Ratio of dynamic moduli and estimation of relaxation times

Abstract

In this paper, the theoretical interrelation between the ratio of dynamic moduli and the number and distribution of relaxation times required to fit the generalized Maxwell model to the data was investigated. Theorems were derived for making interval estimation of the relaxation times of the generalized Maxwell model from the ratio of linear combinations of the dynamic moduli at different frequencies. According to these theorems, given dynamic moduli (G′ and G″) at two frequencies a and b or three frequencies a, b, and (ab)1/2, one must select at least one relaxation time in the relevant interval (τA,τB) for the model to fit the data precisely. As a result, from a set of dynamic data G′ and G″, one can determine a series of (τA,τB) from which the minimum number (Nmin) and distribution (interval estimation of τi) of relaxation times of the model can be estimated. The approach was applied to polystyrene data reported in the literature. The results were discussed and compared with those of relevant work, especially the nonlinear regression model-fitting procedure.