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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Decreased Interfacial Charge Recombination Rate Constants with N3-Type Sensitizers
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Effect of Local Heterogeneity on Dielectric Segmental Relaxation of Poly(vinyl acetate) in Concentrated Solution
TL;DR: In this article, the authors investigated the α-relaxation of toluene solutions of poly(vinyl acetate) (PVAc) and for undiluted PVAc.
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Nanosecond and microsecond study of probe reorientation in orthoterphenyl
TL;DR: In this article, the rotational correlation time of anthracene was measured from 100 ps to 1 ms for anthanthrene, while correlation functions were observed over a narrower time window for 9−phenylanthracene and 9,10−diphenylanthraschracene.
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Investigation of the dynamical slowing down process in soft glassy colloidal suspensions: comparisons with supercooled liquids
TL;DR: In this paper, the primary and secondary relaxation timescales of aging colloidal suspensions of Laponite are estimated from intensity autocorrelation functions obtained in dynamic light scattering (DLS) experiments.
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Comments on the electric modulus formalism model and superior alternatives to it for the analysis of the frequency response of ionic conductors
TL;DR: In this paper, the authors discuss and demonstrate the theoretical and experimental inadequacies of the original modulus formalism (OMF) for analyzing dispersive frequency-response data of ion-conducting materials.
References
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Journal ArticleDOI
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Kenneth S. Cole,Robert H. Cole +1 more
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Graham Williams,David C. Watts +1 more
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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.
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On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind
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