By using simple mode coupling equations, we investigate the depolarized light scattering spectra of two so-called "fragile" glassforming liquids, salol (phenylsalicylate) and CKN (Ca 0.4 K 0.6 (NO 3 ) 1.4 ), measured by Cummins and coworkers. Nonlinear integrodifferential equations for the time evolution of the density-fluctuations autocorrelation functions are the basic input of the mode coupling theory. Restricting ourselves to a small set of such equations, we fit the numerical solution to the experimental spectra. It leads to a good agreement between model and experiment, which allows us to determine how a real system explores the parameter space of the model, but it also leads to unrealistic effective vertices in a temperature range where the theory makes critical asymptotic predictions. We finally discuss the relevance and the range of validity of these universal asymptotic predictions when applied to experimental data on supercooled liquids. *
Recent experimental studies of the glass transition of molecular liquids have exploited light scattering techniques in order to support the dynamical model proposed by the mode coupling theory. In the framework of the dipole-induced-dipole (DID) formalism and the Stephen’s approximation, we have checked this theory with several memory functions in the microscopic region, where phononlike excitations dominate, i.e., in the frequency window of 5–130 cm−1 accessible by a classical Raman spectrometer. The fitting procedure compares the experimental susceptibility spectra of one of the simplest fragile molecular liquid, m-toluidine, to the theoretical ones and estimates, in each case, the T dependence of the different control parameters as well as the crossing point of the transition line of type B. The agreement observed for spectra from a temperatures above the melting point down to the glass transition temperature Tg suggests, on the one hand, that information about the dynamical behavior of the supercooled liquid are contained in this frequency region and, on the other hand, that vibrational contributions are incorporated in this formalism, independently of the form of the relaxation kernel. Finally, the two-peak shape in the microscopic range of the susceptibility spectra is related to the relaxation of a linear combination of the Fourier components of the two density correlators.
A large ^-direction dependence of the broad band close to the TO peak is observed and explained qualitatively and quantitatively. The TO peak is found to be repelled out of a two-phonon band by a strong third-order anharmonic interaction.In a crystal having the zinc-blende structure, the first-order Raman scattering allows detection of either the TO(g~0) phonon or the LO(#~0) phonon, according to the selected direction q of the transferred momentum. We have measured at 40 K the scattered intensities of a CuCl single crystal for various q directions (Fig. 1). Because all the spectra were recorded with the same spectral slit width (2 cm" 1 ), the heights (eventually above the continuum) of the sharp lines at 171 and 208 cm" 1 could be taken to fix a common intensity scale for the drawings of Fig. 1 by making use of the fact that the chosen geometries impose I B = 0.5(JA+IC)-The unusual features in CuCl are the broad and strong band of the TO spectrum 1 " 3 (curve A) in the 140-170 cm" 1 range, reaching a very sharp line at 171 cm" 1 with a maximum at 151 cm" 1 , and its replacement by a weak and featureless continuum in the LO spectrum (curve C). This observation of ^-dependent, first-orderlike spectra obviously differs from the recent results of Shand et al. 3 and excludes the assignment of the broad band to a pure second-order Raman scattering.We propose to explain these features by the existence of strong anharmonic interactions between one of the <7~0 optical phonons and a twophonon continuum limited on the high-frequency side by a P 3 type of singularity 4 due to a Bril-where i labels the TO or LO phonon with frequency w,, R* y is the usual first-order Raman tensor element, the anharmonic third-order interaction being given by the usual formula 5 :(F 3 0 2 [A(a>) + iT(a>)]^ ^ TJ vfiirqJu -qiJ 2 ) G (u,qih, -Qi^ QsJJs* -(fa^M^', 4^3> -Qs^) • ( 2 ) q 3 ,J 3f i 4
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