Light-Scattering Measurement of Concentration Fluctuations in Phenol-Water near its Critical Point

Abstract

The intensity and spectral width of light scattered by a critical mixture of phenol and water have been measured as a function of temperature both above and below the critical temperature $T_c$. The temperature dependence of the scattered intensity was fitted to $I\propto {(T-T_c)}^{-\gamma }$ for $T>\mathrm{}{T}_c$ and $I\propto {(T_c-T)}^{-{\gamma }^{\prime }}$ for $T<\mathrm{}{T}_c$. Also measured was the ratio $R_I\equiv \frac{I\left(\Delta T\right)}{I(-\Delta T)}$ of intensities scattered at a given temperature interval $\Delta T$ above and below $T_c$. The measured values of $\gamma$, ${\gamma }^{\prime }$, and $R_I$ were quite close to the predictions of the $3-D$ lattice gas model. The spectral width $\Gamma$ was measured using a photon correlation method, and the data were fitted to $\Gamma =D{K}^2 (1+K^2{\xi }_{\Gamma }^2)$, with the diffusion constant $D=D_0{|T-T_c|}^{\gamma *}$ and ${\xi }_{\Gamma }={\xi }_{0\Gamma }{|T-T_c|}^{{\nu }_{\Gamma }}$ The Fixman term $K^2{\xi }_{\Gamma }^2$ ($K$ being the photon momentum transfer) was observed only above the critical temperature. The value of $\nu$ and the values of ${\gamma }^{*}$ both above and below $T_c$ were in fairly good agreement with the theory of Kadanoff and Swift. The spectral width measurements also provided the ratio $R_D\equiv \frac{D(-\Delta T)}{D\left(\Delta T\right)}$, a quantity for which no theoretical prediction exists. Comparison of this work on phenol-water with that of Swinney and Cummins and others on ${\mathrm{CO}}_2$ near its gas-liquid critical point reveals remarkable similarities between the two systems.