J . Phys. Chem. 1988, 92, 1664-1667
1664
a +complex configuration. This is in contradiction to the experimental evidence, which poses a challenge for further quantum chemical studies. The complex Al[C&,] poses another interesting prdbiem. Here ESR studies3indicate a novel bonding arrangement in which the AI atom interacts with just two carbon atoms rather than with the full aromatic ring. The description of the bonding is then entirely analogous to the A1[C,H4] case. A further intriguing aspect of these a-complexes is the tendency for formation of monoligand as opposed to diligand complexes. This is in -~ contrast to the case of A1 CO, for which e ~ p e r i m e n t a l ~and
+
theoreticals studies indicate a preference for the diligand complex Al(C0)z. Note Added in Proof. Recent ab initio CI calculations (ref 37) for AI[C2H,] in a r-complex configuration find a binding energy of 1.89 kcal.mol-l, significantly lower than our experimental value of > 16 kcal-mol-'. Registry No. AI, 7429-90-5; CO, 630-08-0; C2Hz, 74-86-2; C&b, 74-85-1;1-butene,106-98-9;2-butene, 107-01-7; 2,3-dimethyl-2-butene, 563-79-1; 1,3-cyclohexadiene,592-57-4; benzene, 71-43-2; toluene, 10888-3; o-xylene, 95-47-6.
Rdantion in Supercrltlcal FluM Chromatography:
Influence of the Partial Molar Volume
of tho sdlute in the Stationary Phase Clement R. Yonker* and Richard D. Smith Chemical Methods and Separations Group, Chemical Sciences Department, Pacific Northwest Laboratory (Operated by Battelle Memorial Institute), Richland, Washington 99352 (Received: June 9, 1987)
Theoretical models for retention in supercritical fluid chromatography have described solute retention based on statistical thermodynamics or classical thermodynamic models of mobile-phase interactions with the solute. The shortcomings of these models largely reside in the assumption of pressure-independentsolutestationary phase interactions with supercritical fluids. The pressure dependence of the partial molar volume of the solute in the stationary phase and the role of the partial molar volume of the solute in the stationary phase on retention in supercritical fluid chromatography are discussed based upon experimental studies with C 0 2 over a wide range of fluid pressures.
IMradUction
Ecktrt, C . A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J . Phys. Chem. 1986,90,2738. (2) Ziger, D.H. Ph.D. Thesis, University of Illinois, Urbana, 1983.
description of solute retention far applicable systems can be obtained. The mathematical complexity of the Lee-Kesler EOS constitutes the major drawback of this approach8~~Martire and Martire and Boehmlos'l have developed an alternative unified theory of chromatographic retention based on a statistical thermodynamic treatment using established lattice-gas models to describe the solute partition coefficient. Previous theoretical work by Martire et al.l2-I4for liquid chromatography has been expanded and applied to retention in supercritical fluid chromatography. Solute retention in Martire's work is related to molecular parameters that control retention. Yonker et aI.l5 have used a simple thermodynamic model of solute retention in SFC as a function of pressure to describe the chromatographic retention process, using the bulk macroscopic properties of partial molar volume of the solute in the mobile and stationary phases. The partial molar volume of the solute in the mobile phase at infinite dilution was calculated by using the Peng-Robinson EOS, which is a simple two-parameter, cubic EOS. Correlation with actual solute retention is similar to that seen for the more complex statistical thermodynamic model of Martirelo-" and has the advantage of ease of calculation as compared to Schoenmakers methodology. All the models discussed above determine the stationary-phase contribution to retention through an initial reference retention value to which all other calculated retention values are related. One reason for this approach is the difficulty in determining the interactions between the solute and the stationary phase, as well as uncertainties in the actual stationary-phase volume. These models all assume that the effect of pressure upon the interaction of the solute with the stationary phase is negligible. This as-
(3) Kim, S.; Johnston, K. P. AIChE J . 1987, 33, 1603. (4) Yonker, C . R.; Wright, B. W.; Petersen, R. C.; Smith, R. D. J . Phys. Chem. 1985,89, 5526. ( 5 ) Chester, T. L.; Innis, D. P. J. High Resolut. Chromatogr. Chromatogr. Coinmun. 1985, 8, 561. (6) Van Wasen, J.; Schneider, G. M. Chromatographia 1975, 8, 214. (7) Van Wasen, J.; Swaid, I.; Schneider, G. M. Angew. Chem., Int. E d . Engl. 1980, 19, 575. (8) Schoenmakers, P. J. J . Chromatogr. 1984, 315, 1.
(9) Lee, B. I.; Kesler, M. G. AIChE J . 1975, 21, 510. (10) Martire, D. E. J . Liq. Chromatogr. 1987, 10, 1569. (11) Martire, D. E.; Bochm, R. D. J . Phys. Chem. 1987, 91, 2433. (12) Martire, D. E.; Boehm, R. E. J . Phys. Chem. 1983, 87, 1045. (1 3) Jaroniec, M.; Martire, D. E. J . Chromatogr. 1986, 351, 1. (14) Martire, D. E.; Locke, D. C . Anal. Chem. 1971, 43, 68. (15) Yonker, C . R.; Gale, R. W.; Smith, R. D. J . Phys. Chem. 1987, 91, 3333.
The evcpanding applications of supercritical fluids in extraction, chromatography, and chemical reaction processes are primarily due to the ability to control solvent strength and other physicochemical properties as a function of density. The capability to alter the intermolecular interactions in the mobile phase for supetcritical fluid chromatography (SFC) is reflected in the partial molar voluihe of a solute as a function of density at infinite dilution.'S2 This solvation of the solute by a fluid can influence local fluid density and extend over multiple solvent shell^.^ The elucidation of the detailed retention mechanism in S F C is a complex problem. Yonker et aL4 have developed a simple thermodynamic model for solute retention as a function of temperature at constant pressure. Chester and InnisS developed an ehpirical thermodynamic model relating retention with temperature for SFC. Van Wasen et al.637have developed a simple thermodynamic model describing solute retention in S F C as a function of pressure. Schoenmakerss also derived a simple thermodynamic equation describing solute retention as a function of density and ressure based upon the Lee-Kesler equation of statb (EOS). hese workers calculated the fugacity coefficient of the solute at infinite dilution in the supercritical fluid mobile phase, which was used to determine solute retention. Although this method cannot yield retention for a solute a priori, once a reference retention value for a system is measured, a quantitative
.F
~~
(1)
0022-3654/88/2092-1664$01.50/0
0 1988 American Chemical Society
Retention in Supercritical Fluid Chromatography
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1665
sumption leads to the interesting predictionlO,lsof a retention minima as a function of pressure or density for solute retention in SFC. This minima is predicted to be dependent on temperature and solute type.I0 This paper describes a study of solute retention in SFC through the density region where the retention minima is predicted for various solute molecules. Open tubular capillary columns are utilized to eliminate any perturbation to retention caused by the pressure drop across a packed column. Correlation of solute retention as a function of density is based upon the macroscopic solute properties at infinite dilution of the partial molar volume of the solute in the fluid mobile phase and stationary phase.ls The effect of pressure on both the fluid mobile phase and stationary phase are examined to elucidate the retention mechanism in SFC.
behavior for the solute and the fluid. The direct calculation of k'cannot be accomplished a priori due to the unknown stationary-phase volume and related uncertainties. Once a reference k' value is determined by experiment under any pressure and temperature condition, retention at other conditions can be calculated. In this work, B1sP-"'o was estimated to give the best fit to the experimental data in the low-pressure regime, assuming the pressure dependence of the stationary phase to be negligible. At higher pressures (densities) eq 4a or b were invoked to describe . solute rethe effect of pressure or density on B ~ ~ P ~ "Therefore, tention could be studied as a function of density from low densities to nearly liquidlike densities by using the thermodynamic equations derived in our model.
Theory
The experimental system and methodology have been described in detail elsewhere.1sJ9 The retention factors, using carbon dioxide, were determined for naphthalene at 35 "C from 82.2 to 403.2 bar and for phenanthrene, chrysene, 2-naphthol, 6aminochrysene and dotriacontane from 101.3 to 403.2 bar at 35 "C. The capillary column used in these studies was coated with a cross-linked 5% methylphenylpolysiloxane (SE-54) stationary phase. A Varian 8500 high-pressure syringe pump was operated under microprocessor control, providing a pulse-free solvent flow and an accurate control of fluid pressure. Column temperature was controlled with a constant-temperature air bath to an accuracy of fO.l "C. The system pressure was measured with a straingauge pressure transducer in line between the pump and the column in the oven (Setra Systems, Model 204). The retention times of the solutes as a function of pressure were measured by using a reporting integrator with an accuracy of a tenth of a second. Solute samples were injected with a Valco C14W HPLC injection valve (0.2-pL rotor volume), which was mounted outside the oven and connected to the chromatographic column through a flow splitter. A flow restrictor was connected to the end of the column, which controlled the mass flux of the mobile phase through the column.20 Detection of the solute was accomplished, after expansion through the restrictor, by using a flame-ionization detector. *
Retention in SFC as a function of pressure a t constant temperature is shown in eq l,637J5where k' is the solute retention
(a In k'//aP),
= 1/R7&mp-m
- DlSP,"J
-K
(1)
factor, T i s temperature, R is the gas constant, Blmp." and DlsP." are the partial molar volumes of the solute in the fluid mobile phase and stationary phase at infinite dilution, respectively, and K is the isothermal compressibility of the supercritical fluid solution. The assumptions made in the derivation of eq 1 are that the molar volumes of the mobile and stationary phase and the volume of the stationary phase are independent of pressure. At infinite dilution the isothermal compressibility of the fluid solution can be approximated by the isothermal compressibility of the pure fluid. The density dependence of solute retention in SFC at constant temperature is (a In k'/ap), = (a In k ' / d P ) , ( a P / d p ) , = l / R q D l m P ~ " - Dl"P")(aP/ap), - l / p (2) where p is the density of the pure fluid when assuming infinite dilution of the solute in the mobile phase. The partial molar volume of the solute in the mobile phase at infinite dilution can be evaluated through a triple-product relationshipI6 v p 3 -
= (aV/anl)T,P,n,= -(aV/aP),,,,,~,(dP/anl),,,,,, = K2 V2(dP/ an1 ) T,V,n2 (3)
where Vis the total volume, nl and n2 represent the number of moles of solute and solvent, respectively, K2 is the isothermal compressibility of the pure fluid, and V, is the molar volume of the pure fluid.' The Peng-Robinson EOS7 was used to calculate the solute's partial molar volume in the fluid following eq 3.2JsJ6 This EOS was used to evaluate K, p, ( d P / d p ) n and (dP/dn,),,,,, in eq 1 , 2 and 3 to calculate solute retention as a function of density or pressure in SFC. The partial molar volume of the solute in the stationary phase at infinite dilution can be estimated as D,SP,"" = fllsP~'*o + A P ( B , S P ~ " / a P ) , (4a) or DISP'"
= ~,SP,",O
+ Ap(D1sP'"/ap),
(4b)
where o ~ ~ isP a *chosen ~ ~ ~reference value, which fits the experimental data in the low-pressure (density) regime and the second term is the pressure or density dependence of the solute's partial molar volume in the bonded polymeric stationary phase. The lack of an accurate EOS for the P,V, and T behavior of a chemically bonded phase precludes the direct calculation of DlsP~' for the stationary phase. The partial molar volume of the solute in the fluid (Dlmp,") can be calculated by use of an EOS that describes the P, V, and T (16) Wu, P. C.; Ehrlich, P. AIChE J . 1973, 19, 533. (17) Peng, D.Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59.
Experimental Section
Results and Discussion
A prediction of solute retention in SFC can be obtained from eq 1 or 2 as a function of pressure or density, respectively. Calculated retention values were initiated with the lowest pressure datum, which determined the contribution of the stationary phase to solute retention under a set of particular experimental conditions (Le., stationary phase, pressure, temperature, and solute). Naphthalene was used as the solute for modeling studies because the binary interaction parameter with C 0 2 is available from bulk solubility data.zJ5 Thus the partial molar volume of naphthalene at infinite dilution in C 0 2 at 35 "C can be readily calculated by using the Peng-Robinson EOS.2JS The solute partial molar volume in the stationary phase was assumed to be independent of pressure, and solute retention for naphthalene as a function of pressure and density was calculated by using eq 1 and 2, respectively. The experimental retention data for naphthalene are shown in Figure 1 and Table I. In Figure 1 the calculated solute retention is plotted against pressure and density of C 0 2 , with the experimental data. The calculated retention values are referenced to the initial (lowest density) measured k'value contained in Table I. The partial molar volume of the solute in the stationary phase was chosen to be -200 cm3/mol which fit the data in the low-pressure and density region quite accurately. As apparent in Figure 1, the thermodynamic model predicts a minimum in retention in a similar range of density as reported by Martire,Io but the experimental retention values (18) Wright, B. W.; Smith, R. D. Chromatographia 1984, 18, 542. (19) Smith, R. D.; Kalinoski, H. T. Udseth, H . R.; Wright, B. W. Anal. Chem. 1984, 56, 2476. (20) Smith, R. D.; Fulton, J. D.; Petersen, R. C.; Kopriva, A. J.; Wright, B. W. Anal. Chem. 1986, 58, 2057.
Yonker and Smith
1666 The Journal of Physical Chemistry, Vol. 92, No. 6, 1988
TABLE I: Retention Factors of Naphthalene as a Function of Pressure and Density at 35 OC with C02
0
0
Pressure (Bar)
Y
-C 0
0.5
OO
1 .o
Density (g/cm3)
Figure 1. Dependence of solute retention (In k') on pressure (A) and density (B) for naphthalene-CO, at 35 O C . The solid line is calculated solute retention with BlSP~' = -200 cm3/mol;the binary interaction parameter is 0.1082; (0)experimental data points.
of the solute continue to decrease, as a function of pressure and density for C02. Table I1 contains experimental data for other solutes, both polar and nonpolar, which show similar retention behavior as a function of density. No retention minimum is seen for these solutes, as predicted by the thermodynamic model shown in Figure 1, within the experimental pressure limitations of our work. Maxima in bulk solubility with supercritical fluid solvents has been demonstrated in the work of Czubryt et alJ1 and Bowman.22 Giddings uses a description of supercritical fluid solvent strength based on the Hildebrand regular solution theory, solubility parameter concept and demonstrates excellent qualitative agreement between the maximum bulk solubility of a solute with the corresponding solubility parameter of the fluid. These data reflect the changes in the microscopic solvent environment with density. (21) Czubryt, J. J.; Myers, M. N.; Giddings, J. C. J. Phys. Chem. 1970, 74, 4260. (22) Bowman, L. M. Ph.D. Thesis, University of Utah, Salt Lake City, UT, 1976.
pressure, bar
density, g/cm3
82.2 87.2 92.2 102.4 203.7 305.2 403.2
0.491 0.565 0.606 0.663 0.865 0.954 1.012
naphthalene k' 0.271 0.137 0.11 7 0.091 0.052 0.049 0.044
*
0.002 f 0.001 f 0.002 f 0.002 f 0.003 f 0.002 f 0.003
At low densities, attractive solute-solvent interactions predominate and bulk solubility increases linearly with d e n ~ i t y . ~At ~ .high ~~ densities the molecules are packed closely together and the solvent-solute interactions can become repulsive.25 Therefore, one would predict a maximum in bulk solute solubility as a function of density, which is shown experimentally.21~22 An argument based directly on bulk saturated solute solubilities in supercritical fluids affecting solute retention in SFC is invalid because of the infinite dilution regime of solute concentration used; one is always below the bulk solubility limit (linear distribution isotherm region). The local solvent structure about the solute molecule changes, as reflected in bulk solubility behavior and solvatochromic data for supercritical fluids.26 If only fluid mobile phase solventsolute interactions controlled retention in SFC, then one might expect a retention minimum as the solvent-solute interactions changed from attractive to repulsive interactions (due to the exclusion of the solute from the fluid mobile phase into the stationary phase, resulting in an increase in solute retention). The statistical thermodynamiclo-" and cubic, t ~ o - p a r a m e t e r ' ~ (Peng-Robinson) EOS estimate this point to occur at approximately the same density. This description of solute retention in SFC based only on fluid mobile phase solvent-solute retention interactions seems valid at low to moderate pressures and densities but apparently fails at higher densities (see Figure 1). The assumption that 81sP*" is independent of pressure neglects the dynamic role of the stationary phase in the retention process. Modification of the stationary phase in SFC as a function of pressure by the supercritical fluid has been reported by Sie et aL2' and Springston et The role of stationary-phase modification by the supercritical fluid on solute retention has not been elucidated but has been demonstrated to at least involve swelling of even cross-linked phases. The effect of pressure on the term [~~"'p," - ijlsP,"] (which will be defined as ADl) is of primary importance in the discussion of the role of BIsP," on solute retention in SFC. The assumption that D ~ ~ Pis~independent " of pressure leads to ml being constant beyond 140 bar for the C02-naphthalene system. The partial molar volume of a gas in a liquid solvent a t infinite dilution has been described by Brelvi and O'ConnellZ9using a corresponding-states correlation for liquid compressibilities and partial molar volumes. Their correlation holds to within a few percent over the reduced density range of 2-4.29*30In some systems their calculations have shown changes of 30% in the partial molar volume of a solute in a liquid solvent as a function of pressure. For the chromatographic system discussed above, with naphthalene a t infinite dilution in both the mobile and stationary phase, B,~P*" could be expected to change as a function of pressure as shown by the work of Brelvi and O'Connell, if one assumes the bonded stationary phase has liquidlike characteristics. Therefore, AD1 would not be constant as a function of pressure, due to the weak dependence of ijlsP3"
-
(23) Heyes, D. M. Chem. Phys. 1984, 82, 285. (24) Tsekhanskaya, Y. V.;Iomtere, M. B.; Mushkina, E. V. Russ. J . Phys. Chem. (Engl. Trans/.) 1964, 38, 1173. (25) Shing, K. S.; Chung, S . T. J . Phys. Chem. 1987, 91, 1674. (26) Yonker, C. R.; Frye, S . L.; Kalkwarf, D. R.; Smith, R. D. J . Phys. Chem. 1986, 90, 3022. (27) Sie, S . F.; van Beersam, W.; Rijnders, G. W. A. Sep. Sci. 1966, I, 459. (28) Springston, S. R.; David, P.; Steger, J.; Novotny, M. Anal. Chem. 1986, 58, 997. (29) Brelvi, S . W.; O'Connell, J. P. AZChE J . 1972, 18, 1239. (30) Gubbins, K. E.; O'Connell, J. P. J. Chem. Phys. 1974, 60, 3449.
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988
Retention in Supercritical Fluid Chromatography
1667
TABLE II: Retention Factors for Select Solutes as a Function of Pressure and Density at 35 O C and C02 k' pressure, bar
density, g/cm3
phenanthrene
chrysene
2-naphthol
6-aminochrysene
101.3 151.9 202.7 203.9 403.2
0.658 0.793 0.864 0.954 1.012
0.209
0.590
0.163
0.570
0.099 0.072 0.067
0.201 0.152 0.123
0.076 0.061 0.056
0.164 0.102 0.090
"-
t
0.199 0.137 0.108 0.089
volume of the solute in the stationary phase and its effect on solute retention is shown in Figure 2. The partial molar volume of the solute in the stationary phase was allowed to increase as a linear function of density (pressure) from -200 to 100 cm3/mol. The predicted solute retention, as a function of density, follows experimental data, with an asympototic approach to zero solute retention at high-density values. The method of calculation of from the Peng-Robinson EOS was held constant for the calculated solute retentions shown in Figures 1 and 2; only ijIsP'" was varied between the two figures. The experimental solute retention, measured by using capillary SFC, is more accurately predicted by allowing the bulk thermodynamic macroscopic P with ~ ~pressure, as DlmPv" does for a suproperty of D ~ to~ vary percritical fluid.
0
L
-C
0.5
dotriacontane
1 .o
Density (g/cm31
Figure 2. Dependence of solute retention (In k') on density for naphthalene-CO, a t 35 "C. The solid line is the calculated solute retention, using eq 4 (slope = 390 cm6/(mol.g)) for B1*P*DIdependence on pressure, and the binary interaction parameter is 0.1082; (0)experimental data points.
on pressure. Thus for dense solvents ijlsP*"should increase weakly as pressure increase^.^^ The pressure or density dependence of i j I s P ~ " is approximated by eq 4a and b, where i j l s P ~ m ~iso referenced to solute retention at low densities or pressure and the slope is small to approximate with pressure or density. In the a weak dependence of calculation of solute retention as a function of density, the slope (dBISP~"/dp)T was held constant; therefore, ijIsP*" was a linear function of density. We know of no requirement for this to be true for the system studied; however, as an initial assumption, the constant slope simplified the calculational procedure for solute retention. The effect of density (pressure) on the partial molar DlsPgm
(31) Hamann, S. D. High Pressure Physics and Chemistry; Bradley, R . S., Ed.; Academic: New York, 1963; Vol. 2, Chapter 7.
Conclusion Previous models of solute retention in SFC, where the solute partial molar volume in the stationary phase is independent of pressure, accurately fit solute retention data at low to moderate densities but predict minimum in solute retention as density increases. In contrast, experimental data for open tubular capillary SFC show no minimum in solute retention as a function of density for selected model systems, only an asymptotic approach to a limiting retention value (essentially a k' of zero). Solute retention in SFC is a dynamic process depending on both the mobile-phase and stationary-phase intermolecular interactions with the solute molecule. In terms of the bulk macroscopic physicochemical parameters of ijlmP," and 81sP",ijlmP~" has a large dependence on pressure near the critical point of the supercritical fluid, whereas DIsP~" was shown to have a weak dependence on pressure. At low pressures (densities), ijlmP," controls the retention process in SFC. As pressure (density) increases, the role of the stationary-phase contribution becomes more evident. The detailed mechanisms and implications for S F C of such stationary-phase phenomena remain to be addressed, particularly for the more complex situations encountered for mixed (modified) fluid systems. Acknowledgment. This work has been supported by the U S . Department of Energy, Office of Basic Energy Sciences, under Contract DE-AC06-76RLO 1830. We thank A. J. Kopriva for technical assistance. Registry No. C02, 124-38-9; naphthalene, 91-20-3; phenanthrene, 85-01-8; chrysene, 218-01-9; 2-naphthol, 135-19-3; 6-aminochrysene, 2642-98-0; dotriacontane, 544-85-4.
