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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Kinetics of morphological transition in Polystyrene–block‐ polybutadiene–block‐polystyrene triblock copolymer melt
TL;DR: In this paper, the kinetics of morphological transition from cylinders to lamellae were studied using a time-resolved small-angle x-ray scattering (SAXS) technique with synchrotron radiations.
Journal ArticleDOI
Total internal reflection fluorescence microscopy: a powerful tool to study single quantum dots
TL;DR: In this paper, total internal reflection fluorescence microscopy (TIRFM) measurements of colloidal CdSe quantum dots (QDs) are presented, which provides the advantage of recording the time-resolved fluorescent signal of many single QDs simultaneously, thus allowing data with high statistical confidence to be obtained in relatively short time.
Journal ArticleDOI
Static and Dynamic Light Scattering of a Nematic Side-Group Polysiloxane
TL;DR: In this paper, the elastic constants of a nematic side-group polymer have been analyzed using two different scattering geometries, and the depolarized scattering due to thermally excited fluctuations of the nematic director was analyzed.
Journal ArticleDOI
Dielectric relaxation processes in solid and supercooled liquid solutions of acetaminophen and nifedipine
Tarek El Goresy,Roland Böhmer +1 more
TL;DR: In this article, the authors used dielectric spectroscopy to study supercooled liquid and glassy mixtures of acetaminophen and nifedipine and found that the steepness index m characterizing the α-relaxation as well as the dispersion width of this process were almost independent of x.
Journal ArticleDOI
Molecular Dynamics of Graphene–Electrolyte Interface: Interfacial Solution Structure and Molecular Diffusion
TL;DR: In this article, the aqueous solutions of electrolytes (LiCl, NaCl, KCl, MgCl2, and CaCl2) near the interface with a graphene sheet using classical molecular simulations are studied.
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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