Journal ArticleDOI
Detailed comparison of the Williams–Watts and Cole–Davidson functions
C. P. Lindsey,G. D. Patterson +1 more
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.read more
Citations
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Computer simulation studies of soliton models for dielectric relaxation in crystalline polyethylene and related polymers. I. Continuum and pinned limits
TL;DR: In this article, the sine-Gordon soliton model of the dielectric α relaxation in polyethylene and similar polymers is studied and a stochastic molecular dynamics computer simulation for a wide range of coupling constants is performed.
Journal ArticleDOI
Charge Recombination to Oxidized Iodide in Dye-Sensitized Solar Cells
TL;DR: In this paper, the authors used time-resolved absorption spectroscopy to quantify the yield of I2•− disproportionation under conditions where I2− reduction by electrons photoinjected into TiO2, TiO 2(e−)s, could be competitive.
Journal ArticleDOI
Viscoelastic properties of a cross-linked polysiloxane near the sol–gel transition
TL;DR: In this article, the zero frequency and dynamic properties of a cross-linked polysiloxane near gelation threshold were investigated in the framework of linear viscoelasticity.
Journal ArticleDOI
Energy criterion in interacting cluster systems
TL;DR: In this paper, a rigorous formulation of the energy-criterion argument is proposed in the frame of a new probabilistic approach to derive the Havriliak-Negami (HN) and Kohlraush-Williams-Watts (KWW) responses.
Journal ArticleDOI
Enthalpy recovery in glassy materials: Heterogeneous versus homogenous models
TL;DR: This work compares models in terms of the nature of the relaxation dynamics, heterogeneous versus homogeneous, with focus on the Kovacs-Aklonis-Hutchinson-Ramos (KAHR) and the Tool-Narayanaswamy-Moynihan (TNM) approaches, and identifies the situations for which experimental data are capable of discriminating the heterogeneous from the homogeneous scenario.
References
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Journal ArticleDOI
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
Kenneth S. Cole,Robert H. Cole +1 more
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.
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Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function
Graham Williams,David C. Watts +1 more
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
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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
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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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