Glass transition thermodynamic considerations

Continuous transition of state is possible only between isotropic states it may thus occur between amorphous glass (i.e., supercooled liquid of great viscosity) and liquid ( sealing-wax type of fusion ), or between liquid and vapour, but probably never between anisotropic forms, or between these and isotropic states. This conclusion, derived from purely thermodynamic considerations, is also supported by molecular theory. 

The so-called glass transition temperature, Tg, must be considered below this temperature the liquid configuration is frozen in a structure corresponding to equilibrium at Tg. Around Tg a rather abrupt change is observed of several properties as a function of temperature (viscosity, diffusion, molar volume). Above 7 , for instance, viscosity shows a strong temperature dependence below Tg only a rather weak temperature dependence is observed, approximately similar to that of crystal. Notice that 7 is not a thermodynamically defined temperature its value is determined by kinetic considerations it also depends on the quenching rate. 

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. 

As mentioned at the beginning of the chapter, it is not feasible to cover all aspects of the pharmaceutical uses of DSC in the space available hence, emphasis has been placed on what are probably the most important applications of the technique. Clearly, DSC may be used as a simple screening method, for example, in the identification of polymorphs or glass transitions. However, there are numerous ways in which the approach can yield a more sophisticated analysis with comparatively little additional effort. Examples outlined here include the predictability of the thermodynamic parameters associated with polymorphic transitions and the assessment of the relaxation behavior of glassy pharmaceuticals. Both these examples have very tangible practical implications for the prediction of stability hence, such studies are not simply academic exercises but may be of considerable benefit in formulation optimization. 

Based on the considerations summarized above, it is not surprising to find that most theories of the glass transition [11-29] describe it, either explicitly or implicitly, in terms of key physical ingredients whose values strongly depend on the chain stiffness and/or the cohesive forces. These theoretical treatments invariably treat the observed value of Tg as a kinetic (rate-dependent) manifestation of an underlying thermodynamic phenomenon. However, they differ significantly in their description of the nature of this phenomenon at a fundamental level. 

Considerable effort has been made during the last two decades to develop a "microscopic" description of gas diffusion in polymers, which is more detailed than the simplified continuum viewpoint of Fick s laws. It has been known for a long time that the mechanism of diffusion is very different in "rubbery" and "glassy" polymers, i.e., at temperatures above and below the glass-transition temperature, Tg, of the polymers, respectively. This is due to the fact that glassy polymers are not in a true state of thermodynamic equilibrium, cf. refs. (1,3,5,7-11). Some of the models and theories that have been proposed to describe gas diffusion in rubbery and glassy polymers are discussed below. The models selected for presentation in this review reflect only the authors present interests. 

Another more recent a model to correlate Tg of plasticized systems was proposed by DiMarzio and Gibbs. They took into consideration the intramolecular interactions of polymer-plasticizer (but not the intermolecular interactions) via an iso-entropic model. In this model the glass transition occurs at a temperature at which the configurational entropy of the system becomes zero. Considering the effect of these interactions and based on thermodynamics, other models were developed, as those presented by Gordon et al and Couchman. " The expression obtained by Couchman for polymer blends or polymer-plasticizer mixtures has been applied successfiilly to plasticized PVC in a range of composi-... 

The crystallization of blends tends to depend on the level of mutual miscibility of the components. In miscible blends, the general result is that suppression or otherwise of crystallization with miscibility is dependent on the relative glass transition temperatures of both phases [33, 34]. For example, in a blend of an amorphous and semicrystalline polymer, if the amorphous material has the higher Tg, the miscible blend will also have a higher Tg than that of the semicrystalline homopolymer and, at a given temperature, the mobility and thus the efficacy of the semicrystalline phase molecules to crystallize is reduced. The converse is often true if the amorphous phase has a lower glass transition. Effects such as chemical interactions and other thermodynamic considerations also play a role and the depression of the melting point in a miscible blend can be used to determine the Flory interaction parameter x [40]. 

Earlier measurements on the moist transitions of extracted hemicelluloses were made by differential scanning calorimetry (DSC) (4). This enables the glass transition to be studied from a thermodynamic point of view, but information relevant for mechanical considerations such as the effect of load frequency is lacking. Some measurements in temperature scans in dynamic mechanical tests have been performed on carbohydrates such as amylopectin (13-15). The problem with such measurements on moist samples is the evaporation of water at the high temperatures. To avoid such problems, a technique for humidity scans... 

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