Global thermodynamic behavior of fluids in the critical region

Thermal Density Fluctuations and Polymorphic Phase Transitions of Ethane (C2D6) in the Gas/Liquid and Supercritical States

The phase behavior of the liquid C2D6 below and above the critical point was investigated using small-angle neutron scattering (SANS) in temperature and pressure ranges from 10 to 45 °C and 20 to 126 bar, respectively. The scattering of thermal fluctuations of the molecular density was determined and thus the gas-liquid and Widom lines. At the same time, we observed additional scattering of droplets of more densely packed C2D6 molecules above the gas-liquid line and in the supercritical fluid regime from just below the critical point for all temperatures at about ΔP = 10 bar above the Widom line. This line is interpreted as the Frenkel line. These results are consistent with our previous studies on CO2 and thus indicate a universal phase behavior for monomolecular liquids below and above the critical point. The interpretation of the Frenkel line as the lower limit of a polymorphic phase transition is in contrast to the usual interpretation as the limit of a dynamic process. The correlation lengths (ξ) of the thermal density fluctuations at the critical point and at the Widom line are determined between 20 and 35 Å and thus in the range of the droplet radius between 60 and 80 Å. These long-range fluctuations appear to suppress the formation of droplets, which can only form at about 10 bar above the critical point and the Widom line when ξ becomes smaller than 10 Å.

Reference Correlation for the Viscosity of Carbon Dioxide

A comprehensive database of experimental and computed data for the viscosity of carbon dioxide (CO2) was compiled and a new reference correlation was developed. Literature results based on an ab initio potential energy surface were the foundation of the correlation of the viscosity in the limit of zero density in the temperature range from 100 K to 2000 K. Guided symbolic regression was employed to obtain a new functional form that extrapolates correctly to T → 0 K and to 10 000 K. Coordinated measurements at low density made it possible to implement the temperature dependence of the Rainwater-Friend theory in the linear-in-density viscosity term. The residual viscosity could be formulated with a scaling term ργ /T the significance of which was confirmed by symbolic regression. The final viscosity correlation covers temperatures from 100 K to 2000 K for gaseous CO2, and from 220 K to 700 K with pressures along the melting line up to 8000 MPa for compressed and supercritical liquid states. The data representation is more accurate than with the previous correlations, and the covered pressure and temperature range is significantly extended. The critical enhancement of the viscosity of CO2 is included in the new correlation.

Improved renormalization group theory for critical asymmetry of fluids

We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.

Critical asymmetry in renormalization group theory for fluids

The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

Heat can cool near-critical fluids

We report experiments with very compressible fluids near the liquid-gas critical point. These experiments are performed (i) under microgravity in low Earth orbit by using SF(6) at liquidlike density and (ii) under Earth's gravity with CO(2) at gaslike density. The sample fluid is filled in an interferometer cell with its walls maintained at constant temperature. In situ thermistors measure the local fluid temperature. One of the thermistors is also used as a heat source to generate heat pulses. With no gravity-induced fluid convection, the evolution of fluid temperature is governed by the balance of heat flux between the thermal boundary layer of the heat source, which compresses the bulk fluid, and the thermal boundary layer at the wall, which expands it. When heat pulses are applied to the fluid under weak or Earth's gravity, a long thermal transient is observed at the end of the heat pulse where the bulk fluid temperature reaches significantly below the initial temperature. This unconventional cooling originates from the fast decompression of the fluid, which is induced by the rapid convectively disappearing hot boundary layer at the heat source, and the persistence of an anomalously thin cold boundary layer convectively induced at the cell wall. This striking phenomenon is observed in a large range of temperature, density, and various thermodynamic conditions. This anomalous cooling effect persists for an appreciable period of time corresponding to the diffusive destruction of the cold boundary layer. We found that the effect is also more pronounced when the free fall acceleration is large. We have analyzed the result by using a simple one-dimensional model with ad hoc convective heat losses.

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.

Universality and quantum effects in one-component critical fluids

Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within phi (4)(d = 3) (n = 1)the model, or based on the crossover parametric equation of state for Ising-like systems.

Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, which corresponds to the limit N-->0 of an N-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed by using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions for the critical crossover functions, finding good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of our data for any finite range.

Crossover parametric equation of state for Ising-like systems

We present a parametric equation for the thermodynamic properties in the critical region of three-dimensional Ising-like systems which include fluids and fluid mixtures. The equation of state incorporates a crossover from singular Ising behavior asymptotically close to the critical point to classical (mean-field) behavior further away from the critical point, characterized by two physical crossover parameters: a coupling constant related to the strength and range of molecular interactions and a "cutoff" wave number for the critical fluctuations. In the asymptotic Ising limit, the crossover equation reproduces the most recent theoretical estimates for the universal ratios of the leading and correction-to-scaling critical amplitudes. The equation has been tested by comparing it with recent experimental thermodynamic-property data for 3He near its vapor-liquid critical point.

Crossover behavior in the isothermal susceptibility near the 3He critical point

We present high-resolution measurements of the isothermal susceptibility of pure 3He near the liquid-gas critical point. PVT measurements were performed in the single-phase region over the reduced temperature range 3 x 10(-5)<T/Tc-1<1.5 x 10(-1). The crossover behavior of the susceptibility along the critical isochore was analyzed using a field-theoretical renormalization-group calculation based on the phi4 model. A similar crossover analysis was performed on previously obtained Xe susceptibility measurements. A comparison of the rescaled susceptibility for 3He and Xe shows theoretically predicted universal crossover behavior.

Frequency-dependent shear viscosity, sound velocity, and sound attenuation near the critical point in liquids. III. The shear viscosity

We compare theoretical results for the shear viscosity calculated in one-loop order within the field-theoretical method of the renormalization-group theory with experiments. Our expressions describe the nonasymptotic crossover in both temperature and density, and allow us to consider effects of finite gravitation and finite frequency at which the experiments are performed. In doing so we treat the critical exponent x(eta) of the shear viscosity as an independent parameter, keeping the one-loop value of the Kawasaki amplitude fixed. Within our model we also consider the temperature and density dependence of the thermal diffusion including gravitational effects.