Free volume quantities and viscoelasticity of polymer glasses

Abstract

We have investigated, in terms of the Cohen-Turnbull theory, a relationship for polycarbonate (PC) glasses between average stress relaxation times, , and average free volume sizes, , obtained from positron annihilation lifetime spectroscopy. This examination suggests that the minimum free volume required for stress relaxation, υ*, decreases with decreasing temperature and that, near the glass transition temperature, only a subset of extremely large free volume elements contributes to the stress relaxation of PC glasses. This suggestion is consistent with the idea that near the glass transition temperature, the viscoelastic response is dominated by large-scale, main-chain motion, whereas at lower temperature it is controlled by local motion. Moreover, comparison with the υ* value estimated from gas diffusivity through various PC species at room temperature shows that the required free volume size for stress relaxation in the glass transition region is much larger than that for gas diffusion. Previously we showed that the Doolittle equation fails to correlate viscoelastic relaxation times of polymer glasses with changing temperature ; determining the free volume fraction, h, from theoretical analysis of volume recovery data and theory, the Doolittle equation is shown to be valid in PC above 135°C (T g - 14°C) irrespective of temperature and physical aging times. This result supports the idea suggested in the previous article that, as glassy polymers approach the transition region, viscoelastic properties increasingly tend to be controlled by free volume.