THE RELATIONSHIP BETWEEN THE POLEY ABSORPTION AND FRACTIONAL POWER-LAW RELAXATION IN THE CLUSTER MODEL

The response function derived for the cluster model possesses an analytical form over the whole time range form zero to infinity. Previous work has concentrated upon its behaviour in the non-inertial (relaxation) regime where it predicts a non-Debye decay consisting in general of two power laws, namely t(-n) at t < 1/omega(p) and t-(m+1) for t > 1/omega(p) with omega(p) the loss peak frequency. Here it is shown that the exact response function of this model gives an absorption peak in the inertial region (Poley absorption) as well as a relaxation loss peak. Furthermore the relative magnitude of the predicted Poley absorption is shown to decrease with the value of the exponent n (< 1) appropriate to the relaxation peak, leading to an isolated Debye peak for n = 0. A comparison with the experimental data will be made and the relationship between the Cluster Model and other models for the Poley absorption discussed.