Supercritical fluids liquid theory

D. E. Martire and R. E. Boehm, Unified molecular theory of clrromatography and its application to supercritical fluid mobile phases. 1. Eluid-liquid (absorption) clrromatography , J. Phys. Chem. 91 2433-2446 (1987). 

D. E. Martue, Unified theory of absorption clrromatography gas, liquid and supercritical fluid mobile phases , ]. Liq. Chmmatogr. 10 1569-1588 (1987). 

D. P. Poe and D. E. Marthe, Plate height theory for compressible mobile phase fluids and its application to gas, liquid and supercritical fluid cliromatography , 7. Chromatogr. 517 3-29(1990). 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the complexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often necessary to treat the solvent as a continuous homogeneous medium characterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. For an example of this tool with supercritical fluids see Ting et al., 1993. 

To understand any extraction technique it is first necessary to discuss some underlying principles that govern all extraction procedures. The chemical properties of the analyte are important to an extraction, as are the properties of the liquid medium in which it is dissolved and the gaseous, liquid, supercritical fluid, or solid extractant used to effect a separation. Of all the relevant solute properties, five chemical properties are fundamental to understanding extraction theory vapor pressure, solubility, molecular weight, hydrophobicity, and acid dissociation. These essential properties determine the transport of chemicals in the human body, the transport of chemicals in the air water-soil environmental compartments, and the transport between immiscible phases during analytical extraction. 

Statistical mechanics, the science that should yield parameters like A/x , is hampered by the multibody complexity of molecular interactions in condensed phases and by the failure of quantum mechanics to provide accurate interaction potentials between molecules. Because pure theory is impractical, progress in understanding and describing molecular equilibrium between phases requires a combination of careful experimental measurements and correlations by means of empirical equations and approximate theories. The most comprehensive approximate theory available for describing the distribution of solute between phases—including liquids, gases, supercritical fluids, surfaces, and bonded surface phases—is based on a lattice model developed by Martire and co-workers [12, 13]. 

The Diels-Alder cycloaddition reaction of maleic anhydride with isoprene has been studied in supercritical-fluid CO2 under conditions near the critical point of CO2 [759]. The rate constants obtained for supercritical-fluid CO2 as solvent at 35 °C and high pressures (>200 bar) are similar to those obtained using normal liquid ethyl acetate as the solvent. However, at 35 °C and pressures approaching the critical pressure of CO2 (7.4 MPa), the effect of pressure on the rate constant becomes substantial. Obviously, AV takes on large negative values at temperatures and pressures near the critical point of CO2. Thus, pressure can be used to manipulate reaction rates in supercritical solvents under near-critical conditions. This effect of pressure on reacting systems in sc-fluids appears to be unique. A discussion of fundamental aspects of reaction kinetics under near-critical reaction conditions within the framework of transition-state theory can be found in reference [759],... 

They showed that the Peng-Robinson equation of state using mixing rules based on conformal solution theory can predict the fluid phase equilibrium of high molecular weight liquids in supercritical fluids more accurately than others (18.19). 

Dee, G.Y, The application of EoS theories to polar-nonpolar liquid mixtures, J. Supercritical Fluids, 4, 152, 1991. 

The theories of the viscosity of ordinary liquids are mainly scaling relationships there is no first-principles theory for their viscosities. An important scaling relationship is that the viscosity is related to the ratio of the occupied volume to the free volume. The usefulness of variable-pressure studies lies in their ability to probe this directly. Such studies of low-density fluids (gases and supercritical fluids), interpreted through extensions to the kinetic gas theory, have provided a quantitative understanding of their viscosities. How-... 

Anton, K. Berger, C., Ed. Supercritical Fluid Chromatography Marcel Dekker, Inc. New York, 1998. Ardrey, R.E. Liquid Chromatography—Mass Spectrometry, An Introduction Wiley New York, 2003. Berthold, et al. Micellar Liquid Chromatography Marcel Dekker, Inc. New York, 2000. Camilleri, P. Capillary Electrophoresis Theory and Practice CRC Press Boca Raton, EL, 1998. Cazes, J. Encyclopedia of Chromatography Marcel Dekker Inc. New York, 2001. 

This brief survey begins in Sec. II with studies of the aggregation behavior of the anionic surfactant AOT (sodium bis-2-ethylhexyI sulfosuccinate) and of nonionic pol-y(ethylene oxide) alkyl ethers in supercritical fluid ethane and compressed liquid propane. One- and two-phase reverse micelle systems are formed in which the volume of the oil component greatly exceeds the volume of water. In Sec. Ill we continue with investigations into three-component systems of AOT, compressed liquid propane, and water. These microemulsion systems are of the classical Winsor type that contain water and oil in relatively equal amounts. We next examine the effect of the alkane carbon number of the oil on surfactant phase behavior in Sec. IV. Unusual reversals of phase behavior occur in alkanes lighter than hexane in both reverse micelle and Winsor systems. Unusual phase behavior, together with pressure-driven phase transitions, can be explained and modeled by a modest extension of existing theories of surfactant phase behavior. Finally, Sec. V describes efforts to create surfactants suitable for use in supercritical CO2, and applications of surfactants in supercritical fluids are covered in Sec. VI. 

Stability of phase boundaries depends on the surface tension. Surface tension in a supercritical fluid system is of major importance for drying, surfactant eflicacy, and extraction. The surface tension of a gas increases with pressure and approaches zero at the critical point while the surface tension of liquid decreases with pressure resulting in dissolution of supercritical components in the liquid phase. The mefliods useful in correlating surface tension include Macleod-Sugden correlation and corresponding states theory. ... 

Both adsorption from a supercritical fluid to an adsorbent and desorption from an adsorbent find applications in supercritical fluid processing. The extrapolation of classical sorption theory to supercritical conditions has merits. The supercritical conditions are believed to necessitate monolayer coverage and density dependent isotherms. Considerable success has been observed by the authors in working with an equation of state based upon the Toth isoterm. It is also important to note that the retrograde behavior observed for vapor-liquid phase equilibrium is experimentally observed and predicted for sorptive systems. 

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