Solid-SCF system

Shown in figure 3.12a is the P-T-x diagram for the type of solid-SCF system described in the previous paragraph. The phase behavior depicted in figure 3.12c is observed if a P-x diagram is experimentally determined at Ti, a temperature below the critical temperature of the lighter component Tc,- At low pressure solid-vapor equilibria are observed until the three-phase SLV line is intersected. Three equilibrium phases exist at this pressure a pure solid, a liquid, and a gas. 

Numerous examples of this type of solid-SCF phase behavior are reported in the literature. Normally this type of phase behavior occurs for mixtures whose components are chemically similar. Figure 3.13 shows one example of such a solid-SCF system (Donnelly and Katz, 1954). 

We can now explain the sudden increase in the solubility of naphthalene in supercritical ethylene reported at 50 bar and 12°C. This solubility increase is a result of being very close to the LCEP for this system, which is 51.9 bar and 10.7°C (Diepen and Scheffer, 1948a). As shown in table 3.3, the LCEP usually occurs very close to the critical point of the pure SCF for most of the solid-SCF systems reported in the literature even though there is a large solubility enhancement, the amount of solid in the SCF phase at the LCEP is quite low. 

The differences in the solubility behavior of the naphthalene-ethylene and biphenyl-carbon dioxide systems near their mixture UCEPs can be readily explained by considering the P-T trace of the three-phase SLV line for each system. Shown in figure 3.16b is the P-T trace of the SLV line along with the P-x isotherms for the naphthalene-ethylene system. Similar diagrams for the biphenyl-carbon dioxide system are shown in figure 3.17b. The biphenyl-carbon dioxide SLV line exhibits a temperature minimum with increasing pressure, whereas the naphthalene-ethylene SLV line exhibits no such minimum. The different shapes of the SLV lines are a consequence of the amount of like or dislike the components have for each other. The reason for the differences in the solubility behavior for these two systems near their UCEPs is directly related to the mutual solubility of the mixture components. Let us examine the phase behavior characteristics of these two solid-SCF systems in more detail. 

A number of solid-SCF systems have been reported in which a temperature minimum exists in the three-phase SLV line (van Hest and Diepen, 1963 McHugh and Yogan, 1984). Some examples are shown in figure 3.21. The UCEP for the methane-naphthalene system is at very high pressures compared to the carbon dioxide-naphthalene system. The large difference in UCEP conditions for these two systems is a direct manifestation of the much reduced solvent power of methane compared to carbon dioxide. Simply put, methane is behaving more like an ideal gas, since its reduced temperature, Tr ==... 

Solid propellants, fractionation of polymer binders for, 250-257 Solid-SCF calculations, 127-134 Solid-SCF equilibria, 45, 59, 61, 131, 133 Solid-solid-SCF systems, 80 Solomon, H. J., 316, 317 Solubility, 367... 

The effect of temperature on solubility is more complex and involves both a consideration of the solute vapor pressure as well as the density of the SCF. The solubility isotherms shown in Figure 1.2-9 are typical of most solid-SCF systems in that they intersect within a narrow range of pressure. For any two isotherms, the point of intersection, or crossover pressure, represents a change in the temperature dependence of solubility. 

Most reactions that have been investigated using PTC in supercritical fluids have been solid-SCF systems, not liquid-SCF. The first published example of PTC in an SCF is the displacement reaction of benzyl chloride 1 with potassium bromide in supercritical carbon dioxide (SCCO2) with 5 mol % acetone, in the presence of tetraheptylammonium bromide (THAB) [19-20] (Scheme 4.10-1) to yield benzyl bromide 2. The effects on reaction rate of traditional PTC parameters, such as agitation, catalyst type, temperature, pressure, and catalyst concentration were investigated. The experimental technique is described below. PTC appeared to occur between an SCF phase and a solid salt phase, and in the absence of a catalyst the reaction did not occur. With an excess of inorganic salt, the reaction was shown to follow pseudo-first order kinetics. 

Figure 2. Depression of eutectic melting point by a supercritical fluid in an A-B-SCF system, where A,B are immiscible solids and Pj < Pa < Ps- 5 upper lines represent first freezing and the lower lines represent first melting (o Pi A - Pa, - Ps) ...

Type II (Solid-Fluid) System. In type II systems (when the solid and the SCF component are very dissimilar in molecular size, structure, and polarity), the S-L-V line is no longer continuous, and the critical (L = V) mixture curve also is not continuous. The branch of the three-phase S-L-V line starting with the triple point of the solid solute does not bend as much toward lower temperature with increasing pressure as it does in the case of type I system. This is because the SCF component is not very soluble in the heavy molten solute. The S-L-V line rises sharply with pressure and intersects the upper branch of the critical mixture (L = V) curve at the upper critical end point (LfCEP), and the lower temperature branch of the S-L-V line intersects the critical mixture curve at the lower critical end point (LCEP). Between the two branches of the S-L-V line there exists S-V equilibrium only (13). 

SCF and the solubility of the solid in the SCF. Therefore, the isothermal solubility curves deviate from linearity as the SCF approaches a highly compressed constant density, at which point the solid solubility reaches a limiting value. The solubility curves also deviate from linearity as the UCEP for the solid-SCF mixture is approached. This deviation from linearity near the system UCEP is clearly shown in the work of Schmitt and Reid (1984) for the naphthalene-ethylene system. Finally, the solubility curves will deviate from linearity if there are specific solute-solvent interactions, such as acid-base interactions or hydrogen bonding (Schmitt, 1984). 

Another series of cubic clusters of general composition M9(/.i4-E)6Lg (M = Ni or Pd E = Ge, P, As, Te) incorporates a metal atom in the center of the cube. The bonding in these cluster compounds is also analyzed by means of EH and SCF-MS-Xa calculations. The number of MVE ranges from 130 to 121. Examination of the electronic structures has shown that the cluster compounds are at the interface between molecular and solid state materials. In the cubic clusters, closed-shell electron configurations of stable molecular systems with a significant HOMO-LUMO gap coexist with open-shell electron configurations of solid-state systems with no significant gap between the skeletal frontier orbitals. 

In separation equilibrium involving a supercritical fluid (SCF), the two systems commonly used are solid-SCF and liquid-SCF. A solute or solutes are distributed between the two immiscible phases. A supercritical fluid is normally... 

The Rh-Rh distance is 3.12 A, long compared with Rh-Rh single bonds (2.624A in Rh2(MeCN) J([, 2.73 A in Rh4(CO)12) there is a weaker (3.31 A) intermolecular attraction. Dipole moment and IR studies indicate that the structure is retained in solution and is, therefore, a consequence of electronic rather than solid-state packing effects. Furthermore, it is found for some other (but not all) [RhCl(alkene)2]2 and [RhCl(CO)(PR3)]2 systems. SCF MO calculations indicate that bending favours a Rh-Cl bonding interaction which also includes a contribution from Rh—Rh bonding [56b]. 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

Supercritical fluids represent a different type of alternative solvent to the others discussed in this book since they are not in the liquid state. A SCF is defined as a substance above its critical temperature (Tc) and pressure (Pc)1, but below the pressure required for condensation to a solid, see Figure 6.1 [1], The last requirement is often omitted since the pressure needed for condensation to occur is usually unpractically high. The critical point represents the highest temperature and pressure at which the substance can exist as a vapour and liquid in equilibrium. Hence, in a closed system, as the boiling point curve is ascended, increasing both temperature and pressure, the liquid becomes less dense due to thermal expansion and the gas becomes denser as the pressure rises. The densities of both phases thus converge until they become identical at the critical point. At this point, the two phases become indistinguishable and a SCF is obtained. 

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