Free volume theory, glass transition polymers

According to the glass transition theory, lipids are dispersed in the free volume of the food matrix composed of carbohydrates and protein polymers. In the rubbery state, the lipids react readily with oxygen and become oxidized. In the glassy state, however, the lipids are stable to oxidation because they are encapsulated and there is no free volume. The glass transition temperature, which determines when the food matrix changes from one state to the other, increases with a decrease in moisture and water activity. In many foods the... 

We believe the difficulty is that the free-volume theory as applied to the glass-transition does not take account of the essential role of intra- and intermolecular interaction in the system and the flexibility of the polymer chains, all of which factors play an important role in the glass-transition phenomena. 

We therefore believe one of the most pressing problems in the field of free-volume theory and glass-transition theory to be the development of new concepts and obtaining of new parameters for the corresponding states. Miller37 as early as 1968 introduced the idea that the glass transition corresponds to the iso-relaxation state, which at molecular weights of polymers below the critical ones may be replaced by an iso-viscous state. 

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). 

As seen in Table 1, the decrease in permeability can be directly attributed to a dramatic reduction in the effective diffusion coefficient, while there is a much smaller effect on the apparent solubility. A similar dependence of the solubility and diffusion coefficients on the draw ratio has been observed in other uniaxially oriented polymers (35-37). Because the glass transition and density of the polystyrene samples were found independent of the draw ratio, they concluded that the reduction in diffusivity was due to anisotropic redistribution of the free volume during drawing. Using an expansion coefficient related to draw ratio, the polystyrene data were successfully correlated using the Cohen-Turnbull free volume theory. However, the situation was found to be more complex for PVC (i ) ... 

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. 

For these polymers the following equation for Tg (absolute) can be deduced from the free-volume theory of the glass transition (see section 7.5.3) ... 

Several theories have been developed to describe glass transition, such as the thermodynamic theory [24, 25], free volume theory [26], or kinetic theory [27]. The former employs the lattice model to establish the partition function and the entropy of polymer can be calculated through this partition function. The latter takes the volume changes during the glass transition stage into account. 

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... 

In dense polymers, the self-diffusion of small plasticising solvent molecules has been measured PGSE methods [105]. For polymers above the glass-transition temperature, it is common to model the solvent diffusion using the free volume theory as modified for polymer systems by Fujita [122] and by Vrentas and Duda [123]. For solvent diffusion in dense polymers below Tg, an alternative model has been given by Frisch and Stern [124]. 

A comprehensive analysis of the free volume theories of glass transitions of high polymers has recently been published by Kanig (121). 

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