Models of the glass transition

The concept of free volume, Vi, and the idea that the mobility of molecules at any temperature is primarily controlled by the free volume, was brought forth by Doolittle [45] in explaining the non-Arrhenius temperature dependence of the viscosity, rj, of liquids of low molecular weight. The free volume is defined as the difference between the total specific volume v and an occupied volume, Vo. The Doolittle equation. 

Williams, Landel, and Ferry (52) found that the temperature dependences of the empirical values of log aj of many polymers are well described by their (WLF) equation. 

Free volume or hole volume is ostensibly measured experimentally by positronium-annihilation-lifetime spectroscopy (PALS). In organic glasses, including amorphous polymers, the ortho-positronium (o-Ps) bound state of a positron has a strong tendency to localize in heterogeneous regions of low electron density. In vacuo, an 

The experimentally observed glass transition is observed to be a kinetic phenomenon and the glass-transition temperature Tg is determined by kinetics. Nevertheless, one cannot exclude the possibility of the existence of a true thermodynamic transition responsible for the slowing down of the molecular motions. The thermodynamic transition, if it exists, would occur at some temperature below Tg, had kinetics 

If ACp(T) were independent of temperature, the equilibrium configurational entropy SdT) from Eq. (2.21) would be given by AC (T)ln(T/r2). This expression is the origin of Eq. (2.6), which, together with Eq. (2.5), introduces nonlinearity into structural recovery. If the temperature dependence of ACp(T) is well approximated by the hyperbolic expression, ACp(T) = A/T, which is the case for some glass-formers [75], then AS(T) = A(T — T2)/ TT2), which, after substitution into Eq. (2.20), leads to the equation 

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To keep the liquid at metastable equilibrium while cooling it to T2 Tq, the cooling rate would have to be infinitely slow. It has been argued that in this hypothetical limit a thermodynamic transition of some kind, possibly second order, intervenes to prevent the excess entropy from becoming catastrophically negative. However, another possibility is that the true dependence of excess entropy on temperature deviates from the linear extrapolation to zero, and the excess entropy varies much more slowly with temperature near Tb than it does at higher temperatures. This latter possibility is found in some simple models of the glass transition discussed below. 

Accordingly, since the dispersion and xa are obtained independently as separate and unrelated predictions, in such models the dispersion (or the time/frequency dependence) of the structural relaxation bears no relation to the structural relaxation time. This means it cannot govern the dynamic properties. As have been shown before [2], and will be further discussed in this chapter, several general properties of the dynamics are well known to be governed by or correlated with the dispersion. Therefore, neglect of the dispersion means a model of the glass transition cannot be consistent with the important and general properties of the phenomenon. The present situation makes clear the need to develop a theory that connects in a fundamental way the dispersion of relaxation times to xa and the various experimental properties. 

We now discuss the impact of this general property on theories and models of the glass transition. The primary concern of most theories is to explain the temperature and pressure dependences of the structural relaxation time ra. The dispersion (n or >kww) °f the structural relaxation is either not addressed or... 

Jenkins and Hay [205] discussed kinetic modeling of the glass transition and of enthalpic relaxation resulting from physical aging, as observed by differential scanning calorimetry. 

Jackie, J., Models of the glass transition. Rep. Prog. Phys.,49,171-231 (1986). 

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. 

C. Ligand Field Model of the Glass Transition in Macromolecule-Metal Complexes... 

Fig. 5.15. Storage shear moduli measured for a series of fractions of PS with different molecular weights in the range M = 8.9 10 to M = 5.81 10. The dashed line in the upper right corner indicates the slope corresponding to the power law Eq. (6.81) derived for the Rouse-model of the glass-transition. Data from Onogi et...

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