Accurate determination ofαandΔexponents in critical binary fluids by refractive-index measurements

Abstract

The critical behavior of the refractive index $n$ of three critical mixtures, nitroethane-isooctane (N-I), isobutyric-acid-water (I-W), and triethylamine-water (T-W), has been investigated u$\stackrel{\mathrm{`}}{\mathrm{s}}$ing a very sensitive and reliable interferometric method which enables gravity effects to be ignored. An accuracy $\frac{\ensuremath{\delta}n}{n}\ensuremath{\simeq}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ has been obtained in the range $T\ensuremath{-}{T}_{c}=5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\ensuremath{-}20\ifmmode^\circ\else\textdegree\fi{}$C [$t=\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}=1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\ensuremath{-}7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$]. All anomalies can be interpreted in terms of density or specific-heat anomalies. Thus, for the first time in binary fluids, the $\ensuremath{\alpha}$ exponent could be accurately determined, and was found very close to the renormalization-group (RG) value (${\ensuremath{\alpha}}_{\mathrm{RG}}=0.110\ifmmode\pm\else\textpm\fi{}0.003$ for $n=1$ and $d=3$, to be compared with ${\ensuremath{\alpha}}_{\mathrm{N}\ensuremath{-}\mathrm{I}}=0.10\ifmmode\pm\else\textpm\fi{}0.02$, ${\ensuremath{\alpha}}_{\mathrm{I}\ensuremath{-}\mathrm{W}}=0.12\ifmmode\pm\else\textpm\fi{}0.05$, and ${\ensuremath{\alpha}}_{\mathrm{T}\ensuremath{-}\mathrm{W}}=0.113\ifmmode\pm\else\textpm\fi{}0.005$). In the T-W system, the nonanalytical corrections are sufficiently high to allow, also for the first time, the critical exponent $\ensuremath{\Delta}$ to be determined accurately. The experimental value ${\ensuremath{\Delta}}_{\mathrm{T}\ensuremath{-}\mathrm{W}}=0.50\ifmmode\pm\else\textpm\fi{}0.03$ is in good agreement with the value obtained by RG theory ($\ensuremath{\Delta}=0.493\ifmmode\pm\else\textpm\fi{}0.007$). The amplitude values of the diverging part are in agreement with the two-scale-factor universality and allow the universal constant $X={({R}_{\ensuremath{\xi}}^{+})}^{3}$ to be determined, here also in agreement with the RG values [${X}_{\mathrm{I}\ensuremath{-}\mathrm{W}}=(2.0\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, ${X}_{\mathrm{RG}}\ensuremath{\simeq}1.76\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$]. In the systems studied here, the regular variation was found to be close to ideal variation, suggesting that the mixing anomaly is due mainly to the critical behavior of the specific heat. In addition, we review the results for other systems which have been studied by density, volume, thermal diffusivity, and specific-heat measurements. Although the data are not generally very accurate or reliable, they all support the same general conclusions derived from the analysis of the present data.