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
Neutron scattering study on dynamics of water molecules in MCM-41. 2. Determination of translational diffusion coefficient.
Shuichi Takahara,Naoya Sumiyama,Shigeharu Kittaka,Toshio Yamaguchi,Marie-Claire Bellissent-Funel +4 more
TL;DR: It was shown that the translational diffusion of water molecules in the pores is decelerated by confinement and that the deceleration becomes marked with a decrease in pore size.
Journal ArticleDOI
Novel Dendritic Chromophores for Electro-optics: Influence of Binding Mode and Attachment Flexibility on Electro-optic Behavior
Philip A. Sullivan,Andrew J. P. Akelaitis,Sang Kyu Lee,Genette Mcgrew,Susan K. Lee,Dong Hoon Choi,Larry R. Dalton +6 more
TL;DR: Four dendritic electro-optic chromophores were designed, prepared, and evaluated to explore the effects on EO behavior of end-on relative to side-on Chromophore attachment geometry as well as differing chromophore-to-dendrimer core tether groups.
Journal ArticleDOI
Effect of Molecular Weight on the Ion Transport Mechanism in Polymerized Ionic Liquids
Fei Fan,Fei Fan,Weiyu Wang,Weiyu Wang,Adam P. Holt,Adam P. Holt,Hongbo Feng,Hongbo Feng,David Uhrig,David Uhrig,Xinyi Lu,Xinyi Lu,Tao Hong,Tao Hong,Yangyang Wang,Yangyang Wang,Nam-Goo Kang,Nam-Goo Kang,Jimmy W. Mays,Jimmy W. Mays,Alexei P. Sokolov,Alexei P. Sokolov +21 more
TL;DR: In this article, seven polymerized ionic liquids (PolyILs) were synthesized having degrees of polymerization ranging from 1 to 333, corresponding to molecular weights (MW) from 482 to 160 g/mol.
Journal ArticleDOI
Fluorescence enhancement, blinking suppression, and gray states of individual semiconductor nanocrystals close to gold nanoparticles.
TL;DR: Time-resolved photoluminescence spectroscopy investigates CdSe multishell nanocrystals coupled to self-assembled films of Au nanoparticles that showed increased fluorescence intensity, a decreased fluorescence lifetime, strong blinking suppression, and fluorescence from gray states.
Journal ArticleDOI
Two‐dimensional exchange NMR of powder samples. II. The dynamic evolution of two‐time distribution functions
TL;DR: In this paper, the evolution of the two-time distribution S2'0 (ω1,ω2 ;tm) as a function of the mixing time tm is presented, where S2`0 is identical with the 2D absorption spectrum rendered by 2D exchange NMR spectroscopy of static powder samples.
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