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.     

Local density augmentation and dynamic properties of hydrogen-and non-hydrogen-bonded supercritical fluids: a molecular dynamics study

The local density inhomogeneities in neat supercritical fluids were investigated via canonical molecular dynamics simulations. The selected systems under investigation were the polar and hydrogen-bonded fluid methanol as well as the quadrupolar non-hydrogen-bonded carbon dioxide one. Effective local densities, local density augmentation, and enhancement factors were calculated at state points along an isotherm close to the critical temperature of each system (T(r)=1.03). The results obtained reveal strong influence of the polarity and hydrogen bonding upon the intensity of the local density augmentation. It is found that this effect is sufficiently larger in the case of the polar and associated methanol in comparison to those predicted for carbon dioxide. For both fluids the local density augmentation values are maximized in the bulk density region near 0.7rho(c), a result that is in agreement with experiment. In addition, the local density dynamics of each fluid were investigated in terms of the appropriate time correlation functions. The behavior of these functions reveals that the bulk density dependence of the local density reorganization times is very sensitive to the specific intermolecular interactions and to the size of the local region. Also, the estimated local density reorganization time as a function of bulk density of each fluid was further analyzed and successfully related to two different time-scale relaxation mechanisms. Finally, the results obtained indicate a possible relationship between the single-molecule reorientational dynamics and the local density reorganization ones.     

Analysis to obtain precise density fluctuation of supercritical fluids by small-angle X-ray scattering

A procedure of analysis for small-angle X-ray scattering (SAXS) data has been established to obtain density fluctuation of supercritical fluids near the critical point. It is indispensable for the certain analysis to utilize both of high-quality SAXS data measured under stable thermodynamic condition and accurate P–ρ–T data in supercritical region. As a standard example, SAXS measurements have been performed for supercritical CO₂, which is a suitable sample satisfying the condition for both experiment and analysis. The measurements were carried out along four isothermal conditions at reduced temperature of T_r = T/T_c = 1.020, 1.022, 1.043 and 1.064. Comparing the experimental density fluctuation with calculated one from the most reliable equation of state, the differences are within 8% at most.     

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.     

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: a density functional approach

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.     

Degradation of polycaprolactone in supercritical fluids

The degradation of polycaprolactone (PCL) was studied in subcritical and supercritical toluene from 250 to 375 °C at 50 bar. The degradation was also investigated in various solvents like ethylbenzene, o-xylene and benzene at 325 °C and 50 bar. The effect of pressure on degradation was also evaluated at 325 °C at various pressures (35, 50 and 80 bar). The variation of molecular weight with time was analyzed using gel permeation chromatography and modeled using continuous distribution kinetics to evaluate the degradation rate coefficients. PCL degrades by random chain scission in subcritical conditions (250-300 °C) and by chain end scission (325-375 °C) in supercritical conditions in toluene. The degradation of PCL in other solvents at 325 °C was by chain end scission under both subcritical and supercritical conditions indicating that the mode of scission depends on the temperature and not on the supercriticality of the solvent. The thermogravimetric analysis of PCL was investigated at various heating rates (2-24 °C/min) and the activation energy was determined using Friedman, Ozawa and Kissinger methods. It was shown that PCL degrades by random scission at lower temperatures and by chain end scission at higher temperatures again indicating that the mode of scission is dependent on the temperature.     

Use of supercritical fluids in inorganic analysis

The possibilities, advantages, shortcomings, and prospects of using supercritical fluids for separating and extracting metal complexes with organic reagents are considered. The theoretical bases of supercritical fluid chromatography and factors influencing the separation of metal complexes (nature of the organic reagent, solubility of reagents and complexes in a supercritical fluid, type of column, motionless phase, addition of a modifier into the mobile phase, and the test solvent) are discussed. The processes occurring in complexes during chromatography are discussed. The bases of supercritical fluid extraction and factors influencing extraction of metals (nature and solubility in a supercritical fluid of an organic reagent and complexes; concentration and ways of introducing the reagent into the system; addition of the modifier, water, and surfactants; the collector; and the matrix) are considered. The possibilities of methods for determining metals in various objects are shown.     

Solubility of solid mixtures in supercritical fluids

Kurnik, R.T. and Reid, R.C., 1982. Solubility of solid mixtures in supercritical fluids. Fluid Phase Equilibria, 8: 93-105Supercritical fluids are receiving widespread attention as possible extraction agents for relatively non-volatile solids and liquids. Previous studies of the solubility of solids in supercritical fluids have been limited to pure solids. These pure-component data are interesting and indicate novel properties of supercritical fluids in this respect. The more general problem, however, lies in determining the solubility of multicomponent solids in supercritical fluids. Experimental data have now been obtained on the solubilities of binary, solid hydrocarbon mixtures in both supercritical carbon dioxide and supercritical ethylene. Most of the behavior exhibited by pure solids in supercritical fluids still exists for multicomponent solid solute systems (e.g., retrograde solidification, solubility extrema), but new phenomena were also found. The most interesting finding is that the solubility of a solid component when in a multicomponent solute system can be as much as 300% higher than the component solubility in a pure solid system at the same operating conditions. The multicomponent-solid-fluid data usually correlate well with thermodynamic theory.     

Comparison of eluents in supercritical fluid chromatography as based on density and free volume

A comparative study of chromatographic properties of different supercritical eluents has been performed by considering the retention at equal density or at equal free volume for different mobile phases. At equal density, the temperature dependence of the capacity ratios of aromatic hydrocarbons is the same for different alkane mobile phases, whereas significant deviations are observed when carbon dioxide is employed as the mobile phase. At equal free volume, a comparison of the capacity ratios measured in carbon dioxide and in alkane eluents showed a pronounced similarity for the different mobile phases when the free volume was low, i.e., at high densities. With increasing free volume, the chemical differences of the alkanes on the one hand and carbon dioxide on the other become more apparent in their elution behavior. Furthermore, it is demonstrated that the free volume can also be used as a reference basis for the data of solvatochromic shift experiments.     

Efficient cooling in supersonic jet expansions of supercritical fluids: CO and CO2

Pulsed, supersonic beams of pure carbon monoxide and carbon dioxide at stagnation conditions above their critical point have been investigated by time-of-flight measurements as a function of pressure and temperature. Although both molecules form clusters readily in adiabatic expansions, surprisingly large speed ratios (above 100) indicative of very low translational temperatures (below 0.1 K) have been achieved. In particular, the supersonic expansion of CO(2) at stagnation temperatures slightly above the phase transition to the supercritical state results in unprecedented cold beams. This efficient cooling is attributed to the large values of the heat capacity ratio of supercritical fluids in close vicinity of their critical point.     

Phase equilibrium modeling of triglycerides in supercritical fluids

To design a reactor and separator for a supercritical biodiesel process, phase equilibria of multi-component mixtures in supercritical fluids should be determined using group contribution with association equation of state (GCA-EOS) as a thermodynamics method. The model is considered for two systems of reactants and products. System 1 is comprised of methanol and triglycerides from two sources (palm and Jatropha oils); and System 2 is unconverted methanol, FAME (product) and glycerol (by-product). Pressure and temperature diagrams were developed at different mole fraction of methanol (x_MeOH). As x_MeOH increased, the critical temperature (T_c) and pressure (p_c) increased. The increasing temperature causes the immiscibility region and the amount of methanol at the plait point to decrease. The maximum plait point pressure was observed at 19.20 MPa for palm and 19.33 MPa for Jatropha oil systems.     

Oscillating repulsive force between macroscopic surfaces as a consequence of the fluctuation of the density in the gap region

We try to explain the short-range repulsive force between surfaces as a consequence of a decrease in the configurational entropy of liquid molecules in the gap region as the width of the gap decreases. A simple model shows that the density has an oscillating variation when the surfaces are pushed towards each other. As a consequence, an oscillating repulsive force appears between the macroscopic surfaces, which is the result of a loss of configurational freedom of the liquid molecules because of their orientation in the gap. Received: 14 August 2000 Accepted: 30 January 2001     

Enhancement of Structural fluctuation in the region connecting two kinds of critical points in temperature-pressure-composition three-dimensional phase diagram: Raman studies of benzene/CO2 binary systems up to supercritical region

Pressure dependence of Raman spectra of benzene/CO2 two-component systems was systematically studied at different temperatures and compositions. We estimated the magnitude of inhomogeneous component in Raman bandwidth to get information on the structural fluctuation in the system. It was found that the inhomogeneous bandwidth attains a maximum on an isothermal plane in the temperature-pressure-composition three-dimensional phase diagram when the state point crosses the line connecting the region where the density fluctuation is large (the vicinity of the critical point of neat CO2) and the region where the concentration fluctuation in a binary system is enhanced (the vicinity of the critical solution point). By accumulating such data, we found that the points of large structural fluctuation comprise a sheet that includes the extension line of the gas-liquid equilibrium line in the phase diagram of neat CO2 and the line connecting critical solution points of the two-component system at different temperatures. Interaction between benzene and CO2 molecules in the supercritical region is briefly discussed.     

Significant substitution effects in dipolar and non-dipolar supercritical fluids

Vibrational Raman spectra of C=C stretching modes of ethylene derivates (cis-C(2)H(2)Cl(2), cis-stilbene, and trans-stilbene) were measured in supercritical fluids along an isotherm as functions of their densities. The substitution effect of the Raman shift is so significant that a difference among three solutes can be 20 times and is observed similarly in dipolar (CHF(3)) and non-dipolar (CO(2)) fluids. In particular, the shifts of trans-stilbene were enormously large among all systems for studies of vibrational spectroscopies of supercritical fluids and were equivalent to those of typical hydrogen-bonded fluids. Such large shifts arising from the significant attractive energy between solute and solvent molecules were attributed to a site-selective solvation around a phenyl group, which was driven by a dispersion force in the absence of steric hindrance. We found that the absence of steric hindrance causes the significant local density augmentation. To the best of our knowledge, Raman experiments and their theoretical analysis are the first ones quantifying how the difference of steric hindrance produces solvation structures in solution as well as supercritical solutions.     

Properties and reactions of charged species in nonpolar supercritical fluids

This review focuses on the properties and reactions of charged species in supercritical fluids. The techniques of pulse conductivity and transient absorption are used to follow the behavior of charged species. We begin with a discussion of the mobilities, yields, and energy levels of electrons. Studies of the pressure dependence of electron attachment reactions lead to information on the magnitude of activation volumes. This as well as diffusion and energetics are factors that influence the rates of electron attachment. The free energy changes in electron attachment-detachment equilibrium reactions decrease rapidly at pressures where the compressibility maximizes. The transport properties of ions in supercritical fluids are also discussed, as these studies provide a straightforward indication of the degree of interaction between ions and the medium. We conclude with a review of electron transfer reactions in supercritical fluids.     

Thermodynamic modeling of the solubilities of fatty acids in supercritical fluids

Modeling the solubilities of fatty acids is important because these compounds are used in various industries. In this work, a thermodynamic model based on Redlich–Kwong equation of state with Kwak–Mansoori mixing rules was used to model the solubilities of fatty acids in supercritical carbon dioxide. The model uses only one adjustable parameter and this parameter varies linearly with the chain length of the fatty acid. Therefore, this model can be potentially used to predict the solubilities of various fatty acids in supercritical carbon dioxide.     

Simultaneous extraction and derivatization of 2-chlorovinylarsonous acid from soils using supercritical and pressurized fluids

Supercritical carbon dioxide and pressurized fluids are compared for the extraction with in situ derivatization of 2-chlorovinylarsonous acid (CVAA) from a series of seven spiked soils. Samples are allowed to age (up to 42 days) and periodically extracted. Sample ageing leads to a recovery decrease due to the development of strong interactions between CVAA and matrix active sites, as time elapses. A similar behavior is observed when usual ultrasonic extraction is performed. Supercritical fluid extraction (SFE) with in situ derivatization leads to the highest recovery. Moreover, SFE allows a solvent consumption reduction. A limit of detection of 0.2 microg/g is reached with the SFE method.     

Density dependence of the Stokes shift and solvent reorganization energy in supercritical fluids

The Stokes shifts of coumarin 153 (C153) in CF₃H, CO₂ and C₂H₆ have been measured at several reduced densities (0.3–1.8). For C153 in CF₃H, the shifts increase with a decrease in reduced density and show a maximum value at a reduced density of 0.5. In non-polar solvents, the shifts are not dramatically altered as a function of reduced density but slightly increase with a decrease in the reduced density.