Cole–Davidson dynamics of simple chain models

Abstract

Rotational relaxation functions of the end-to-end vector of short, freely jointed and freely rotating chains were determined from molecular dynamics simulations. The associated response functions were obtained from the one-sided Fourier transform of the relaxation functions. The Cole-Davidson function was used to fit the response functions with extensive use being made of Cole-Cole plots in the fitting procedure. For the systems studied, the Cole-Davidson function provided remarkably accurate fits [as compared to the transform of the Kohlrausch-Williams-Watts (KWW) function]. The only appreciable deviations from the simulation results were in the high frequency limit and were due to ballistic or free rotation effects. The accuracy of the Cole-Davidson function appears to be the result of the transition in the time domain from stretched exponential behavior at intermediate time to single exponential behavior at long time. Such a transition can be explained in terms of a distribution of relaxation times with a well-defined longest relaxation time. Since the Cole-Davidson distribution has a sharp cutoff in relaxation time (while the KWW function does not), it makes sense that the Cole-Davidson would provide a better frequency-domain description of the associated response function than the KWW function does.

Effect of chain flexibility on master curve behavior for diffusion coefficient

“…3,7,[28][29][30] Previously, freely jointed and freely rotating, tangent site chains were explored. In the current paper, rotational restrictions on the dihedral angle ("torsional" chains) are introduced resulting in well defined gauche and trans states.…”

Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation

“…If taken as a correlation function, the function exp{−(R*t) β } cannot be Fourier transformed in closed form for arbitrary β and much effort has gone into relating it, or its numerically determined Fourier transform, to other functions such as the phenomenological Davidson-Cole function. 75,86,87 Also, much effort has gone into determining a distribution of exponential relaxation rates that gives the stretched exponential. 88,89 The best one can do is to relate R* to a distribution function describing the fraction of relaxors with (an exponential) relaxation rate below R* and the fraction above R*.…”

Grain size dependence of dielectric relaxation in cerium oxide as high-k layer

“…The CD and KWW models have certain links in both high frequency and low frequency approximations. Besides, the CD model is widely used in glass-forming materials to explain the frequency dependence of the dielectric constants [20]. Here, dielectric relaxation can be described by the CD law for all of the CeO 2 samples.…”