Adam-Gibbs theory

Whereas the kinetic approach embodied in the WLF equation and the equilibrium treatment of the G-D theory have both been successful in their way, the one-sided aspect of each probably masks the fact that they are not entirely incompatible with one another. An attempt to rennite both channels of thought has been made by Adam and Gibbs (1965), who have ontlined a molecular kinetic theory. 

Resnlts plotted according to the WLF eqnation could be predicted also from the molecular kinetic equation and show that the two approaches are compatible. The Adam-Gibbs equations also lead to a value of (Fg - Fj) = 55 K, so the theory appears to resolve most of the differences between the kinetic and thermodynamic interpretations of the glass transition. 

These theories point to the fundamental importance of Tj as a true second-order transition temperature and to the experimental as the temperature governed by the time scale of the measuring technique. The latter value has great practical significance, however, and is a parameter that is essential to the imderstanding of the physical behavior of a polymer. 

In region II, Tg is dependent on the molar mass and can be described by Equation 12.22, but, on entering region III where the decrease in Tg accelerates, this is no longer true. The latter region incorporates the material that is ohlgomeric, and the 

FIGURE 12.6 Plot of the glass transition temperature as a function of log r, where x is the number of chain atoms or bonds in the backbone. Data for (-0-) poly(a-methyl styrene), (-A-) poly(methyl methacrylate) (- -) polystyrene, (- -) poly(vinylchloride), (-A-) isotactic poly-propylene, (- -) atactic polypropylene, and (- -) poly(dimethylsiloxane). (From Cowie, J.M.G., Eur. Polym. J., 11, 297, 1975. With permission of Pergamon Press.) 

if is the activation energy for relaxation of 1 mol of conformers, then zEl is the barrier to relaxation in the Uquid near Tg. Thus, the relaxation time is 

The excess entropy A 5 5 is related to the heat capacity difference ACp between 

The Adam-Gibbs equation (4-10) can be tested directly by using the calorimetrically measured entropy difference AS to compute the temperature-dependence of the relaxation time, with B then being a fitting parameter. This has been done, for example, with the data for o-terphenyl shown in Fig. 4-11, and the predicted temperature-dependence of the viscosity is found to be in qualitative, but not quantitative, agreement with the measured viscosity (see, for example. Fig 4-12). The main reason for the failure in Fig. 4-12 is that the temperature Tj at which the entropy extrapolates to zero for o-terphenyl lies below the VFTH temperature Tq required to fit the viscosity data hence the predicted viscosity does not vary as rapidly with temperature as it should. 

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Using the specific entropy determined in the simulations, one can test this theoretical approach by fitting this expression to the temperature dependence of D observed in the simulations. It has been concluded that the Adam-Gibbs theory cannot predict the temperature dependence of the dynamics from the thermodynamic information contained in the temperature dependence of the... 

At equilibrium. Tf = T, and the equilibrium version of the Adam-Gibbs theory, discussed earlier, is recovered. For a glass that is not able to relax, T/ is constant, and then follows an Arrhenius temperature-dependence, which accords well with experimental measurements on deeply quenched glasses. 

Figure 4.26 The log of the average relaxation time versus Adam-Gibbs exponent U jlTS for the facilitated Ising model on the square lattice. The points are from Monte Carlo simulations and the straight line through the points is the prediction of the Adam-Gibbs theory. (From Fredrickson 1988, with permission from the Annual Review of Physical Chemistry, Volume 39, 1988, by Annual Reviews, Inc.)...

Thus, the main problem with the various inferences drawn from Adam-Gibbs theory seems to emanate from the fact that the evaluation of the configurational entropy on the basis of ACp values is erroneous. This... 

The departure from Arrhenius behavior of the relaxation time arises, in the Adam-Gibbs theory, from the temperature dependence of the Sc term in equation (1), which itself is a consequence of the excess heat capacity ACp of equation (2). For constant Ap in equation (2), the degree of non-Arrhenius character, now called the fragility, is determined by the magnitude of ACp. A general but incomplete accord seems to exist between the fragility and ACp and exceptions, like the alcohols, can be rationalized by the presence of unusual Ap terms. 

Combination of the Seif-Concentration Approach with the Adam/Gibbs Theory... 

Soluiiov H A (2006) The dynamic crossover temperature and the characteristic length of glass transition in accordance with the extended Adam-Gibbs theory, J Non-Oryst Solids 352 4871-4876. 

As said before, to study the density fluctuations in polymer matrices, the fluorescence decay time of a probe molecule has to be followed for a sufficiently long time. This has allowed researchers to determine the number of polymer segments Ns rearranging cooperatively (Adam-Gibbs theory) around a single probe molecule by fitting a histogram of the fluorescence decay times (for more details see ref ). 

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