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 three-parameter function of the form lambda=lambda0+lambda1G(k) leads to an analytic solution for the function G in the time domain. This assumption also allows one to express the function G as an infinite series of Lorentzians in the frequency domain. This model has been applied to Mossbauer absorption spectra of aqueous FeCl2 Solutions in glycerol (14.4-keV line of Fe-57) and higher temperature quasielastic (Rayleigh) scattering data obtained by the scattering of the W-183 46.5-keV Mossbauer line from pure glycerol. The model describes the Mossbauer data as well as the empirical Kohlrausch or Cole-Davidson (CD) laws. Also, the function lambda(G) can be expressed in a two-parameter form as lambda0exp(alphaG). It has been shown, however, that a closed-form expression 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 this form and implies that small changes in G are proportional to fractional changes in lambda. It has been found that the parameter alpha has some universal meaning as it remains constant over a significant low-temperature range accessible experimentally, decreasing to the zero value with increasing temperature. Our analysis suggests that the parameter alpha may change in steps as sample temperature is increased. Such a behavior suggests that some processes (degrees of freedom) are ''freezing out'' at well-defined temperatures.