Density fluctuations mode coupling theory

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. 

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]. 

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. 

A mode coupling theory is recently developed [135] which goes beyond the time-dependent density functional theory method. In this theory a projection operator formalism is used to derive an expression for the coupling vertex projecting the fluctuating transition frequency onto the subspace spanned by the product of the solvent self-density and solvent collective density modes. The theory has been applied to the case of nonpolar solvation dynamics of dense Lennard-Jones fluid. Also it has been extended to the case of solvation dynamics of the LJ fluid in the supercritical state [135],... 

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. 

Of these models, the mode-coupling theory has the clearest direct coimection to liquid-state structure it attempts to describe nonhnear density fluctuations in dense liquids. 

There are rival theories of the glass transition the Gibbs Dimarzio theory assumes that the configurational entropy of the chains approaches zero at Tg. Other researchers prefer a mode coupling theory (MCT), based on the dynamics of density fluctuations. However, it is difficult to extract a simple physical meaning from the complex equations that describe correlations between density fluctuations. Neither theory, at its current state of development, is particularly useful in understanding the properties of glassy polymers. 

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],... 

In the presence of both order-disorder and displacive, as in the KDP family, the two dynamic concepts have somehow to be merged. It could well be that the damping constant Zs becomes somewhat critical too (at least in the over-damped regime of the soft mode), because of the bihnear coupling of r/ and p. It would, however, lead too far to discuss this here in more detail. The corresponding theory of NMR spin-lattice relaxation for the phase transitions in the KDP family has been worked out by Blinc et al. [19]. Calculation of the spectral density is here based on a collective coordinate representation of the hydrogen bond fluctuations connected with a soft lattice mode. Excellent and comprehensive reviews of the theoretical concepts, as well as of the experimental verifications can be found in [20,21]. 

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