Glass transition and free volume

At the time of development of free volume theory, two important empirical equations of viscosity were known. They are the Doolittle (1951) equation (3.01) and the Vogel, Tamman and Fulcher (VTF) equation (3.02) (Vogel, 1921, Fulcher, 1923, Tammann and Hesse, 1926), which are given below. 

In equation (3.01), A and B are empirical constants, Vocc is the volume occupied by the constituent particles and v/ is the free volume. In equation (3.02), r]a, C and To are constants. VTF equation implies that viscosities of glass forming supercooled liquids are non-Arrhenius and To is the temperature which linearizes the data of the non-Arrhenius plot. Cohen and Turnbull (Cohen and Turnbull, 1959 Turnbull and Cohen, 1961, 

Equation (3.06) suggests that as V/ decreases, r increases exponentially and the transport is severely curtailed. Correspondingly, the motion of the particle gets confined to the Voronoi polyhedron and as expected the motion becomes more and more oscillatory. The empirical VTF equation (3.02) may be recovered from equation (3.06) by a proper substitution of Vf. One plausible assumption is that v/ s v, - Vg s Aa(T-Tg) where Vi is the 

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Kilburn, D., Bamford, D., Liipke, T., Dlubek, G., Menke, T. J., and Alam, M. A., Free volume and glass transition in ethylene/l-octene copolymers positron lifetime studies and dynamic mechanical analysis, Polymer, 43, 6973-6983 (2002). 

Figure 2.1. Frozen fraction of free volume vs. glass transition temperature. Full triangles — values for different polymers at ambient pressures [Simha and Wilson, 1973], Squares — PS data at pressures P = 0 - 400 MPa (data [Rehage, 1980] calculations [Utracki and Simha, 1997]).

The kinetics of migration of additives from the package into the (food) contents depends on the characteristics of the plastics such as density or free volume, crystallinity, glass transition temperature (Tg), as well as the polarity, molecular mass, and boiling point of the migrant species. Migration rates also depend on the temperature, relative humidity, pH value, and the composition of the food contents (Sajilata et al., 2007). Given the number of variables that can affect the results, reported data must be compared cautiously. 

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... 

Lipatov, Y. S. The Iso-Free-Volume State and Glass Transition in Amorphous Polymers New Development of the Theory. Vol. 26, pp. 63 —104. 

The Iso-Free-Volume State and Glass Transitions in Amorphous Polymers ... 

It was found that Afi Tg and Aa Tg are not constant and therefore the SB equation has limited applicability. Hie results indicate an increase in Aa Te with increasing Tg. Therefore it is inadmissible to use the product A a Tg as a universal value in any theoretical discussion of the glass-transition phenomenon. At the same time, this conclusion in no way excludes the free-volume theory and the role of free-volume in the transition from the glassy to the liquid or rubberlike state. 

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. 

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