Structural relaxation, mode coupling theory

A. Comments on the Relaxation Equation Vm. Structure of Mode Coupling Theory as Applied to Liquid-State Dynamics... 

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 relaxation equations for the time correlation functions are derived formally by using the projection operator technique [12]. This relaxation equation has the same structure as a generalized Langevin equation. The mode coupling theory provides microscopic, albeit approximate, expressions for the wavevector- and frequency-dependent memory functions. One important aspect of the mode coupling theory is the intimate relation between the static microscopic structure of the liquid and the transport properties. In fact, even now, realistic calculations using MCT is often not possible because of the nonavailability of the static pair correlation functions for complex inter-molecular potential. 

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. 

Leutheusser 1984 Bentzelius et al. 1984), has stirred both excitement and controversy (Mezei et al. 1987 Richter et al. 1991 Retry et al. 1991 Schonhals et al. 1993 Mezei 1991 Kim and Mazenko 1992). While the details of the mode-coupling theory are beyond the scope of this chapter, the main idea is that at high fluid densities there is a nonlinear feedback mechanism by which fluctuations in the structure (or local density) of the fluid become arrested and cannot relax to equilibrium. The point at which this occurs is then a purely dynamic glass transition. 

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 ... 

Slow relaxation of water was further discussed in more broad contexts. In particular, since the IS picture is expected to become appropriate as the temperature is decreased, special attention has been paid to water in supercooled states, and dynamics in supercooled states has been investigated in relation to applicability of the mode-coupling theory [51]. It was found that the bond lifetime of individual molecules obeys the thermal process, whereas the bond correlation function shows power-law behavior [52,53], The behavior below or above the temperature at which the mode-coupling theory can be applied was also studied and the transition between IS structures, which is just the network rearrangement dynamics just mentioned above, has clearly been identified in supercooled regions. 

Gdtze. W., and Sjogren, L., The mode coupling theory of structural relaxations. Transp. Theory Stat. Phys lA, 801 (1995). 

To what extent the schematic model systems A and B for a polymer melt show this typical relaxation behavior will be addressed in this subsection, by calculating various structural correlation functions that probe the dynamical changes of the melt on different length scales (Section 6.3.2.1). From these correlation functions it is possible to extract relaxation times the temperature dependence of which can be studied and compared to that of transport coefficients, such as the diffusion coefficient. This will be done in Section 6.3.2.2. The final paragraph of this subsection then deals with the calculation of the incoherent intermediate scattering function and its quantitative interpretation in the framework of the idealized mode coupling theory (MCT). " ... 

When an atomic system is cooled below its glass temperature, it vitrifies, that is, it forms an amorphous solid [1]. Upon decreasing the temperature, the viscosity of the fluid increases dramatically, as well as the time scale for structural relaxation, until the solid forms concomitantly, the diffusion coefficient vanishes. This process is observed in atomic or molecular systems and is widely used in material processing. Several theories have been developed to rationalize this behavior, in particular, the mode coupling theory (MCT) that describes the fluid-to-glass transition kinetically, as the arrest of the local dynamics of particles. This becomes manifest in (metastable) nondecaying amplitudes in the correlation functions of density fluctuations, which are due to a feedback mechanism that has been called cage effect [2],... 

Hinze, G., Brace, D.D., Gottke, S.D. and Payer, M.D. (2000). A detailed test of mode-coupling theory on all time scales Time domain studies of structural relaxation in a supercooled liquid. J. Chem. Phys. 113 3723-3733. 

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