Static inhomogeneity of supercritical ethylene studied by small-angle X-ray scattering

Structure and Properties of Supercritical Water: Experimental and Theoretical Characterizations

Water in the supercritical region of the phase diagram exhibits a markedly different structure and properties from that at ambient conditions, which is useful in controlling chemical reactions. Nonetheless, the experimental, as well as theoretical, characterization of the substance is not easy because the region is next to the critical point. This article reviews the experimental as well as theoretical studies on water in the supercritical region and its properties as a solvent for chemical reactions, as carried out by the authors and based on small-angle X-ray scattering and the statistical mechanics theory of molecular liquids, also known as reference interaction-site model (RISM) theory.

Structural difference between liquidlike and gaslike phases in supercritical fluid

Density fluctuation structures of supercritical carbon dioxide along the isothermal and isochoric lines were observed with small-angle neutron scattering (SANS). All the scattering intensities in the low-Q range were well described with the Ornstein-Zernike (OZ) equation. It was confirmed that there exists a locus where the OZ correlation length and scattering intensity at Q=0 exhibit extrema on the isothermal lines: this locus, named the ridge, was interpreted as the boundary by which the supercritical state is divided into liquidlike and gaslike phases. In order to clarify the difference of the fluctuation structure between the liquidlike and the gaslike phases, a real-space molecular distribution was obtained with a reverse Monte Carlo (RMC) method. Number density distributions of CO2 molecules at all measured states were calculated with the real-space molecular distributions obtained. In addition, the statistical parameters of the number density distributions, the standard deviations, and the skewnesses, were examined. The standard deviations of the number density distributions almost coincide with the results of the OZ analysis. On the other hand, the skewnesses, which describe the asymmetric nature of the number density distribution, clearly showed a difference between the two phases: the skewness became negative in the liquidlike phase, positive in the gaslike phase, and almost zero at the nearest state to the ridge in all isotherms. It was proved with simple equations of statistical mechanics that the skewness is described as the first differential of the magnitude of the density fluctuation with respect to the pressure. We conclude that the skewness, obtained with a RMC analysis for SANS data, is an important structural parameter distinguishing between the liquidlike and gaslike phases.

Simulations of solvation free energies and solubilities in supercritical solvents

Computer simulations are used to study solvation free energies and solubilities in supercritical solvents. Solvation free energies are calculated using the particle insertion method. The equilibrium solvent configurations required for these calculations are based on molecular dynamics simulations employing model solvent potentials previously tuned to reproduce liquid-vapor coexistence properties of the fluids Xe, C(2)H(6), CO(2), and CHF(3). Solutes are represented by all-atom potentials based on ab initio calculations and the OPLS-AA parameter set. Without any tuning of the intermolecular potentials, such calculations are found to reproduce the solvation free energies of a variety of typical solid solutes with an average accuracy of +/-2 kJmol. Further calculations on simple model solutes are also used to explore general aspects of solvation free energies in supercritical solvents. Comparisons of solutes in Lennard-Jones and hard-sphere representations of Xe show that solvation free energies and thus solubilities are not significantly influenced by solvent density fluctuations near the critical point. The solvation enthalpy and entropy do couple to these fluctuations and diverge similarly to solute partial molar volumes. Solvation free energies are also found to be little affected by the local density augmentation characteristic of the compressible regime. In contrast to solute-solvent interaction energies, which often provide a direct measure of local solvent densities, solvation free energies are remarkably insensitive to the presence of local density augmentation.

Density dependences of long-range fluctuations and short-range correlation lengths of CHF3 and CH2F2 in supercritical states

Small-angle x-ray scattering (SAXS) measurements are carried out for supercritical polar fluorocarbons, CHF3 and CH2F2, along the isotherm of 1.04 in reduced temperatures with the density range from 0.3 to 1.5 in reduced units. A novel apparatus for determination of absorption factors of the sample fluids is used in the present measurements. The apparatus enables us to detect simultaneously the accurate factors during the observation of the SAXS signals. Long-range fluctuations such as density fluctuations and correlation lengths are evaluated from the obtained SAXS data. The reduced correlation lengths are obtained by normalization by each molecular size, in order to discuss the fluctuations independent of the difference of the individual molecular size. The density fluctuations and the reduced correlation lengths of CHF3 and CH2F2 are compared with those of CO2 and H2O. The results are as follows: H2O>CH2F2>CHF3 approximately CO2 in the order of magnitude. The fluctuations of CH2F2 are significantly distinguishable from those of CHF3 and show intermediate aspect between H2O and a group of CO2 and CHF3. In addition, the short-range correlation lengths, i.e., the Ornstein-Zernike direct correlation lengths, are firstly discussed from both viewpoints of density and substance dependences. The reduced short-range correlation lengths normalized by individual molecular size are found to trace a universal curve as a function of the reduced density.

Time Evolution of Density Fluctuation in Supercritical Region. I. Non-hydrogen-bonded Fluids Studied by Dynamic Light Scattering

The time evolution of the density fluctuation of molecules inhomogeneously dispersing in a mesoscopic volume is investigated by dynamic light scattering in several fluids in supercritical states. This study is the first time-domain investigation to compare the dynamics of density fluctuation among several fluids. The samples used are non-hydrogen-bonded fluids in the supercritical states: CHF(3), C(2)H(4), CO(2), and xenon. These four molecules have different properties but are of similar size. Under these conditions, the relationship between dynamic and static density inhomogeneities is studied by measuring the time correlation function of the density fluctuation. In all cases, this function is characterized by a single exponential function, decaying within a few microseconds. While the correlation times in the four fluids show noncoincidence, those values agree well with each other when scaled to a dimensionless parameter. From the results of this scaling based on the Kawasaki theory and Landau-Placzek theory, the relation between dynamics and static structures is analyzed, and the following four insights are obtained: (i) viscosity is the main contributor to the time evolution of density fluctuation; (ii) the principle of corresponding state is observed by the use of time-domain data; (iii) the Kawasaki theory and the Landau-Placzek theory are confirmed to be applicable to polar, nonpolar, and nondipolar fluids that have no hydrogen bonding, at temperatures relatively far from critical temperature; and (iv) the density fluctuation correlation length and the value of density fluctuation are estimated from the time-domain data and agree with the values from other experiments and calculations.

Dynamics of Density Fluctuation of Supercritical Fluid Mapped on Phase Diagram

A time evolution of polar molecules inhomogeneously dispersing in mesoscale is investigated by dynamic light scattering around the gas-liquid critical point. The dynamics evaluated on phase diagrams produces a contour map of critical slowing down and suggests a ridge to be a trace of intermediate lines between gas and liquid states. A good coincidence between dynamics and static inhomogeneities is confirmed in the wide density, and it is consistent with theoretical expressions.