J . Phys. Chem. 1988, 92, 235-238
235
Solvatochromlsm: A Dielectric Continuum Model Applied to Supercritical Fluids C. R. Yonker* and R. D. Smith Chemical Methods and Separations Group, Chemical Sciences Department, Pacific Northwest Laboratory, Richland, Washington 99352 (Received: May 4, 1987; In Final Form: July 29, 1987)
The solvatochromic behavior of nonpolar supercritical fluids, in terms of the a* Kamlet and Taft polarity/polarizability parameter, is compared to the McRae-Bayliss model. A break in the plot of a* against the Onsager reaction field (F,) is seen for the fluids studied at low reaction field values (low densities). The relationship between a* and the Onsager reaction field (F,)shows two regions of nearly linear behavior. The transition from the low-density region to a higher density region, where a smaller dependence of a* upon (F,)is observed, is tentatively attributed to extensive solvent clustering about the solute. This hypothesis is supported by the behavior previously observed for the partial molar volume of the solute in the fluid 0," as a function of pressure. The rapid change in 02-is also shown to occur in the same region where the solvatochromic behavior of the fluid changes and the solute's solubility increases dramatically.
Introduction Solvent effects on chemical reaction rates and solvatochromic behavior of solutes have been well Theoretical models for solvent polarity effects, ranging from simple continuum reaction fields3v4to individual solventsolute dipolar interactions for l i q ~ i d shave , ~ been used to correlate solvatochromic behavior with various solvent polarity One of the more versatile of the solvent polarity scales is that developed by Kamlet, Taft, and co-workers,8-11which is based on the solvatochromic shift seen for the a-a* electronic transition of the solute. Recent interest in supercritical fluids as solvents in extraction processes,I2 c h r ~ m a t o g r a p h y , ' ~and * l ~ chemical reactions15 has stimulated interest in the relationship between density and the solvent properties of these fluids, as measured by using various solvent scales.16-20 Yonker and co-workers have adopted the Kamlet-Taft x* polarity scale and applied it to a wide range of supercritical fluids at various temperatures and pressure^,'^*^^ but limited theoretical analysis of the solvatochromic behavior for supercritical fluids has been presented to date. Leffler and Sigman have presented initial results correlating the solvatochromic behavior of COzwith the McRae-Bayliss model using four different densities of CO2.lSThese authors reported experimental a* values for C 0 2 higher (less negative) than those calculated from their (1) Abraham, M. H.Pure Appl. Chem. 1985, 57, 1055. (2)Symons, M. C. R. Pure Appl. Chem. 1986, 58, 121. (3) Brady, J. E.; Carr, P. W. J . Phys. Chem. 1985, 89, 5759. (4) Abboud, J.-L. M.; Taft, R. W. J . Phys. Chem. 1979,83, 412. ( 5 ) Ehrenson, S. J . A m . Chem. SOC.1981, 103, 6036. (6) Kamlet, M.J.; Abboud, J.-L. M.; Taft, R. W. Prog. Phys. Org. Chem. 1980, 13, 485. (7) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983, 48, 2877. (8) Kamlet, M. J.; Doherty, R. M.; Taft, R. W.; Abraham, M. H. J . A m . Chem. SOC.1983. 105. 6741. (9) Abraham,'M. H.;Kamlet, M. J.; Taft, R. W.; Weathersby, P. K. J . A m . Chem. SOC.1983, 105, 6797. (10)Taft, R. W.; Abboud, J.-L. M.; Kamlet, M. J. J . Ora. Chem. 1984, 49, 2001. (11) Abboud, J.-L. M.; Guiheneuf, G.; Essfar M.; Taft, R. W.; Kamlet, M. J. J. Phvs. Chem. 1984. 88. 4414. (12) Pailaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Rev. Chem. Eng. 1983, 1 , 179. (13) Peaden, P. A.; Lee, M. L. J . Liq. Chromatogr. 1982, 5 , 179. (14)Wright, B. W.: Kalinoski. H. T.: Udseth. H. R.: Smith. R. D. HRC CC;J.' High-Resol. Chromatogr. Chromatogr. Commun. 1986, 8 , 145. (15) Amestica, L. A.; Wolf, E. E. Supercritical Fluid Technology; Penninger, J. M. L.: Radosz, M.; McHugh, M. A.; Krukonis, V. J., a s . ; Elsevier: Amsterdam, 1985;p 331. (16) Hyatt, J. A. J . Org. Chem. 1984, 49, 5097. (17) Sigman, M. E.;Lindley, S. M.; Leffler, J. E. J. Am. Chem. Soc. 1985, 107, 1471. (18) Sigman, M. E.;Leffler, J. E. J. Phys. Chem. 1986, 90, 6063.
7,91, 3059.
0022-3654/88/2092-0235$01.50/0
regressed equation based on a dielectric continuum model. In this study more extensive solvatochromic results for supercritical C 0 2 , SF6, and ethane are compared with the McRae-Bayliss model of solvatochromism (which is based on Onsager's reaction field theory). Through studying a broader set of data for supercritical fluids, greater insight is obtained into the role of dipolar/polarizability interactions and cluster formation on solvation as a function of fluid density. In the broader sense, these studies begin to bridge the gap between the gas and liquid states by exploiting the unique properties of supercritical fluids.
Theory Models for dipole solvation can be microscopic or macroscopic in approach. The microscopic case involves the evaluation of individual solute-solvent intermolecular interactions, where the electric field along the dipole axis of the solute molecule is induced by the presence of the solvent molecules.21 In the macroscopic approach the reaction field is based on a continuum model which recognizes no specific solvent molecule or localization of solvent structure and, in its original form as stated by Onsager,22assumes no difference in solvent orientation close to or far removed from the solute molecule. Inclusion of dielectric saturation, involving the alignment of solvent molecules in the region surrounding the polar solute molecule, was described by Block-Walker in their modification to the Onsager reaction field theory.23 The McRae-Bayliss model of solvatochromic b e h a v i ~ isr ~ ~ ~ ~ ~ based on a continuum model of dipole solvation similar to that proposed by Onsager. The equilibrium energy of solvation of the ground state of the solute molecule is determined by the dipole interaction with the solvent molecules. On excitation of the solute molecule to the a* state, the dipole orientation of the solvent molecules remains frozen in the ground-state configuration because the solvent dielectric relaxation time is orders of magnitude greater than the lifetime of the excited ~ t a t e .Thus, ~ ~ ~the~ inductive component of solvation will be in equilibrium with the excited-state dipole. Therefore, the McRae-Bayliss model of solvatochromism is composed of dipolar and inductive components in equilibrium with the ground and excited states of the solute dipole. A simplified expression of the McRae-Bayliss model iszs
(21) Bottcher, C. J. F. Theory ofElectric Polarization, 2nd ed.; revised by Van Belle, 0. C.; Rip, A,; Elsevier: Amsterdam, 1973; Vol 1, p 18. (22) Onsager, L. J. Am. Chem. SOC.1936, 58, 1486. (23) Block, H.;Walker, S. M. Chem. Phys. Lett. 1973, 19, 363. (24) Bayliss, N.S.; McRae, E. G. J . Phys. Chem. 1954, 58, 1002. (25) McRae, E.G. J . Phys. Chem. 1957, 61, 562.
0 1988 American Chemical Society
236 The Journal of Physical Chemistry, Vol. 92, No. 1 , 1988
Yonker and Smith
where Av is the difference in the absorbance maximum in a solvent compared to a gas-phase reference spectrum measured in reciprocal centimeters, A and B are polarizability effect constants, Lo is a weighted mean wavelength, C and D are dipolar effect constants, t is the dielectric constant of the solvent, and n is the solvent’s refractive index. For solvent molecules having no per. ~ ~ , manent dipole (e.g., CO2, SF,, and ethane), e = t ~ ~ Therefore, eq 1 reduces to
and Carr have shown linear relationships between P* and F0.3 As more nonpolar solvents were added, the correlation became poorer, as reflected by changes in the slope and intercept. For different solvent sets there was wide variability in the reported slope and intercept, which demonstrates a problem with the theory as applied to some solvents. An interesting point of the n-alkane data reported by Brady and Carr3 is the excellent agreement between ~ the gas-phase limit for the solvent series and the experimental value of -1.06.29 The failure of the continuum model to describe the solvatochromic behavior of some solvent classes is probably because this model ignores any dielectric saturation effect on the macroscopic level and ultimately ignores discrete solvent-solute pair interactions on the molecular level. The radial distribution function for a liquid (Le., the ordering of solvent molecules about the solute), defined as specific pair interactions, has been used in describing the statistical mechanical partition function for an equation of state that describes on a molecular level the local density and composition of a solvent about the solute for pure and binary liquid mixture^.^"-^^ The excellent correlation of the continuum model seen for the nonpolar n-alkanes supports this simple physicochemical description as appropriate for some nonpolar solvent classes using bulk properties such as refractive index. In this work we examine the applicability of the McRae-Bayliss theory for the nonpolar supercritical fluids of c o 2 , SF6, and ethane. Because the solvent powers of supercritical fluids can be varied continuously from essentially the gas-phase limit to a liquid-phase limit at high densities, these studies offer the potential for bridging the gap between these two states and may offer new insights into solvation processes in general.
where the polarizability of the solvent molecule, which is a function of the refractive index of the solvent (the Lorentz-Lorenz equation2*),is important in determining the solvatochromic behavior of the solute molecule. The relationship between the MacRaeBayliss theory and the Onsager reaction field theory can be seen from eq 3, where the reaction field as defined by Onsager is6
(3) is the dipole moment of the solute molecule in the ground state and a is the radius of the cavity occupied by the solute molecule which is assumed to be a point dipole. The distribution of solvent molecules about the solute molecule creates the electrostatic field, ER, felt by the solute molecule. The distribution of the solvent molecules is influenced not only by solute-solvent interactions, but also by solvent-solvent interactions and thermal agitation. Therefore, for a dielectric continuum model, the solvatochromic effect of the solvent will be a linear relationship in 2(n2 - 1)/(2n2 1). Defining the constant Fo as 2(n2 - 1)/(2n2 + 1) and substituting into eq 2, one obtains p
+
Av = Y2(AL + B)Fo
(4)
Substituting the appropriate relationship for B from the McRae-Bayliss theory of solvatochromism:
where p* is the solute excited-state dipole moment, h is Planck‘s constant, and c is the speed of light. From eq 5 , the relationship between the polarizability of the solvent (Fo)and the excited-state dipole moment of the solute molecule is apparent. The Kamlet and Taftbs scale of solvent polarity/polarizability defines a* as
where s is the susceptibility of the solute molecule to the solvent and vo is the reference absorbance maximum in cyclohexane. Equation 6 is only applicable to solvent-solute systems where no specific interactions occur, such as hydrogen bonding or charge-transfer effects. Therefore, rearranging and substituting eq 6 into eq 5 , one obtains
where a*gas is the vapor-phase limit (Po= 0). Thus a plot of a* versus Fo (proportional to the Onsager reaction field) should yield of -1.06.19.29 a straight line with an intercept value (a*gas) The relationship between a* and Fohas been tested for different ~ ~ ~ ~ ~certain solvent classes liquids with reasonable S U C C ~ S S .Within including the solvent set of pentane through hexadecane, Brady (26) Michels, A,; Kleerekoper, L. Physica (Amsterdam) 1939, 6, 586. (27) Keyes, F. G.; Kirkwood, J. G. Phys. Rev. 1930, 36, 754. (28) Sinnock, A. C. J. Phys. C: Solid State Phys. 1980, 13, 2375. (29) Essfar, M.; Guiheneuf, G.; Abboud, J.-L. M. J . Am. Chem. SOC.1982, 104, 6786.
~
Experimental Section The solvatochromic probe molecule in this work was 2-nitroanisole (Aldrich Chemical Co.). The s value reported for 2nitroanisole is -2.428 f 0.195.33 One can calculate the change in the supercritical fluids a* value using eq 6 as a function of pressure, holding temperature constant. The reference absorbance maximum for 2-nitroanisole in cyclohexane (YO) is 32 560 cm-I. Absorption spectra of 2-nitroanisole in supercritical C o 2 , SF6, and ethane were obtained with a Varian Model 2200 spectrophotometer operated in the dual beam mode. The gases used as supercritical solvents were of the highest purity commercially available. The supercritical fluid spectra were obtained with an air reference. The high-pressure cell was constructed from stainless steel (SS 304) with dimensions of 8.25 cm wide X 5.0 cm high X 14.0 cm long. The optical path along the axis of the cell was 5.0 cm long X 1.9 cm in diameter with a sapphire window at each end of 2.5 cm in diameter X 1.3 cm thick. The high-pressure seal between the stainless steel cell body and the sapphire windows were made by using silver-coated, metal C-rings (Helicoflex). The volume of the sample cell was 14.5 cm3. The cell was thermostated to 0.1 OC, and a magnetic stir bar provided rapid mixing of the solute and solvent components. The supercritical fluid was delivered to the cell by a high-pressure syringe pump (Varian 8500) which was operated in a pressure-regulated mode and was connected to the sample cell via a high-pressure liquid chromatographic sampling valve (Valco). The sampling valve had an internal sample loop volume of 0.2 pL, which allowed for easy introduction of 2-nitroanisole into the absorption cell. A pressure transducer (Model 204, Serta Systems) provided pressure measurements (f10 psi). The experimental arrangement allowed the supercritical fluid to flow through and purge the cell or to be stopped during experimental measurement of the solvatochromic shifts. Spectra at different pressures and temperatures were obtained after ap-
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~~~~
~~
(30) Sander, S. I. Fluid Phase Euilib. 1985, 19, 233. (31) Lee, K.-H.; Lombardo, M.; Sandler, S. I. Fluid Phase Equilib. 1985, 21, 177. (32) Lee, K.-H.; Sandler, S. I.; Patel, N. C. Fluid Phase Equilib. 1986, 25, 3 I . (33) Kamlet, M. J.; Abboud, J.-L. M.; Taft, R. W. J . Am. Chem. SOC. 1977, 99, 6027.
The Journal of Physical Chemistry, Vol. 92, No. I , 1988 237
Solvatochromism in Supercritical Fluids 0.2
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propriate equilibration periods during which the contents of the absorption cell were continuously stirred. Background spectra were obtained before sample introduction to ensure no interference absorption from the pure fluids.
Results and Discussion Supercritical fluids are versatile solvents for polar and nonpolar solutes, whose solvent strength is a function of pressure. This has been demonstrated by the solubility of various compounds in supercritical fluids as a function of pressureI2 and can be rationalized in terms of the change in the Hildebrand solubility parameter with pressure.34 The McRae-Bayliss description of solvatochromism provides a basis for considering supercritical fluid solvation using a continuum reaction field model. Taking into account the simplifying assumptions made in the Onsager reaction field theory, on which the McRae-Bayliss model is based, one may still gain appreciable insight into supercritical fluid solvation processes from the study of their solvatochromic effects. Equation 7 relates the supercritical fluid P* value to the Onsager reaction field, Fo. For fluid molecules having no dipole moment such as C 0 2 ,SF6,and ethane, the polarizability of the molecule (which is related to refractive index) is important in the stabilization of the excited-state dipole of the solute molecule. Knowledge of the refractive index of the supercritical fluids CO,, SF6, and ethane is necessary to use eq 7 . The refractive index can be determined from a virial expansion of the Lorentz-Lorenz equation in terms of the molar density for the supercritical fluids. The refractometric virial coefficients of the supercritical fluids studied have been reported in the l i t e r a t ~ r e . ~ ~ - ~ ' Figure 1 is a plot of a* versus F, for supercritical C 0 2 at 35 and 50 OC, supercritical SF, at 50 "C, and supercritical ethane (34) Bowman, L. M. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1976. (35) St-Arnaud, J. M.; Bose, T. K. J . Chem. Phys. 1979, 71, 4951. (36) Kholodor, E. P.; Timoshenko, N. I.; Yamnov, A. L. Therm. Eng. (English Transl.) 1972, 19, 126. (37) Besserer, G. J.; Robinson, D. B. J . Chem. Eng. Data 1973, 18, 137.
at 50 OC. There are three important points to be seen in Figure 1: (1) there are two linear regions for a* as a function of Fo; (2) the region where the slope changes is dependent on the fluid; and (3) the least-squares regressions of the intercepts for supercritical C 0 2 at 35 and 50 OC and ethane in the low-Fo(low-density) region have values of -0.84, -1.02, and -0.94, respectively, for P * ~ ~ , , which correlates reasonably well with the value of a*gas = -1.06 reported by Essfar, Guiheneuf, and Abboud.,' The correlation between a* and the Onsager reaction field is linear in the two regions seen in Figure 1. One region occurs at low densities (Fo 5 0.08), and the other occurs at higher densities (Fo > 0.08). Leffler et al. do not report a break in their x* correlation, possibly because their limited data set was obtained at mostly higher density value^.^^^'* They do note that their calculated P* values are lower than those observed experimentally; this may be due to the change in slope shown in Figure 1. The reason for the two regions seen in P* versus Fo is not clear when considered in the framework of the McRae-Bayliss theory of solvatochromism. With supercritical fluids, the density can be varied over a wide range; one must be concerned with the type of interaction between the solute and solvent, as well as with the number of interactions that occur due to changes in the average intermolecular distances (local density). Clearly the number of solute-solvent interactions will be density-dependent and change as a function of Fo. With a supercritical fluid, one should be able to sample the entire range of solute-solvent interactions from zero (or a small number) to saturation in the cybotactic region (region of solvent molecules whose solvation structure is determined by the presence of the solute molecule) of the solute molecule as a function of density (Fo). The partial molar volume of the solute, which is the change in the solute's chemical potential as a function - ~ ~partial of pressure, is a fundamental solution p r ~ p e r t y . ~ *The molar volume of the solute molecule should reflect the range of interactions, with the minimum of the solute partial molar volume occurring at a density where the number of solute-solvent interactions increases the greatest, and the cybotactic region of the solute becomes saturated. Therefore, the break seen in the plot of T* against Fo might be expected to occur at a density where the solvent molecules saturate the cybotactic region, which is reflected by the minimum in the partial molar volume of the solute in the supercritical fluid, occurring at a transition between gaslike and liquidlike behavior. The slope of the plots of P* versus Fo seen in Figure 1 for the supercritical fluids in the high-Fo region (Fo > 0.08) for C 0 2 at 50 "C is 1.76 f 0.13, for SF, at 50 OC is 1.42 f 0.10, and for ethane at 50 'C is 1.13 f 0.04. The slopes for ethane and SF, are roughly parallel to one another due to the similarity of their interactions with the solute molecule. The greater slope and n* value seen for C 0 2most likely reflects the greater polarity of C02, due either to the large quadrupole moment of C 0 2 or the "local" dipole of the C 0 2 molecule. The slope of x* versus Fo for a homologous series of n-alkane solvents is 2.88 f 0.06.40 The reason for the difference between the slopes of the liquid n-alkanes and the supercritical fluids is uncertain at this time. It may be caused by a difference in structure of the solvent molecules in the cybotactic region due to the supercritical fluid having a lower local density than the liquid n-alkane solvents. Both the solvatochromic technique and the solute partial molar volume provide measures of the extent of interaction in the solute's cybotactic region. The solute's solvatochromic behavior reflects the solvent environment of the immediate cybotactic region whereas the solute's partial molar volume is the change due to the attractive interactions which can extend over a somewhat greater volume. The partial molar volumes for several solutes in supercritical fluids have been reported by Eckert et aL4' and by Ziger.42 Figure 2 is a plot of P* vs Fo and C2-, the partial (38) Chang, R. F.; Morrison, G.; Levelt Sengers, J. M. H. J . Phys. Chem. 1984, 88, 3389.
(39) Gubbins, K. E.; O'Connell, J. P. J . Chem. Phys. 1974, 60, 3449. (40) Brady, J. E.; Carr, P. W. J . Phys. Chem. 1985, 89, 1813. (41) Eckert, C. A,; Ziger, D. H.; Johnston, K. P.; Kim, S . J . Phys. Chem. 1986, 90, 2738.
238 The Journal of Physical Chemistry, Vof.92, No. I, 1988
Yonker and Smith 3 012
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molar volume of naphthalene in supercritical C 0 2 at 35 "C. The onset of the rapid decrease in the partial molar volume of the solute occurs very near the transition point of a* with F,. At densities above this region, the local density of the fluid in the cybotactic region of the solute is greater than in the bulk solution. This change in the solvent environment of the cybotactic region is seen spectroscopically as the shift in the solvatochromic behavior changing from a gas-phase-like solvent environment to that of a liquidlike solvation sphere due to the attractive interactions between the solvent and s o l ~ t e . ~ ~ , ~ ~ The transition between gaslike and liquidlike behavior at F, = 0.07 is also supported by the solubility behavior of naphthalene in supercritical C 0 2 at 35 O C . Figure 3 is a plot of both A* and solubility of naphthalene vs density of supercritical C 0 2 at 35 OC.4' Figure 3 shows that the mole fraction of naphthalene remains relatively constant at low density; beyond a threshold density the solubility increases at a rapid rate. This is consistent with the linear relationship between In (solubility) and density for supercritical C 0 2 and naphthalene a t 35 0C.45 The change in solubility also coincides with the change in slope of A* values for CO, as a function of density. The relationship between the (42) Ziger, D. H . Ph.D. Dissertation, University of Illinois, Urbana, IL, 1983. (43) Castleman, A. W.; Keesee, R. G. Acc. Chem. Res. 1986, 19, 413. (44) Meot-Ner, M.; Speller, C. V. J . Phys. Chem. 1986, 90,6616. (45) Wong, J. M.; Pearlman, R. S.; Johnson, K. P.J . Phys. Chem. 1985, 89, 2671.
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Figure 2. Plot of ?r* and partial molar volume ( D 2 - ) for naphthalene versus Onsager reaction field (Fo)for C 0 2 at 35 0C.37
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at 35 OC. solvatochromic behavior and the partial molar volume of the solute in the fluid at infinite dilution remains to be described on a quantitative basis.
Conc1usion The relationship between a* and the Onsager reaction field showed two linear regions over the temperature and pressure range studied. The applicability of the Block-Walker model for more polar supercritical solvents such as NH3is being investigated. The McRae-Bayliss model of solvatochromism does not predict a break in the slope of r * versus Foas observed in this work. A possible mechanism for the break in the slope is due to cluster formation of the solvent about the solute and the transition from gaslike to liquidlike behavior. Similar phenomena constitute an area of active study for pure and binary liquid mixtures where the density-dependent local composition model has achieved success in the thermodynamic description of these ~ystems.~*~* The approximate correlation of solubility and the partial molar volume of naphthalene in C 0 2 at 35 "C with the break in a* at 35 "C for the 2-nitroanisole probe molecule provides qualitative support for this hypothesis. It appears that supercritical fluids provide a basis for studying the transition between gas and fluid behavior and that solvatochromic techniques present one approach to bridging the gap between these states and to understanding solvation processes better. Acknowledgment. This work has been supported by the U S . Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC06-76RLO 1830.
