Thermal diffusivity of CO2 in the critical region

We have measured the Rayleigh linewidth in C${\mathrm{O}}_{2}$ in the critical region using a self-beat spectrometer. The linewidth was measured as a function of both temperature and cell height. The thermal diffusivity $\ensuremath{\chi}$ calculated using the Landau-Placzek equation is in excellent agreement with the values that have been obtained by thermodynamic measurements at three temperatures within the temperature range we investigated ($T\ensuremath{-}{T}_{c}=\ensuremath{-}1.04$, +1.06, and +3.8C\ifmmode^\circ\else\textdegree\fi{}). Thus the Landau-Placzek equation is directly verified in the critical region, at least for temperatures not too close to ${T}_{c}$. However, we find that very near ${T}_{c}$ [for $\ensuremath{\epsilon}\ensuremath{\equiv}\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}\ensuremath{\lesssim}{10}^{\ensuremath{-}4}$], the correlation length in C${\mathrm{O}}_{2}$ is of sufficiently long range (\ensuremath{\sim}250 \AA{} at $\ensuremath{\epsilon}={10}^{\ensuremath{-}4}$) to require that the Fixman-modified linewidth equation be used in order to correctly describe the linewidth behavior. The thermal diffusivity was obtained along the critical isochore for the temperature range $0.02\ensuremath{\le}(T\ensuremath{-}{T}_{c})\ensuremath{\le}5.3{\mathrm{C}}^{\ensuremath{\circ}}$ and along both the gas and liquid sides of the coexistence line for $0.02\ensuremath{\le}({T}_{c}\ensuremath{-}T)\ensuremath{\le}2.3$ C\ifmmode^\circ\else\textdegree\fi{}. The results are (in units of ${\mathrm{cm}}^{2}$/sec): along the critical isochore, $\ensuremath{\chi}=(18.1\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{(T\ensuremath{-}{T}_{c})}^{0.73\ifmmode\pm\else\textpm\fi{}0.02}$; along the gas coexistence line, $\ensuremath{\chi}=(36.0\ifmmode\pm\else\textpm\fi{}3.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{({T}_{c}\ensuremath{-}T)}^{0.66\ifmmode\pm\else\textpm\fi{}0.05}$; and along the liquid coexistence line, $\ensuremath{\chi}=(34.8\ifmmode\pm\else\textpm\fi{}2.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{({T}_{c}\ensuremath{-}T)}^{0.72\ifmmode\pm\else\textpm\fi{}0.05}$. These exponents are in reasonable quantitative agreement with the prediction of Kadanoff and Swift that $\ensuremath{\chi}\ensuremath{\sim}{|\ensuremath{\epsilon}|}^{\ensuremath{-}\ensuremath{\nu}}(\ensuremath{\nu}\ensuremath{\approx}\frac{2}{3})$. Our exponents are also in accord with the thermal-conductivity divergence $\ensuremath{\lambda}\ensuremath{\sim}{\ensuremath{\epsilon}}^{\frac{\ensuremath{-}1}{2}}$ predicted by Fixman and by Mountain and Zwanzig, if the isothermal compressibility diverges as ${\ensuremath{\epsilon}}^{\frac{\ensuremath{-}5}{4}}$, as predicted by the Ising model. Thus both theory and experiment indicate a stronger divergence in the thermal conductivity than has heretofore been assumed. Our subcritical exponents are also in agreement with the linewidth measurements by Saxman and Benedek in S${\mathrm{F}}_{6}$; however, above the critical temperature they obtained an exponent of 1.27, in definite disagreement with our result.