Deformations and Molecular Motions in Polymers Above the Glass Transition Temperature

Abstract

Time-dependent deformations of polymers above the glass transition temperature are related to spectra of relaxation times which reflect certain modes of configurational motion of the macromolecules. The spacings and magnitudes of these characteristic times, even as determined from experiments in small deformations, are important in understanding large deformations and processes of rupture, since the rates of molecular motions will set the time scale for these as well. In very dilute solution, all relaxation times (except perhaps the shortest) are proportional to solvent viscosity; their spacings have been derived theoretically and checked experimentally for a variety of linear and branched molecules. In concentrated and undiluted systems, the presence of entanglement coupling sharply differentiates the time or frequency scale into characteristic zones of viscoelastic behavior. In the transition zone, the relaxation times reflecting local motions are proportional to a monomeric friction coefficient. The dependence of the friction coefficient on temperature, pressure, diluent concentration, and other variables can be described and formulated with an auxiliary parameter, the fractional free volume. The spacing of the transition-zone relaxation times in concentrated systems is less well understood, though the Rouse spectrum is a first approximation. In the terminal zone, relaxation times of uncross-linked polymers are enormously prolonged by entanglement coupling and appear to be quite closely spaced. In lightly cross-linked systems, effects of trapped and untrapped entanglement loci may be distinguished. The dependence of contributions to modulus or compliance on concentration, molecular weight, and other variables must be considered separately for each zone of viscoelastic behavior.