Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 352

Relaxation times that depend only on temperature and pressure have been considered. Nevertheless, the complexity of microscopic structures in glasses implies the existence of a distribution of relaxation times. Relaxation processes then also depend on the instantaneous state of the system itself and, thus, on its history as, for instance, described by the Tool–Narayanaswamy–Moynihan model (Chapter 3.7, [22, 23]). A consequence is that some nontrivial relaxation processes can take place well below the glass transition range. Hence, it is interesting to study such a time‐dependent process termed physical aging, which has a practical relevance through its possible effects on glass properties.

The process can be illustrated with DSC scans for PVAc (Figures 2 and 6). If the sample is cooled down at some rate to 297 K, i.e. about 10 K below the calorimetric T_g, and its temperature is kept constant for a time interval t_a, then its enthalpy (and entropy) relax to their lowest equilibrium values for the temperature (and pressure) considered. Experimentally, physical aging manifests itself as differences between the areas of DSC scans upon heating recorded for samples annealed (72 hours at 297 K) and not annealed. For the experiment without annealing, the lowest temperature of 278 K has been directly reached (see cooling curve in Figure 6). The amount of enthalpy relaxed during aging is equal to the difference between the light gray and dark gray areas in Figure 6. Of course, for a given annealing temperature, such a difference increases with the aging duration. As recently carried out on polymeric glass‐formers annealed at relatively low aging temperatures for a very long time, calorimetry (DSC) can bring to light two different timescales for glass equilibration, revealing the complexity and richness of relaxation processes well below T_g [24].

Figure 6 Effect of aging on the heat capacities of PVAc recorded upon heating at the same rate. Heat capacity after a cooling (solid circle with line) and heat capacity after cooling and 72‐hour annealing at 297 K (empty circle with line). The enthalpy released during aging estimated by the difference between the two areas included between these two curves. Heat capacities upon continuous cooling shown as solid circles.

Phenomenologically, however, in simple cases aging can be accounted for with the same approach as developed in previous sections. It is related to the relaxation of the order parameter ξ toward its equilibrium value ξ_eq(P,T) whereas the affinity A is relaxing at the same time toward zero. When applicable, the lattice‐hole theory can be used to solve Eq. (16) at constant P and T to reproduce the observed process. As done for o‐terphenyl [19], the order parameter is calculated at constant pressure and aging temperature T = 229.5 K with Eq. (16) and a temperature‐ and pressure‐dependent relaxation time [19]. The affinity has been calculated upon heating at 60 K/min, either after cooling at 6 K/min without aging, or after cooling at the same rate but with an aging process at 229.5 K (Figure 7). Upon isothermal aging, the affinity increases markedly (see the arrow in Figure 6) and then increases at the same rate as without aging. The difference is that the zero line is crossed at a lower temperature so that a much bigger peak is observed when the affinity finally recovers its zero equilibrium value at high temperatures. Since the affinity is an integrated measure of the heat capacity, the large peaks either calculated or observed for these properties are clear signatures of aging [19]. More complex calculations can of course be made to deal with at least two separate timescales [24], or a more realistic distribution of relaxation times.

Figure 7 Effect of aging on affinities calculated with the lattice‐hole model upon heating at the same rate of 60 K/min, first after a continuous cooling at 6 K/min (black line with solid circle), and second after annealing at 229.5 K (black line with empty circle). The black arrow simulating the relaxation of affinity upon aging at 229.5 K. Affinity upon continuous cooling shown as solid circles.