Probability distribution of singly and multiply scattered light near the critical point of a binary mixture

The probability density function p(I) is theoretically and experimentally investigated in the case of single, double, and multiple light scattering near a second-order transition (demixing of the binary mixture nitrobenzene and n-hexane). Experimentally we find no differences between the statistics of singly, doubly or multiply scattered light, and as expected from theory, p(I) shows an exponential variation. These results justify the use of either heterodyne or homodyne techniques for studying single or multiple scattering close to a critical point. We also describe a particularly simple way of determining whether homodyne or heterodyne detection occurs.     

Spectral measurements of the depolarized multiple scattered light from a binary mixture near its critical point

We report the first spectral measurements of the depolarized multiple scattered light from a binary mixture near its critical point. Spectral analysis of the depolarized light allows to separate rigorously the multiple scattering from the light scattered by the anisotropy fluctuations. The results are in very good agreement with a recent theory by Oxtoby-Gelbart.     

Spectrum of depolarized light scattered from nitroethane-isooctane mixture near its critical point

We present the results of a study of the spectrum of depolarized light scattered from the critical nitroethane—isooctane mixture which has a very weak critical opalescence. Near the critical point only slight narrowing of the spectrum is observed.     

Spectral linewidth of light quasi-elastically scattered from xenon along the coexistence curve near the critical point

We have measured the linewidth of the central component of light scattered from xenon in both the liquid and vapor phases from 1 to 900 mK below the critical point, and compared our results with the predictions of the mode-mode coupling theory. By taking proper account of the “noncritical” background, using independent measurements of all parameters in both the singular and background parts of the theoretical linewidth, we find satisfactory agreement for 0.03<qξ<6.     

Spectra of Rayleigh scattered light near the gas-liquid critical point of 3He

Spectra of the Rayleigh scattered light near the gas-liquid critical point of ³He have been measured. The correlation length, ξ, the critical exponent corresponding to ξ, v, and the high-frequency shear viscosity, n¹, have been determined.     

Intensity of rayleigh scattered light near the gas-liquid critical point of 3He

Intensities of the Rayleigh scattered light near the gas-liquid critical point of ³He have been measured. The critical exponents, γ, γ′, v and v′ and the parameter, ξ₀ and ξ_±, have been determined.     

Growth rate of critical nuclei near the critical point of a fluid

The growth rate of critical nuclei for a fluid near its critical point is discussed on the basis of the stochastic equation for the probability distribution function of the local order parameter, which was derived previously by the author. The growth rate was found to depend on , the range of correlation of the order parameter fluctuation, andR, the radius of critical nuclei, as ⁰ R ^–3, in conformity with dynamical scaling. The rate of nucleation at the liquid-gas transition near the critical point is also discussed on the basis of this result.     

Ultrasound propagation near the critical mixing point of sodium-ammonia solutions

Ultrasonic absorption and dispersion measurements near the critical mixing point of sodium-ammonia solutions are reported. The results are interpreted in terms of a coupling of the ultrasonic wave and mass diffusional modes. The critical behavior of sound propagation shows features not observed in organic binary mixtures.     

Depolarized light scattered from a fluid near its Bénard instability

Bilinear response theory is extended and applied to a fluid of non-spherical molecules in a gravitational field and with time independent different temperatures on its upper and lower boundaries. The spectral line-shape of the depolarized component in a light-scattering experiment is worked out. It is found that there are two dips in the central peak and that one of these dips becomes infinitely sharp as the external constraints approach their critical values. It is hoped that this kind of experiment will provide relevant information about the dynamics of fluctuations near hydrodynamical instabilities.     

Molecular dynamics simulations of a fluid near its critical point

We present computer simulations for the static and dynamic behavior of a fluid near its consolute critical point. We study the Widom-Rowlinson mixture, which is a two component fluid where like species do not interact and unlike species interact via a hard core repulsion. At high enough densities this fluid exhibits a second order demixing transition that is in the Ising universality class. We find that the mutual diffusion coefficient DAB vanishes as DAB approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from renormalization-group and mode coupling theory predictions for model H, which are DAB approximately xi(-1.065) and DAB approximately xi(-1), respectively.     

Anomaly in electric resistance of binary liquids near the critical point

Electric resistance in critical solutions of nitrobenzene inn-hexane,n-heptane andn-octane was measured. The resistance near the critical point was studied and divergence in the temperature derivative measured.     

Transport properties of a Van der Waals fluid near the critical point

The behaviour of the transport coefficients of a Van der Waals fluid is studied in the one-phase region along the critical isochore of the liquid-vapour phase transition. When $\text{?=}\text{(T?T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}\text{→0}$ the strongest singularity is found in the case of the bulk viscosity (??^?2). The divergence of the heat conductivity is shown to be weaker than $\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$. The shear viscosity tends to a finite limit. The coefficients of the asymptotic laws are explicitly given. All the results are established in the region where the Ornstein-Zernike theory applies.     

Properties of the adsorption layer in a binary liquid mixture near the critical point

A method for the determination of parameters of the surface layer (thickness and refraction index) at the liquid-vapor interface in binary liquid mixtures was developed. The parameters of the surface layer for the C₇H₁₄-C₇F₁₄ liquid mixture in the vicinity of the critical point, which was studied by means of ellipsometry in [1], were calculated using the proposed method. The temperature dependences of the thickness and refraction index that were determined in the homogeneous isotropic layer approximation at the interface liquid-vapor, show structural peculiarities that were not observed earlier. Their appearance is explained by the possible influence of hydrodynamic processes at the boundary.     

Depolarized light scattering in a 2.6-lutidine-water solution near the critical point

The spectra of depolarized Rayleigh light scattering, i.e., the Rayleigh line wing (RLW), and Raman scattering in a solution with the lower critical point in the phase separation diagram is experimentally studied. The Rayleigh line wing is studied to 30 cm^?1 from the exciting light frequency; the Raman scattering line (RSL) is studied in the near profile region. In the vicinity of the lower critical point, as well as in solutions with the upper critical point, strong narrowing of the RLW and RSL is observed. In this case, the conditions arise for the manifestation of the profile in the Rayleigh line spectrum, which is caused by the interaction of concentration and anisotropy fluctuations. Previously, this spectral line was theoretically predicted by I. A. Chaban in [1].     

Contraction and reswelling of a polymer chain near the critical point of a binary liquid mixture

We have studied the conformation change of a flexible linear polymer chain near the critical point of a binary liquid mixture using fluorescence correlation spectroscopy, which measured the hydrodynamic radius of the chains. Our results indicate that as the critical temperature (Tc) is approached, the chain size decreases. The polymer attains its most compact conformation when the correlation length of the critical fluctuations becomes comparable to the coil size. At very close to Tc, the polymer reexpands dramatically. To our knowledge, this is the first experimental evidence supporting the prediction of Brochard and de Gennes that a polymer chain will collapse and subsequently reswell on approaching Tc.     

Bounds on the mixing enhancement for a stirred binary fluid

The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss stirring strategies that homogenize the binary fluid. By measuring fluctuations of the composition away from its mean value, we quantify the amount of homogenization achievable. We find upper and lower bounds on our measure of homogenization using only the Cahn-Hilliard equation and the incompressibility of the advecting flow. We compare these theoretical bounds with numerical simulations for two model flows: the constant flow, and the random-phase sine flow. Using the sine flow as an example, we show how our bounds on composition fluctuations provide a measure of the effectiveness of a given stirring protocol in homogenizing a phase-separating binary fluid.     

Features of the spectral intensity of scattered light near the phase transition point in quartz crystals

The isofrequency dependences of inelastic light scattering in quartz crystals near the phase transition point are calculated taking into account both spatially inhomogeneous fluctuations of the order parameter and the finite spectral width of the spectrometer slit. It was found that the theory is in satisfactory agreement with the experimental data on dynamic opalescence observed in quartz crystals during phase transformations.     

Anisotropy of correlations and its influence on the scattering of light near a critical point

Various manifestations of the anisotropy of correlation properties near a critical point are investigated, and numerical estimates are made for the ranges of variation of the thermodynamic variables in which the influence of anisotropy is important.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 31–35, March, 1981.