Mode-Coupling Theory temperature dependence

The temperature dependence of the dynamic fluctuations which contribute to the effective pore size may be estimated by means of mode coupling theory, which views a gel as consisting of N pores of diameter t, over which the density fluctuations are correlated [4, 20, 21]. 

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... 

Another type of kinetics pattern currently under discussion is related to the so-called Mode-Coupling Theory (MCT) developed by Gotze and Sjogren [74], In the MCT the cooperative relaxation process in supercooled liquids and amorphous solids is considered to be a critical phenomenon. The model predicts a dependence of relaxation time on temperature for such substances in the form... 

Crossover Temperature for Various Glass Formers as Reported by the Different Methods From the Temperature Dependence of the Stretching Parameter y(T), Scaling the Time Constant xa — xa(r) [cf. Eq. (42)], Non-ergodicity Parameter 1 —f(T) Obtained from Spectra Analysis, Electron Paramagnetic Resonance (EPR), and from Tests of the Asymptotic Laws of Mode Coupling Theory ... 

The time-resolved solvation of s-tetrazine in propylene carbonate is studied by ultrafast transient hole burning. In agreement with mode-coupling theory, the temperature dependence of the average relaxation dme follows a power law in which the critical temperature and exponent are the same as in other relaxation experiments. Our recent theory for solvation by mechanical relaxation provides a unified and quantitative explanation of both the subpicosecond phonon-induced relaxation and the slower structural relaxation. 

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... 

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).

Li et al. employed Eqs. (40) and (41) to fit the temperature-dependent OHD-OKE data on mesogens in the isotropic phase [91]. Equation (40) is identical to the one use in the analysis of the supercooled liquid data. The difference between the schematic model developed by Li et al. and the one applied to supercooled liquids is Eq. (41). The schematic mode coupling theory developed by Li et al. was found to be successful in reproducing the OHD-OKE data on three mesogens in the isotropic phase on all timescales and at all temperatures investigated [91]. 

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. 

To what extent the schematic model systems A and B for a polymer melt show this typical relaxation behavior will be addressed in this subsection, by calculating various structural correlation functions that probe the dynamical changes of the melt on different length scales (Section 6.3.2.1). From these correlation functions it is possible to extract relaxation times the temperature dependence of which can be studied and compared to that of transport coefficients, such as the diffusion coefficient. This will be done in Section 6.3.2.2. The final paragraph of this subsection then deals with the calculation of the incoherent intermediate scattering function and its quantitative interpretation in the framework of the idealized mode coupling theory (MCT). " ... 

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