Anal. Chem. 1996, 68, 4474-4480
Thermodynamic Prospects of Alternative Refrigerants as Solvents for Supercritical Fluid Extraction Michal Roth
Institute of Analytical Chemistry, Academy of Sciences of the Czech Republic, CZ-61142 Brno, Czech Republic
Wide-range thermodynamic formulations for four hydrofluorocarbons (R32, R125, R134a, and R152a) and two hydrochlorofluorocarbons (R22 and R123) are employed to derive the properties relevant to the use of these alternative refrigerants as solvents in supercritical fluid extraction (SFE). The calculated solubility parameters indicate that, in the high-pressure, low-compressibility region, the solvating powers of all the six refrigerants are superior to that of carbon dioxide. Regions of near-critical enhancement in compressibility are identified in carbon dioxide and in the refrigerants. A simple thermodynamic analysis suggests the possibility to employ the compressibility enhancement in alternative refrigerants to boost the selectivity of extraction of thermally stable, nonvolatile, environmentally sensitive analytes. In SFE with carbon dioxide, this mode of operation is not practical because of insufficient volatility of such analytes at temperatures near the critical temperature of carbon dioxide. Because of its nontoxicity, nonflammability, and affordable price, carbon dioxide is the most frequently used solvent in analytical supercritical fluid extraction (SFE). A significant portion of SFE applications involves thermally stable, relatively polar, nonvolatile, environmentally sensitive compounds such as polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins (PCDDs), or polychlorinated dibenzofurans (PCDFs). However, solubility of polar and/or less volatile analytes in pure, supercritical CO2 is often too low to result in an efficient extraction. In the case of polar analytes, the solvating power of carbon dioxide has customarily been increased by adding a polar modifier (cosolvent). The fact that the solvent becomes a binary mixture may then result in some instrumental problems. In the case of nonvolatile analytes, extractions with pure CO2 have often been performed at elevated temperatures (∼100 °C), far above the solvent’s critical temperature, in order to promote solubility through the increased vapor pressure of the analyte(s). To secure sufficient density and solvating power of CO2 at the elevated temperature, it is necessary to work at rather high pressures (>300 bar). At the high pressures, CO2 becomes relatively incompressible; the low compressibility results in the loss of one of the main advantages of SFE, i.e., the possibility to generate significant changes in solubility by modest shifts in pressure. It will also be shown below that, in the low-compressibility region alone, it is impossible to exploit the potential selectivity of SFE to its full extent. It follows from the above considerations that, for the extraction of thermally stable analytes such as PCBs, PCDDs, or PCDFs, single-component, polar solvents with critical temperatures ex4474 Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
ceeding that of CO2 are desirable. Alternative refrigerants, i.e., hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs), are a family of such solvents. Unlike their perhalogenated predecessors (CFCs), which have been destined for an ultimate phaseout under the Montreal Protocol, alternative refrigerants display ozone-depleting potentials and global-warming potentials low enough to make these compounds environmentally acceptable. Because of the growing applications of HFCs and HCFCs (e.g., in automotive air conditioners and domestic refrigeration), their thermophysical properties have been relatively well characterized. The aim of this paper is to evaluate and discuss the thermodynamic properties relevant to the use of alternative refrigerants as solvents for SFE. For this purpose, high-pressure equilibrium data on a binary system composed of a refrigerant and a PCB, PCDD, or PCDF would be highly helpful; unfortunately, binary data on such systems are absent.1,2 Therefore, the evaluation can only be performed with the properties of the pure refrigerant fluids. Nevertheless, the encouraging results obtained when using some alternative refrigerants as solvents in SFE3-5 and as mobile phases in supercritical fluid chromatography6-8 justify such efforts. The refrigerants covered in this paper will be those for which wide-range thermodynamic formulations are available: difluoromethane (R32),9 1,1-difluoroethane (R152a),10 1,1,1,2-tetrafluoroethane (R134a),11 pentafluoroethane (R125),9 chlorodifluoromethane (R22),12 and 2,2-dichloro-1,1,1-trifluoroethane (R123).13 The term “thermodynamic formulation” includes a high-accuracy, wide-range equation of state (EOS) and expressions describing the vapor pressure, the densities of saturated liquid and saturated vapor, and the isobaric ideal-gas heat capacity as functions of temperature. (1) Fornari, R.; Alessi, P.; Kikic, I. Fluid Phase Equilib. 1990, 57, 1-33. (2) Dohrn, R.; Brunner, G. Fluid Phase Equilib. 1995, 106, 213-282. (3) Hawthorne, S. B.; Langenfeld, J. J.; Miller, D. J.; Burford, M. D. Anal. Chem. 1992, 64, 1614-1622. (4) Howard, A. L.; Yoo, W. J.; Taylor, L. T.; Schweighardt, F. K.; Emery, A. P.; Chesler, A. N.; MacCrehan, W. A. J. Chromatogr. Sci. 1993, 31, 401-408. (5) Hillmann, R.; Ba¨chmann, K. J. Chromatogr. A 1995, 695, 149-154. (6) Ong, C. P.; Lee, H. K.; Li, S. F. Y. Anal. Chem. 1990, 62, 1389-1391. (7) Blackwell, J. A.; Schallinger, L. E. J. Microcolumn Sep. 1994, 6, 551-556. (8) Cantrell, G. O.; Blackwell, J. A.; Weckwerth, J. D.; Carr, P. W. Oral & Poster Abstracts, 7th International Symposium on Supercritical Fluid Chromatography and Extraction, Indianapolis, IN, March 31-April 4, 1996; p A-07. (9) Outcalt, S. L.; McLinden, M. O. Int. J. Thermophys. 1995, 16, 79-89. (10) Tillner-Roth, R. Int. J. Thermophys. 1995, 16, 91-100. (11) Tillner-Roth, R.; Baehr, H. D. J. Phys. Chem. Ref. Data 1994, 23, 657-729. (12) Kamei, A.; Beyerlein, S. W.; Jacobsen, R. T. Int. J. Thermophys. 1995, 16, 1155-1164. (13) Younglove, B. A.; McLinden, M. O. J. Phys. Chem. Ref. Data 1994, 23, 731779. S0003-2700(96)00609-9 CCC: $12.00
© 1996 American Chemical Society
(
THEORY Pressure Dependence of Selectivity in SFE. To explain the motivation for the present study, it is necessary to turn briefly to thermodynamic principles of SFE. In a binary system composed of a solvent 1 and a solid analyte 2, the solubility (mole fraction) of the analyte in the solvent is given by14
y2 )
(∫
P2sat φ2sat exp P φ2
)
ν20 dP P2satRT P
( )
)
T
ν20 - νj2 RT
(2)
where νj2 is the partial molar volume of the analyte in solution. Suppose now that there are two analytes, A and B, and that the fluid solution is sufficiently dilute in both analytes that the presence of one analyte does not affect the solubility of the other. Then, it follows from eq 2 that the isothermal change in selectivity of extraction of the analytes A and B with pressure may be expressed as
(
)
∂ ln(yA/yB) ∂P
νjB - νjA νB0 - νA0 RT RT
) T
T
≈
[ ( )
ν10β1T ∂P lim RT yBf0 ∂yB
β1T ) -
(
)
νjB∞ - νjA∞ ≈ T RT
P)
(5)
T,v
T
a RT ν - b ν(ν + b) + b(ν - b)
a)
(6)
(7)
∑∑y y a
(8)
∑y b
(9)
i j ij
j
and
b)
i i
i
where aij is the interaction parameter between components i and j, bi is the size parameter of component i, and the summations are over all components of the mixture. Applying eqs 7-9 separately to the solvent-analyte A and solvent-analyte B binary mixtures and assuming that bA ) bB for isomers A and B, one obtains
lim yBf0
(14) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1986; Chapters 5 and 10. (15) Reference 14, Chapter 6. (16) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.; Butterworth: London, UK, 1982; Chapter 4. (17) Reference 16, p 13, eq 2.21.
∂P ∂yA
where v is the molar volume of the mixture. The interaction parameter a and the size parameter b are related to composition of the mixture through conventional mixing rules,
(4)
Employing the definition of partial molar volume15,16 and the identity connecting the three mutual derivatives of P, v, and T in the single-phase region,17 one may rewrite eq 4 as
( )]
( )
0 1 ∂ν1 ν10 ∂P
i
∂ ln(yA/yB) ∂P
yAf0
The two limits on the rhs of eq 5 reflect the pressure changes that result from adding a single molecule of the analytes B and A, respectively, to the pure solvent 1 at a constant temperature and density. The value of such a limit at the critical temperature and critical pressure of the solvent has been termed the Krichevskii parameter and shown to play an important role in the thermodynamics of dilute solutions near the solvent’s critical point.18 The composition derivatives of pressure on the rhs of eq 5 are not related to any fundamental thermodynamic property; consequently, they have to be evaluated from a suitable EOS describing the particular solvent-analyte mixture. The mixtures of interest in SFE have often been modeled with the PengRobinson EOS,19
(3)
In SFE, selectivity to isomeric analytes is of particular interest (e.g., selectivity to PCB congeners containing the same number of chlorine atoms); if A and B are isomers, the molecular volumes of A and B are the same, so that one can assume that νB0 ≈ νA0, and the second term on the right-hand side (rhs) of eq 3 vanishes. Further, assuming again very low solubilities of both analytes, the difference in their partial molar volumes may be replaced by the difference in the partial molar volumes at infinite dilution of the respective analyte. For isomeric analytes A and B, therefore, eq 3 reduces to
- lim T,v
where ν10 is the molar volume of pure solvent 1 and β1T is the isothermal compressibility of the pure solvent:
(1)
where R is the molar gas constant, T the absolute temperature, P the total pressure, P2sat the vapor pressure of the analyte, ν20 the molar volume of the pure solid analyte, φ2 the fugacity coefficient of the analyte in the mixture with the solvent, and φ2sat the fugacity coefficient of the pure analyte vapor. For the change in solubility with pressure at a constant temperature, one obtains
∂ ln y2 ∂P
)
∂ ln(yA/yB) ∂P
( ) ∂P ∂yB
- lim T,v
yAf0
( ) ∂P ∂yA
a1A - a1B )2 0 0 ν1 (ν1 + b1) + b1(ν10 - b1) T,v (10)
Consequently, if both solvent-analyte A and solvent-analyte B mixtures conform to the Peng-Robinson EOS, eq 10 shows that the term in brackets on the rhs of eq 5 is proportional to the difference in the solvent-analyte interaction parameters. Moreover, as the parameter aij for a particular i-j pair depends on (18) Levelt Sengers, J. M. H. J. Supercrit. Fluids 1991, 4, 215-222. (19) Peng, D.-Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59-64.
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4475
temperature but not on density,19 the interaction parameter difference a1A - a1B is constant on an isotherm. For considerations of selectivity of SFE to isomeric analytes, it is important to note the different behaviors of the separate terms on the rhs of eq 5 as the temperature and pressure approach the vapor-liquid critical point of pure solvent 1. While the difference in brackets and the solvent’s molar volume are well-behaved, finite quantities, the solvent’s isothermal compressibility assumes very high values; at the critical point of the pure solvent, the compressibility diverges (β1T f +∞). Equation 5, therefore, suggests that the solvent’s compressibility serves as an amplifier of the difference in the interactions of the solvent with the isomeric analytes A and B, thus producing a compressibility-driven enhancement in the pressure slope of selectivity near the critical point of the pure solvent. Figure 1 shows the schematic presentation of the enhancement for carbon dioxide as a solvent at two different, supercritical temperatures; the properties of the pure solvent have been calculated from the EOS by Ely et al.,20 and the bracketed term in eq 5 has been obtained from eq 10 assuming a single value of the interaction parameter difference a1A - a1B for the two mutually close temperatures concerned. It should, of course, be admitted here that, as the solvent’s critical point is approached, the approximations embedded in eq 5 become questionable. First, there are experimental, theoretical, and computer simulation indications21 that, in a system composed of a solvent and two different analytes at a temperature and pressure close to the vapor-liquid critical point of the pure solvent, mutual interactions of the two analytes are not negligible, even at very high dilution of both analytes. Second, replacing the difference in the partial molar volumes of the two analytes (eq 3) with the difference in their infinite dilution partial molar volumes (eq 4) also becomes problematic near the critical point of the pure solvent.22 However, the existence of a supercritical enhancement in the pressure slope of selectivity is not qualified by the validity of the two assumptions which have been called in to make the problem tractable at a sufficiently general level. Within the classification of high-pressure phase equilibria by Scott and van Konynenburg,23,24 most of the highly asymmetric analytesolvent systems encountered in environmental SFE probably belong to type III phase behavior.25-27 In effect, derivation of eq 5 from eq 1 is based on neglect of the distinction between the vapor-liquid critical point of the pure solvent and the upper critical end point terminating the solvent-rich branch of the analytesolvent critical line. In this sense, the above assumptions receive some marginal support from the fact that, in the highly asymmetric analyte-solvent systems of interest in SFE, the two critical points are often quite close to each other. (20) Ely, J. F.; Haynes, W. M.; Bain, B. C. J. Chem. Thermodyn. 1989, 21, 879894. (21) Chialvo, A. A. J. Phys. Chem. 1993, 97, 2740-2744. (22) Levelt Sengers, J. M. H. In Supercritical FluidssFundamentals for Application; NATO ASI Series E, Vol. 273; Kiran, E., Levelt Sengers, J. M. H., Eds.; Kluwer: Dordrecht, 1994; pp 3-38. (23) Scott, R. L.; van Konynenburg, P. H. Discuss. Faraday Soc. 1970, 49, 8797. (24) van Konynenburg, P. H.; Scott, R. L. Phil. Trans. R. Soc. London, Ser. A 1980, 298, 495-540. (25) Reference 16, Chapter 7. (26) de Loos, Th. W. In Supercritical FluidssFundamentals for Application; NATO ASI Series E, Vol. 273; Kiran, E., Levelt Sengers, J. M. H., Eds.; Kluwer: Dordrecht, 1994; pp 65-89. (27) Peters, C. J. In Supercritical FluidssFundamentals for Application; NATO ASI Series E, Vol. 273; Kiran, E., Levelt Sengers, J. M. H., Eds.; Kluwer: Dordrecht, 1994; pp 117-145.
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Figure 1. Pressure derivative of selectivity (arbitrary units) to a pair of isomeric analytes as a function of pressure in CO2 at 35 (a) and 41 °C (b).
Solubility vs Selectivity in SFE. A good solvent for a given analyte should provide favorable interaction with the analyte in order to promote solubility by minimizing the fugacity coefficient φ2 in eq 1. A selective solvent for a given pair of isomeric analytes, A and B, should maximize the solubility difference between the two analytes. To this end, the difference in the intensities of the solvent-analyte A and the solvent-analyte B interactions (as measured, for example, by the difference in the Peng-Robinson interaction parameters, a1A - a1B) should obviously be maximum. However, the simplest-level treatment above suggests that, in SFE, selectivity may also be exploited in an alternative, analyteindependent way that is not available in essentially incompressible liquid solvents. Such a way consists of performing extractions of equivalent samples at a constant, near-critical temperature and at two (or more) different pressures bracketing the maximum in the pressure slope of selectivity, i.e., at two or more pressures on the opposite sides of a peak such as those shown in Figure 1. The basis for this suggestion comes from the following consideration. In the zero pressure limit, the solvent behaves like an ideal gas, and the selectivity to a pair of nonvolatile analytes approaches the ratio of their vapor pressures:
lim yA/yB ) PAsat/PBsat
(11)
Pf0
The selectivity to a pair of analytes A and B at an elevated pressure P is, therefore, given by
ln(yA/yB) ) ln(PAsat/PBsat) +
∫( P
0
)
∂ ln(yA/yB) ∂P
T
dP
(12)
The integral in eq 12 is equal to the area under the isotherm such as shown in Figure 1 between zero pressure and the pressure P. The size of the area between zero and a practical upper limit of the operating pressure defines the selectivity space offered to the particular pair of analytes by the particular solvent at the particular temperature. Equations 5 and 10 suggest that the selectivity space expands with increasing disparity between the solvent-analyte A and solvent-analyte B interactions. At a near-critical temperature, a large part of the selectivity space is concentrated into a relatively narrow range of pressures, e.g., between 50 and 120 bar for isotherm a in Figure 1. The current practice of SFE leaves this selectivity space virtually unexploited. The reason is that the analytes of prevailing interest (PAHs, PCBs, PCDDs, PCDFs, etc.)
are too nonvolatile and poorly soluble in pure CO2 at temperatures near the critical temperature. Another reason is the current emphasis on complete rather than selective extraction. In the particular case in which the analytes A and B are isomers and both the solvent-analyte A and the solvent-analyte B mixtures conform to the Peng-Robinson EOS, the specific form of eq 12 is
ln(yA/yB) ) ln(PAsat/PBsat) +
a1A - a1B RTb1x2
ln
ν10 + b1(1 + x2) ν10 + b1(1 - x2) (13)
0
where ν1 is the molar volume of pure solvent at the particular temperature and the pressure P (ν10 f ∞ as P f 0). The above manner of exploiting the potential selectivity of SFE employs the enhanced compressibility of the pure solvent to boost the effect of the difference in the solvent-analyte A and solventanalyte B interactions (eq 5). Since both the pressure slope of selectivity and the solubility of (at least) one analyte are important here, it is essential to consider also the solubility parameter of the particular solvent at the particular conditions of temperature and pressure. The solubility parameters of alternative refrigerants will be compared to those of carbon dioxide in the high- and lowcompressibility regions separately, and the behavior of these solvents on adiabatic expansion will also be examined. CALCULATIONS The expressions for the required properties of the supercritical solvents have been obtained by applying standard thermodynamic relationships28 to the particular EOS.9-13,20 The respective computer codes have been written in Turbo Pascal and run on an IBM-compatible PC. In addition to the data sources specified above, the saturation properties of CO2 have been those published by Duschek et al.,29 and the temperature dependence of the isobaric heat capacity of CO2 in an ideal-gas state has been taken from Reid et al.30 Vapor pressure of R152a has been calculated from the correlation of Iglesias-Silva et al.31 RESULTS AND DISCUSSION High-Compressibility Region. Figure 2 shows the pressure courses of compressibility of 1,1-difluoroethane (R152a) at three different supercritical temperatures. At very low pressures, the fluid’s compressibility approaches that of an ideal gas (β1T f 1/P); in the zero pressure limit, therefore, compressibility becomes infinite. With the pressure (and density) increasing from zero, compressibility initially declines. At a temperature slightly above the critical (curve a in Figure 2), the decline is followed by an increase, and β1T passes through a sharp maximum. With the increasing temperature, the “compressibility peak” gradually becomes lower and wider (curve b), and then it disappears (curve c). The peak in a compressibility isotherm may be characterized by the minimum, maximum, and the arbitrarily set right margin according to Figure 3, and one can use the fluid’s EOS to map (28) Reference 14, Chapter 3. (29) Duschek, W.; Kleinrahm, R.; Wagner, W. J. Chem. Thermodyn. 1990, 22, 841-864. (30) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1986; Appendix A. (31) Iglesias-Silva, G. A.; Miller, R. C.; Ceballos, A. D.; Hall, K. R.; Holste, J. C. Fluid Phase Equilib. 1995, 111, 203-212.
Figure 2. Compressibility isotherms in R152a (tc ) 113.38 °C): (a) 114, (b) 130, and (c) 180 °C.
Figure 3. Characteristic points of the pressure course of compressibility at a constant temperature.
the region of enhanced compressibility into P-T or P-F planes as shown in Figure 4a,b, respectively, for CO2. Within the region bordered by curves 2, 3, and the critical isotherm, compressibility increases with increasing pressure at a constant temperature; this situation is unique to the near-supercritical state. The overall shapes of the P-T and P-F projections are common to all fluids, as illustrated in Figures 5 and 6 for refrigerants R134a and R123, respectively. Table 1 lists the critical data and characteristics of the end point of the locus of compressibility maxima for CO2 and for the six alternative refrigerants. Table 2 shows the relevant properties of each fluid at the point lying in one-fourth of the temperature span of the locus of compressibility maxima, starting from the critical point. At that point, the solvating powers of HFCs and HCFCs as measured by their solubility parameters appear to be somewhat lower than that of CO2. However, it is important to note that the solubility parameters of alternative refrigerants pertain to progressively increasing temperatures and, consequently, to progressively increasing vapor pressure of any analyte. Therefore, an analyte with a vapor pressure insufficient for extraction with highly compressible CO2 may still be amenable to extraction in the high-compressibility region of a properly selected refrigerant. Besides, the solubility parameters in Table 2 have been calculated strictly according to their thermodynamic definition, i.e., they are square roots of the cohesive energy densities of the solvents at the particular temperature and pressure. It follows from the regular solution theory32 that these pure-component properties cannot be directly used to describe nondispersion intermolecular interactions between the analyte and (32) Reference 14, Chapter 7.
Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
4477
a
a
b
b
Figure 4. Region of enhanced compressibility of CO2 in P-T (a) and P-F (b) projections: C, critical point; E, end point of the locus of compressibility maxima; 1, vapor-liquid coexistence curve; 2, locus of compressibility minima; 3, locus of compressibility maxima; 4, locus of right margins of compressibility peaks. Lower pressure ends of curves 2 and 4 are connected by a portion of the critical isotherm.
the solvent. Dipole moments of the refrigerants covered in this study range from 1.40 to 2.30 D.33 As compared with CO2, the relatively high polarity of refrigerants promotes the selectivity to a pair of isomeric analytes differing in their dipole moments by increasing the difference in the solvent-analyte interaction parameters (see eq 13). Therefore, both polarity and elevated critical temperatures make HFCs and HCFCs suitable solvents for SFE of environmentally sensitive analytes in the region of high compressibility of the solvent. Among the solvents covered here, R123, R152a, and R134a appear to be the most promising. To fully exploit the compressibility-driven enhancement in the pressure slope of selectivity, it is advisable to operate at near-critical temperatures, because the maximum compressibility declines steeply with increasing temperature (see Figure 7). Instrumental aspects of the operation in high-compressibility region will be discussed below. Low-Compressibility Region. To secure sufficient solubility of nonvolatile analytes, extractions with CO2 are usually performed at high pressures, where the solvent’s compressibility is relatively low. It is, therefore, useful to compare the relevant properties of CO2 and alternative refrigerants in this region as well. Table 3 shows such a comparison for two pairs of fixed values of temperature and pressure. Among the six alternative refrigerants at the particular conditions, the lowest solubility parameters are those of pentafluoroethane (R125), because R125 contains the largest portion of low polarizability, carbon-fluorine bonds that (33) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman & Co.: San Francisco and London, 1963.
4478 Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
Figure 5. Region of enhanced compressibility of R134a in P-T (a) and P-F (b) projections. Symbols have the same meaning as in Figure 4.
a
b
Figure 6. Region of enhanced compressibility of R123 in P-T (a) and P-F (b) projections. Symbols have the same meaning as in Figure 4.
detract from the cohesive energy. The solubility parameters also suggest that, at the particular conditions, even the solvating power of R125 will be still superior to that of CO2.
Table 1. Critical Data and Characteristics of the End Point of the Locus of Compressibility Maxima critical data solvent
t (°C)
CO2 R125 R32 R22 R134a R152a R123
30.99 66.18 78.20 96.15 101.03 113.26 183.68
end-point data
Table 3. Densities, Isothermal Compressibilities, and Solubility Parameters at 100 °C, 300 bar and at 200 °C, 400 bar 100 °C, 300 bar
P (bar) F1 (g cm-3) t (°C) P (bar) F1 (g cm-3) 73.75 36.29 57.95 49.90 40.57 45.16 36.62
0.468 0.571 0.427 0.524 0.508 0.368 0.550
65.3 102.2 121.2 135.4 138.8 154.6 231.8
100.6 49.32 82.14 65.46 54.17 60.97 49.48
0.266 0.321 0.230 0.282 0.278 0.198 0.308
Table 2. Densities, Isothermal Compressibilities, and Solubility Parameters at One-Fourth of the Temperature Span of the Locus of Compressibility Maxima
200 °C, 400 bar
β1T δ1 [(cal F1 β1T δ1 [(cal F1 solvent (g cm-3) (bar-1) cm-3)1/2] (g cm-3) (bar-1) cm-3)1/2] CO2 R125 R32 R22 R134a R152a R123
0.663 1.161 0.862 1.105 1.130a 0.839a 1.383a
0.001 84 0.000 64 0.000 69 0.000 49 0.000 45 0.000 40 0.000 22
4.95 5.28 6.88 6.33 6.32 6.80 6.85
0.497 0.982 0.659 0.914 0.949 0.703 1.227
0.001 90 0.000 89 0.001 22 0.000 83 0.000 73 0.000 69 0.000 36
3.59 4.30 5.19 5.07 5.12 5.53 5.91
a The solvent is a subcritical, compressed liquid at the particular conditions.
solvent t (°C) P (bar) F1 (g cm-3) β1T (bar-1) δ1 [(cal cm-3)1/2] CO2 R125 R32 R22 R134a R152a R123
39.6 75.2 88.9 106.0 110.5 123.6 195.7
86.3 42.5 68.7 58.5 47.5 53.3 42.7
0.403 0.491 0.351 0.472 0.448 0.326 0.471
0.068 0.135 0.084 0.112 0.136 0.124 0.139
3.37 2.46 3.29 2.96 2.78 2.98 2.49
Figure 8. Isentropic expansion of CO2: C, critical point; vap, vapor part of the coexistence curve; liq, liquid part of the coexistence curve; 1, constant entropy curve starting at the locus of compressibility maxima (t ) t1/2); 2, constant entropy curve starting at 100 °C and 300 bar; D, dew point.
Figure 7. Decay of the supercritical enhancement in compressibility of R22 with increasing temperature (see Figure 3 for the meaning of symbols βmax and βmin).
Further, the ability of HFCs and HCFCs to interact with analytes through dipole-dipole forces may shift their solvating powers above those indicated by the solubility parameters in Table 3. Moreover, considerations of the solubility of a pure analyte in a solvent constitute only a part of the extraction problem. Another part is due to interactions between the analyte(s) and the sample matrix. Owing to their polar character, alternative refrigerants will be more effective than CO2 in displacing the analytes from the active sites within the matrix by competitive sorption. Expansion Behavior. Detailed information on the temperature and pressure course of decompression of fluid solutions would be highly helpful in delineating and exploiting the mechanism of analyte trapping after SFE. Although both the presence of small concentrations of analyte(s) and the use of liquid solvents for trapping affect the decompression, the expansion behavior of a pure solvent can also yield some useful insights. A reasonable description of the rapid decompression of a pure fluid in a restrictor is provided by the isentropic (constant entropy) expansion. Development of a numerical model of the expansion path requires some mathematical manipulation of the EOS and of the
Figure 9. Isentropic expansion of R32: B, bubble point; other symbols have the same meaning as in Figure 8.
temperature dependence of the isobaric ideal-gas heat capacity of the fluid. Figures 8-10 illustrate the isentropic expansion of CO2, R32, and R123, respectively, from the high- and lowcompressibility regions. The high-compressibility region is represented by the midpoint of the temperature span of the locus of compressibility maxima. In all three fluids, the paths of isentropic expansion from that point hit the vapor part of the coexistence curve. Consequently, isentropic expansion from the highcompressibility region proceeds through a dew point (D), in which small droplets of liquid appear in the subcritical vapor. The expansion paths from the low-compressibility region differ in CO2 and the two refrigerants. In the refrigerants, the paths arrive at the liquid part of the coexistence curve, indicating the occurrence Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
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Table 4. Normal Boiling Points and Vapor Pressures at 20 °C
a
Figure 10. Isentropic expansion of R123: 3, constant entropy curve starting at 200 °C and 300 bar; other symbols have the same meaning as in Figure 8.
of a bubble point (B), in which a first portion of vapor appears in the subcritical liquid. The two distinct paths of isentropic expansion of refrigerants R32 and R123 from the high- and lowcompressibility regions could differentiate between the mechanisms of trapping after SFE in the two regimes. Table 4 lists vapor pressure data that are relevant to the final, equilibrium stage of solvent expansion; at ambient conditions, all fluids in Table 4 except R123 are gases. Instrumental Considerations. To make use of the compressibility-driven enhancement in the pressure slope of selectivity, it is necessary to operate also at a pressure below the maximum of the compressibility peak (see curve a in Figure 2). The fluid’s compressibility at that pressure may still be several orders of magnitude larger than that encountered in the current highpressure practice of SFE. Consequently, the required precision of the pressure and temperature controls may exceed the current standard. The enhanced compressibility could even result in the
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solvent
normal boiling point (°C)
vapor pressure at 20 °C (bar)
CO2 R125 R32 R22 R134a R152a R123
a -48.11 -51.66 -40.83 -26.07 -23.90 27.83
57.29 12.04 14.75 9.10 5.72 5.12 0.76
Triple-point pressure is 5.18 bar.29
static extraction as the only practical operating mode, because it would be prohibitively difficult to control the temperature and pressure with sufficient accuracy in a flow (dynamic) experiment. A more fundamental problem follows from the present lack of reliable theoretical tools for an a priori prediction of the difference in the intensities of the solvent-analyte A and the solvent-analyte B interactions. These adverse (but not fatal) circumstances are a natural price to pay for the unique possibility to employ the enhanced compressibility of near-critical solvents to boost the selectivity of SFE. ACKNOWLEDGMENT This work was supported by the Grant Agency of the Academy of Sciences of the Czech Republic under Project No. A4031503. Received for review June 19, 1996. Accepted September 16, 1996.X AC960609B X
Abstract published in Advance ACS Abstracts, October 15, 1996.
