Dynamics of Fluids near the Critical Point: Decay Rate of Order-Parameter Fluctuations

Abstract

The decay rate of the order-parameter fluctuations in fluids near the critical point can be determined by measuring the linewidth of the central component in the spectrum of the scattered light, and many such experiments have been reported in the past eight years. In the past two years the dynamical theories developed by Kawasaki and Ferrell to describe the decay rate have been modificed to take into account the anomaly in the shear viscosity and the effect of departures of the correlation function from the Ornstein-Zernike form, and at the same time new accurate measurements of the parameters which enter the theory (the correlation length $\ensuremath{\xi}$ and the shear viscosity ${\ensuremath{\eta}}_{s}$) have been reported. Thus we are able to present here an absolute comparison of the refined mode-mode coupling and decoupled-mode theories with the linewidth data for seven fluids: carbon dioxide, xenon, sulfur hexafluoride, isobutyric acid-water, 3 methylpentane-nitroethane, aniline-cyclohexane, and 2,6 lutidine-water. These linewidth data were obtained in many different laboratories over the past few years; however, in addition to linewidth data previously reported, we also include in our analysis new data which we have obtained for carbon dioxide and xenon and a tabulation and detailed error analysis for all our data for these two fluids. The theories describe only the "critical part" of the decay rate ${\ensuremath{\Gamma}}^{C}$; hence the nonanomalous background contributions are first substracted from the measured linewidths to obtained ${\ensuremath{\Gamma}}^{C}$. Then it is shown that the resultant values for a quantity we call the "scaled linewidth," ${\ensuremath{\Gamma}}^{*}\ensuremath{\equiv}(\frac{6\ensuremath{\pi}{\ensuremath{\eta}}_{s}{\ensuremath{\Gamma}}^{C}}{{k}_{B}T{q}^{3}})$, are described by a single universal curve as a function of $q\ensuremath{\xi}$, for all fluids and every thermodynamic path that has been investigated near the critical point. This universal curve is described remarkably well by the modified mode-mode-coupling expression of Kawasaki and Lo and the similar decoupled-mode-theory expression of Perl and Ferrell. The accuracy of this comparison, which involves no adjustable parameters, is limited to $\ensuremath{\sim}10%$ by the uncertainties in the background corrections, linewidths, viscosities, and correlation lengths, and by the uncertainties in the various modifications to the theories. The two theories differ significantly only in the extreme nonhydrodynamic region ($q\ensuremath{\xi}\ensuremath{\gg}1$), where the decoupled-mode values for ${\ensuremath{\Gamma}}^{*}$ are $\ensuremath{\sim}10%$ smaller than those predicted by the mode-mode-coupling theory. Although the available data in the extreme nonhydrodynamic region appear to be described somewhat better by the decoupled-mode theory than the mode-mode-coupling theory, this result is suggestive rather than conclusive since the data in this region are sparse and exhibit considerable scatter.