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Journal ArticleDOI

Detailed comparison of the Williams–Watts and Cole–Davidson functions

C. P. Lindsey, +1 more
- 01 Oct 1980 - 
- Vol. 73, Iss: 7, pp 3348-3357
TLDR
In this paper, the distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole-Davidson distribution function, and several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.
Abstract
The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole–Davidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the Cole–Davidson and Williams–Watts parameters was determined which may be used to compare data analyzed using the two fitting functions. Although the relaxation functions are similar to each other, the distribution functions are quite dissimilar. The Cole–Davidson distribution shows a sharp long time cutoff, while the Williams–Watts distribution decays approximately exponentially at long times. Finally, several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.

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Citations
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Manipulation of Photoluminescence from Semiconductor Nanocrystals by Bandgap Engineering and Surface Plasmons

Xuedan Ma
TL;DR: In this article, the optischen Eigenschaften von Halbleiter-Nanokristallen sind stark abhangig von Ladungstrager-Zustanden an der Nanokistalloberflache oder in the Nanokistsumgebung, was wiederum zum sogenannten Blinken von Nanokrists, dem zeitliche Wechseln zwischen Emission and Nicht-Emission von Licht, fuhren kann.
Journal ArticleDOI

Theoretical Aspects of Non-Debye Relaxation in Ionic Conductors

TL;DR: In this article, the authors investigated the collective transport properties of ionic conductors in a lattice-gas model of charged particles and found that the interplay of Coulomb-interactions among diffusing ions and structural disorder in the material provides a general mechanism for non-Debye relaxational effects commonly observed by experiment.
References
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Journal ArticleDOI

Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.
Journal ArticleDOI

Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function

TL;DR: In this article, the empirical dielectric decay function γ(t)= exp −(t/τ 0)β was transformed analytically to give the frequency dependent complex dielectrics constant if β is chosen to be 0.50 in the range log(ωτ0) > −0.5.
Journal ArticleDOI

Analysis of Structural Relaxation in Glass Using Rate Heating Data

TL;DR: In this paper, a method was developed to determine the kinetic parameters controlling structural relaxation in the glass transition region from data acquired during continuous heating or cooling, where the data were linearized using the method of Narayanaswamy, and the continuous temperature variation during heating and cooling was dealt with by invoking the superposition principle.
Journal ArticleDOI

Further considerations of non symmetrical dielectric relaxation behaviour arising from a simple empirical decay function

TL;DR: The empirical dielectric decay function ϕ(t)= exp −(t/τ0)β, 0 0, but significant corrections may have to be applied for β > 0.5 and log ωτ0 < 0.
Journal ArticleDOI

On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind

J G McWhirter, +1 more
- 01 Sep 1978 - 
TL;DR: In this article, the Laplace transform and other dilationally invariant integral equations of the first kind were derived for the eigenfunctions and eigenvalues, and the maximum possible amount of information was obtained when solving the inverse problem numerically.
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