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
Interpretation of 1H and 2H spin-lattice relaxation dispersions: insights from molecular dynamics simulations of polymer melts.
TL;DR: It is demonstrated that molecular dynamics simulations are a versatile tool to ascertain the interpretation of spin-lattice relaxation data and the range of validity of experimental approaches, which often assume Gaussian dynamics, is determined.
Journal ArticleDOI
Dynamics of Hydrophobic Core Phenylalanine Residues Probed by Solid-State Deuteron NMR.
Liliya Vugmeyster,Dmitry Ostrovsky,Toni Villafranca,Janelle Sharp,Wei Xu,Andrew S. Lipton,Gina L. Hoatson,Robert L. Vold +7 more
TL;DR: The analysis of the widths of the distributions, in combination with the earlier results on the dynamics of flanking methyl groups, suggests that the hydrophobic core undergoes slow concerted fluctuations and points to the role of solvent in softening the core and highlights aromatic residues as markers of the protein dynamical transitions.
Journal ArticleDOI
Dynamic site heterogeneity in amorphous maltose and maltitol from spectral heterogeneity in erythrosin B phosphorescence.
TL;DR: In this article, the authors used phosphorescence from erythrosin B (tetraiodofluorescein) dispersed in thin films of either maltose or maltitol to investigate the physical properties of these amorphous pure sugar matrixes.
Journal ArticleDOI
Stochastic Tools Hidden Behind the Empirical Dielectric Relaxation Laws
TL;DR: In this article, the authors present probabilistic implications for the study of the relaxation-rate distribution models in complex systems, in which relaxing entities form random clusters interacting with each other and single entities.
Journal ArticleDOI
Stochastic Model for Volume Relaxation in Glass Forming Materials: Local Specific Volume Model
TL;DR: In this paper, a stochastic model for structural relaxation in glassy materials is developed, where the rate of relaxation in a mesoscopic domain depends upon the state in that meso-domain.
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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