|The physical stage of a substance of fixed composition can be described by a phase diagram, as shown in Figure 1. In this pres sure-temperature (PT) diagram for CO 2 there are three lines describing the sublimation, melting, and boiling processes. These lines also define the regions corresponding to the gas, liquid, and.solid states. Points along the lines (between the phases) define the equilibrium between two of the phases. The vapor pressure (boiling) starts at the triple point (TP) and ends at the critical point (CP). The critical region has its origin at the critical point. At this point we can define a SF as any substance that is above its critical temperature (Tc) and critical pressure (Pc). The critical temperature is therefore the highest temperature at which a gas can be converted to a liquid by an increase in pressure. The critical pressure is the highest pressure at which a liquid can be converted to a traditional gas by an increase in the liquid temperature. In the so-called critical region, there is only one phase and it possesses some of the properties of both a gas and liquid. Subcritical (liquid) CO 2 is found in the triangular region formed by the melting curve, the boiling curve and the line that defines the critical pressure.
Supercritical and liquid CO 2 can both be used as solvents. In contrast to sub- Critical CO 2 (i.e., liquid), the solvating power of the supercritical fluid is highly dependent on its temperature and pressure.
Fig. 1. Phase (pressure-temperature) diagram for CO 2: CP = critical point, TP = triple point, Pc = critical pressure, 7^ = critical temperature.
Figure 2 illustrates that at low pressure the solvent power of CO 2 surprisingly decreases with rising temperature; whereas at high pressures it increases in a straightforward fashion as measured by naphthalene solubility. If we replace the parameter "pressure" by the parameter "density," the solubility-temperature relationship becomes much simpler, as shown in Figure 3. This anomaly comes about because density decreases dramatically with an increase in temperature at low pressure; whereas at higher pressure, changes in temperature have much less effect on density. Thus density, not pressure, to a first approximation is proportional to the solvent power of the SF. (Supercritical fluid technology would be better served if all scientists discussed experiments in terms of density rather than pressure.) The following trends are based upon many solubility measurements in the region from ambient conditions up to 1000 bar and 100°C:
Fig. 2. Solubility (mole fraction) of Naphthalene in CO 2 as a function of temperature at various pressures.
Fig. 3. Solubility (mole fraction) of Naphthalene in CO 2 as a function of density at various temperatures.
• Solvent power of a supercritical fluid increases with density at a given temperature
• Solvent power of a supercritical fluid increases with temperature at a given density
For a material at temperatures just above the critical temperature of the substance, liquid-like densities are rapidly approached with modest increases in pressure, (i.e., approximately 0.7-2 times the critical pressure). Higher pressures are required to attain liquid-like densities for temperatures further above the critical temperature. Table 4 lists the densities at the critical point and at 400 atm and Tc for various fluids employed for SFE. The critical densities for all fluids except xenon fall below 1 g/mL. A rough correlation of increasing critical density with increasing fluid molecular weight appears to exist. The most polar substances ( H2O and NH3) exhibit some of the lowest listed critical densities. The density at 400 atm and Tc is curiously double the critical density in most all cases where data are available. Thus one could expect a doubling of the solvent power of each fluid over this pressure range at Tc. Table 5 gives a more detailed listing of the pressure (in bar) requirements necessary to achieve specific CO 2 densities at various temperatures (Fig. 3). The listing once again emphasizes the need for higher pressures at higher temperatures to achieve a specified density. Table 6 contains conversion factors for other pressure units used in SFE/SFC.
From van der Waal's Law of Corresponding States18 one would expect that these temperature-pressure-density relationships would be applicable to all substances. In this regard, it is convenient to define the PT region in terms of reduced pressure (P acbl/Pc = PR), reduced temperature (7 actual/Tc = Tr) and re-
Table 4 Densities (g/mL) of Selected Fluids
"At Pc, Tc.
'Density calculated from compressibility data at approximately Tc and 400
Table 5 Density-Temperature-Pressure Relationship for CO 2
Pressure is given in bar.
Duced density (pacluai/pc = pR) (Fig. 4).* The region just above 7*R = 1.0, PR = 1.0 is the traditional operational supercritical region. At high values of TR the fluid density may be reduced to the point where solvent properties are no longer favorable if restricted by the pump to a relatively low pressure. Because of safety concerns arising from equipment limitations, reduced pressures above 5 or 6 may be difficult to achieve in the analytical laboratory. The region of condensed phase between TR= 1.0 and TR = 0.95 is termed the subcritical (or near-critical)
*P and p may be in any units. 7" must be in Kelvin. TABLE 6 SFC/SFE Pressure Unit Conversion Factors
Table 6 SFC/SFE Pressure Unit Conversion Factors
"Strictly, kg/cm2 is not a pressure unit. Its use assumes standard acceleration of gravity. region. A continuum of properties between the subcritical and supercritical regions exists and in many extraction experiments using modified SFs, it is not uncommon for conditions to become subcritical.
It is important to recognize, regardless of the fluid, how density (i.e., solvat-ing power) changes with changes in pressure/temperature. As Figure 4 attests, a very small increase in pressure at TR = 1.0-1.2 results in a dramatic increase in density. The same change in pressure at TR > 1.5 hardly changes the fluid density. Such knowledge is important when performing SF fractionation, where small incremental changes in density are invoked with successive extractions, as opposed to general analytical SFE, where a single density is employed. One should also note that the density of the SF practically never exceeds the density of the comparable liquid regardless of the pressure. The density of liquid CO 2 is generally considered to be approximately 0.92 g/mL, for example.
Fig. 4. Reduced pressure (PR) - reduced density (pR) diagrams at various reduced temperatures (7"R). SCF = supercritical fluid region. NCL = near critical liquid region.
Fig. 5. Solubility (mole fraction) of naphthalene in ethylene versus pressure at 12"C and 35^C. Tt for ethylene = 9.3"C.
The previous points are illustrated by the solubility behavior of solid naphthalene in supercritical ethylene (Tc = 9.3°C, Pc = 49.8 atm) at 12°C and 35°C versus pressure (Fig. 5).20 The 35°C isotherm (TK = 1.09) is less sensitive to pressure changes in the region near 50 atm than is the 12°C isotherm (TR = 1.01). In other words, changes in density (or solvent power) are more pronounced with changes in pressure at 12°C in the vicinity of the critical point than at 35°C. This results in naphthalene solubility being greater at lower temperatures up to 100 atm. This behavior is referred to as retrograde vaporization. The much lower solubility at 35°C, at pressures less than 100 atm, reflects the large decrease in ethylene density relative to its density at 12°C (100 atm). At pressures greater than 150 atm, the difference in the densities of SF ethylene at 12 and 35°C is not very large. The higher naphthalene solubility at 35°C and at elevated pressure can be explained only by the increase in sublimation pressure of naphthalene on heating from 12 to 35°C. Thus two competing factors affect the solubility of solids in SFs:
• SF density
• Solid sublimation pressure
An increase in either parameter while holding the other parameter constant will result in enhanced solubility. The increase in density enhances solute-fluid interaction. The increase in analyte sublimation pressure decreases solute-solute interaction. A comparison of the experimental solubility of naphthalene in SF eth-ylene versus the calculated solubility under the same conditions but assuming ethylene behaves as an ideal gas is impressive. For example, at 100 atm and 12°C, the ratio of observed naphthalene solubility to calculated naphthalene solubility is approximately 16,000 to I.
The phase diagram in Figure 1 shows that there is no phase transition between either the SF and the liquid phase or the SF and the gaseous phase because there are no phase transition lines corresponding to the boiling line. This means that no physical property of the phase undergoes a sudden change when moving from the supercritical to the liquid or gaseous state. The rules given previously for the solvent power of a SF must therefore be valid in a limited way for the liquid or gaseous solvent also, as long as they are not applied too far from the region where they have been experimentally verified.