Theory of Relaxation Phenomena in Polymers. I. Rotational Motion of Side Elements around the Backbone

Abstract

Dielectric relaxation in polymers is investigated by means of an extension of Glauber's dynamical theory of the Ising model. The theory is applied to a linear chain of rotators with arbitrary interactions between neighbors, and the frequency dependence of the complex electric susceptibility is found to be simply expressed in terms of the Fourier—Laplace transform of a correlation function. The latter is related to the extent of correlated motion of nearby segments. If the correlation function contains a time dependence of the form (1/τ1) exp(—t/τ1), where τ1 is the time constant for the establishment of the equilibrium correlation function, then both the effective dielectric relaxation time and the effective dipole moment of the dipolar rotators are frequency dependent. A time dependence of this form may introduce asymmetry or even a bimodal structure into the dielectric loss spectrum. The temperature dependence of the spectrum is discussed within the framework of the theory, and application is made to mechanical-relaxation phenomena. The direction of continuing efforts to extend the theory to other modes of internal motion is indicated.