Supercritical densities

Junkel-Vives GC, Abdallah Jr. J, Blasco F, Dorchies F, Caillaud T, Bonte C, Stenz C, Salin F, Faenov AYa, Magunov AI, Pikuz TA, Skobelev IYu (2002) Evidence of supercritical density in 45-fs-laser-irradiated Ar-cluster plasmas. Phys. Rev. A 66 0332041-0332045... 

Figure 16-9. Snapshots of molecular configurations for the solvated electron polymer at two supercritical densities of water at 645 K. Left 1.0 g/cm3 Right. 0.05 g/cm3...

At reservoir conditions, the fluid is supercritical (density approximately 385 kg/m3 or 24.0 lb/ft3) and as we move up the injection well the fluid becomes a liquid (the pressure is greater than the bubble point pressure). 

Cases la, lb, and Ic illustrate the difficulties which can arise if one incorporates experimental values of Zc into a cubic equation of state. Excellent representation of the critical isotherm is obtained up to a reduced density of about 0.4, because of the realistic value for Bc built into the equation. Between pT = 0.4 and 1.0, the predicted pressures are a little low, but not unreasonably so. For supercritical densities, however, the quality of the representation deteriorates badly, increasingly so the smaller one makes parameter bc. A large value of bc is not the answer to the problem as indicated by the results of Case Ic, a value of bc = 0.150 improves the predictions up to pT = 1.8, but yields negative pressures for the two highest densities. The reason for this behavior is that for this case the limiting reduced volume (the value of Vr for which Pr —> oo ) is Vr = c/fc = 0.150/0.291 = 0.5155, a number larger than the last two volume entries in the table for Vr < 0.5155, one lands on a physically meaningless branch of the isotherm. 

In order to interpret and offer an explanation for the weak temperature dependence exhibited by I>2i( P Pc) w analyze its link with two closely related quantities, (V (SR) and p i(C"2 - Cfi) (e.g., see Equation 8.6 and Equation 8.10), that also exhibit negligible temperature dependence for supercritical densities as illustrated in Eigure 8.11. The link becomes clearer if we rewrite the quantity >21, after invoking Equation 8.4 through Equation 8.8, in the following four alternative forms. 

Figure 4. Pressure dependence of the average number of hydrogen bonds per water molecule according to the geometric (G), energetic (E), and combined (E+G) criteria. The corresponding open symbols for ambient water are plotted at P = l(X)0MPa, at which the supercritical density is Ig/cm. ...

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

The second type of solution polymerization concept uses mixtures of supercritical ethylene and molten PE as the medium for ethylene polymerization. Some reactors previously used for free-radical ethylene polymerization in supercritical ethylene at high pressure (see Olefin POLYMERS,LOW DENSITY polyethylene) were converted for the catalytic synthesis of LLDPE. Both stirred and tubular autoclaves operating at 30—200 MPa (4,500—30,000 psig) and 170—350°C can also be used for this purpose. Residence times in these reactors are short, from 1 to 5 minutes. Three types of catalysts are used in these processes. The first type includes pseudo-homogeneous Ziegler catalysts. In this case, all catalyst components are introduced into a reactor as hquids or solutions but form soHd catalysts when combined in the reactor. Examples of such catalysts include titanium tetrachloride as well as its mixtures with vanadium oxytrichloride and a trialkyl aluminum compound (53,54). The second type of catalysts are soHd Ziegler catalysts (55). Both of these catalysts produce compositionaHy nonuniform LLDPE resins. Exxon Chemical Company uses a third type of catalysts, metallocene catalysts, in a similar solution process to produce uniformly branched ethylene copolymers with 1-butene and 1-hexene called Exact resins (56). 

Certain boilers employ forced circulation, whereby a pump helps impart the circulation through the downcomer lines to the waterwaH header, particularly to improve or control circulation at low loads. Forced-circulation pumps are also required in high pressure and supercritical pressure boilers, because once the pressure within a boiler approaches the critical pressure, 22.1 MPa (3208 psia), the densities of the water and steam become similar, limiting or eliminating the potential for natural circulation. 

Production of net-shape siUca (qv) components serves as an example of sol—gel processing methods. A siUca gel may be formed by network growth from an array of discrete coUoidal particles (method 1) or by formation of an intercoimected three-dimensional network by the simultaneous hydrolysis and polycondensation of a chemical precursor (methods 2 and 3). When the pore Hquid is removed as a gas phase from the intercoimected soHd gel network under supercritical conditions (critical-point drying, method 2), the soHd network does not coUapse and a low density aerogel is produced. Aerogels can have pore volumes as large as 98% and densities as low as 80 kg/m (12,19). 

A paiticularly attiactive and useful feature of supeicritical fluids is that these materials can have properties somewhere between those of a gas and a hquid (Table 2). A supercritical fluid has more hquid-hke densities, and subsequent solvation strengths, while possessiag transport properties, ie, viscosities and diffusivities, that are more like gases. Thus, an SCF may diffuse iato a matrix more quickly than a Hquid solvent, yet still possess a Hquid-like solvent strength for extracting a component from the matrix. 

In terms of the solubilities of solutes in a supercritical phase, the following generalizations can be made. Solute solubiUties in supercritical fluids approach and sometimes exceed those of Hquid solvents as the SCF density increases. SolubiUties typically increase as the pressure is increased. Increasing the temperature can cause increases, decreases, or no change in solute solubiUties, depending on the temperature effect on solvent density and/or the solute vapor pressure. Also, at constant SCF density, a temperature increase increases the solute solubiUty (16). 

The fugacity coefficient of thesolid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity ia brackets ia equation 2, is defined as the real solubiUty divided by the solubihty ia an ideal gas. The solubiUty ia an ideal gas is simply the vapor pressure of the sohd over the pressure. Enhancement factors of 10 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 10. Solubihty data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting ia a fairly linear relationship (52). 

Reactions. Supercritical fluids are attractive as media for chemical reactions. Solvent properties such as solvent strength, viscosity, diffusivity, and dielectric constant may be adjusted over the continuum of gas-like to Hquid-like densities by varying pressure and temperature. Subsequently, these changes can be used to affect reaction conditions. A review encompassing the majority of studies and apphcations of reactions in supercritical fluids is available (96). 

Supercritical Fluid Chromatography. Supercritical fluid chromatography (sfc) combines the advantages of gc and hplc in that it allows the use of gc-type detectors when supercritical fluids are used instead of the solvents normally used in hplc. Carbon dioxide, -petane, and ammonia are common supercritical fluids (qv). For example, carbon dioxide (qv) employed at 7.38 MPa (72.9 atm) and 31.3°C has a density of 448 g/mL. 

For supercritical temperatures, it is satisfactory to ever-higher pressures as the temperature increases. For pressures above the range where Eq. (4-190) is useful, but below the critical pressure, the virial expansion in density truncated to three terms is usually suitable ... 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

Thermodynamic Properties The variation in solvent strength of a supercritical fluid From gaslike to hquidlike values may oe described qualitatively in terms of the density, p, or the solubihty parameter, 6 (square root of the cohesive energy density). It is shown For gaseous, hquid, and SCF CO9 as a function of pressure in Fig. 22-17 according to the rigorous thermodynamic definition ... 

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