Mode-coupling temperature

The two different temperature regimes of occurring below 7a are separated from each other by a precisely determined crossover temperature T) (denoted by crosses in Fig. 6), which is defined by an inflection point in the product J c(T ) T as a function of T. As discussed later, this crossover or inflection temperature T) appears to conform to the phenomenology of the experimentally estimated mode coupling temperature T p (denoted also as T] ). 

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. 

Being in the temperature regime below the mode coupling temperature, T, the dynamics are dominated by activated processes. As the system ages, the potential energy surface evolves and the barriers between the adjacent IS potential energy... 

FIG. 7 Intermediate incoherent scattering function of a bead-spring pol5mer of length 10 beads, approaching the mode coupling temperature which is r=0.45 in Lennard-Jones units [26]. 

Figure 3. Example of Graphical Output from Analysis Mode. Reaction progress for water-jacketted reactor, with Cascade coupled temperature controllers, both in self-tuning mode.

Figure 9 Chain center of mass self-diffusion coefficient for the bead-spring model as a function of temperature (open circles). The full line is a fit with the Vogel-Fulcher law in Eq. [3]. The dashed and dotted lines are two fits with a power-law divergence at the mode-coupling critical temperature. 

Dynamics of a Supercooled Polymer Melt Above the Mode-Coupling Critical Temperature Cage Versus Polymer-Specific Effects. 

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 ... 

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