Glass transition thermodynamic approach

It would be an advantage to have a detailed understanding of the glass transition in order to get an idea of the structural and dynamic features that are important for photophysical deactivation pathways or solid-state photochemical reactions in molecular glasses. Unfortunately, the formation of a glass is one of the least understood problems in solid-state science. At least three different theories have been developed for a description of the glass transition that we can sketch only briefly in this context the free volume theory, a thermodynamic approach, and the mode coupling theory. 

The thermodynamic theories [7,8] deny the pure kinetic nature of the glass transition and link it directly to thermodynamic quantities like the configurational entropy of the material. Some recent results suggest a correlation between kinetic quantities and thermodynamic parameters [9]. Also recently, this theory was successfully merged with a potential landscape approach [10]. The thermodynamic approach is interesting since it reflects the different configurations that are allowed not only for the whole ensemble but also for the internal conformations... 

A comparative study of the kinetic and thermodynamic approaches to the glass transition phenomenon was made by Vijayakumar and Kothandaraman (1987). 

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

A fundamental property that determines the state of a reacting system is its extent of cure or chemical conversion (a). Several papers have shown that there is a unique relationship between the glass-transition temperature (Tg) and a that is independent of cure temperature and thermal history. This may imply that molecular structures of materials cured with different histories are the same or that the changes in molecular structure do not affect Tg. There are generally accepted to be two approaches to modelling glass-transition-conversion relationships, namely thermodynamic and viscoelastic approaches. These are summarized in Table 3.8. 

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. 

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