The freezing-in of non-equilibrium values of the limiting compliances as a mechanism of physical ageing

Abstract

The theory of a new method for measuring the temperature dependence of the limiting compliances, J R and J U , is described. The method is based on the observation of secondary creep; this is a small effect generated in a stressed specimen by a T-jump. In the experiment, the specimen is maintained isothermally under a constant stress until the primary creep rate is negligible. A T-jump of several degrees, positive or negative, is then imposed and this generates the secondary creep. If J R and J U are independent of temperature there is no secondary creep. The secondary creep has the same time dependence as primary creep. A comparison of the magnitudes of secondary and primary creep — at equivalent reduced times — leads by means of the theory of thermoviscoelasticity to the determination of α and β, the temperature coefficients of ( J R - J U ) and J U . For isotactic polypropylene in the α-region at 40°C both coefficients are positive: α = 0.7 × 10 −2 and β = 0.1 × 10 −2°C −1. It is clear from the positive sign for the coefficient of ( J R - J U ) that the α-relaxation is of the type in which stress increases the entropy. The magnitudes of the coefficients support the conclusion that the use of un-normalized time-temperature superposition to determine activation energy in polypropylene will be highly erroneous. The magnitude of the coefficient of ( J R - J U ) is sufficiently large to account partially for physical ageing in crystalline polymers. Quenching from T down to T 0 will freeze in a non-equilibrium value of ( J R - J U ), considerably in excess of the equilibrium value at T 0. Storage at T 0 permits the equilibrium value to be slowly attained, so that with increasing ageing time the polymer becomes stiffer and exhibits lower creep rates.