Autocorrelation spectroscopy studies of single and multiple scattered light from a critical fluid mixture

Abstract

We describe photon autocorrelation studies of both the depolarized and polarized components of light scattered from the critical binary mixture methanol-cyclohexane, carried out to $k\ensuremath{\xi}\ensuremath{\cong}80$, in an effort to differentiate between the Rayleigh linewidth predictions of the mode theories and the dynamic droplet model, and to assess the validity of our treatment of the autocorrelation function of light which undergoes double scattering from a critical fluid. (Here $k$ is the scattering wave number and $\ensuremath{\xi}$ the Orstein-Zernike correlation length.) We achieved sample temperature control of \ifmmode\pm\else\textpm\fi{}15 \ensuremath{\mu}\ifmmode^\circ\else\textdegree\fi{}C for periods of 24 hours and reduced sample temperature gradietns to \ensuremath{\lesssim} \ifmmode\pm\else\textpm\fi{}40 \ensuremath{\mu}\ifmmode^\circ\else\textdegree\fi{}C/cm. We developed a technique for measuring the effects of laser heating upon the temperature of the fluid within the scattering volume. These latter measurements enabled us to determine the critical temperature of our system to an accuracy of \ifmmode\pm\else\textpm\fi{}60 \ensuremath{\mu}\ifmmode^\circ\else\textdegree\fi{}C. We find agreement between the predictions of our theory of the double-scattered autocorrelation function and the measured depolarized intensity autocorrelation function. The double-scattered contribution becomes significant for the methanol-cyclohexane system at $k\ensuremath{\xi}\ensuremath{\cong}0.6$, and higher than second-order scattering becomes important for $k\ensuremath{\xi}\ensuremath{\gtrsim}1$. Despite the large multiple-scattered component in the light scattered from the fluid in the nonhydrodynamic regime, the Rayleigh linewidth is affected only slightly. We show how to estimate the amount of multiple scattered light from depolarization-ratio measurements, and make qualitative assessments of the modifications of the Rayleigh linewidth due to higher-order scattering. Despite the small effect of multiple scattering upon the Rayleigh linewidth at large values of $k\ensuremath{\xi}$, the uncertainty introduced is large enough to obscure the differences between the fits of the mode theories and the dynamic droplet model to our experimental results.