Liquid-glass transition, 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. 

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]. 

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. 

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).

Another strong point of the simulation approach is its ability to selectively change parts of the model Hamiltonian. In this way one can compare a chemically realistic model of PB with a freely rotating chain version of the same polymer and does not have to switch to a completely different polymer with some of the same properties like is unavoidable in experiments [33]. With this approach we could establish that identical structure on the two-body correlation function level (single chain and liquid structure factors) does not imply identical dynamics which raises questions on the applicability of the mode-coupling theory of the glass transition to polymer melts. 

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