Mode-Coupling Theory temperature

Y. Brumer and D. R. Reichman, Phys. Rev. E 69, 041202 (2004). This paper indicates that the theoretically determined mode coupling temperature Z ,c is near Za, while fits of the mode coupling theory parameters to experimental data, as well as the results of our calculations, suggest that the experimentally estimated Z / actually or nearly coincides with Zj. 

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]. 

Mode coupling theory provides the following rationale for the known validity of the Stokes relation between the zero frequency friction and the viscosity. According to MCT, both these quantities are primarily determined by the static and dynamic structure factors of the solvent. Hence both vary similarly with density and temperature. This calls into question the justification of the use of the generalized hydrodynamics for molecular processes. The question gathers further relevance from the fact that the time (t) correlation function determining friction (the force-force) and that determining viscosity (the stress-stress) are microscopically different. 

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... 

Figure 47. Diffusion coefficient D as obtained from a molecular dynamics simulation study of a binary Lennard-Jones system reaching temperatures below the crossover temperature of mode coupling theory (MCT). Solid line represents interpolation by MCT power law note the large temperature range covered by the power law. (From Ref. 371.)...

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. 

Figure 4.6 l/logio(/oo//p) versus temperature for propylene carbonate. Here logjQ foo = InjToo -13.11, where too (in sec) is the high-frequency relaxation time in Eq. (4-3). Ta is the crossover temperature between Arrhenius and VFTH behavior. The prediction of the mode-coupling theory MCT (see Section 4.6) is also shown, where 7). is the critical temperature. (From Schbnhals et al. 1993, with permission.)... 

Figure 4.7 Cole-Davidson exponent as a function of temperature for glycerol (circles), propylene glycol (squares), and propylene carbonate (triangles). is the temperature at which the crossover from Arrhenius to VFTH behavior is observed, while is the best fit to the critical temperature of the mode-coupling theory (see Section 4.6). (From Schonhals et al. 1993, reprinted with permission from the American Physical Society.)...

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... 

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