Mode coupling theory prediction

These experiments have shown that the slower component of solvation is linked to the overall structural dynamics of the liquid, and that mode coupling theory predicts many of the overall features of these dynamics. Dielectric solvation, which is the most widely studied solvation mechanism, does not play a major role for this nonpolar solute. Two theories of nonpolar solvation give better agreement with the data. Bagchi s theory is more rigorously derived, but our model permits a more detailed and rigorous comparison with experiment. 

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... 

Another approach towards a thermodynamics of steady-state systems is presented by Santamaria-Holek et al.193 In this formulation a local thermodynamic equilibrium is assumed to exist. The probability density and associated conjugate chemical potential are interpreted as mesoscopic thermodynamic variables from which the Fokker-Planck equation is derived. Nonequilibrium equations of state are derived for a gas of shearing Brownian particles in both dilute and dense states. It is found that for low shear rates the first normal stress difference is quadratic in strain rate and the viscosity is given as a simple power law in the strain rate, in contrast to standard mode-coupling theory predictions (see Section 6.3). 

The mode-mode coupling theory predicts the universality of the dimensionless vvidth of the central (diffusional) spectrum line... 

The only currently existing theory for the glass transition is the mode coupling theory (MCT) (see, e.g. [95, 96, 106]). MCT is an approach based on a rather microscopic description of the dynamics of density fluctuations and correlations among them. Although the theory was only formulated originally for simple (monatomic) fluids, it is believed to be of much wider applicability. In this review we will only briefly summarize the main basis and predictions of this theory, focusing on those that can be directly checked by NSE measurements. 

While the hydrodynamic theory always predicts this near equivalence of the friction and the viscosity, microscopic theories seem to provide a rather different picture. In the mode coupling theory (MCT), the friction on a tagged molecule is expressed in terms of contributions from the binary, density, and transverse current modes. The latter can of course be expressed in terms of viscosity. However, in a neat liquid the friction coefficient is primarily determined not by the transverse current mode but rather by the binary collision and the density fluctuation terms [59]. Thus for neat liquids there is no a priori reason for such an intimate relation between the friction and viscosity to hold. 

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 ... 

Figure 8. The ratio of the self-diffusion coefficient of the solute (Di) to that of the solvent molecules (D ) plotted as a function of the solvent-solute size ratio (

Dephasing Times Predicted from Fundamental Overtone of the C-I Stretching Mode in CH3I and C-H Stretching Mode in CHCL3 Using Mode Coupling Theory (MCT), the Hydrodynamics Theory (HT) [125], and the Experimental (Exptl)... 

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... 

Triggered by predictions of the mode coupling theory (MCT see Chapter 4), the dynamics of super-cooled liquids was also studied by NS58 60 and LS61 65 revealing details of the susceptibility in the GHz regime. The spectra give evidence that a further fast-relaxation contribution has to be taken into account to explain in particular the shape of the susceptibility minimum, a feature also seen in the DS... 

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.)... 

The relaxation that is not quenched at the glass transition, which is responsible for the partial relaxation in /(, t) even at 0 above 0, is referred to as the yS relaxation. It exists because of incompletely arrested structural relaxation. The longest relaxation time Tp of this /S process is predicted by the mode-coupling theory to become singular at the critical glass concentration, according to the power law ... 

Thus, in the fluid state, there are two relaxation processes, the a and the with relaxation times that scale with proximity to the critical point with differing exponents, -y and — l/2fl, respectively. For spherical particles, y — 2.58 and l/2a = 1.66 thus the a process is predicted to slow more dramatically as the transition is approached than the process. Figure 4-22 shows the relaxation times t and extracted from the relaxation data of Fig. 4-20 for the colloidal fluids. The power laws given by Eqns. (4-33) and (4-34) fit these experimental concentration dependencies well, supporting the mode-coupling theory of this transition. 

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