The determination of apparent memory functions from dielectric relaxation data for amorphous polymers and glass-forming liquids: Theory and experiment

Interrelationships between time-correlation functions for molecular reorientation, their apparent memory functions and dielectric permittivity for the α relaxation in glass-forming liquids and amorphous polymers are considered briefly and a method is given for the determination of an apparent first-order memory function K̃1(ω) in the frequency domain from dielectric relaxation data. For the Kohlrausch–Williams–Watts (KWW) function and the Cole–Cole function and for experimental data for three amorphous polymers it is shown that the real and imaginary components of K̃1(ω) increase without limit as frequency f(=ω/2π) is increased. The physical significance of such apparent memory functions is considered in view of this behavior and the recent experimental studies of the α relaxation in polymers by Schmidt–Rohr and Spiess and in glass-forming liquids by Cicerone and Ediger, who suggest that a ‘‘dynamic heterogeneity’’ is present that leads to a broad distribution of relaxation times where each elementary process has no proper memory. For such cases it appears that the apparent memory functions are simply related to the parameters characterizing the distribution and may have no physical significance for the α process in glass-forming materials.