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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Lagrangian and impedance spectroscopy treatments of electric force microscopy
TL;DR: In this article, the authors used Lagrangian mechanics to derive coupled equations of motion for the cantilever position and charge, and then used first-order perturbation theory to relate the frequency shift and dissipation to the sample impedance.
Journal ArticleDOI
Formation of Photoluminescent Lead Bromide Nanoparticles on Aluminoborosilicate Glass
TL;DR: In this article, a multicomponent aluminoborosilicate photoluminescent glass was synthesized by introducing Pb(II) and NaBr in its composition, with an anisotropy equal to 0.19 at room temperature.
Journal ArticleDOI
Effects of polydispersity on the glass transition dynamics of aqueous suspensions of soft spherical colloidal particles
TL;DR: In this article, the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles were investigated using dynamic light scattering and scanning electron microscopy (SEM).
Journal ArticleDOI
Structural relaxation and anharmonicity in polymer electrolytes: Effect of the thermal history
TL;DR: In this paper, the effects of the storage at room temperature of PEO-KSCN polymer electrolytes have been studied by differential scanning calorimetry (DSC) and dynamical mechanical analysis.
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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