Kinetic Theory of Glass

Experiments indicate that the smooth variations of thermodynamic properties (e.g., V, Ky, and the specific heat at constant pressure Cp) with temperature are intermpted by the kinetic process of glass formation, leading to cooling rate dependent kinks in these properties as a function of temperature. In our view, these kinks cannot be described by an equilibrium statistical mechanical theory, but rather are a challenge for a nonequilibrium theory of glass formation. Nonetheless, some insight into the origin of these kinks and the qualitative... 

F30. Friedenwald, J. S., and Maengwyn-Davies, G. D., Elementary kinetic theory of enzymatic activity first order theory. In The Mechanism of Enzyme Action (W. D. McElroy and B. Glass, eds.), p. 163. Johns Hopkins Press, Baltimore, Maryland, 1954. 

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. 

When the degree of cross-linking is low (H, is large), the glass transition temperature increases slightly as cross-linking proceeds. As approaches values in the hundreds, T becomes a sensitive measure of cure. Equation 10 can be derived in its essential features from the kinetic theory of rubber elasticity (62). giving... 

There is no one structure of glass any more than there is one crystal structure. Almost any solid can be produced in a glassy state if the melt is cooled sufficiently quickly. To some extent, glass can be thought of a product of kinetics, and the structure of a glass can depend on the rate at which the hquid is cooled. Theories of glass stracture and formation must consider this (see also Section 6.3). 

One must be carefiil here because one can prove too much. The entropy theory of glasses, also called the Gibbs-Di Marzio (GD) theory, is a theory of equilibrium thermodynamic quantities only, it is not a theory of the kinetics of glasses. Polymer viscosities do in fact get so large at the glass transition that the relaxation times in the material equal and exceed the time scale of the experiment. At such temperatures one should not expect to have a perfect prediction of the various thermodynamic quantities. It is sensible to suppose that our predictions should not accord perfectly with experiment in these high viscosity regions. 

The intensity of the glass transitions in semi-crystalline polycarbonate measured by DSC, has been found to be governed by the extent of primary crystallization. Crystallization induced by annealing, by organic solvents, and in the presence of plasticizers have all been reported. In this last paper, using the kinetic theory of Hoffmann and Lauritzen, it was found possible to determine concentrations of seeds inducing crystallization. Texturization in the form of surface roughness has also been found to cause microstructural order. ... 

For larger changes in the time or frequency frame, values of 6-l°C are obtained from equation (8.48), in agreement with experiment. For example, if Ar = 1 X 10 °, an average value of 6.9°C per decade change in Tg is obtained. The kinetic theory of the glass transition, to be developed in this section, considers the molecular and macroscopic response within a varying time frame. 

All the foregoing discussion is a presentation of the kinetic theory of the glass transition. It has many merits, not least being that it is the theory most easily understood by persons with a background in a molecular science. However, it is not the only theory, and we should be aware of the existence of alternative explanations of the processes that we have just described. 

The kinetic theory of polymers and the TTSP are only valid above the glass transition temperature. However, many feel that the procedure, in a modified form, is valid below the glass-transition temperature but exactly how far below is uncertain. The WLF equation, on the other hand is known to be only valid above the Tg because below this temperature the material can no longer be considered a super cooled liquid. In fact. Ferry, (1980) notes that the slope of the shift factor curve should be discontinuous at the Tg for the same reason that the coefficient of thermal expansion suffers a discontinuity at the Tg. 

Inspection of Figure 5 shows a very broad glass-to-rubber transition range which extends from below -100°C to above 0°C for the polyurethane adhesive. The relaxation modulus E(t) - 400 Kg/cm which occurs at the rubbery inflection temperature - 40°C - 313 K describes an effective molecular weight M as defined by kinetic theory of rubber elasticity ... 

Some chemical reactions involving gases are performed in sealed glass tubes that do not melt at high temperatures. The tubes have thin walls and can easily break. Use the kinetic theory of gases to explain why the tubes should not be heated to high temperatures. 

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