Experimental determinations of universal amplitude combinations for binary fluids. I. Statics

Abstract

The amplitudes of the correlation length (${\xi }_0^{+}$,${\xi }_0^{-}$) and (${\xi }_0^c$) on the critical isotherm, the susceptibility ($C^{+}$,$C^{-}$) and ($D$) on the critical isotherm, the order parameter ($B$), and the specific heat ($A^{+}$,$A^{-}$), have been obtained for eight binary fluids in the homogeneous (+) or the heterogeneous region (-). All the values have been inferred using the universal values of critical exponents. An accurate approximation for the correlation function, which however does not include corrections to scaling, has been used to deduce ${\xi }_0^{+}$ and $C^{+}$ from light scattering measurements. Spectral analysis of the scattered light allows absolute values of $C^{+}$ to be obtained from the Rayleigh-Brillouin ratio without any assumptions concerning the Reyleigh factor expression. The critical anomaly of the refractive index has been used in several cases to estimate the specific-heat anomaly. Values have been obtained for height amplitude combinations, $\frac{A^{+}}{A^{-}}$, $\frac{C^{+}}{C^{-}}$, $\frac{{\xi }_0^{+}}{{\xi }_0^{-}}$, $R_c^{+}=\frac{A^{+}{C}^{+}}{B^2}$, $R_{\chi }^{+}=C^{+}D{B}^{\delta -1\mathrm{}}$, $R_{\xi }^{+}={\xi }_0^{+}{\left(A^{+}\right)}^{\frac{1}{3}}$, $R_{\xi }^{+}{\left(R_c^{+}\right)}^{-\frac{1}{3}}={\xi }_0^{+}{\left(\frac{B^2}{C^{+}}\right)}^{\frac{1}{3}}$, and $Q_2=\left(\frac{C^{+}}{C_c}\right)\left(\frac{{\xi }_0^c}{{\xi }_0^{+}}\right)$. The universality of these ratios is well supported, and the values found are in agreement with those given by the high-temperature series and the renormalization-group approaches. The experimental values of $\frac{C^{+}}{C^{-}}$ and $R_{\xi }^{+}$ are found to be closer to the renormalization-group prediction.