Relaxation physical aging

However, it is expected the reaction rates below Tg may be affected also by volume relaxation (physical aging) which was not taken into account and which will result in the dependence of k-p not only on T and a but also on time t. If we take the positive deviations of experiments in Figure 14 as a measure of the volume relaxation effect then the physical aging increases the apparent mobility although it leads also to a denser (and less mobile) state. 

Figure 4.4 shows a dilatometric or calorimetric experiment to show structural relaxation (physical aging) and glass transition hysteresis. The sample is cooled from T0 to T it is kept at Tj for a certain time and heated again to T0. During the cooling step, the material vitrifies at B, resulting in an abrupt decrease in both the expansion coefficient and the specific heat. 

To summarize, most of the experimental results on the yielding of thermosets may be interpreted by stating that the structure affects chemical structure, secondary relaxations, physical aging, etc., on the proportionality constant are still to be explored. 

The main consequence of this reduced mobility is an extension of the glass transition region towards the high temperature side it will show a lower and an upper value, viz. Tg(L) and Tg(U), the values of the undisturbed amorphous region and that of regions with reduced mobility. By means of this model, Struik could interpret his measurements on volume relaxation (physical ageing) and creep in semicrystalline materials. 

We have reviewed the recent development of a nonequilibrium statistical mechanical theory of polymeric glasses, and have provided a unified account of the structural relaxation, physical aging, and deformation kinetics of glassy polymers, compatible blends, and particulate composites. The specific conclusions are as follows ... 

Tyrosine-derived polycarbonates provided a convenient model system to study the effect of pendent chain length on the thermal properties and the enthalpy relaxation (physical aging). It is noteworthy that enthalpy relaxation kinetics are not usually reported in the biomedical literature and that a recent study by Tangpasuthadol (Tangpasuthadol, 1995) represents one of the first attempts to evaluate physical aging in a degradable biomedical polymer. 

Fig. 3.1 a Tempraatme dependence of volume or enthalpy for an amtnphous polymer. The vertical lines denote Tg determined using fast and slow cooling rates. The vatical arrow denotes glassy-state structural relaxation (physical aging) of the glass ftnmed on slow cooling, b Normalized Arrhenius plot of the average alpha-relaxation time fra- an amorphous polymer. Above Tg, polymer relaxation exhibits a non-Anhenius tempaature dependence while below Tg, polymer relaxation exhibits an Arrhenius 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. 

The kinetic character of the glass transition and the resulting non-equilibrium character of the glassy state are responsible for the phenomena of structural relaxation, glass transition hysteresis, and physical aging (Kovacs, 1963 Struik, 1978). 

Kinetic models of physical aging are available in the literature (Kovacs et al., 1979). During this process, volume changes are very low, typically less than 1 m3 kg but they affect a component of free volume that plays a crucial role in creep, relaxation, yielding and fracture (see Chapter 12). 

From a practical point of view, the main consequence of physical ageing by structural relaxation is embrittlement (decrease in fracture resistance Chapter 12). For the other aspects of mechanical behavior, ageing has either no effect or a favourable effect (increase of relaxation times, leading to a decrease of creep or relaxation rates). This is the reason why, in most thermoset applications, the knowledge of short-term properties is considered to be sufficient for engineering design, as far as fracture and durability are not concerned. 

As discussed in Chapter 10, network polymers - as linear polymers - obey the time-temperature equivalence principle in the domain where they are stable, both chemically (no postcure, no thermal degradation), and physically (no orientation relaxation, water desorption, physical aging, etc.). 

---