Effect of the Distribution of Free Volume on the β Relaxation in Poly (Vinylidene Fluoride)

Abstract

A simple theory is presented to explain the temperature variation of the loss permittivity vs frequency curve for the β relaxation in poly (vinylidene fluoride), which is caused by the micro-Brownian motion of amorphous chains. If it is assumed that (1) there exists a distribution of free volume in the amorphous region of the crystalline polymer; (2) the relaxation time for the β relaxation depends on the free volume according to a Doolittle-type equation; (3) the loss permittivity vs frequency curve for a sample without the free-volume distribution is represented by a Williams-Watts decay function with an appropriate parameter, the theory satisfactorily reproduces the characteristics of the experimental loss permittivity vs frequency curve. The application of the theory to the case of mechanical relaxation is also discussed.