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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Journal ArticleDOI
Heat capacity and glass transition of ethylene oxide clathrate hydrate
TL;DR: In this article, a glass transition related to the proton configurational mode in the hydrogen-bonded host was observed around 90 K. This glass transition was similar to the one observed previously for the structure II tetrahydrofuran hydrate but showed a wider distribution of relaxation times.
Journal ArticleDOI
Analysis of multiexponential decay by a linear programming method: Application to light scattering spectroscopy
TL;DR: In this paper, a linear programming (LP) method is applied to the analysis of multiexponential decay (in other words, to the Laplace inversion problem) and a statistical study of the sequences of residuals is proposed which leads to an evaluation of the goodness of fit.
Journal ArticleDOI
Frequency-dependent magnetic permeability of Fe10Co90 nanocomposites
TL;DR: In this paper, the frequency and temperature-dependent magnetic permeability of a compacted Fe10Co90 nanocomposite was measured over a range of temperatures (77?873?K) and frequencies (0.1?100?kHz).
Journal ArticleDOI
Spectral shape simplicity of viscous materials.
TL;DR: A broad survey of viscoelastic data demonstrates that van der Waals, hydrogen-bonded, and ionic liquids, as well as polymeric, inorganic, and metallic melts share a structural relaxation pattern virtually insensitive to their morphological details as mentioned in this paper.
Journal ArticleDOI
Perpendicularly Aligned, Size-and Spacing-Controlled Nanocylinders by Molecular-Weight Adjustment of a Homopolymer Blended in an Asymmetric Triblock Copolymer
Dae Up Ahn,Erol Sancaktar +1 more
TL;DR: In this article, the preference for perpendicular orientation or hexagonal ordering of the nanocylinders over a large area in the asymmetric block copolymer can be controlled by adjusting the molecular weight of the blended homopolymer.
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.
Journal ArticleDOI
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
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,E R Pike +1 more
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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