A multi-state barrier model for the multiple dielectric relaxations of bulk amorphous polymers and related glass-forming systems

The dynamics of a fluctuation model, broadly based on an earlier model of Bueche, is considered for the motion of a molecule in a glass-forming material. The molecule is assumed to occupy a number of local states in four equivalent manifolds and relaxes by motion between the local states and between manifolds. The dipole-moment correlation function, and hence the dielectric relaxation behaviour, is calculated for a range of relaxation parameters. Two general processes are found being (i) a family of ‘fast’ relaxation modes due to motion between the local states and (ii) a single ‘slow’ relaxation mode due to motion out of one manifold into adjacent manifolds. This pattern is qualitatively in accord with observations of and α processes in glass-forming systems but the observed α-processes are generally rather broader than a ‘slow’ single relaxation-time process which results from the present model.