Physical aging temperature dependence

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

Fig. 14 Temperature dependence of yield stress, cry, and plastic flow stress, crpf, for quenched and physically aged PMMA. Strain rate is 2 x 10-3 s-1 (From [32])...

It is worth pointing out that hindering of the ft-a cooperativity due to physical ageing leads to quite a different temperature dependence of nSSA, as shown in Fig. 27, compared to the case of quenched PMMA shown in Fig. 24. Instead of a plateau, a large increase of nSSA is observed in the temperature range 30-80 °C. 

Fig. 27 Temperature dependence of nSSA of physically aged PMMA at a strain rate of 2 x 10 3 s 1...

Fig. 40 Temperature dependence of nSSA of quenched and physically aged PMMA and various CMIMx copolymers...

In 1901 Planck finally explained the frequency and temperature dependence of blackbody radiation, and ushered in the age of quantum physics, by introducing the quantization of the oscillators that Rayleigh had discussed. (Planck assumed that these oscillators were in the walls of the Hohlmum and that the radiation was in equilibrium with them.) The energy density (energy per unit volume) [m(v, T)/V] dv at the temperature i, in the frequency range between v and v + dv, is given by... 

Fig. 17. Calculated dependence of the physical aging rate on temperature for three glassy polymers...

In the vicinity of glass transition, both Eqs. (47) and (48) become Eqs. (42) and (43), respectively. The calculated dependence of the physical aging rate on temperature for polystyrene (PS), poly(vinyl chloride) (PVC), and poly(vinyl acetate) (PVAc) is shown in Fig. 17. There are five parameters (e, p, f xr, 7 ) in Eqs. (23), (2), (15) and (19). We have chosen p = 1/2. ft = 1/30, and xr = 30 min for these linear polymers in our theoretical calculation. The other two parameters r. = h and Tr are listed in Table 1. The calculation reveals that the Struik exponent (p) increases from zero above 7 to a constant below Tg, and then decreases to zero at 200 K below Tg. The three polymers all show a similar type of temperature dependence of physical aging rate, which compares well with the reported observations (see Fig. 15 of Ref. 2). 

In addition to the well known dependence of yield stress on temperature and strain rate, Eq. (51) provides a functional relationship between the plastic yield, physical aging, and type of stresses applied. 

The master curves and shift factors of transient and dynamic linear viscoelastic responses are calculated for linear, semi-crystalline, and cross-linked polymers. The transition from a WLF dependence to an Arrhenius temperature dependence of the shift factor in the vicinity of Tg is predicted and is related to the temperature dependence of physical aging rate. 

The temperature dependence of iq in physical aging may be expressed in terms of the Adam-Gibbs equation (27,28)... 

---