Critical dynamics near plait points in mixtures

We set up a dynamical model describing the critical dynamics near a plait point considering the entropy density as the order parameter. This leads to model H' of Siggia, Halperin and Hohenberg, which we treat within a field theoretic renormalization group theory. The temperature dependence of the hydrodynamic transport coefficients is calculated in the crossover region from background to the asymptotic critical region. The asymptotic behavior is described by the same universal values of the amplitude ratios and exponents as in the pure fluid and at the consolute point. Thus agreement with mode-coupling theory in the asymptotic region is shown. We define an experimental expression for the Kawasaki amplitude at the plait point and calculate its theoretical counterpart. The theoretical expression agrees with corresponding result at the consolute point, the nonasymptotic expression for the Kawasaki amplitude is different from the pure fluid. The main reason for the nonuniversal behavior of mixtures at the plait point lies not in a slow flow to the asymptotics of the dynamical parameters of the model, but in the nonuniversal prefactor appearing before the singular part in the transport coefficients.     

Nonlinear dielectric effect of critical liquid mixtures: Propylene carbonate + monoalkylbenzene systems

The nonlinear dielectric effect (NDE) is measured in the one-phase region of propylene carbonate + monoalkylbenzene systems. The deviations from the regular molecular behavior are determined by the reference solution method at a very wide temperature distance, up to 180 K, from the critical point. The data are analyzed under the assumption of the universality of the precritical NDE by making use of empirical crossover functions. The precritical NDE anomalies are large. The critical exponent =0.396±0.01 and the correction exponent =1.02±0.1 both differ from the theoretical values.     

Critical Light Scattering in Pure Liquids

Light-scattering experiments near the critical point (T _c, _c) in fluid systems and, in particular, the central Rayleigh peak in the frequency spectrum are reviewed. Within a nonasymptotic renormalization-group theory, the crossover function is calculated between several regions: (i) from the background to the asymptotic region, (ii) from the hydrodynamic region (wave lengthcorrelation length) to the critical region (wave lengthcorrelation length), and (iii) from critical densities to noncritical densities. Contrary to the mode-coupling expression, the appropriate scaling function is well defined in all limits of its arguments. At T _c the crossover in the wave-vector dependence of the linewidth is also considered. Theoretical results are compared with experiments for pure liquids. Nonuniversal parameters are chosen consistent with the transport coefficients (i.e., the shear viscosity) for the same substance which can be evaluated within the same formalism.     

Transport properties of fluid mixtures in the critical region

Transport properties of fluid mixtures exhibit anomalous behavior near the vapor-liquid critical line. These anomalies are a result of long-range fluctuations in the system in the vicinity of a critical point. We use mode-coupling theory to describe the critical enhancements of the thermal conductivity, the viscosity, the mutual diffusivity, and the thermal-diffusion coefficients of binary mixtures. The resulting expressions not only are valid in the asymptotic critical region but also describe the crossover to regular behavior far away from a critical point. The crossover functions depend on the thermodynamic properties of the mixtures, background values of all transport coefficients, and two concentration-dependent cutoff wave numbers. We compare the proposed crossover model with experimental thermal-conductivity data for mixtures of carbon dioxide and ethane in the critical region and find good agreement between theory and experiment.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

Abstact The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field ( = 1/2 in the immediate vicinity of the critical point to Ising-like (= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.Invited paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder. Colorado, U.S.A.     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).     

Transport properties of critical dilute solutions

On the basis of the isomorphism of critical phenomena, the behavior of transport properties of binary mixtures in the vicinity of the vapor-liquid critical line is considered. In particular, the renormalization of the singularity of the thermal conductivity in dilute critical solutions has been analyzed in detail. It is shown that the behavior of the thermal conductivity is determined by the critical background, i.e., the fluctuation-induced regular part, which diverges at the critical point of a solvent.     

Nonasymptotic Transport Properties in Fluids and Mixtures Near a Critical Point

We review the critical dynamics of fluids and mixtures. Special attention in the comparison with experiment is paid to nonasymptotic effects. Our theoretical results are based on the complete model H of Siggia, Halperin, and Hohenberg including the sound mode variables. Using the dynamic renormalization group theory, we calculate the temperature dependence of the transport coefficients as well as the frequency-dependent sound velocity and sound attenuation. In mixtures a time ratio between the Onsager coefficients related to the diffusive modes, which is directly related to the critical enhancement of the thermal conductivity near a consolute point, has to be taken into account. The sound mode contains, besides the dynamic parameters, a static coupling related to the logarithmic derivative of the weakly diverging specific heat. The deviation from the asymptotic value of this coupling at finite frequencies and temperature distance from T _c leads to additional nonasymptotic effects. Our theory, which derives the phenomenological ansatz of Ferrell and Bhattacharjee for pure fluids and mixtures near a consolute point, is also applicable near a plait point.     

Dielectric study of the two-phase region of binary liquid mixtures near the consolute point

We present new experimental results for the static dielectric constant as a function of temperature for the coexisting phases of the binary liquid mixtures benzonitrile-isooctane and nitroethane-cyclohexane near their consolute points. From the difference of the dielectric constants of the coexisting phases as well as from the temperature dependence of the dielectric constant in each phase, a critical exponent value =0.325+-0.005 is obtained. The average of the dielectric constant shows curvature arising from a critical contribution with an exponent of 2.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Magnetic hysteresis of the zero-resistance critical temperature of high-Tc granular superconductors

We have found a notorious hysteretic behavior in the dependence of the zero-resistance critical temperature obtained through resistivity () versus temperature (T) measurements with applied field (H _e ) in High-T _c granular superconductors. This behavior is explained semi-quantitatively based on the analogy between the present observation and a similar hysteresis found in the field dependence of the transport critical current in these materials.     

Measuring Turbidity in a Near-Critical, Liquid–Liquid System: A Precise, Automated Experiment

A ground based (1g) experiment is in progress that measures the turbidity of the density-matched, binary fluid mixture methanol–cyclohexane extremely close to its liquid–liquid critical point. By covering the range of reduced temperatures t (T–T _c)/T _c from 10^–8 to 10^–2, the turbidity measurements should allow the Green–Fisher critical exponent to be determined. This paper reports measurements showing ±0.1 % precision of the transmitted and reference intensities, and ±4K temperature control near the critical temperature of 320 K. Preliminary turbidity data show a nonzero consistent with theoretical predictions. No experiment has precisely determined a value of the critical exponent , yet its value is significant to theorists in critical phenomena. Relatively simple critical phenomena, as in the liquid–liquid system studied here, serve as model systems for more complex behavior near a critical point.     

Interfacial tension near the tricritical point in3He-4He mixtures

The interfacial tension ₁ of phase-separated³He-⁴He mixtures has been measured between 0.5 K and the tricritical point. The observed decrease of _i on approaching the tricritical point is much stronger than for ordinary critical points. Our data are consistent with a critical exponent =2.     

Crossover behavior of the transport coefficients of critical binary mixtures

The behavior of the transport coefficients related to diffusion, heat conduction, and their cross-processes in fluid mixtures near the consolute point and the liquid-vapor critical line is investigated. Simple crossover equations for the critical enhancement of those coefficients are developed by incorporating a finite cutoff and time-dependent correlation functions of the order parameter and of the entropy into decoupled-mode theory integrals. It is shown that the thermal conductivity of a binary mixture is nondivergent and the crossover from the critical background in the critical point to the regular background far from the critical point is elucidated. The crossover to the behavior of the thermal conductivity in the one-component limit is also discussed.     

Thermodynamics of hydrogen-bonding mixtures 2.G E,H E,andS E of 1-propanol +n-heptane

A metal ebulliometcr was used to measure total vapor-pressure (PTx) data on 18 mixtures of 1-propanol +n-heptane (and the pure components) between 380 and 445 K. Bubble-point data were measured at seven pressures between 200 kPa and I MPa. These data cover an intermediate region between previous data reported near atmospheric pressure and below and high-temperature data extending to the critical region. A Redlich--Kister G' model fit isotherms between 373.15 and 463.15 K via Barker's method with an average standard error of 0.2 to 0.5% in pressure. The system exhibits large positive deviations from ideality (derived =2.7–10.5) which decrease with temperature. EquimolarG ^E/T values thus derived also decrease with increasing temperature, which predicts a positiveH ^E An azeotrope exists under all conditions studied: the azeotropic composition increases in alcohol content with increasing temperature. These mixture thermodynamic data show that, above 345 K, the system 1-propanol +n-heptane belongs to the class of mixtures whereG ^E > 0,H ^E >0. andTS ^E > 0. This probably occurs because the 1-I orientational effect (in this case, hydrogen-bonding of the alcohol molecules) is more readily disrupted in the inert solvent than it would be a( lower temperatures, where the effect of hydrogen-bonding is stronger.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Turbidity of a near-critical ionic fluid

We report the critical behavior of osmotic compressibility (% _T ), that was deduced from turbidity, in an ionic fluid mixture comprised of tetra-n-butyl ammonium picrate in a low dielectric solvent, 1-dodecanol. The liquid-liquid phase separation in this system is driven, predominantly, by Coulombic interactions. Measurements covered the reduced temperature, t, range 7 x 10⁵ / 7 × 10^{– 2}. The critical behavior of Z, indicates acrossover from the mean-field to the Ising critical exponent, as the critical temperature (T _c) is approached.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Tricritical Dynamics at the Demixing-λ-Transition in 3He-4He Mixtures

We calculate in two loop order the dynamical critical behavior at the tricritical point occuring in ³He-⁴He mixtures. Model F^′ introduced by Siggia and Nelson (Phys. Rev. B 15:1427, [1977])—already problematic in one loop order—is shown in two loop order to lead to a divergence of the mass diffusion D in contradiction to experiments. Within the complex symmetric version of this model (model E ^⋆′) the dynamical critical exponents of the kinetic coefficients can be calculated exactly leading to a mass diffusion going to zero at the tricritical point as D(t _X )∼t _X ^1/2 (t _X is the relative temperature distance at constant concentration) and the thermal diffusion ratio k _T ∼t _X ⁻¹ diverges proportional to the concentration susceptibility in the experimental region. We also discuss effective dynamical critical exponents and compare them with recent simulations of the vector Blume-Emery-Griffths model.      

The Nearly Classical Behavior of a Pure Fluid on the Critical Isochore Very Near the Critical Point Under the Influence of Gravity

Comprehensive measurements of the isothermal compressibility along the critical isochore in the critical region of pure sulfur hexafluoride (SF₆) and pure carbon dioxide (CO₂) were carried out. All measurements were performed with a multicell apparatus, especially designed for pT measurements in the critical region. The height of the measuring cells was either 30 or 11 mm. Independent of the cell height, we found for both fluids nearly classical values for the critical exponent in the limiting approach to the critical point. However, at a certain distance from the critical point {(T – T _c) 90 mK or 2.82 × 10^–4 for SF₆ and (T – T _c) 55 mK or 1.81 × 10^–4 for CO₂}, we observed a transition to values of the critical exponents which nearly meet the predictions of the renormalization-group theory. Since in the fitting range (T – T _c 1 mK) the correlation length ( 0.5 m) is very much smaller than the geometrical dimensions of the measuring cells, we conclude that the reason for the different behavior is an explicit gravity effect governing the inner critical region. The two different loci of the transition points for sulfur hexafluoride and carbon dioxide can be attributed to the different gravity impact on the fluid corresponding to the different critical densities of the two substances.     

Viscosity of steam in the critical region

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.Nomenclature a critical region equation of state parameter - a _k coefficients in equation for ₀ - a _ij coefficients in equation for ¯ - b critical region equation of state parameter - c _p specific heat at constant pressure - c _v specific heat at constant volume - k critical region equation of state parameter - k _B Boltzmann constant - P pressure - P _r 22.115 MPa - P ^* P/P _r - P _c critical pressure - P _i coefficients in critical region equation of state - R~P (P-P _c )/P _c - q parameter in equation for critical viscosity enhancement - r parametric variable in critical region equation of state - T temperature in K (IPTS-48) - T _r 647.27 K - T ^* T/T _r - T _c critical temperature - T (T–T _c )/T _c - V volume - critical exponent of specific heat - critical exponent of coexistence curve - critical exponent of compressibility - critical exponent of chemical potential at T=T _c - dynamic viscosity - ₀ lim ₀ - ¯ normal viscosity - critical viscosity enhancement - ¯ thermal conductivity - normal thermal conductivity - critical thermal conductivity enhancement - parametric variable in critical region equation of state - correlation length - ₀ correlation length amplitude above T _c at = _c - critical exponent of correlation length - density - _r 317.763 kg/m³ - ^* / _r - _c critical density - (– _c )/ _c - _p estimated error of pressure - _T estimated error of temperature - estimated error of viscosity - exponent of critical viscosity enhancement - _t (/P) _T symmetrized compressibility - _T ^* _T P _r / _r ² - _{t t} P _c / _c ²     

The Viscosity Anomaly Near the Lower Critical Consolute Point

Shear viscosity measurements for a critical mixture of 3-methylpyridine + heavy water near a lower critical consolute point are reported. The background contribution was determined from viscosity measurements of mixture at a noncritical composition. In the entire investigated temperature range T _c – T 15.6 K, the viscosity of the critical mixture exceeds the background contribution, and the critical enhancement is important. The increase of the viscosity near critical is found in the temperature range T _c–T 1.82 K. The critical exponent y = 0.0415 ± 0.002 and the wave number Q = (0.40 ± 0.07) nm^–1 are determined.