Loss tangent (internal friction) for high relaxation strengths and a lognormal distribution of relaxation and retardation times

Abstract

The loss tangent (internal friction) is evaluated numerically for a lognormal distribution of retardation or relaxation times and high relaxation strengths. It is shown that the loss tangent peak becomes more asymmetrical and the peak width, at half-maximum, decreases as the relaxation strength increases, dropping down to values corresponding to a Debye peak at very large relaxation strengths. Furthermore, the asymmetry of the peak can be used to establish if the lognormal distribution is in the retardation or in the relaxation spectrum. Finally, a procedure which can be used to obtain the relaxation strength, the geometrical parameter of the distribution and the average retardation or relaxation time, from the experimental loss tangent vs. frequency curves, is described. This procedure is applied to actual experimental data reported in the literature for polystyrene.