Transition mode coupling

Simulation of the Glass Transition in Polymer Melts Extended Mode-Coupling Analysis. 

It would be an advantage to have a detailed understanding of the glass transition in order to get an idea of the structural and dynamic features that are important for photophysical deactivation pathways or solid-state photochemical reactions in molecular glasses. Unfortunately, the formation of a glass is one of the least understood problems in solid-state science. At least three different theories have been developed for a description of the glass transition that we can sketch only briefly in this context the free volume theory, a thermodynamic approach, and the mode coupling theory. 

The mode coupling theory [11] has emerged from the hydrodynamics of liquids. This theory is able to explain the splitting of molecular mobility into relaxation modes that are frozen at the glass transition and molecular motion that is still possible below Tg. 

Thereby, the features of the a-relaxation observed by different techniques are different projections of the actual structural a-relaxation. Since the glass transition occurs when this relaxation freezes, the investigation of the dynamics of this process is of crucial interest in order to understand the intriguing phenomenon of the glass transition. The only microscopic theory available to date dealing with this transition is the so-called mode coupling theory (MCT) (see, e.g. [95,96,106] and references therein) recently, landscape models (see, e.g. [107-110]) have also been proposed to account for some of its features. 

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. 

G. Biroli and J. P. Bouchaud, Diverging length scale and upper critical dimension in the mode coupling theory of the glass transition. Europhys. Lett. 67, 21 (2004). 

Fig. 15. Absorption line shapes for an Alg - > Tlu transition, (a) Coupling due to the rasl vibration. (b) Coupling due to both t2g and al9 vibrational modes. These absorption profiles were calculated by Toyozawa and Inoue (123) invoking the semiclassical approximation.

Sometimes, this sharp peak in S(q) was used to explore the stability of the liquid [29]. This de Gennes narrowing forms the basis for the current mode coupling theory explanation of the glass transition [30]. 

As discussed by Kirkpatrick [10], this slow mode is important in the theories that include mode coupling effects. Such theories have been used to quantitatively understand the anomalous long-time tails of the stress-stress correlation function and the shear-dependent viscosity [3, 30, 34], observed in computer simulations. As mentioned earlier, a theory of glass transition has also been developed based on the softening of the heat mode. 

It can be instructive to compare the two rather different mode coupling theory expressions for the viscosity one valid near the critical point and other near the liquid-glass transition point. 

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 ... 

We have not dwelt on the limitations of the mode coupling theory near the glass transition due to the acivated or rare events—these have been discussed at length at many places. Instead, we emphasized the applications of MCT to liquid-state dynamics. 

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