Transition, glass, hole model modeling

The hole model discussed above is different from the hole model proposed by Ramachandrarao et al. (1977) and also used by Hirata (1979). In the latter model the hole formation energy is estimated from experimental data on the changes in specific heat and thermal expansion at the glass transition. Also in this hole model a linear relationship is found between the hole formation energy and the glass transition temperature, although the model lends itself less easily for making predictions. 

The hole model of the glass transition. To get a better feeling for the nature of the glass transition to polymers, the simple, 70-year old hole-model of the liquid [8,9] was used for its description [10,11]. The model is shown schematically on the upper right of Fig. 6.5. The main distinction between liquid and solid is the low viscosity of the liquid (see Sect. 5.6). This low viscosity is linked to the long-range mobility of the holes through their ability to diffuse or, after collapse, to reform elsewhere. 

This modeling reveals a glass-transition-like behavior in systems describable with the hole model. It also shows that the reversing heat capacity by TMDSC is only approximately the apparent reversible heat capacity. In addition, it was shown in Sect. 

Plasticized Polymers. As mentioned above the glass transition temperature Tg is lowered by adding certain organic liquids, the so called plasticizers. The illustration of polymers above T0 by means of a model remains valid also for plasticized systems. The configuration that is built up at the transition from the melt to the glass, in this case, remains below the glass temperature, too. Thus, we have an extended structure containing holes. ... 

In a further development of the above model, Kalospiros and Paulaitis [101] use the glass-transition temperature of the pure polymer to calibrate the value of the order parameter (fraction of holes in the lattice). This value is kept constant, even if a swelling agent is added to the system, so the glass transition-temperature depression induced by the SCF can be predicted. 

The entropy theory of the glass transition was developed by Gibbs and DiMarzio and by Adams and Gibbs to describe polymeric systems. By mixing the polymer links with holes or missing sites on a lattice to account for thermal expansion as in a lattice gas model, they could determine the entropy of mixing and the configurational entropy of the polymer. They found a second-order transition at a temperature They then pointed... 

The simplest model for the representation of the glass transition, perhaps, is the hole theory. With it the larger expansivity of liquids and the slower response to external forces is said to be due to changes in an equilibrium of holes. These holes are assumed to be all of equal size, and their number depends on temperature. The equilibrium number of holes at a given T is N, each contribnting an energy to the enthalpy. The hole contribution to Cp is then given under equilibrium conditions by ... 

The simplest model to represent the glass transition is based on the hole theory which was developed by Frenkel and Eyring some 60 years ago and is described in more detail in Sect. 6.1.3 (see also Sect. 4.4.6). The equilibrium number of holes at T is N and each contributes an energy e, to the enthalpy. As given on Fig. 6.5, the hole contribution to the vibrational heat capacity Cp and its kinetics is represented by ... 

The dual-mode model has also been applied with some success to the sorption and transport behavior of small- and intermediate-size organic molecules in glasses (75). Above some size, however, the penetrant may be too large to be accommodated solely within individual holes, and two truly distinct environments may not actually exist for these penetrants. Even in this case, however, the concept of unrelaxed free volume remains valid, and observations of sorption and dilation behavior that apply to gases also apply qualitatively to larger penetrants up to the point of extreme plasticization where an actual glass transition occurs. 

The glassy zone is accounted for by Eyring s free-volume model. In this model, liquid is regarded as a mixture of molecular particles and holes, and at the glass-transition point, the fraction of the hole volume available for translation of a molecule that is, the free volume, becomes a constant value of 2.5% [10]. 

After observing quite a few anomalous properties of optical transitions in glasses and attributing them to the dynamics of TLS [14], the tunneling model was adopted by Reinecke [15] to explain the low-temperature line widths of optical transitions in amorphous solids using the concept of spectral diffusion. This concept had originally been developed for the description of spin resonance experiments [16] and had already been applied to the theoretical treatment of the above mentioned ultrasonic properties of glasses [17]. Soon after this step, the possibility of a connection between thermal and optical properties of amorphous solids was supported by the observation of time dependence of spectral hole widths [18]. 

Figure 19 Variation of glass transition temperature with composition for solutions of polystyrene in styrene monomer. The lines represent calculations from the Gibbs-DiMarzio lattice model upper line calculation allows for holes while the lower...

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