SIMPLE-MODEL OF THE DIFFUSIVE SCATTERING LAW IN GLASS-FORMING LIQUIDS

We found that the decay rate, lambda, of the correlation function, G, in glass-forming liquids can be expressed in terms of G itself. A thre e-parameter function of the form lambda=lambda0+lambda1G(k) leads to a n analytic solution for the function G in the time domain. This assump tion also allows one to express the function G as an infinite series o f Lorentzians in the frequency domain. This model has been applied to Mossbauer absorption spectra of aqueous FeCl2 Solutions in glycerol (1 4.4-keV line of Fe-57) and higher temperature quasielastic (Rayleigh) scattering data obtained by the scattering of the W-183 46.5-keV Mossb auer line from pure glycerol. The model describes the Mossbauer data a s well as the empirical Kohlrausch or Cole-Davidson (CD) laws. Also, t he function lambda(G) can be expressed in a two-parameter form as lamb da0exp(alphaG). It has been shown, however, that a closed-form express ion for the function G does not exist in the time or frequency domain for this latter form. On the other hand, the exponential form gives a two-parameter fit to existing data, suggesting a physical basis to thi s form and implies that small changes in G are proportional to fractio nal changes in lambda. It has been found that the parameter alpha has some universal meaning as it remains constant over a significant low-t emperature range accessible experimentally, decreasing to the zero val ue with increasing temperature. Our analysis suggests that the paramet er alpha may change in steps as sample temperature is increased. Such a behavior suggests that some processes (degrees of freedom) are ''fre ezing out'' at well-defined temperatures.