Rayleigh-Brillouin Light Scattering: Spectral Moments and Sum Rules

Abstract

We present experimental and theoretical results concerning the spectral moments of Rayleigh-Brillouin light scattering spectra of pure liquids and gas mixtures. First we derive a general equation for the second and fourth moment of the dynamic structure factor. Second, we derive explicit expressions for these moments for the Gaussian limit and models that predict Lorentzian line shapes. Our experimental results for the normalized second moment agree with the theoretical expressions. The n = 3 sum rule seems to be satisfied. The results for the normalized fourth moment do not agree with theory, but this can be shown to be caused by frequency cutoff effects in the spectrum. The contribution of the instrumental function to the spectral moments is also investigated. Our results indicate that in the analysis of Rayleigh-Brillouin light scattering spectra use can be made of higher order sum rules (at least up to n = 3), provided that the free spectral range of the interferometer is chosen large enough. This would allow for a significant reduction in the number of fitting parameters needed to analyze such a light scattering spectrum. Rayleigh-Brillouin light scattering spectra of fluids contain a wealth of information concerning the thermodynamic and transport properties of the fluid.' The information gained in an experiment can be used to solve fundamental questions, e.g., to test the validity of and kinetic theory,s7to study molecular relaxation in ionic mixtures* or the dynamical behavior of a supercooled fluid9 or a polymer solution,lo as well as more practical questions, e.g., to study the thermodynamics of the scattering medium.11-13 The shape of the Rayleigh-Brillouin triplet is determined by many parameters which can be extracted from the spectrum. Although this is straightforward in some cases, it is a difficult task in other cases. In this paper we will describe some tools that may be used in these difficult cases. We will show how the analysis of spectral moments can be used to reduce the number of fitting parameters in a hydrodynamic model when applied to a Rayleigh-Brillouin triplet. Furthermore, we will investigate whether our approach to data analysis has been stretched to its limits or can be extended still further.