Theory mode coupling

The mode coupling theory [60] is an example of theories based on kinetic ideas that deals not with the glass transition but with the transition at Tmc- Thus, it is not 

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. 

Above Tc the first component/Q (t) relates to the structural relaxation while below Tc it measures the amount of structural arrest. The second part describes fast motional processes (that would take place in the picosecond range, not accessible by NSE) not related to transport phenomena, is the characteristic time of such fast microscopic dynamics. Concerning the structural relaxation, the following predictions are made  

Qualitatively, the Q -dependence of/q resembles that of Spair(Q). However, no analytical expression is available. 

The ampHtude and the timescale of the structural relaxation are related through  

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The friction coefficient of a large B particle with radius ct in a fluid with viscosity r is well known and is given by the Stokes law, Q, = 67tT CT for stick boundary conditions or ( = 4jit ct for slip boundary conditions. For smaller particles, kinetic and mode coupling theories, as well as considerations based on microscopic boundary layers, show that the friction coefficient can be written approximately in terms of microscopic and hydrodynamic contributions as ( 1 = (,(H 1 + (,/( 1. The physical basis of this form can be understood as follows for a B particle with radius ct a hydrodynamic description of the solvent should... 

Rostov, K.S. Freed, K.F., Mode coupling theory for calculating the memory functions of flexible chain molecules influence on the long time dynamics of oligoglycines, J. Chem. Phys. 1997,106, 771-783... 

R. Schilling, J. Pbys. Condens. Matter, 12, 6311 (2000). Mode-Coupling Theory for... 

Scattering Function in the Framework of the Idealized Mode-Coupling Theory A Monte Carlo Study for Polymer Melts. 

Poly butadiene Mode-Coupling Theory Analysis of Molecular Dynamics Simulations Using a Chemically Realistic Model. 

D. R. Reichman and P. Charbonneau,/. Stat. Mech., P05013 (2005). Mode-Coupling Theory. 

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. 

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). 

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. 

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