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
More filters
Journal ArticleDOI
Heat capacity and transition phenomena of structure i and ii trimethylene oxide clathrate hydrates
TL;DR: In this article, the authors measured the heat capacity of trimethylene oxide (TMO) clathrate hydrates doped with small amount of potassium hydroxide (x=1.8×10−4 to water) in the temperature range 11-300 K.
Journal ArticleDOI
Molecular Dynamics in Supercooled Di-Isobutyl Phthalate Close to the Glass Transition
TL;DR: In this article, the dynamics of α-relaxation in a glass-forming low-molecular-weight system, di-isobutyl phthalate (DIBP), has been studied by means of dielectric, nuclear magnetic and mechanical spectroscopies.
Journal ArticleDOI
The cage effect in systems of hard spheres
W. van Megen,H. J. Schöpe +1 more
TL;DR: This paper identifies and distinguishes these mechanisms in existing data from experiments and computer simulations on systems of particles with hard sphere interactions that incur delay or stretching of time correlation functions, in particular the particle number and flux densities.
Journal ArticleDOI
Thermal Recovery of Colloidal Quantum Dot Ensembles Following Photoinduced Dimming.
TL;DR: Colloidal CdSe quantum dot core ensembles were photodimmed and allowed to recover in the dark using ambient thermal energy at a range of temperatures to intuitively describe the distributed kinetics observed and complements commonly proposed blinking mechanisms.
Journal ArticleDOI
Time-domain dielectric relaxation of poly(methyl methacrylate) and nitrile rubber
TL;DR: In this article, the after effect of poly(methyl methacrylate) (PMMA) and nitrile butadiene rubber (NBR) to a voltage step (100 V) was measured at varying temperatures.
References
More filters
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.
Related Papers (5)
Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function
Graham Williams,David C. Watts +1 more
On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids
Gerold Adam,Julian H. Gibbs +1 more