Glass temperature free volume theory

Styrene-Divinylbenzene Networks. Using ionic polymerization methods, Rietsch et al. (1976) prepared polystyrene (PS) networks with a well-controlled length of elastically active chains and crosslinks of variable functionality. In a given series, the glass transition temperature obeys the classical free volume theory ... 

Using the classical hypotheses of the free volume theory, the glass transition temperature for a polymer (p) and solvent (s) solution, with a volume fraction of solvent, v, is given by (Kelley and Bueche, 1960) ... 

Free Volume Theory. Free volume theory suggests that the glass transition temperature is observed for polymers when their viscosity approaches that of their liquid state. Following a derivation based on the Doolittle expression for polymer viscosity (r ) as a function of free volume (Eisenberg, 1984)... 

Similarly to Fig. 5-4 for other glassy polymer-solvent systems also the predictions of this free-volume theory are in general agreement with experimental data on the temperature dependence of D in the vicinity of Tg2. In particular, the theory predicts a step change in Ed at Tg2, and this is consistent with most experimental investigations of polymer-solvent diffusion at temperatures just above and below the glass transition temperature (6,11,15). 

The assumptions and restrictions of the free-volume theory, as well as the significance of its parameters, are discussed in detail by Vrentas and Duda (5.61. For temperatures close to the glass transition temperature, the diffusion process is free-volume dominated and the energy term can be absorbed in the pre-exponential term. Equation 36 becomes... 

A major property improvement achieved through plasticization is the enormous reduction in the glass transition temperature, T, of PVC so that pliability and impact resistance of the plasticized composition is retained over a wide temperature range. Lowering of T is so important in the free volume theory that it is considered by some synonymous with plasticization. Many essential commercial applications of flexible vinyl depend upon this property modification. Without low-temperature flexibility, some of the... 

Free-volume theories of the glass transition assume that, if conformational changes of the backbone are to take place, there must be space available for molecular segments to move into. The total amount of free space per unit volume of the polymer is called the fractional free volume Vf. As the temperature is lowered from a temperature well above Jg, the volume of the polymer falls because the molecules are able to rearrange locally to reduce the free volume. When the temperature approaches Tg the molecular motions become so slow (see e.g. fig. 5.27) that the molecules cannot rearrange within the time-scale of the experiment and the volume of the material then contracts like that of a solid, with a coefficient of expansion that is generally about half that observed above Tg. 

The free volume theory originated some years later than the lubricity and the gel theories, when the evolution of different properties of polymers as a function of temperature, specific volume, thermal expansion coefficients, or viscosity was attempted to be explained.The relationships between these properties and some variables corresponding to polymer stracture, such as molecular weight or terminal groups content, the presence of another monomer and, of course, the presence of plasticizers, was also explained. For plasticized polymers the theory attempted to explain the diminution of the glass transition temperature with the plasticizer content. This theory is a contribution of different authors, but it was postulated by Fox and Floiy. The theory is still being used to explain some properties of plasticized polymers, i.e., viscoelastic properties. ... 

The extent to which the plasticizer decreases the glass transition temperature of a polymer (measured by DSC or DMA) has been used by different authors as a function of the type and/or the concentration of plasticizer. According to the free volume theory, the addition of the plasticizer to the polymer creates a large free vol-mne in the polymer (Chapter 5), and so diminishing the glass transition temperature of the plasticized polymer. Compatible... 

Theory must account for these properties of fluids, their temperature dependence, the glass transition, and the properties of the amorphous solid. The two most widely accepted theories are the entropy theory, as formulated by Gibbs and Di Marzio (1958), Gibbs (1960), and Adam and Gibbs (1965), and the free-volume theory as developed by Eyring (1936), Fox and Flory (1950), Williams, Landel and Ferry (1955), Cohen and Turnbull (1959), and Turnbull and Cohen (1961, 1970). 

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