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
Kinetic Ising model for polymer dynamics. II. Generalized transition rates and the Williams–Watts nonexponential function
J. Budimir,James L. Skinner +1 more
TL;DR: In this article, the Williams-Watts empirical function φ(t)=exp[−(t/τ)β] with 1/2≤β≤1 provides a good fit to this correlation function.
Journal ArticleDOI
Bioinspired Histidine–Zn2+ Coordination for Tuning the Mechanical Properties of Self-Healing Coiled Coil Cross-Linked Hydrogels
TL;DR: These findings reveal that His–metal coordination can be used as a versatile cross-linking mechanism for tuning the viscoelastic properties of biomimetic hydrogels.
Journal ArticleDOI
Molecular dynamics study of the thermal and the density effects on the local and the large-scale motion of polymer melts: Scaling properties and dielectric relaxation
TL;DR: Results from a molecular dynamics simulation of a melt of unentangled polymers are presented and Detectable cross-correlation between the "normal-mode" and the "segmental" dielectric relaxations is found and contrasted with the usual assumption of independent modes.
Journal ArticleDOI
Slow Dielectric Relaxation of Supercooled Liqutos Investigated by Nonresonant Spectral Hole Burning
TL;DR: In this article, the authors show that the non-debye response is due to a distribution of relaxation times and that the spectral hole is preserved during recovery, indicating negligible interaction between the degrees of freedom that responded to the field.
Journal ArticleDOI
Complex desorption of mucin from silica.
TL;DR: It is shown that the large glycoprotein mucin not only adsorbs in distinctively different ways according to the bulk concentration but also, strikingly, that the law of desorption, established with the help of high-resolution molecular microscopy, depends on the Bulk concentration during adsorption.
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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