Glass transition temperature mode coupling theory

It appears, however, that the mode-coupling theory is not able to explain some of the most significant slow-relaxation processes of these more complex glass formers. In particular, it cannot explain the success of the Vogel-Fulcher-Tammann-Hesse (VFTH) equation for the temperature-dependence of the relaxation time near the glass transition. The mode-coupling theory predicts instead a power-law dependence of the longest relaxation... 

The most important prediction of the mode coupling theory is the temperature or the density dependence of the relaxation time, tmc(< )- MCT predicts that this relaxation time grows as a power law as the glass transition is approached (from the supercooled liquid side). This is because the diffusion coefficient Do of the liquid goes to zero in the following fashion ... 

In Sec. IV we discuss another TPM dye, malachite green (MG), which was used as a molecular probe for glass transition of alcohols and polymers [11,12], Analysis of the temperature dependence of nonradiative relaxation in MG shed light on the understanding of the mechanism of glass transition. Novel experimental observations are divided into two classes. (1) The critical temperature (Tc) predicted by the mode-coupling theory (MCT) was undoubtedly... 

Figure 3.15 Test of the mode coupling theory power law predictions for viscosity temperature dependence for a variety of molecular and ionic liquids. Tg is the glass transition temperature determined by thermal analysis at 10 K/min scanning (After Angell, 1998).

Deviations from harmonic behaviour are also found above about 200 K, however, only for the amorphous samples. These high temperature anharmonicities occur often far below Tg, which is typically around 300-350 K. They are supposed to be caused by residual solvents in the polymer matrix. We have also studied / T) for some polymers with a relatively low Tg of 250-300 K. In f T) decreases rapidly following a V c - T dependence as predicted by mode coupling theory (MCT). This is interpreted as the onset of local processes. Tc represents the transition from non-ergodic to ergodic behaviour, which occurs typically 30-150 K above the macroscopic glass transition temperature Tg. In Fig. 15.10 we show f T) for PROPS. The MCT fit is indicated by the broken line yielding Tc = 306 12 K whereas Tg k, 240 K. Simultaneously with the onset of anharmonic behaviour of/the Mofl-bauer resonance lines broaden and quasi-elastic lines appear close to Tc. 

When an atomic system is cooled below its glass temperature, it vitrifies, that is, it forms an amorphous solid [1]. Upon decreasing the temperature, the viscosity of the fluid increases dramatically, as well as the time scale for structural relaxation, until the solid forms concomitantly, the diffusion coefficient vanishes. This process is observed in atomic or molecular systems and is widely used in material processing. Several theories have been developed to rationalize this behavior, in particular, the mode coupling theory (MCT) that describes the fluid-to-glass transition kinetically, as the arrest of the local dynamics of particles. This becomes manifest in (metastable) nondecaying amplitudes in the correlation functions of density fluctuations, which are due to a feedback mechanism that has been called cage effect [2],... 

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