Free volume glass transition requirements

While the WLF equation is based on the free-volume theory of glass transition which is concerned with the introduction of free volume as a requirement for coordinated molecular motion, the equation also serves to introduce some kinetic aspects into the quantitative theory of glass transition. 

The free-volume theory of the glass transition, as developed in Section 8.6.1, is concerned with the introduction of free volume as a requirement for coordinated molecular motion, leading to reptation.The WLF equation also serves to introduce some kinetic aspects. For example, if the time frame of an experiment is decreased by a factor of 10 near Tg, equations (8.47) and (8.48) indicate that the glass transition temperature should be raised by about 3°C ... 

The viscosity dependence of intramolecular excimer formation is complex. As in the case of molecular rotors (Section 8.2), most of the experimental observations can be interpreted in terms of free volume. However, compared to molecular rotors, the free volume fraction measured by intramolecular excimers is smaller. The volume swept out during the conformational change required for excimer formation is in fact larger, and consequently these probes do not respond in frozen media or polymers below the glass transition temperature. 

The method is based on the fact that the rate of conformational change required for excimer formation depends on the free volume induced by the segmental motions of the polymer occurring above the glass transition. DIPHANT (compound 3 in Figure 8.3) was used as an excimer-forming probe of three polymer samples consisting of polybutadiene, polyisoprene and poly(dimethylsiloxane).a)... 

As shown in Figure 1.7 there is a decrease in the coefiicient of thermal expansion, a, to values lower than extrapolated from the polymer melt (dotted line). This results in the polymer having a lower density than would be predicted and there is thus a measurable free volume, Vf, which has an important bearing on the properties of the amorphous region of the polymer. This and the detailed analysis of the glass transition are considered after the molecular requirements for polymer crystallization and the structure of the crystalline region. 

Vrentas and Duda s theory formulates a method of predicting the mutual diffusion coefficient D of a penetrant/polymer system. The revised version ( 8) of this theory describes the temperature and concentration dependence of D but requires values for a number of parameters for a binary system. The data needed for evaluation of these parameters include the Tg of both the polymer and the penetrant, the density and viscosity as a function of temperature for the pure polymer and penetrant, at least three values of the diffusivity for the penetrant/polymer system at two or more temperatures, and the solubility of the penetrant in the polymer or other thermodynamic data from which the Flory interaction parameter % (assumed to be independent of concentration and temperature) can be determined. An extension of this model has been made to describe the effect of the glass transition on the free volume and on the diffusion process (23.) ... 

Given that (see Fig. 9.8) at the glass transition temperature, the specific volume Vs and entropy S are continuous, whereas the thermal expansivity a and heat capacity Cp are discontinuous, at first glance it is not unreasonable to characterize the transformation occurring at Tg as a second-order phase transformation. After all, recall that, by definition, second-order phase transitions require that the properties that depend on the first derivative of the free energy G such as... 

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