Thermal Diffusivity of CO2in 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 $\chi$ 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 ($T-T_c=-1.04\mathrm{}$, +1.06, and +3.8C°). 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 $\epsilon \equiv \frac{(T-T_c)}{T_c}\lesssim {10}^{-4\mathrm{}}$], the correlation length in C${\mathrm{O}}_2$ is of sufficiently long range (∼250 Å at $\epsilon ={10}^{-4\mathrm{}}$) 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 $0.02\le (T-T_c)\le 5.3{\mathrm{C}}^{\circ }$ and along both the gas and liquid sides of the coexistence line for $0.02\le (T_c-T)\le 2.3$ C°. The results are (in units of ${\mathrm{cm}}^2$/sec): along the critical isochore, $\chi =(18.1\mathrm{}\pm 0.5)\times {10}^{-6\mathrm{}}{(T-T_c)}^{0.73\pm 0.02}$; along the gas coexistence line, $\chi =(36.0\mathrm{}\pm 3.0)\times {10}^{-6\mathrm{}}{(T_c-T)}^{0.66\pm 0.05}$; and along the liquid coexistence line, $\chi =(34.8\mathrm{}\pm 2.5)\times {10}^{-6\mathrm{}}{(T_c-T)}^{0.72\pm 0.05}$. These exponents are in reasonable quantitative agreement with the prediction of Kadanoff and Swift that $\chi \sim {\left|\epsilon \right|}^{-\nu }\left(\nu \approx \frac{2}{3}\right)$. Our exponents are also in accord with the thermal-conductivity divergence $\lambda \sim {\epsilon }^{\frac{-1\mathrm{}}{2}}$ predicted by Fixman and by Mountain and Zwanzig, if the isothermal compressibility diverges as ${\epsilon }^{\frac{-5\mathrm{}}{4}}$, 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.