scispace - formally typeset
Journal ArticleDOI

Detailed comparison of the Williams–Watts and Cole–Davidson functions

C. P. Lindsey, +1 more
- 01 Oct 1980 - 
- Vol. 73, Iss: 7, pp 3348-3357
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

Dielectric dispersion interpretation of single enzyme dynamic disorder, spectral diffusion, and radiative fluorescence lifetime.

TL;DR: A previously derived relation between the observables and the electric field fluctuations is used to calculate the autocorrelation functions of the fluorescence lifetime and of spectral diffusion using dielectric dispersion data for proteins and the Onsager regression hypothesis.
Proceedings ArticleDOI

A new vision of photodarkening in Yb 3+ -doped fibers

TL;DR: In this article, the authors showed that thulium impurities, present at the parts-per-billion (ppb) level in the raw doping material, can induce UV emission which in turn creates defects responsible for photodarkening in ytterbium-doped continuous-wave fiber lasers.
Journal ArticleDOI

Remarkable non-exponentiality of the enthalpy relaxation in fast ion conducting glass (AgI)0.5 (AgPO3)0.5 far from equilibrium☆

TL;DR: In this paper, the spontaneous enthalpy-evolution processes of AgI-based fast ion conducting glass (AgI) 0.5 precooled at different rates were precisely measured by using an adiabatic calorimeter in the temperature range of 290-373 K.
Journal ArticleDOI

Probing Heterogeneity and Bonding at Silica Surfaces through Single-Molecule Investigation of Base-Mediated Linkage Failure

TL;DR: Kinetic analysis elucidates the role of thermal annealing and addition of blocking layers in increasing stability and demonstrates that the innate structural diversity of the silica surface is likely the cause of observed heterogeneity in surface-linkage disruption kinetics.
Journal ArticleDOI

Effect of H bond removal and changes in the position of the iron–sulphur head domain on the spin–lattice relaxation properties of the [2Fe–2S]2+ Rieske cluster in cytochrome bc1

TL;DR: Comparison of electron spin-lattice relaxation studies of the 2Fe-2S iron-sulphur (Fe-S) cluster embedded in a large membrane protein complex - cytochrome bc1 - suggests that H bond removal influences the geometry leading to increased strength of antiferromagnetic coupling between two Fe ions of the cluster.
References
More filters
Journal ArticleDOI

Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

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

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, +1 more
- 01 Sep 1978 - 
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)