**Cole-Davidson dynamics of simple chain models**

TC Dotson and J Budzien and JD Mccoy and DB Adolf, JOURNAL OF CHEMICAL PHYSICS, 130, 024903 (2009).

DOI: 10.1063/1.3050105

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.

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