = ε_{\infty} + sans-serifΔ ε \int_{0}^{\infty} \frac{sans-serifG (τ) normald τ}{1 + ı ω τ} \end{matrix}

where ε ,

ε_{\infty}

and

Δ ε

are the complex permittivity, permittivity at optical frequencies and dielectric strength, respectively; and

ı \equiv \sqrt{- 1}

. The quantities ω and τ are the angular frequency and relaxation time, respectively.…”

Section: Spectral Density Representationmentioning

confidence: 99%

Geometrical Description in Binary Composites and Spectral Density Representation

Tuncer

2010

Materials

View full text Add to dashboard Cite

show abstract

“…Examples of such codes are LEVM written by one of the present authors (Macdonald and Potter, 1987;Macdonald, 2000a) and the first and most comprehensive one (see LEVMW, web information), EQC written by B. A. Boukamp, ZView from Scribner Associates Inc., ZSimpWin from EChem Software, and MEISP from Kumho Chemical Laboratories.…”

Section: Data Analysis Elements and Codesmentioning

confidence: 99%

Impedance Spectroscopy of Dielectrics and Electronic Conductors

Bonanos

Pissis

Macdonald

2012

Characterization of Materials

View full text Add to dashboard Cite

Impedance spectroscopy is used for the characterization of materials, such as electroceramics, solid and liquid electrochemical cells, dielectrics and also fully integrated devices, such as fuel cells. It consists of measuring the electrical impedance ‐ or a closely related property, such as admittance or dielectric constant ‐ as a function of frequency and comparing the results with expectations based on physical, chemical, and microstructural models. This article reviews the principles and practical aspects of the technique, the representations of the results, the analysis of data, and procedures for the correction of measurement errors. The applications of impedance spectroscopy are illustrated with examples from electroceramics and polymer‐based dielectric systems. The way in which the technique is applied to the two classes of materials is compared with reference to the different models used.

show abstract

“…Noise amplification coefficients (8) greater than 1 are responsible for the ill-posedness of inversion (1). A mechanism of the ill-posedness is quite straightforward to understand in the (Mellin) frequency-domain.…”

Section: Mechanism Of the Ill-posednessmentioning

confidence: 99%

“…This particularly, concerns the determination of continuous RRS by the so-called nonparametric methods [1] when no assumption has been made about the parametric form of the spectrum.…”

Section: Introductionmentioning

confidence: 99%

“…Although a considerable success has been reached for the determination of the relaxation and retardation spectrum (RRS) within the last decade [1][2][3][4][5][6][7][8][9][10], the problem has not become yet the routine and safe procedure and still presents a lot of theoretical and practical challenges for computational rheology. This particularly, concerns the determination of continuous RRS by the so-called nonparametric methods [1] when no assumption has been made about the parametric form of the spectrum.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of relaxation and retardation spectrum by inverse functional filtering

Shtrauss¹

2010

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

Comparison of Parametric and Nonparametric Methods for the Analysis and Inversion of Immittance Data: Critique of Earlier Work

Cited by 66 publications

References 29 publications

Geometrical Description in Binary Composites and Spectral Density Representation

Geometrical Description in Binary Composites and Spectral Density Representation

Impedance Spectroscopy of Dielectrics and Electronic Conductors

Determination of relaxation and retardation spectrum by inverse functional filtering

Contact Info

Product

Resources

About