Light scattering from a binary liquid mixture above its critical consolute point

Abstract

Light scattering measurements were performed on the binary liquid mixture carbon tetrachloride–perfluoromethylcyclohexane at its critical concentration and immediately above its critical consolute temperature. Measurements of time averaged intensities as a function of scattering angle and temperature distance from the critical consolute temperature, T−Tc, yielded the critical parameters γ = 1.220±0.018, ξ0 = 2.28±0.21 Å, and ν = 0.626±0.013. Here γ describes the temperature dependence of the susceptibility χ according to the relation χ∝ε−γ, where ε = (T−Tc)/Tc. ξ0 and ν characterize the correlation length with ξ = ξ0ε−ν, which is a measure of the spatial extent of local concentration fluctuations. These values of γ and ν agree well with the scaling and universality hypothesis. Time dependence of the intensity as a function of scattering angle and of T−Tc was determined by measuring the photocurrent autocorrelation function. These measurements yielded decay rates for concentration fluctuations. Combination of decay rates, correlation lengths, and viscosities allowed a direct comparison with the mode–mode coupling theory of Kawasaki. Excellent coincidence of theory and experiment was found except in the vicinity of Kξ = 1, where decay rates were high when compared to theory. K is the magnitude of the momentum transfer vector. Sources of error in the critical parameters obtained from light scattering intensity measurements were analyzed in detail. A useful equation is derived which relates the actual scattering angle inside a cylindrical cell to eight experimental parameters including five ’’alignment’’ parameters which are subject to error. Graphical criteria are presented for estimating uncertainties in critical parameters γ, ξ0, ν, and η.

A Laser Scattering Photogoniometer

“…and should be suppressable to some extent by rotating the cell until the flares at these points of the cell become minimum. We found that the upturn of 1 (8) the cells when the flares were minimized. Figure 6 shows the difference between the scattered light intensities (corrected for the scattering volume by multiplying sin 8) of benzene placed in two arbitrarily chosen cells.…”

“…We found that the upturn of 1 (8) the cells when the flares were minimized. Figure 6 shows the difference between the scattered light intensities (corrected for the scattering volume by multiplying sin 8) of benzene placed in two arbitrarily chosen cells. This difference vanishes within deviations of ± 1% in the angular range 5-150°.…”

“…Other causes of stray light in the bath are reflection at the interface between the cell wall and the test liquid or the bath liquid, and also the flareback of light reflected on the edge surface of the aperture stop (6). The view field of the photomultiplier is so limited by slits (8) and (9) that, even at an angle as low as 2°, the photomultiplier does not see the points at which the beam enters and leaves the cell. Nevertheless, it still catches the flares reflected from these points, although they can be diminished visually by rotating the cell adequately.…”

“…Scattered intensities /(8) times sin 8 relative to that at 90° are also plotted against 8 in Figure 5. The values remain constant, with deviations of ±0.6%, for angles higher than 14°, suggesting that the photomultiplier caught no appreciable stray light in this range of angles.…”

“…Vertically polarized laser light of 632.8 nm is in part reflected by a half-mirror (2) to a monitor. The remaining light travels through a converging lens (4), pinholes (5), a glass rod (6), and a light shield (7) and enters a test liquid placed in a highly polished cylindrical cell (8). The cell, made of Pyrex glass, is immersed in a refractive-indexmatching solvent, xylene.…”