Other glass transition theories

All the foregoing discussion is a presentation of the kinetic theory of the glass transition. It has many merits, not least being that it is the theory most easily understood by persons with a background in a molecular science. However, it is not the only theory, and we should be aware of the existence of alternative explanations of the processes that we have just described. 

A quite different approach is adopted in the statistical mechanical theory expounded by Gibbs and DiMarzio. They considered that the rotating unit could exist in two stable conformations (which might correspond to the trans and gauche conformers discussed earher), separated by a standard state energy difference, AE°, called the flex energy. Using the techniques of statistical thermodynamics, they calculated the partition of the units between these two forms. In theory, the 

The asymptotic approach to a limiting low temperature value is apparent. However, in its simple form, the theory assumes that this is an equilibrium value of the distribution and order, whereas we know that the glass is a nonequilibrium state. The theory has been extended using non-equilibrium thermodynamics, but is not as useful in technological applications as is the simple kinetic theory elaborated above. 

---

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

It has been noted that although non-equilibrium situations exist in semi-moist food products, observed a values may predict microbial and biochemical activities fairly well (Chirife and Buera, 1994 Chirife and Buera, 1995 Chirife and Buera, 1996 Chirife et al., 1996 Cardona, 1997). The glass transition theory, on the other hand, remains inconclusive as more counter challenging data have been published (Chirife et al., 1996 Cardona, 1997 Buera et al., 1998). In this report, the investigation into water mobility has provided additional insights on the molecular dynamics of water (mobility) since water is the key solvent carrying nutrients and oxygen to cells. 

According to the glass transition theory, lipids are dispersed in the free volume of the food matrix composed of carbohydrates and protein polymers. In the rubbery state, the lipids react readily with oxygen and become oxidized. In the glassy state, however, the lipids are stable to oxidation because they are encapsulated and there is no free volume. The glass transition temperature, which determines when the food matrix changes from one state to the other, increases with a decrease in moisture and water activity. In many foods the... 

It should be pointed out that the view of the glass transition temperature described above is not universally accepted. In essence the concept that at the glass transition temperature the polymers have a certain molecular orientation time is an iso-elastic approach while other theories are based on iso-viscous. 

Other theories proposed dissipation of energy through crack interaction localised heating causing the material to be raised to above the glass transition temperature in the layers of resin between the rubber droplets and a proposal that extension causes dilation so that the free volume is increased and the glass transition temperature drops to below the temperature of the polyblend. 

The measured G(x) value of representative epoxy polymers is approximately 10, but this value depends strongly on the structure of the polymer, its glass transition temperature and other characteristics. Since the crosslinking reaction that characterizes the COP resist functionality is a chain reaction, in theory, a single, electron-initiated event could result in the insolublization of an entire film of the resist material. Fortunately, because of the existence of chain terminating reactions, this does not occur and high resolution imaging of the resist material can be accomplished. 

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. 

As early as 1950 Fox and Fiery19 put forward the idea that the glass temperature corresponds to the iso-free-volume state. This hypothesis was developed by other authors20 21 and has won wide acceptance. It has been used with minor modifications as the basis for a number of sophisticated theories of the glass-transition... 

It can be instructive to compare the two rather different mode coupling theory expressions for the viscosity one valid near the critical point and other near the liquid-glass transition point. 

Similarly to Fig. 5-4 for other glassy polymer-solvent systems also the predictions of this free-volume theory are in general agreement with experimental data on the temperature dependence of D in the vicinity of Tg2. In particular, the theory predicts a step change in Ed at Tg2, and this is consistent with most experimental investigations of polymer-solvent diffusion at temperatures just above and below the glass transition temperature (6,11,15). 

---