Rayleigh-linewidth measurements on thin critical fluid films

We describe photon autocorrelation measurements of the Rayleigh linewidth in thin binary liquid films near the critical point. Measurements were made on four films of thickness 13.1, 4.1, 2.1, and 0.5 μm. The films were formed by trapping and sealing samples of a 2,6-lutidine + water critical mixture between fused-silica optical flats. Dynamic scaling arguments predict that the Rayleigh linewidth dependence upon $k\xi$ for the films should be indistinguishable from that for otherwise identical large-volume samples, until conditions defined by both $\xi \simeq \frac{s}{2}$ and $\Lambda \simeq s$ are satisfied. Here, $s$ is the film thickness, $\xi$ is the correlation length, and $\Lambda \equiv 2\pi k^{-1\mathrm{}}$ is the sampling length probed at wave number $k$. We find that, for the three thicker films to within 0.1 mK of their phase-separation temperatures and for the 0.5-μm film to within 2 mK of an extrapolated critical temperature, our data agree with the predictions of renormalization-group theory for binary liquid mixtures in three spatial dimensions—with no adjustable parameters. No evidence of finite-size effects was seen, although both conditions are at least marginally satisfied for the 0.5-μm film ($\Lambda \simeq s$, and eight linewidths measured with $\xi >\frac{s}{2}$) and for the 2.1-μm film ($\Lambda \simeq \frac{s}{4}$, and fourteen linewidths measured with $\xi >\frac{s}{2}$). No effects were seen that could be traced to the presence of surface wetting layers. Finally, we observe a time- and film-thickness-dependent drift in the critical temperature which is not a critical phenomenon, and we find evidence for a noncritical phase transition in the thinnest film.