Study of Interactions in Supercritical Fluids and Supercritical Fluid

the retention process in supercritical fluid chromatogra- phy (SFC) and to gain ... poly(dimethylsiloxane) stationary phase with pure carbon dioxide a...
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Anal. Chem. 1998, 70, 1404-1411

Study of Interactions in Supercritical Fluids and Supercritical Fluid Chromatography by Solvatochromic Linear Solvation Energy Relationships Jeff D. Weckwerth† and Peter W. Carr*

Department of Chemistry, Kolthoff and Smith Halls, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455

Linear solvation energy relationships were used to study the retention process in supercritical fluid chromatography (SFC) and to gain a better understanding of intermolecular interactions in supercritical fluids. Correlation of SFC retention data with a set of solute solvatochromic parameters, which are also applicable to gas and liquid chromatography, yields information regarding the relative contributions of dispersion, cavity formation, dipolar, and hydrogen-bonding processes to retention. Dispersion interactions and cavity formation processes dominate retention on an open tubular poly(dimethylsiloxane) stationary phase with pure carbon dioxide as the mobile phase. Dipolar interactions and hydrogen-bonding interactions are of decidedly less importance but do contribute significantly to retention. Based on prior solvatochromic studies of poly(dimethylsiloxane) and carbon dioxide, the changes in the regression coefficients with temperature and pressure are interpreted chemically. The relative importance of these contributions changes with temperature and pressure. As pressure increases, the carbon dioxide becomes more dense, and dispersion interactions between the solute and the mobile phase increase. A temperature increase at constant pressure decreases dispersion interactions with the stationary phase, as in gas chromatography, but also decreases dispersion interactions with the mobile phase, due to a decrease in carbon dioxide density. On the basis of the solvatochromic coefficients, carbon dioxide acts as both a Lewis base and a Lewis acid. The quality of fit for these correlations is very high and compares favorably with similar studies in gas chromatography and liquid chromatography, permitting the prediction of retention behavior from a solute’s solvatochromic parameters. As evidenced by several recent reviews, interest in supercritical fluids (SCFs) continues to grow as the existing technology matures and new applications are developed.1-4 Perhaps most importantly, SCFs are being explored as alternatives to conven† Present address: Eastman Chemical Co., Kingsport, TN 37662-5150. (1) Eckert, C. A.; Knutson, B. L.; Debenedetti, P. G. Nature 1996, 383, 313. (2) Bowadt, S.; Hawthorne, S. B. J. Chromatogr. 1995, 703, 549.

1404 Analytical Chemistry, Vol. 70, No. 7, April 1, 1998

tional solvents.5 For example, liquid-solid extraction processes that use conventional organic solvents have two major problems. Frequently a large volume of hazardous waste is produced and it is either hard to reclaim the solvent or costly to dispose of it.6 Additionally, liquid-solid extractions are often slow, taking hours, or even days, to reach completion.6 Supercritical fluid extraction (SFE), especially with carbon dioxide or carbon dioxide-based fluids, may be a solution to both of these problems, not only on an analytical scale6 but also for industrial-scale processing.7 SFE remains one of the most widely used and investigated SCF techniques, especially in the area of analytical sample preparation.8 SFE is used, particularly in environmental analysis, for the extraction of hydrocarbons, polyaromatic hydrocarbons, polychlorinated biphenyls, and other compounds from soils, sediments, airborne particulates, and related materials.9 For example, Eckert-Tilotta et al. used supercritical carbon dioxide to extract soil samples contaminated by heavy fuel oil, diesel fuel, light crude oil, gasoline, or kerosene spills. The method compared favorably to Soxhlet extraction with Freon-113.10 A related industrial-scale application of SFE involves the use of supercritical carbon dioxide for tertiary oil recovery in the petroleum industry.11 Regardless of the nature of any specific application of SCFs, it is obvious that a thorough understanding of the molecular level interactions that take place in these fluids is required.12 This work studies the intermolecular interactions responsible for retention in supercritical fluid chromatography (SFC). This information can possibly be extended to other systems, such as SFE. Recently, Yang and Griffiths used SFC retention times to predict solubility (3) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E. AIChE J. 1995, 41, 1723. (4) Palmer, M. U.; Ting, S. S. T. Food Chem. 1995, 52, 345. (5) Anastas, P. T.; Farris, C. A. Benign By Design. Alternative Synthetic Design for Pollution Prevention; ACS Symposium Series 577; American Chemical Society: Washington, DC, 1994. (6) Hawthorne, S. B. Anal. Chem. 1990, 62, 2, A633. (7) Eggers, R.; Wagner, H. J. Supercrit. Fluids 1993, 6, 31. (8) Chester, T. L.; Pinkston, J. D.; Raynie, D. E. Anal. Chem. 1996, 68, 487R. (9) Chester, T. L.; Pinkston, J. D.; Raynie, D. E. Anal. Chem. 1994, 66, 106R. (10) Eckert-Tilotta, S. E.; Hawthorne, S. B.; Miller, D. J. Fuel 1993, 72, 1015. (11) Abdulagatov, I. M.; Abdulkadyrova, K. S.; Dadashev, M. N. High Temp. 1993, 31, 765. (12) McNally, M. E. P.; Bright, F. V. In Supercritical Fluid Technology: Theoretical and Applied Approaches to Analytical Chemistry; ACS Symposium Series 488; Bright, F. V.; McNally, M. E. P., Eds.; American Chemical Society: Washington, DC, 1992; pp 1-15. S0003-2700(97)00673-2 CCC: $15.00

© 1998 American Chemical Society Published on Web 03/04/1998

in SCFs.13 The chromatographic approach to the study of intermolecular processes is attractive for the many reasons outlined in the classic monograph on physicochemical interactions in GC by Conder and Young.14 Chromatographic measurements are rapid and precise, require little solute, and inherently separate impurities from the solute.14 SFC has previously been used to measure thermodynamic properties, such as partial molar volumes and enthalpies, in SCFs.15-17 SFC is becoming an important analytical technique in its own right, especially for the analysis of oligomers and polymers.12 It occupies a significant niche intermediate between gas and liquid chromatography.12 However, since SFC is a newer technique and SCFs are more difficult to study than are liquids, the factors that govern retention in SFC are not nearly so well-understood as the retention controlling interactions in gas and liquid chromatography.12 The solvatochromic comparison method, in conjuction with linear solvation energy relationships (LSERs) as developed by Kamlet, Abraham, Taft, and their co-workers,18-22 has been very successful in rationalizing the chemical and physical factors, such as cavity formation, dispersion, dipolar, and Lewis acid-base (especially hydrogen-bonding) interactions that control retention in various modes of gas and liquid chromatography of nonelectrolytes.22-26 The current work extends this method to study and rationalize the major intermolecular processes that contribute to retention in SFC. The so-called solvatochromic comparison method was originally developed to study the effect of solvent on UV-visible spectra.18-20 Kamlet and Taft used a variety of spectroscopic methods, including UV-visible electronic spectroscopy, NMR, and IR, to develop the π*, R, and β scales of solvent strength. These three, highly selective, nearly orthogonal scales represent a solvent’s dipolarity/polarizability, hydrogen bond acidity, and hydrogen bond basicity, respectively.18-20 These sets of solvent parameters are used in a LSER, such as eq 1, to relate some

∆E ) ∆E0 + sπ* + aR + bβ

∆E0, represents that property in some reference phase that has all three solvatochromic parameters, R, β, and π* equal to zero. As originally established by Kamlet and Taft,20 π* of cyclohexane was defined as zero as were the hydrogen bond acidities and basicities of all saturated alkanes. Thus the intercept refers to the value of the property under study in cyclohexane. Subsequently the π* of the gas phase, that is, a noninteracting medium was measured at about -1.4.28 Supercritical carbon dioxide, being nonpolar and of low density, has π* values ranging from -0.5 to 0.0, depending on its density and temperature.29 The coefficients s, a, and b are determined by linear regression analysis, and they represent the susceptibility of the property under study (∆E) to changes in solvent dipolarity/polarizability, hydrogen bond acidity, and hydrogen bond basicity, respectively.27 Subsequently, Kamlet, Taft, and co-workers inverted the solvatochromic approach, so that a solute property could be correlated with a set of solute parameters.30 Initially the solute parameters were taken for non-self-associating fluids to be equal to the solvent parameters; however, a great deal of work has since gone into the development of methods for measuring solute parameters,31-35 and now their actual values are only loosely related to the corresponding parameters as bulk species. However, the chemical meaning of the solute parameters is the same as their meaning as solvent parameters. The current work is based on the second approach and thus it is analogous to prior solvatochromic work such as the study of solubility in water,36 retention in reversed-phase liquid chromatography (RPLC),23,24 and retention in gas chromatography (GC).25,26 In this work retention in GC and in SFC is treated as a simple partitioning process represented by the following equilibria.

GC: SFC:

Agas S Astat

(2)

ASCF CO2 S Astat

(3)

(1)

observable solvent-dependent energy-related property (denoted ∆E) to the various molecular interactions that the solvent can exert on the probe solute.20 In this LSER, ∆E is a free-energy-related solvent property, such as a spectroscopic frequency shift, a logarithmic reaction rate constant, or a logarithmic equilibrium constant.27 The intercept, (13) Yang, J.; Griffiths, P. R. Anal. Chem. 1996, 68, 2353. (14) Conder, J. R.; Young, C. L. Physicochemical Measurement by Gas Chromatography; Wiley: New York, 1979. (15) Olesik, S. V.; Kiba, N.; Novotny, M. V.; Roth, M.; Steger, J. L. J. Chromatogr. 1987, 392, 165. (16) Shim, J. J.; Johnston, K. P. J. Phys. Chem. 1991, 95, 353. (17) Schneider, G. M. J. Chem. Therm. 1991, 23, 301. (18) Kamlet, M. J.; Taft, R. W. J. Am. Chem. Soc. 1976, 98, 377. (19) Kamlet, M. J.; Taft, R. W. J. Am. Chem. Soc. 1976, 98, 2886. (20) Kamlet, M. J.; Taft, R. W. J. Am. Chem. Soc. 1977, 99, 6027. (21) Kamlet, M. J.; Taft, R. W. J. Am. Chem. Soc. 1977, 99, 8325. (22) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. J. Chem. Soc., Perkin Trans. 2 1990, 1451. (23) Sadek, P. C.; Carr, P. W.; Doherty, R. M.; Kamlet, M. J.; Taft, R. W.; Abraham, M. H. Anal. Chem. 1985, 57, 2971. (24) Tan, L. C.; Carr, P. W.; Frechet, J. M. J.; Smigol, V. Anal. Chem. 1994, 66, 450. (25) Li, J. J.; Dallas, A. J.; Carr, P. W. J. Chromatogr. 1990, 517, 103. (26) Li, J. J.; Carr, P. W. J. Chromatogr., A 1994, 659, 367.

Specifically, open tubular GC and SFC are used to measure capacity factors (k′) for a set of solutes (A), which can be related to the partition coefficient (K) and the free energy of transfer (∆G0) as shown in eqs 4 and 5. In eq 5, φ is the phase ratio of the

∆G° ) -RT ln K

(4)

ln k′ ) ln K + ln φ

(5)

chromatographic column, which for a pure phase partition process can be defined as Vstat/Vmob, where Vstat and Vmob denote the (27) Carr, P. W. Microchem. J. 1993, 48, 4. (28) Essfar, M.; Guiheneuf, G.; Abboud, J. L. M. J. Am. Chem. Soc. 1982, 104, 6786. (29) Yonker, C. R.; Frye, S. L.; Kalkwarf, D. R.; Smith, R. D. J. Phys. Chem. 1986, 90, 3022. (30) Taft, R. W.; Abraham, M. H.; Doherty, R. M.; Kamlet, M. J. J. Am. Chem. Soc. 1985, 107, 3105. (31) Li, J. J.; Zhang, Y.; Dallas, A. J.; Carr, P. W. J. Chromatogr. 1991, 550, 101. (32) Li, J. J.; Zhang, Y.; Carr, P. W. Anal. Chem. 1993, 65, 1969. (33) Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J. J. Chromatogr. 1991, 587, 213. (34) Abraham, M. H.; Whiting, G. S. J. Chromatogr. 1992, 594, 229. (35) Abraham, M. H. J. Chromatogr. 1993, 644, 95. (36) Abraham, M. H.; Andonianhaftvan, J.; Whiting, G. S.; Leo, A.; Taft, R. S. J. Chem. Soc., Perkin Trans. 2 1994, 1777.

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volume of stationary phase and mobile phase, respectively, in the column. With a few exceptions,37 it is possible to treat both open tubular GC38 and open tubular SFC on polymer films as partition processes.39,40 We will use the LSER given by eq 6 to correlate GC and SFC retention. In eq 6, the parameters π2H, ΣR2H, and Σβ2H represent

log k′ ) log k′0 + l log L16 + sπ2H + aΣR2H + bΣβ2H + rR2 (6) the solute’s dipolarity/polarizability, hydrogen bond acidity, and hydrogen bond basicity, respectively. The Σ notation denotes the important distinction that the hydrogen-bonding parameter is measured in the presence of a much larger amount of the complementary hydrogen-bonding agent and thus all available donor and acceptor sites on the solute are utilized. These solute scales were developed by Abraham34-36 from GC data. In this investigation, Abraham’s parameters were chosen over other available parameters31,32 because they are available for many more solutes and can be estimated for many others. The logarithm of a solute’s gas-to-hexadecane partition coefficient, log L16, is used to model dispersion interactions and cavity formation processes.34 Because one term is used to model both processes, a correction factor is needed for solutes with different polarizability/volume ratios.35 Abraham defined and used the excess molar refractivity, R2 as this correction factor.35 The purpose of this work is to relate retention in SFC to the intermolecular interactions discussed above. The role of the supercritical mobile phase is rationalized on the basis of the LSER coefficients and previous solvatochromic studies of SCFs.41 Previously, Kim and Johnston measured solvatochromic shifts of phenol blue in supercritical CO2, C2H4, CHF3, and CF3Cl, as well as binary mixtures of carbon dioxide and several modifiers.42,43 Yonker and Smith used the solvatochromic approach to measure π* for supercritical carbon dioxide44 and for a few binary mixtures of carbon dioxide.45,46 They also used their spectroscopic results to rationalize changes in SFC retention with changes in mobile-phase conditions.46 Similarly, Deye et al. measured solvent strength with the solvatochromic dye Nile Red and extended the results to SFC retention.47 Engel and Olesik developed a model for SFC retention on a porous glassy carbon stationary phase using solvatochromic parameters for the carbon dioxide modifiers.48 There are only a few reported applications of LSERs using solute parameters to study retention in SFC.49-51 Each of these (37) Li, J. Ph.D. Thesis, University of Minnesota, 1992. (38) Rohrschneider, L. Anal. Chem. 1973, 45, 1241. (39) Roth, M. J. Phys. Chem. 1992, 96, 8548. (40) Roth, M. J. Phys. Chem. 1992, 96, 8552. (41) Brady, J. E.; Bjorkman, D.; Herter, C. D.; Carr, P. W. Anal. Chem. 1984, 56, 278. (42) Kim, S. W.; Johnston, K. P. AIChE J. 1987, 33, 1603. (43) Kim, S.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1206. (44) Yonker, C. R.; Frye, S. L.; Kalkwarf, D. R.; Smith, R. D. J. Phys. Chem. 1986, 90, 3022. (45) Yonker, C. R.; Smith, R. D. J. Phys. Chem. 1988, 92, 2374. (46) Yonker, C. R.; Smith, R. D. In Supercritical Fluid Extraction and Chromatography: Techniques and Applications; Charpentier, B. A., Stevenants, M. R., Eds.; ACS Symposium Series 366; American Chemical Society: Washington, DC, 1988; pp 161-178. (47) Deye, J. F.; Berger, T. A.; Anderson, A. G. Anal. Chem. 1990, 62, 615. (48) Engel, T. M.; Olesik, S. V. Anal. Chem. 1991, 63, 1830.

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examples involved very complex systems including packed columns and binary mobile phases. In contrast, the current studies involved a nonpolar, polymer-bonded capillary phase using unmodified carbon dioxide. Also, these applications featured severely limited solute sets. On the basis of extensive prior experience, Kamlet and Taft recommended an absolute minimum of three to four judiciously chosen solutes per parameter to obtain chemically meaningful coefficients.52 Furthermore, to obtain chemically meaningful and statistically reliable LSER coefficients (l, s, a, b, r) each of the solute parameters must be varied over a reasonably wide range by judicious choice of the probe solute set.52 This work systematically explores the solvatochromic LSER model as a function of pressure (density) and temperature in SCF carbon dioxide. EXPERIMENTAL SECTION Chromatographic System. The supercritical fluid mobile phase was pressurized and delivered by a Varian 8500 syringe pump (Walnut Creek, CA), and was heated in a Hewlett-Packard 5710 gas chromatograph (Avondale, PA). Samples were introduced with a Valco W-series high-pressure injection valve that was fitted with a 0.2-mL rotor. The split ratio was adjusted to obtain good peak shapes. The flame ionization detector in the Hewlett-Packard 5710 GC was used to detect the compounds. Materials and Column. SFC-grade CO2 was obtained from Scott Specialty Gases (Plumsteadville, PA). The capillary column was a 5 m × 50 mm i.d. SB-Methyl-100 poly(dimethylsiloxane) with 0.25-mm film thickness obtained from Dionex (Sunnyvale, CA). A frit-type restrictor was used. The void volume of the system was taken as the methane peak. Solutes were obtained commercially and were analytical grade in the highest purity available. Solutes were dissolved in ACS grade carbon disulfide. RESULTS AND DISCUSSION Goodness of Fit. Although solvatochromic LSERs have been used to correlate retention data in both LC23,24 and GC,25,26 there are only a few applications of this method to SFC.49-51 The current work, while aimed at understanding retention in SFC, also acts as a test of the generality of the entire LSER methodology. The first test of the LSER methodology for any system involves the goodness of fit.52 SFC retention data for several compounds (Table 1), measured for the poly(dimethylsiloxane)/carbon dioxide system at several temperatures and pressures, were correlated using the LSER given in eq 6. The results of these regressions are given in Table 2. In each regression, the correlation coefficient (R) exceeds 0.996, and the standard error (sd) is less than 0.03. Even for the most poorly fit of these data sets, the calculated values of log k′ compare well with the experimental values, as shown in Figure 1 . These fits are at least as good as any that have been previously reported for GC25,26 or LC.23,24 Clearly, retention in SFC under these conditions is remarkably well-correlated with eq 6. This goodness of fit strongly suggests that the LSER methodology is just as applicable to SFC as it is to GC and RPLC. (49) Heaton, D. M.; Bartle, K. D.; Clifford, A. A.; Klee, M. S.; Berger, T. A. Anal. Chem. 1994, 66, 4253. (50) Pyo, D.; Li, W.; Lee, M. L.; Weckwerth, J. D.; Carr, P. W. J. Chromatogr. 1996, 753, 291. (51) Cantrell, G. O.; Stringham, R. W.; Blackwell, J. A.; Weckwerth, J. D.; Carr, P. W. Anal. Chem. 1996, 68, 3645. (52) Kamlet, M. J. Personal Communication.

Table 1. Solutes and Descriptors no.

solute

R2

π2H

ΣR2H

Σβ2H

log L16

no.

solute

R2

π2H

ΣR2H

Σβ2H

log L16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

octane nonane undecane dodecane tridecane tetradecane pentadecane hexadecane methylcyclohexane cycloheptane cyclooctane 1-nonene 1-decene 1-undecene 1-dodecene 1-octyne 1-dodecyne 1-chloropentane 1-chlorohexane 1-chloroheptane 1-chlorooctane 1-bromohexane 1-iodohexane dibutyl ether hexanal heptanal octanal 2-heptanone 2-nonanone 2-undecanone cyclohexanone butyl acetate pentyl acetate hexyl acetate 1-cyanobutane 1-cyanopentane 1-cyanohexane 1-cyanoheptane 1-cyanooctane 1-cyanononane 1-nitrobutane 1-nitropentane butanoic acid

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.244 0.350 0.413 0.090 0.093 0.091 0.089 0.155 0.133 0.208 0.201 0.194 0.191 0.349 0.615 0.000 0.146 0.140 0.160 0.123 0.119 0.101 0.403 0.071 0.067 0.056 0.177 0.166 0.159 0.162 0.159 0.156 0.227 0.212 0.210

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 0.10 0.08 0.08 0.08 0.08 0.23 0.23 0.40 0.40 0.40 0.40 0.40 0.40 0.25 0.65 0.65 0.65 0.68 0.68 0.68 0.86 0.60 0.60 0.60 0.90 0.90 0.90 0.90 0.90 0.90 0.95 0.95 0.62

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.60

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.07 0.07 0.07 0.10 0.10 0.10 0.10 0.10 0.10 0.12 0.15 0.45 0.45 0.45 0.45 0.51 0.51 0.51 0.56 0.45 0.45 0.45 0.36 0.36 0.36 0.36 0.36 0.36 0.29 0.29 0.45

3.677 4.182 5.191 5.696 6.200 6.705 7.209 7.714 3.323 3.704 4.329 4.073 4.533 5.023 5.515 3.521 5.657 3.223 3.777 4.282 4.772 4.130 4.620 3.924 3.357 3.865 4.361 3.760 4.735 5.732 3.792 3.353 3.844 4.351 3.108 3.608 4.089 4.585 4.970 5.460 3.415 3.938 2.830

44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

hexanoic acid heptanoic acid nonanoic acid 1-pentanol 1-hexanol 1-heptanol 1-octanol 1-nonanol 1-decanol 1-undecanol toluene ethylbenzene o-xylene propylbenzene butylbenzene pentamethylbenzene hexamethylbenzene biphenyl naphthalene chlorobenzene o-dichlorobenzene benzyl chloride bromobenzene benzyl bromide iodobenzene anisole phenetole benzaldehyde acetophenone propiophenone methyl benzoate ethyl benzoate benzonitrile nitrobenzene o-nitrotoluene m-nitrotoluene p-nitrotoluene phenol o-cresol m-cresol p-cresol o-chlorophenol benzyl alcohol

0.174 0.149 0.132 0.219 0.210 0.211 0.199 0.193 0.191 0.181 0.601 0.613 0.663 0.604 0.600 0.850 0.950 1.360 1.340 0.718 0.872 0.821 0.882 1.014 1.188 0.708 0.681 0.820 0.818 0.804 0.733 0.689 0.742 0.871 0.866 0.874 0.870 0.805 0.840 0.822 0.820 0.853 0.803

0.60 0.60 0.60 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.52 0.51 0.56 0.50 0.51 0.66 0.72 0.99 0.92 0.65 0.78 0.82 0.73 0.98 0.82 0.75 0.70 1.00 1.01 0.95 0.85 0.85 1.11 1.11 1.11 1.10 1.11 0.89 0.86 0.88 0.87 0.88 0.87

0.60 0.60 0.60 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.60 0.52 0.57 0.57 0.32 0.33

0.45 0.45 0.45 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.14 0.15 0.16 0.15 0.15 0.20 0.21 0.22 0.20 0.07 0.04 0.33 0.09 0.20 0.12 0.29 0.32 0.39 0.48 0.51 0.46 0.46 0.33 0.28 0.27 0.25 0.28 0.30 0.30 0.34 0.31 0.31 0.56

3.920 4.460 5.550 3.106 3.610 4.115 4.619 5.124 5.628 6.130 3.325 3.778 3.939 4.230 4.730 5.798 6.557 6.014 5.161 3.657 4.518 4.384 4.041 4.672 4.502 3.890 4.242 4.008 4.501 4.971 4.704 5.075 4.039 4.557 4.878 5.097 5.154 3.766 4.218 4.310 4.312 4.178 4.221

Table 2. Effect of Temperature and Pressure on LSER Coefficientsa Pb

Tc

SP0d

ld

1h 1100 1300 1500 1700

100 100 100 100 100

-2.00 ( 0.04 -1.68 ( 0.01 -1.69 ( 0.02 -1.70 ( 0.01 -1.70 ( 0.01

0.559 ( 0.008 0.361 ( 0.002 0.330 ( 0.002 0.299 ( 0.002 0.267 ( 0.003

1300 1300 1300 1300

60 80 100 120

-1.56 ( 0.01 -1.64 ( 0.01 -1.69 ( 0.02 -1.74 ( 0.01

0.315 ( 0.002 0.339 ( 0.002 0.330 ( 0.002 0.316 ( 0.002

rd

bd

Re

sd f

Ng

A. Constant Temperature 0.16 ( 0.04 0.23 ( 0.04 0.16 ( 0.01 0.21 ( 0.01 0.15 ( 0.01 0.21 ( 0.01 0.13 ( 0.01 0.19 ( 0.01 0.12 ( 0.01 0.16 ( 0.01

0.07 ( 0.02 0.050 ( 0.009 0.060 ( 0.009 0.080 ( 0.009 0.10 ( 0.01

0i -0.06 ( 0.02 -0.06 ( 0.02 -0.06 ( 0.02 -0.08 ( 0.02

0.996 0.999 0.998 0.998 0.996

0.058 0.019 0.019 0.018 0.022

47 86 86 86 86

B. Constant Pressure 0.16 ( 0.01 0.27 ( 0.01 0.14 ( 0.01 0.23 ( 0.01 0.15 ( 0.01 0.21 ( 0.01 0.13 ( 0.01 0.16 ( 0.01

0.04 ( 0.01 0.06 ( 0.01 0.060 ( 0.009 0.080 ( 0.008

-0.13 ( 0.02 -0.08 ( 0.02 -0.06 ( 0.02 -0.05 ( 0.02

0.998 0.998 0.998 0.998

0.021 0.020 0.019 0.017

86 86 86 86

sd

ad

a Stationary phase is Dionex SB-Methyl-100; mobile phase is pure CO at the indicated temperature and pressure. b In psi. c In °C. d See eq 6. 2 Coefficient of correlation. f Average residual of fit. g Number of solutes tested. h Stationary phase is DB-1; mobile phase is He at the indicated temperature. Data from ref 46. i Coefficient of solute basicity is statistically insignificant in GC.

e

However, mere goodness of fit is only a necessary but not sufficient condition to consider the model as being an acceptable description of a process. In addition to goodness of fit, according to Kamlet and Taft,52 the coefficients must make chemical sense. Both the pressure and temperature dependence of the LSER

coefficients have been examined and are consistent with the known behavior of the poly(dimethylsiloxane) stationary phase37 and the supercritical carbon dioxide mobile phase.42 This rationalization of coefficients, coupled with the goodness of fit for our data, indicates that the LSER methodology is just as applicable Analytical Chemistry, Vol. 70, No. 7, April 1, 1998

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Figure 1. Calculated vs experimental log k′. Calculated values are from eq 6 and the coefficients in Table 1. Classes of compounds represented: (O) nonpolar aliphatic, (0) polar (aprotic) aliphatic, (4) protic aliphatic, (b) nonpolar aromatic, (9) polar (aprotic) aromatic, and (2) protic aromatic. The solid line is the 1:1 line. The stationary phase is a SB-Methyl-100. The mobile phase is pure CO2 at 1700 psi and 100 °C.

to SFC retention on a polymer-coated capillary as it is to GC and RPLC. LSER Characterization of the Stationary Phase. As mentioned above, the type of stationary phase used in these experiments has already been studied using GC retention data and the solvatochromic comparison method.37 Dimethylsiloxanes have been studied by direct solvatochromism.41 At room temperature this type of medium has a π* and β of 0.07 and 0.15, respectively. In comparison, the π* value for bulk hexadecane is 0.07 and the β value for diethyl ether is 0.47.27 This type of phase is thus about as interactive as bulk hexadecane and is a weak hydrogen bond acceptor. It should have no ability to donate hydrogen bonds (R ) 0) by analogy to chemically similar substances such as diethyl ether. GC retention on a chemically analogous poly(dimethylsiloxane) (DB-1) stationary phase at 100 °C correlates with the solute descriptors as shown in eq 7.37 Note that Abraham’s π2H

log k′GC,100°C ) (-2.00 ( 0.04) + (0.559 ( 0.008) log L16 + (0.16 ( 0.04)π2H + (0.23 ( 0.04)ΣR2H + (0.07 ( 0.02)R2 (7) N ) 47

sd ) 0.058

R ) 0.996

and ΣR2H scales are used here to be consistent with the parameters used in the SFC correlations. Statistically better fits to the GC data can be achieved using Li’s chromatographic solute parameters, π*2C and R2C.37 However, the chemical interpretation of the coefficients (l, s, a, b, r) is not altered by using Li’s parameters. An analysis of the sign and magnitude of the individual coefficients for GC retention will aid in understanding the 1408 Analytical Chemistry, Vol. 70, No. 7, April 1, 1998

coefficients for SFC retention. In GC, because there are no solute interactions with the mobile phase, all of the coefficients reflect one or more properties of the stationary phase. The l coefficient (coefficient of log L16) represents contributions of cavity formation and dispersion interactions in the stationary phase. The positive sign of the l coefficient indicates that dispersive interactions between the solute and the stationary phase outweigh cavity processes.37 If the cavity formation process (an endoergic process) were dominant, the sign of the l coefficient would be negative, and correspondingly, we would observe that small, nonpolar compounds would be more retained than larger, nonpolar compounds. This is clearly not the case in GC. By the same reasoning, the s and a coefficients (coefficients of π2H and ΣR2H) must also be positive, as these represent exoergic processes that cannot occur in the gaseous mobile phase. Both of these coefficients are small, but statistically significant, indicating that the DB-1 phase has a low dipolarity and is a weak hydrogen bond acceptor. This is consistent with the π* and β measurements for bulk poly(dimethylsiloxane). Since DB-1 is not a hydrogen bond donor, retention on this phase does not depend on solute basicity. The r coefficient (coefficient of R2, the excess molar refractivity), which is always small, is difficult to interpret, and no attempt will be made to do so in this work. Retention in GC, as shown in eq 7, is predominantly dependent on the l log L16 term and, therefore, on dispersion interactions with the stationary phase. Not only is the l coefficient larger than any of the other coefficients, but the log L16 descriptor covers a wider range of values (1.0-7.0 for this data set) than do any of the other descriptors (0.0-2.0). For example, even for a small and reasonably polar solute such as 1-propanol (log L16 ) 2.031, π2H ) 0.42, Σa2H ) 0.37, R2 ) 0.236), the l log L16 term accounts for 87% of retention on DB-1 at 100 °C. Assuming that the DB-1 phase described above and the SBMethyl-100 phase used in the current work are chemically nearly identical, then differences in the GC and SFC LSER coefficients can be rationalized by contributions from the mobile phase. For example, the l coefficient represents the following difference:

l ) lstat - lmob

(8)

where lstat is a relative measure of the strength of solute-stationaryphase dispersion forces and cavity processes and lmob is a relative measure of the strength of solute-mobile phase dispersion forces and cavity processes. In GC, the solute does not interact with the mobile phase, so l ) lstat. In SFC, however, there is a contribution (lmob) from the mobile phase. The relative strength of these solute-carbon dioxide dispersion interactions and cavity processes can be quantified from the difference lstat - l, with lstat being determined by GC as described above. However, the assumption that the GC stationary phase and the SFC stationary phase are identical is not valid. It is wellknown53-55 that polysiloxanes in contact with supercritical carbon dioxide swell significantly; that is, a considerable amount of carbon dioxide dissolves in the polysiloxane. Yonker and Smith54 and, (53) Springston, S. R.; David, P.; Steger, J.; Novotny, M. Anal. Chem. 1986, 58, 997. (54) Yonker, C. R.; Smith, R. D. J. Chromatogr. 1990, 505, 139. (55) Strubinger, J. R.; Song, H. C.; Parcher, J. F. Anal. Chem. 1991, 63, 98.

Figure 2. Effect of (A) pressure and (B) temperature on LSER coefficients. Coefficients: (b) l coefficient, (2) a coefficient, (9) s coefficient, (1) r coefficient, and ([) b coefficient. The column is a SB-Methyl-100. The mobile phase is pure CO2. In (A), the temperature is held constant at 100 °C. In (B), the pressure is held constant at 1300 psi.

more recently, Strubinger et al.55 measured the extent of stationary-phase swelling as a function of the pressure and temperature of the carbon dioxide mobile phase. Based on the data from these two studies, in the current work swelling increases with increasing pressure at constant temperature and decreases with increasing temperature at constant pressure. This is not true over the entire range of temperature and pressure, but only in the range of temperature and pressure investigated here. The uptake of carbon dioxide physically and chemically alters the stationary phase, complicating the analysis. Pressure Dependence of Retention. The regression results for SFC retention at 100 °C and 1300 psi are given in eq 9 and in

log k′100°C,1300psi ) (-1.69 ( 0.02) + (0.330 ( 0.002) log L16 + (0.15 ( 0.01)π2H + (0.21 ( 0.01)ΣR2H - (0.06 ( 0.02)Σβ2H + (0.060 ( 0.009)R2 (9) N ) 86

sd ) 0.019

R ) 0.998

Table 2. Comparing eqs 7 and 9, the LSER coefficients are strikingly similar for GC and SFC retention. The coefficients of π2H, ΣR2H, and R2 are statistically equal in GC and SFC at 100 °C when the pressure of the SCF carbon dioxide is 1300 psi. The equality of the s, a, and r coefficients at 100 °C in GC and SFC is not just due to a fortuitous choice of pressure. As shown in Table 2A, the coefficients at constant temperature are virtually independent of the carbon dioxide pressure and therefore its density. The coefficient of log L16, however, is much smaller in SFC than in GC, so it is strongly dependent on the carbon dioxide density (see Table 2A). An unanticipated but not surprising result is the small but statistically real negative coefficient of Σβ2H. The negative coefficient of the solute hydrogen bond basicity suggests that carbon dioxide is acting as a Lewis acid (see below). As shown in Table 2A and Figure 2A, the coefficients l, s, and a decrease as the pressure of carbon dioxide is increased at a

constant temperature of 100 °C. The change in the l coefficient is much greater than in the other coefficients. By extrapolating the l coefficient obtained in GC,37 we see that the temperature would have to be increased by nearly 150 °C to decrease the GC l coefficient to 0.267, which is the value of the l coefficient in SFC at 100 °C and 1700 psi. This pressure is relatively low for SFC. Based on prior interpretation of the GC retention on this phase,37 the l coefficient depends primarily on dispersion interactions. Therefore, the main difference between GC and SFC with pure carbon dioxide is dispersive interactions between carbon dioxide and the solute in the mobile phase. The magnitude of these interactions is given by the difference between the SFC l coefficient and the GC l coefficient, assuming that carbon dioxide does not modify the stationary-phase chemistry. The small decreases in the s and a coefficients are much less significant, but they can also be chemically rationalized. Although carbon dioxide has no dipole moment, the decrease in the s coefficient can be attributed to the presence of dipole/induceddipole or dipole/quadrupole interactions between the solute and the mobile phase. This is consistent with spectroscopic measurements in supercritical carbon dioxide in which Sigman et al.56 and Yonker et al.44 determined that the π* for bulk carbon dioxide is slightly less than that of liquid alkanes and that it increases with the density of the carbon dioxide. The a coefficient is smaller for SFC with carbon dioxide compared to GC because the carbon dioxide acts as a hydrogen bond base. The basicity of carbon dioxide has been observed spectroscopically.56 However, according to the spectroscopic results, the β value of carbon dioxide does not increase significantly with pressure. In contrast, the current work indicates a monotonic but small increase in the effective basicity of carbon dioxide as the pressure increases. The decrease in the l, s, and a coefficients could also be due in part to the uptake of carbon dioxide and concomitant swelling of the stationary phase. This uptake of carbon dioxide will have the effect of “diluting” and/or imparting mobile-phase-like proper(56) Sigman, M. E.; Lindley, S. M.; Leffler, J. E. J. Am. Chem. Soc. 1985, 107, 1471.

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ties to the stationary phase, which could lead to a decrease in the LSER coefficients for SFC relative to GC. It is highly unlikely that these “dilution” effects by themselves can cause the large decrease in the l coefficient relative to that observed in GC. More likely, the decrease in the LSER coefficients is due to a combination of these two effectssincreased interactions with the mobile phase and dissolution of carbon dioxide in the stationary phase. Another difference between the SFC and GC results is the b coefficient. The b coefficient, though insignificant for a poly(dimethylsiloxane) phase (a non-hydrogen bond donating phase) in GC, is significant in SFC. The b coefficient represents the difference in hydrogen bond acidity of the stationary and the mobile phases. The negative sign of the coefficient indicates that carbon dioxide is acting as a hydrogen bond acid, which, of course, is chemically impossible. However, carbon dioxide is a hard, weak Lewis acid, so the negative b coefficient is a measure of its electronaccepting ability. The Lewis acidity of carbon dioxide has been quantified based on solvatochromic shifts.48 For example, Engel and Olesik reported an a value of 0.05 for carbon dioxide at 25 °C and 170 atm.48 The b coefficient was statistically equal at all pressures studied in this work. Temperature Dependence of Retention. The processes which are represented by log L16, π2H, ΣR2H and Σβ2H are exothermic, so these interactions should decrease with increasing temperature.37 In GC, as expected, Li found that an increase in temperature leads to a decrease in all coefficients (l, s, a, b).37 Similarly, in a conventional liquid solvent, as the temperature is increased, the intermolecular interactions will decrease in magnitude. The temperature dependence of LSER coefficients for LC is more complicated than that for GC. This will be demonstrated by analyzing the temperature dependence of the s coefficient for LC. Just as the l coefficient for an interacting mobile phase is given by eq 8, the s coefficient for LC is given by eq 10, where

s ) sstat - smob

(10)

sstat represents the dipolarity/polarizability of the stationary phase and smob represents the dipolarity/polarizability of the mobile phase. As the temperature changes, the dipolarity/polarizability of the stationary phase will change by ∆sstat, and the dipolarity/ polarizability of the mobile phase will change by ∆smob. This leads to an overall change in the s coefficient with temperature as given by eq 11.

( ) ( ) ( ) ∂s ∂T

)

P

∂sstat ∂T

-

P

∂smob ∂T

P

(11)

According to Li,37 the temperature dependence, that is, the magnitude of the ∂sstat/∂T|P and ∂smob/∂T|P terms depends on the magnitude of sstat and smob, respectively. Therefore, if sstat > smob, then ∂sstat/∂T|P > ∂smob/∂T|P and vice versa. In terms of the s coefficient for LC, this means that the magnitude of s will decrease with increasing temperature, but the sign of s will not change. We will refer to this as the “temperature-dependent effect”. This is true for all exothermic processes in LC. One might expect, then, that the LSER coefficients for SFC will behave similarly with increasing temperature. However, unlike a conventional liquid where density is only slightly 1410 Analytical Chemistry, Vol. 70, No. 7, April 1, 1998

temperature dependent, at constant pressure, the density of the supercritical carbon dioxide decreases strongly and monotonically as the temperature increases, thereby causing a decrease in solute-carbon dioxide interactions in the mobile phase.12 This will be referred to as the “density-dependent effect”. Thus, a temperature change has two effects in SFC. As in LC, the “temperature-dependent effect” causes a decrease in the LSER coefficients as temperature is increased, but the “densitydependent effect” causes an increase in the LSER coefficients due to a diminution in the strength of the interactions of the solute with the mobile phase. On the basis of the decrease in the s, a, and b coefficients with increasing temperature (see Figure 2B and Table 2), the “temperature-dependent effect” rather than the “density-dependent effect” is more important. The temperature dependence of the l coefficient is more complicated. At low temperatures under isobaric conditions, an increase in temperature causes a decrease in the density of carbon dioxide. This leads to an increase in retention and, therefore, an increase in the l coefficient due to a diminution in the strength of the interactions of the solutes with the mobile phase due to the density-dependent effect. However, as the temperature is increased further, the retention decreases because the densitydependent effect is overshadowed by the temperature-dependent effect. Just as in GC, then, the l coefficient now decreases with increasing temperature. This interpretation was corroborated by carrying out a constant-density experiment in which the temperature was increased and the pressure adjusted to hold the density constant. At constant density, retention and the l coefficient both decrease monotonically with increasing temperature (see curve c in Figure 3A). The temperature dependence of SFC retention is also compared to that of GC. Figure 3 shows the GC and SFC coefficients as a function of reciprocal temperature. The difference between the GC coefficients and the SFC coefficients represents the contribution of the supercritical carbon dioxide mobile phase. Except for the l coefficient at high temperatures, this difference becomes greater at lower temperatures (higher densities). Again, this could be due to a mobile-phase effect (increased interactions) or a stationary-phase effect (swelling). Test of the Applicability of Other LSER Parameters. In RPLC, better fits are obtained when a volume term, rather than log L16, is used to scale solute size and dispersive interactions. If McGowan’s volume (VX,2), an easily calculated parameter,57 were adequate for correlating SFC retention, L16 values would not need to be determined and many more compounds could be investigated. However, replacing log L16 with VX,2 resulted in much worse fits. This indicates that SFC at the temperatures and densities explored here more closely resembles GC than LC. Furthermore, the fact that the l coefficients (see below) are positive shows that the dispersive interactions in the mobile phase are more important than cavity formation processes. This result is not too surprising since most of the data were collected in a supercritical region that is more like a dense gas than a liquid. The reduced densities (rR), that is, the density divided by the density at the critical point, varied from 0.288 to 0.502 (1.1 < TR < 1.3 1.0 < PR < 1.6). (57) Abraham, M. H.; McGowan, J. C. Chromatographia 1987, 23, 243.

Figure 3. Effect of temperature on the LSER coefficients. Coefficients plotted are (A) l, (B) s, (C) a, and (D) b. The GC coefficients (9) for a DB-1 stationary phase (46) are given by curve a. The SFC coefficients (b) for a SB-Methyl-100 stationary phase and pure CO2 mobile phase are given by curve b, for a constant pressure of 1300 psi and by curve c, for a constant density of 0.25 g/mL. The b coefficient in GC is statistically insignificant.

CONCLUSIONS Based on the excellent fits to the LSER and the chemically reasonable coefficients of these fits, this work demonstrates that the solvatochromic comparison method can be used to correlate and explain retention in SFC. For the poly(dimethylsiloxane)/ carbon dioxide system at low densities, retention of a solute is due primarily to dispersion interactions and cavity formation processes. These processes also govern the changes in retention with pressure and temperature. Solute carbon dioxide dispersion interactions increase with pressure, causing a decrease in retention. At low temperatures, solute carbon dioxide dispersion interactions decrease with increasing temperature, causing an increase in retention. At high temperatures, solute poly(dimethylsiloxane) dispersion interactions decrease faster than solute carbon dioxide dispersion interactions, so a decrease in retention is observed.

Retention in SFC under these conditions is also dependent on a solute’s dipolarity/polarizability, hydrogen bond acidity, and hydrogen bond basicity. The contributions to retention from these types of interactions decrease with increasing pressure and temperature. According to the LSER results, carbon dioxide acts as a weak Lewis acid. ACKNOWLEDGMENT This work was supported in part by grants from the National Science Foundation and the Graduate School of the University of Minnesota.

Received for review June 27, 1997. Accepted January 2, 1998. AC9706739

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