Supercooled liquids, mode coupling theory

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 ... 

Another type of kinetics pattern currently under discussion is related to the so-called Mode-Coupling Theory (MCT) developed by Gotze and Sjogren [74], In the MCT the cooperative relaxation process in supercooled liquids and amorphous solids is considered to be a critical phenomenon. The model predicts a dependence of relaxation time on temperature for such substances in the form... 

These authors noted that the intermediate power law (i.e., t l+y, with a small positive 7) of the OKE data was formally equivalent to the excess wing in the frequency-dependent susceptibility, the latter discussed in the dielectric literature since 1951. Brodin and Rossler argued that the intermediate power law observed in the OKE data was in essence a manifestation of the excess wing of the corresponding frequency-domain data, known long since from broadband dielectric spectroscopy and anticipated from DLS studies of supercooled liquids [83]. More recently, these authors showed that the excess wing was an equally common feature of the DLS data and discussed the merits of the Mode coupling theory analysis of the time and frequency-domain data [84]. 

Li et al. employed Eqs. (40) and (41) to fit the temperature-dependent OHD-OKE data on mesogens in the isotropic phase [91]. Equation (40) is identical to the one use in the analysis of the supercooled liquid data. The difference between the schematic model developed by Li et al. and the one applied to supercooled liquids is Eq. (41). The schematic mode coupling theory developed by Li et al. was found to be successful in reproducing the OHD-OKE data on three mesogens in the isotropic phase on all timescales and at all temperatures investigated [91]. 

The current picture of relaxation behavior of supercooled liquids is complex. Mode coupling theory introduced slow a- and fast -processes, whose existence has been confirmed experimentally in almost all known glass forming liquids. The fast -process takes place on the picosecond time scale at all... 

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. 

Li, J. Wang, L Fruchey, K. Payer, M. D. (2006). Dynamics in supercooled ionic organic liquids and mode coupling theory analysis. Journal of Physical Chemistry A, 110,... 

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