Anal. Chem. 1996, 68, 2353-2360
Prediction of the Solubility in Supercritical Fluids Based on Supercritical Fluid Chromatography Retention Times Jyisy Yang† and Peter R. Griffiths*
Department of Chemistry, University of Idaho, Moscow, Idaho 83843-2343
An improved method for the rapid prediction of solubilities of solutes in supercritical fluids is proposed. The method is based on the measured retention times of solutes eluting from packed and capillary supercritical fluid chromatography (SFC) columns. The solubilities in CO2 of four polycyclic aromatic hydrocarbons were estimated with an average error of about (30% using retention data obtained by packed column SFC. For more polar compounds, which may interact strongly with the stationary phase in packed columns, capillary column SFC gave better results. Agreement to better than 35% was found between the solubilities obtained by this method and those obtained gravimetrically for compounds with a variety of functionalities. Several factors have been investigated, including the relationship between solubility and the reciprocal of the capacity factor, the effect of temperature, and the effect of the stationary phase. Supercritical fluid extraction (SFE) using CO2 as the extracting fluid has received increased attention in recent years because CO2 is a benign substitute for organic liquids and has the potential to reduce the amount of solvent wastes.1-4 The extraction efficiency of SFE is determined by two main factors: the solubilities of solutes in the supercritical fluid (SF) and the effect of the matrix. Several approaches have been used to obtain solubility data, including gravimetric,5,6 spectroscopic,7 and chromatographic methods.8-10 To eliminate the disadvantages of either excessive measurement time or the expense of the instrumentation required for these techniques, predictive methods have been proposed to obtain the solubility data rapidly for the optimization of the SFE process. To evaluate the solubilities of analytes in SFs and the retention behaviors of solutes in SFC, Giddings et al.11 and King12 used the Hildebrand parameter, δ, which is defined as †
Present address: Department of Chemistry, Chung Yuan Christian University, Chung-Li, Taiwan 32023, ROC. (1) Lee, M. L.; Markides, K. E. Analytical Supercritical Fluid Chromatography and Extraction; Chromatography Conferences, Inc.: Provo, UT, 1992. (2) Hawthorne, S. B. Anal. Chem. 1990, 62, 622A. (3) Majors, R. E. LC-GC 1991, 9, 78. (4) Brennecke, J. F.; Eckert, C. A. AIChE J. 1989, 35, 1409. (5) van Leer, R. A.; Paulaitis, M. E. J. Chem. Eng. Data 1980, 25, 257. (6) Johnston, K. P.; Eckert, C. A. AIChE J. 1981, 27, 773. (7) Swaid, I.; Nickel, D.; Schneider, G. M. Fluid Phase Equil. 1985, 21, 95. (8) Kosal, E.; Holder, G. D. J. Chem. Eng. Data 1987, 32, 148. (9) Nakatani, T.; Ohgaki, K.; Katayama, T. J. Supercrit. Fluids 1986, 2, 9. (10) Schafer, K.; Baumann, W. Fresenius Z. Anal. Chem. 1988, 332, 122. (11) Giddings, J. C.; Myers, M. N.; King, J. W. J. Chromatogr. Sci. 1969, 7, 276. (12) King, J. W. J. Chromatogr. Sci. 1989, 27, 355. S0003-2700(96)00371-X CCC: $12.00
© 1996 American Chemical Society
δ ) c1/2 ) (-U/V)1/2 = (∆gl U/V)1/2
(1)
where c is the cohesive energy density, V is the molar volume of solute at its boiling point, U is the cohesive energy, and ∆gl U is the change of cohesive energy between the liquid and gaseous states. For gases, this equation has been simplified to the following equation involving the critical pressure, Pc:
δ ) 1.25Pc1/2
(2)
al.11
Giddings et modified this expression to make it more applicable to supercritical fluids as
δ ) 1.25Pc1/2(Ff/Fl)
(3)
where Ff is the reduced density of the supercritical fluid and Fl is the reduced density of the fluid in the liquid state, which is close to 2.66. King and Friedrich13 defined a reduced solubility parameter as
∆ ) δ1/δ2
(4)
where δ1 is the solubility parameter of the supercritical fluid as evaluated by eq 3 and δ2 is the solubility parameter for the solute in liquid solvents. This solubility parameter may be calculated by the group contribution method of Fedors14 and used to evaluate both cohesive energy and molar volume according to the structure of the molecule. An example of the application of this method for calculation of the solubility parameter of caffeine has been reported by King and Friedrich,13 who showed that the reduced solubility parameter varies smoothly with the logarithm of the weight fraction, i.e., the ratio of the weight of the solute to that of the SF. They used this curve to predict the solubility of any solute with good accuracy from its reduced solubility parameter. Smith et al.15 showed theoretically that the SFC retention time permits a good estimate of the solvent strength of the supercritical fluid to be obtained from the following equation:
( ) ∂ ln k ∂P
T
)
(
)
(Vs - Vistat) ∂ ln Ximob RT ∂P
T
-K
(5)
where k is the chromatographic capacity factor, Vs is the molar volume of the solute, Vistat is the partial molar volume of the stationary phase at infinite dilution, Ximob is the mole fraction of the solute in the mobile phase, and K is the compressibility of the supercritical fluid (which can be obtained from a suitable equation of state). (13) King, J. W.; Friedrich, J. P. J. Chromatogr. 1990, 517, 459. (14) Fedors, R. F. Polym. Eng. Sci. 1974, 14, 147. (15) Smith, R. D.; Udseth, H. R.; Wright, B. W.; Yonker, C. R. Sep. Sci. Technol. 1987, 22, 1065.
Analytical Chemistry, Vol. 68, No. 14, July 15, 1996 2353
Figure 1. Plots of 1/S versus k at 308 K for (A) naphthalene, (B) fluorene, (C) phenanthrene, and (D) pyrene.
Bartle, Clifford, et al.16-18 extended and simplified this theory. They showed that the solubility, Sa, of compound, a, in any SF is inversely proportional to its capacity factor, ka, i.e.,
Sa ) Ca/ka (in g/L)
(6)
Ca is a constant for each compound for a particular column and temperature, given by
Ca ) rcst0 exp[(µs0 - µst0)/RT]
(7)
where r is the phase ratio (the ratio of the amount of stationary phase to that of the mobile phase), cst0 is the standard concentration in the stationary phase, µs0 is the chemical potential of the pure solid solute at standard pressure, and µst0 is the chemical potential of the solute in the stationary phase referred to infinite dilution and the standard concentration and pressure. To obtain a Ca value that is truly constant, six conditions must be fulfilled: (i) infinite dilution, (ii) a low pressure drop across the column, (iii) no absorption of the solvent by the solid solute, (iv) the partial molar volume of solute in the stationary phase must be equal to that of the pure compound at the same temperature, (v) the chemical potential of the solute in the stationary phase at infinite dilution should be independent of mobile phase and pressure of system, and (vi) the value of the activity coefficient should not vary with concentration of the solute. Bartle’s group demonstrated (16) Barker, I. K.; Bartle, K. D.; Clifford, A. A. Chem. Eng. Commun. 1988, 68, 177. (17) Bartle, K. D.; Clifford, A. A.; Jafar, S. A. J. Chem. Soc., Faraday. Trans. 1990, 186, 855. (18) Bartle, K. D.; Clifford, A. A.; Jafar, S. A. J. Chem. Eng. Data 1990, 35, 355.
2354
Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
that a linear relationship between 1/Sa and ka is found in practice for polynuclear aromatic compounds;16-18 their data are reproduced in Figure 1. Equation 7 is extremely useful for interpolating existing experimental solubility data but lacks the capability of predicting the solubilities of analytes for which no experimental solubility data have been obtained by conventional methods. In the following section, a method of predicting the solubilities of solutes in supercritical fluids on the basis of their chromatographic retention times is proposed. This method stems from the concept that the solubility of a compound in a supercritical fluid affects its retention time in an SFC column. DEVELOPMENT OF WORKING EQUATION The chromatographic retention of a given solute in SFC depends on the interaction between the solute and the stationary phase. For strong interactions, the retention time of the analytes is often long, and the peaks are broad. The retention time is a function of the solvent strength of the supercritical mobile phase, which is in turn determined by its density. The logarithm of the capacity factor, k, is inversely proportional to the density of the supercritical fluid. The threshold pressure has been used by several authors19-21 to describe the chromatographic retention behavior of a given solute on a column containing a given stationary phase and held at a constant temperature. This threshold pressure is the pressure at which the solvent strength of the mobile phase overcomes the interaction between the solute and the stationary phase, resulting in a migration of the solute through the column. As indicated by (19) Giddings, J. C.; Myers, M. N.; Keller, R. A. Science 1968, 162, 67-73. (20) Czubryt, J. J.; Myers, M. N.; Giddings, J. C. J. Phys. Chem. 1970, 74, 4260. (21) Smith, R. D.; Chapman, E. G.; Wright, B. W. Anal. Chem. 1985, 57, 28292836.
Smith et al.,15 as the pressure of the mobile phase is increased, peaks will first be observed at very long retention times, in which case measurement of the threshold pressure will depend on the sensitivity and stability of the detector. To describe the migration of a given solute more precisely, we have redefined the threshold density for a certain stationary phase as the density required for the elution of the analyte with k ) 1 at a given temperature. This definition allows comparison of the solvent strengths (or densities) needed to move any solute with capacity factor equal to 1. The threshold density is the result of the interactions of the solute with both the stationary phase and the mobile phase, i.e.,
Ds ) f(Iss,Ism,T)
(8)
where Ds is the threshold density, Iss represents the interaction between the solute and the stationary phase, Ism represents the interaction between the solute and the mobile phase, and T is the temperature of the system. The relationship between the threshold density and these interaction functions is difficult to derive theoretically, but it can be found empirically. To satisfy the criterion that an increased interaction between the solute and the stationary phase leads to a higher value of threshold density, while a stronger interaction between the solute and the mobile phase leads to a lower threshold density, eq 8 can be expressed empirically at a given temperature as
D∝
f(Iss)
(9)
f(Ism)
In eq 7, the value of the constant Ca is related to the chemical potential between the solute and the stationary phase. Rearrangement of this equation yields
(µst0 - µs0) ) RT ln
( ) rcst0 Ca
(10)
Assuming that the phase ratio, r, and the standard concentration of the solute in the stationary phase, cst0, are constants for any solute, the above equation can be simplified to
(µst0 - µs0) ∝ ln(1/Ca)
(11)
The difference of chemical potentials between the solute and the stationary phase can be substituted into eq 9 for the f(Iss) term as follows:
Ds ∝ E/f(Ism)
(12)
where E ) ln(1/Ca). The Hildebrand solubility parameter, δ, was originally used to predict the solubilities of compounds in liquid solvents at ambient temperature. Thus, if CO2 is treated as a “superheated” liquid, then the solubility of any solute in supercritical CO2 will be a function of δ. This parameter can also be used to indicate the interaction between the solute and the supercritical fluid phase. Therefore, if we substitute the solubility parameter, δ, for Ism in eq 12, we obtain
Ds ∝ E/δ
(13)
Rearranging the above equation, the following equation is obtained:
E/δ ) ADs + B
(14)
where A and B are constants for any solute at a given temperature and are related to the chemical nature and thickness of the stationary phase. The effect of temperature has been taken into account in the definition of Ca, as shown in eq 7. Therefore, the values of A and B should be independent of temperature. If we plot the threshold density against E/δ at a given temperature, then the slope is the constant A, and the intercept corresponds to the constant B. Because the solubilities of different compounds are being compared, the molar solubility, rather than the solubility in, e.g., g/L, should be used for all calculations. After determination of the values of A and B, the value of E, and hence the value of Ca, can be calculated for any solute. Entering this value into eq 6 allows the solubility of any compound in the working pressure range of the chromatograph to be predicted. EXPERIMENTAL SECTION The accuracy by which the solubilities of compounds in supercritical fluids can be predicted on the basis of their retention times in packed column SFC was investiged using data published by Bartle et al.17 A Computer Chemical Systems (CCS, Avondale, PA) Model 5000 supercritical fluid chromatograph equipped with a flame ionization detector (FID) and an ultaviolet (UV) detector was used for all capillary SFC separations, with the UV detector mounted between the column outlet and the FID. A bubble gas flowmeter was used to measure the gas flow rate at the outlet of the column. The densities for each pressure and temperature were calculated using the Lee-Kesler equation of state.22 Because the maximum pressure is limited to 320 atm by the CCS 5000, a CCS Model 7000 fluid delivery system, which is rated to higher pressures, was used to generate pressures between 320 and 640 atm. The signals from both detectors were collected at a rate of 1 Hz using an IBM-compatible personal computer and LabCalc software (Galactic Industries, Salem, NH). For precise control of the injection time, a pneumatically switched injection valve that controlled the injection time to better than 1 s was used. An integral restrictor (White Associates, Pittsburgh, PA) was mounted in the FID to maintain the pressure. Two types of capillary column, each 10 m long and having an internal diameter of 100 µm, were used in the study. The first was a DB-5 (95% methyl, 5% phenylpolysiloxane) column (J&W Scientific, Folson, CA) with a 0.4-µm film coating, and the second was a biphenyl-30 (30% biphenyl, 70% methylpolysiloxane) column (Dionex, Salt Lake City, UT) with a 0.2-µm film coating. RESULTS AND DISCUSSION A. Packed Column SFC. Relationship between E/δ and Threshold Density. To obtain the threshold density of solutes from packed column SFC data, the capacity factors were adapted from the report of Bartle et al.,17 who used an ODS2 column, i.e., a packed column with the silica surface-bonded with octadecylsilyl groups, for their work. The density of CO2 was calculated using (22) Lee, B. I.; Kesler, M. G. AIChE. J. 1975, 21, 51.
Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
2355
Figure 2. Plots of ln k versus density for naphthalene (0), fluorene (+), phenanthrene ()), and pyrene(4); all data were obtained using an ODS2 packed column. Table 1. Solubility Parameters and Threshold Densities of Four PAHs compounds naphthalene fluorene phenanthrene pyrene
temp (K)
δ(Fedors)a
δ(lit.)b
Ds
Ca
Ee
308 318 308 323 308 318 328 308 323
9.97
9.92
0.76 0.69 0.83 0.79 0.90 0.88 0.84 1.00 0.98
30.61 40.80 7.04 10.26 6.90 10.73 13.66 2.36 3.06
8.34 8.05 10.07 9.69 10.16 9.72 9.48 11.36 11.10
11.04 10.32 10.57
9.78
c
d
a Solubility parameters calculated by Fedors’s method. b Adapted from ref 24. c Threshold density (g/mL) calculated using data from ref 18. d Ca constant in eq 6. Data were adapted from ref 18. e E values in eq 14. Data were calculated using data from ref 18.
the Lee-Kesler equation of state.22 As shown in Figure 2, a linear variation of ln k with the density of CO2 is seen in the high pressure region but not at low pressures. The variation of ln k with pressure was first noted by Sie et al.23 and is probably caused in part by the magnitude of the pressure drop across the column that occurs in packed columns, which gives rise to large density changes along the column, especially around the critical pressure. In any event, the threshold density was obtained by either interpolation or extrapolation from the linear region of these plots. The Hildebrand solubility parameter was obtained by Fedors’s method, as described above. The cohesive energy and the molar volume were predicted according to the molecular structures. The solubility parameters for naphthalene, phenanthrene, fluorene, and pyrene predicted by Fedors’s method are listed in Table 1. The available literature values for the Hildebrand solubility parameters of these molecules, which were obtained experimentally,24 are also listed for comparison. The calculated Hildebrand parameter agrees with the experimental value very well for naphthalene but less well for phenanthrene. Plots of E and E/δ against threshold density at a given temperature indicate that, for naphthalene, phenanthrene, and (23) Sie, S. T.; van Beersum, W.; Rijnders, G. W. A. Anal. Chem. 1966, 1, 459. (24) Hildebrand, J. H.; Scott, R. L. The Solubility of Nonelectrolytes, Dover Publications: New York, 1964.
2356 Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
Figure 3. Plots of E/δ versus threshold density at different temperatures for naphthalene (0), fluorene (+), phenanthrene ()), and pyrene (4). The equation of the regression line is E/δ ) 0.16 + 0.90Ds.
pyrene, E is proportional to the threshold density. The data for fluorene do not lie on the same line, presumably because fluorene contains an aliphatic CH2 group not contained by the other three molecules, leading to a significantly higher solubility parameter than those for the other molecules (see Table 1). Dividing E by the solubility parameter reduces the error significantly when different classes of compounds are investigated, indicating that it is valid to apply eq 14 to correlate the threshold densities with the E values even for data obtained on packed columns, where there may be a high pressure drop across the column. The equation of the regression line for all four compounds is E/δ ) 0.99Ds + 0.08, with a regression coefficient, R2, equal to 0.999. Effect of Temperature. The A and B constants in eq 14 are invariant with temperature because the value of Ca already includes this effect (see eq 7). The variation of E/δ with threshold density for the same four compounds measured at different temperatures is plotted in Figure 3, which shows that a linear relationship with similar values of constants A and B in eq 14 was obtained even when the temperature was varied. Using the method proposed here to predict the solubility of these four PAHs, the average error is around (30%, which is significantly better than that for the method proposed by King and Friedrich,13 which has an accuracy of about 1 order of magnitude for the estimation of the solubilities of solutes in supercritical fluids. The accuracy to which solubilities could be calculated using retention times obtained by packed column SFC18 is probably determined by the standard deviation of each plot in Figure 1. Validation of This Method. In the method outlined above, the solubility parameter and the values of A and B in eq 14 are needed. The solubility parameter can be calculated to the desired level of accuracy by Fedors’s method, and the values of A and B can be obtained by two methods. In the first, A and B can be obtained directly from a plot of E/δ versus threshold density by calibrating a particular column using several compounds of known solubilities. Because the values of A and B are determined by the stationary phase of the column, they can be used to predict the solubilities of other compounds after measuring their capacity factors with the same column with the mobile phase at the same temperature and pressure. The second method involves coinjecting two standards of known solubilities with the analytes of
Figure 4. Comparison of the solubilities of phenanthrene in CO2 measured in this study (0) and reported previously (+), and corresponding experimental (4) and literature values ()) for pyrene.
interest. The standards must have chemical functionalities similar to those of the unknowns. Since the values of A and B of the standards can be calculated, eq 14 can be used to predict the solubilities of the unknowns. In the first method, the values of A and B are obtained from several compounds of known solubilities; thus, one may have high confidence in the accuracy of the values that are predicted for the unknowns. The second method must be used when such solubility data are unavailable. This approach may provide an easier way of obtaining the A and B values, provided that the compounds of interest can be co-injected and separated without changing the chromatographic conditions. An example where the solubilities of phenanthrene and pyrene have been estimated from their retention times is shown in Figure 4. The values of A and B obtained from the regression line determined above were used, and the solubility parameters were calculated by Fedors’s method. After the threshold densities of phenanthrene and pyrene are computed from the relationship between capacity factor and density, the values of E and Ca can be calculated, after which the solubilities of phenanthrene and pyrene can be predicted using eq 3. B. Capillary SFC Data. The applicability of packed column SFC to obtain estimates of the solubilities of polar molecules is limited by the fact that the stationary phase is rarely perfectly end-capped, so hydrogen-bonding molecules can interact strongly with the active sites on the silica substrate. In addition, there is often a high pressure drop across the column, so the mobile phase cannot be estimated accurately. The use of capillary columns should permit both of these problems to be largely overcome. Eleven compounds with a wide variety of functional groups for which solubility data are available in the literature were investigated. These compounds were naphthalene,18 phenanthrene,18 pyrene,16 phenol,5 β-naphthol,25 cholesterol,26 palmitic acid,27 stearic acid,28 behenic acid,29 caffeine,30 and diphenylamine.31 These compounds can be classified into four classes: (25) Schmidt, W. J.; Reid, R. C. J. Chem. Eng. Data 1986, 31, 204. (26) Wong, J. M.; Johnston, K. P. Biotechnol. Prog. 1986, 2, 29. (27) Kramer, A.; Thodos, G. J. Chem. Eng. Data 1988, 33, 320. (28) Kramer, A.; Thodos, G. J. Chem. Eng. Data 1989, 34, 184. (29) Chrastil, J. J. Phys. Chem. 1982, 86, 3016. (30) Ebeling, H.; Frank, E. U. Ber. Bunsenges. Phys. Chem. 1984, 88, 862.
Figure 5. Plots of ln k versus density for 11 compounds eluted from a DB-5 column.
polycyclic aromatic hydrocarbons (naphthalene, phenanthrene, and pyrene), long-chain acids (palmitic acid, stearic acid, and behenic acid), compounds containing a hydroxyl functional group (phenol, β-naphthol, and cholesterol), and compounds containing a basic nitrogen atom (caffeine and diphenylamine). Solubility values at any temperature were calculated by interpolation or extrapolation of literature values. Investigation of the Relationship between S and k on Capillary Columns. It was noted above that, for a packed column, a plot of ln k against the density of the mobile phase was linear at high density but not at low density. It was postulated that the reason for the behavior at low density was the pressure drop across packed columns at low density. The corresponding plots for isothermal separations of ln k against density of the fluid at 55 °C for capillary columns are shown in Figure 5. For every compound studied, it can be seen that a more linear relationship between ln k and density was obtained for measurements made on capillary columns than was found for packed columns. This result is presumably because the pressure drop across capillary columns is significantly less than that across capillary columns at low pressure. If the reciprocal of the solubility, S, of each analyte given in the references in Table 3 is plotted against k measured using a capillary column, a linear relationship with an intercept at zero is maintained. The slope of this plot yields the value of C, from which E is calculated as ln(1/C), as derived above. The relationship between 1/S and k is obeyed for most compounds investi(31) Tsekhanskaya, Y. V.; Mushkina, E. V. J. Phys. Chem. 1962, 36, 1177. (32) Barton, A. F. M. Handbook of Solubility Parameters and other Cohesion Parameters; CRC Press, Inc.: Boca Raton, FL, 1983.
Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
2357
Table 2. Solubility Parameters for Eleven Compounds compounds
δ(Fedors)a
δ(lit.)b
naphthalene phenanthrene pyrene phenol β-naphthol cholesterol palmitic acid stearic acid behenic acid diphenylamine caffeine
9.97 10.32 10.57 14.60 12.29 9.60 10.17 10.01 9.69 10.83 12.96
9.92 9.78 14.52 9.20
13.69
a Solubility parameters calculated by Fedors’s method. b Adapted from refs 24 and 32.
Table 3. Threshold Density at 55 °C for Compounds Eluted from DB-5 and Biphenyl-30 Columns DB-5 column
biphenyl column
compounds
Ds
Ca
E
Ds
Ca
E
ref
naphthalene phenanthrene pyrene phenol β-naphthol cholesterol palmitic acid stearic acid behenic acid diphenylamine caffeine
0.35 0.49 0.53 0.22 0.43 0.61 0.47 0.50 0.53 0.36 0.43
3.82 0.72 0.14 0.85 0.14 0.34 0.66 1.00 0.50 2.91 0.02
10.42 12.41 14.15 11.61 13.84 13.94 12.87 12.56 13.43 10.97 16.02
0.39 0.59
6.43 2.27
9.90 11.27
0.27 0.51 0.82
1.45 0.38 0.64
11.08 12.86 13.31
18 18 18 5 25 26 27 28 29 30 31
0.50
4.44
10.55
gated by capillary SFC except diphenylamine and behenic acid, for which linear plots with nonzero intercepts were obtained. Since a nonzero intercept would lead to the calculation of an inaccurate value of E, the lines for these two compounds were forced to pass through the origin before the slopes were calculated. The solubility parameters calculated by Fedors’s method14 for these compounds are listed in Table 2, and the values of C and E are listed in Table 3. Relationship between E/δ to Threshold Density. The threshold densities (Ds) were obtained by interpolating each plot of ln k versus density and reading off the density at which ln k ) 0. A plot of E against threshold density is shown in Figure 6A. Although this plot is fairly linear for compounds falling into the same class, several outliers were observed; these points correspond to phenol (1), β-naphthol (2), and caffeine (3), all of which are relatively polar materials. A significantly more linear relationship was obtained for compounds falling into different classes when E was divided by the solubility parameter calculated by Fedors’s method; the results are shown in Figure 6B. The values of A and B obtained from the regression line of this plot are quite different from the values obtained using the packed column. Therefore, characterization of each column to obtain the constants A and B is needed prior to determining the solubility of any compound. The average error for the solubilities of the 11 compounds tested in comparison to the literature values is (37%. In light of the high polarities of several of the compounds tested, the accuracy of the literature values is probably worse than that for the hydrocarbons studied in the first part of this paper. Effect of Temperature. To test the effect of temperature on the solubility of seven of the compounds reported in the previous 2358 Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
Figure 6. Plots of (A) E versus threshold density and (B) E/δ versus threshold density for 11 compounds eluted from a DB-5 capillary column at 55 °C. 1, Phenol; 2, β-naphthol; 3, caffeine. In plot B, the equation of the regression line is E/δ ) 0.41 + 1.74Ds.
Figure 7. Plot of E/δ versus threshold density at 35, 45, 55, and 65 °C obtained using a DB-5 column (2); squares show corresponding data measured at 55 °C from previous measurement. The equation of the regression line is E/δ ) 0.49 + 1.59Ds.
section, capacity factors were obtained at four temperatures and four pressures. Because the capacity factors were obtained at only four pressures in this experiment, and because in most cases k was much less than 1, there was a considerable potential for error in the estimate of the threshold density from the extrapolation process. The plot of E/δ versus threshold density for these seven compounds is shown in Figure 7. It can be seen that the E/δ values are strongly related to their threshold density even at different temperatures. For comparison, the data measured previously at 55 °C are also plotted in this figure. As can be seen, all the data fall onto the same regression line, indicating that A
Figure 8. Plots of 1/S versus k at 55 °C for (A) phenanthrene and (B) phenol eluted from a biphenyl-30 capillary column.
and B in the prediction equation are, indeed, constant for a given stationary phase. Effect of Stationary Phase. To study the effect of the stationary phase on these parameters, a series of measurements was made using the biphenyl-30 column, as it is a more selective stationary phase than DB-5. The high percentage of pendant biphenyl groups leads to a strong interaction between the stationary phase and PAHs, which could cause some difficulty in terms of the correlation of the data obtained for PAHs and nonPAHs. Figure 8 shows the plots of 1/S against k. With the exception of the plot for diphenylamine, each plot has an intercept of approximately zero. Values of the threshold density, the constant Ca, and E are also listed in Table 3. Plots of E and E/δ against threshold density are shown in Figures 9A and B, respectively. It can be seen that the points for naphthalene, phenanthrene, cholesterol, and diphenylamine lie on a straight line, but the points due to phenol and β-naphthol are outliers, possibly because of the presence of the phenolic hydroxyl group. After dividing E by the solubility parameter, δ, the values for all six compounds fall fairly close to a straight line, as shown in Figure 9B. Good agreement between the solubility of phenanthrene at different densities calculated from this regression line and literature values18 is found, as shown in Figure 10. The average error obtained for the solubilities of these six compounds in comparison with the literature values was (13.5%. This is a significant improvement over the data obtained for the same molecules with a less polar column and (not unexpectedly) indicates that the stationary phase should be matched to the polarity of the molecules under investigation. The threshold densities were obtained in the same way as described above for the DB-5 column. A comparison of the linear regression line for the data obtained using the DB-5 (Figure 6) and the biphenyl-30 columns (Figure 9) shows that the values of
Figure 9. Plots of (A) E versus threshold density and (B) E/δ versus threshold density for six compounds eluted from a biphenyl-30 capillary column at 55 °C. In plot A, 1 represents phenol, and 2 represents β-naphthol. In plot B, the equation of the regression line is E/δ ) 0.49 + 1.06Ds.
Figure 10. Comparison of the solubilities of phenanthrene predicted in this work using a biphenyl-30 column (0) and from the literature5 (+).
A and B in the prediction equation are different and indicates that they are related to the chemical nature of the stationary phase. Thus, A and B must be determined for any column that is used to measure solubility using this technique. CONCLUSION The method proposed in this paper provides a faster way to estimate the solubilities of compounds in supercritical fluids than traditional gravimetric approaches. However, because of the complexity of the retention behavior, the inaccuracy of published solubility data, and the approximations involved when the Hildebrand solubility parameter is calculated by Fedors’s method, the Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
2359
accuracy of this method is limited to about (30% (which should still prove to be very useful for SFE). Although a linear relationship between solubility and capacity factor was obtained for polycyclic aromatic hydrocarbons on a packed column with an ODS2 stationary phase, the selectivity of the stationary phase can contribute to the problem of obtaining a good regression line for different classes of compounds. This problem was partially eliminated by using the Hildebrand solubility parameter. It could also possibly be overcome by choosing standards in a chemical class similar to that of the analyte, so that they all have similar values of δ, or (less likely) by choosing a less selective stationary
2360
Analytical Chemistry, Vol. 68, No. 14, July 15, 1996
phase. Because the constants A and B in eq 14 are related to the nature of the stationary phase, their values must be determined before this method can be applied with a new stationary phase. The use of capillary SFC columns eliminates some of these sources of error. Received for review April 16, 1996. Accepted April 25, 1996.X AC960371R X
Abstract published in Advance ACS Abstracts, June 1, 1996.
