Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
of advancement of the configurational change at every temperature:
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6 Physical Aging
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 Tg, and its temperature is kept constant for a time interval ta, 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 Tg [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 ξeq(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.
7 Perspectives
Whether in the form of affinity, fictive temperature, or structural order parameter, additional variables must be introduced to deal with the nonequilibrium thermodynamics of glass‐forming systems and, in particular, with the time dependence of their properties in relaxation regimes. Phenomenological advances now make it possible to predict these properties as a function of time and temperature or to determine accurately the entropy irreversibly produced, but the mechanisms involved at the atomic or molecular level generally remain to be deciphered. The physical nature of the glass transition is a case in point, as are the origins of Kauzmann catastrophe, of the strong variations of the PD ratio, of the diversity of relaxation timescales or of, as illustrated by the well‐known memory effects, the complex nonlinear coupling of the parameters of the differential equations with which these processes are described.
Not only could highly sensitive calorimetric experiments yield valuable original data in this respect but coupling of different techniques such as dielectric spectroscopy and temperature‐modulated calorimetry should bring new insights on the dynamics and thermodynamics of the glass transition. Recent experiments on ultra‐stable organic glasses obtained by vapor deposition techniques are, for instance, promising [25, 26]. And whereas very long aging performed well below Tg should also give new clues on the laws driving complex relaxation processes in the glassy state [24], experiments made at extremely rapid timescales (e.g. spectroscopy) are in contrast needed to investigate relaxation in supercooled liquids where equilibrium is quickly achieved. To give a single example, ultrastable organic glasses obtained by vacuum‐deposition techniques should be of special interest in view of their internal stability that is equivalent of that of hyper‐aged glasses (with aging time of millions of years) obtained by conventional melt cooling [25]. For this particular class of glasses, the aforedefined TM values are so much lower (by a few tens of degrees) than the standard glass transition temperatures that TM and Tg cannot be indiscriminately used in Eq. (9b) [25, 26]. Among other consequences, new insights should then be gained on the non‐unity of the PD ratio. Finally, such experiments should of course be firmly complemented by fundamental work. Microscopic theories and atomistic simulations must be developed and, as stringent tests of their value, their predictions checked in terms of macroscopic physical properties.