J . Phys. Chem. 1986, 90, 3022-3026
3022
fit in this cavity better than in other parts of the lipid bilayer. The proximity of O2would then enhance the effect of paramagnetic relaxation on the fluorine atoms and raise qF. In the meantime, qH of the aliphatic protons near the cavity would also increase. However, this would only contribute to a very small fraction of the weighted average of all protons. Thus, we observe q F > qH in the bilayers. Since the cavity may have a better chance to be located near the middle part of the PFD molecule (Figure 4B), the increase in q F of the l a , le, and 2a fluorine atoms would be larger than that in q F of the 2e fluorine (Table I). This is in contrast to the situation in bulk PFD liquid, in which q F of the 2e fluorine (2.45 f 0.05 s-l atm-' at 75.38 MHz) is slightly larger than q F of other fluorine atoms (2.17 f 0.08 for la, 2.15 f 0.04 for le, and 2.20 f 0.03 for 2a, all in s-l atm-l at 75.38 MHz),'O because the small end of an ellipsoid is sterically more favorable for the approach of o2in an isotropic liquid. The values of q F at 250 MHz (2.05-2.25 s-l atm-I) are smaller, and the differences are also 1 e ~ s . lThe ~ q F values of PFD droplets decrease further at 282.23 MHz (Table I). However, the differences in the q F values for the PFD droplets as well as the decane solution of PFD are too small to be significant, possibly due to the change in medium and larger experimental uncertainties. Since the corresponding F- 19 signals of cis-PFD are very broad and unresolved the interaction between lipid bilayers cannot be at 298 determined by N M R under these conditions. Because of the low solubility of PFD in the lipid bilayers: molecules of the two isomers are not likely to either interact or interfere with each other. PFTPA is a flexible molecule. Therefore, a schematic representation like Figure 4 may not be entirely adequate. However, the lipid bilayer would still experience a local perturbation by a dissolved PFTPA molecule. It is well-known that solutions of fluorocarbons in hydrocarbons exhibit nonideal The K,'2313
(24) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand Reinhold: New York, 1970.
perturbation of the ordering of the lipid bilayer may also create a cavity near a PFTPA molecule, causing the effect of oxygen to be larger on q F than on q H . In this case, the cavities may be less well-defined than those for PFD in the lipid bilayers. Therefore, the decrease in q H / q F (in comparison with decane) is not as pronounced as that for PFD, and there are no anomalous variations in the q F values of individual fluorine atoms within the PFTPA molecule. Whether it is in the bilayer, droplets, or decane solution, q(CF3) is slightly larger than q(CF2) due to a more favorable steric factor for the CF, group in flexible, unordered PFTPA molecules.10~'5 In conclusion, we have studied the effect of molecular oxygen on the fluorine and proton relaxation rates of perfluorodecalin and perfluorotripropylamine in decane solutions and in aqueous dispersions with phosphatidylcholine. The perfluoro chemicals seem to have no specific affinity for oxygen in decane solutions. The enhanced solubility of oxygen in PFC's compared to that in hydrocarbons has been interpreted by the existence of cavities in bulk PFC l i q ~ i d s . ' ~From , ' ~ the N M R data presented here, we postulate that PFC molecules may also create cavities in a lipid bilayer within which the O2 molecule can fit better than in an unperturbed bilayer. However, it should be pointed out that motions in the lipid bilayers are anisotropic and a theory of paramagnetic relaxation in ordered systems is needed to interpret the data quantitatively. Our results can be explained by the hypothesis of cavity formation around the PFC molecules in lipid bilayers but are not conclusive proof of their existence.
Acknowledgment. This work was supported by the Public Health Service under Grant No. H L 32640. (25) Gilmour, J. B.; Zwicker, J. 0.;Katz, J.; Scott, R. L. J . Phys. Chem. 1967, 71, 3259.
(26) Mukerjee, P.; Yang, A. Y . S.J . Phys. Chem. 1976, 80, 1388. (27) Mukerjee, P.; Handa, T. J . Phys. Chem. 1981, 85, 2298.
Characterlzatlon of Supercritical Fluid Solvents Using Solvatochromic Shifts C. R. Yonker,* S. L. Frye, D. R. Kalkwarf, and R. D. Smith Chemical Methods and Separations Group, Pacifc Northwest Laboratory,+ Richland, Washington 99352 (Received: November 4, 1985; In Final Form: February 3, 1986)
Solvatochromic probe molecules, with absorbances in the UV region, were used to examine the cybotactic region of pure and mixed supercritical fluid solvent systems. This approach allowed determination of the relative polarity-polarizability of these fluids and comparison with conventional solvents. The position of maximum absorbance was seen to be density dependent. The solvatochromicshift for the most polar fluid studied, supercritical ammonia, was the most sensitive to changes in solvent density, and at moderate densities it approached that observed for tetrahydrofuran. Supercritical C 0 2 , NzO, and CC1,F showed smaller spectral shifts over a comparable density range. In mixed fluid solvents (C0,-methanol) the spectral shift approached that seen for pure methanol as the percentage of methanol was increased.
Introduction The growing interest in supercritical fluid solvents for and chromatography2,3 has shown the need for better ,,,,derstanding of the effects of pressure and temperature on solventsolute interactions. Since the solvation power of a fluid has been shown to be roughly proportional to d e n ~ i t ythe , ~ interactions are expected to be sensitive to changes in temperature and Dressure. Since changes in solvent densit; may impact both the quantity and qualitative nature of solute-solvent intermolecular interactions, supercritical fluids should be sensitive media for studying solvation Dhenomena. 'Operated by Battelle Memorial Institute.
0022-3654/86/2090-3022$01.50/0
One probe of the immediate environment around a solute molecule is based upon measurements of spectroscopic shift^.^-^ The solvatochromic method utilizes a linear solvation energy relationship to correlate solvent effects on a solute. This relationship can be expressed in the general form XYZ = XYZo acy + bo + SPPE (1)
+
( I ) Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Reu. Chem, Eng, 1983, 79, (2) Wright, B. W.; Smith, R. D. Chromatographia 1984, 18, 542. (3) Yonker, C. R.; Wright, B. W.; Udseth, H. R.; Smith, R. D. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 908. (4) Giddings, J. C.; Meyers, M. N.; McLaren, L.; Keller, R. A. Science 1968, 162, 67.
0 1986 American Chemical Society
The Journal ofPhysica1 Chemistry, Vol. 90, No. 13, 1986 3023
Supercritical Fluid Solvents where XYZ represents some property of the system (e.g., reaction rate constant, position of an absorption maximum in an IR, UV-visible, NMR, or ESR spectrum, etc.), a is a scale of solvent hydrogen-bond donor acidities (HBD), /3 is a scale of solvent hydrogen-bond acceptor basicities (HBA), and SPPE is a parameter based on solvent polarity-polarizability effects5 In a series of papers dealing with the solvatochromic Kamlet, Taft, and co-workers have described a linear solvation energy relationship based on the correlation of peak position of UV-visible absorption maximum of a solute in a liquid solvent with values of HBD, HBA, and SPPE characteristic of these solvents. Kamlet and Taft have shown that for UV-visible spectral data the SPPE term in eq 1 can be correlated with a single parameter, a*. This parameter correlates solvent effects on the p a* and a a* electronic transitions, establishing a a* scale of solvent polarities. The success of this method has led to the characterization of roughly 250 solvent^.^ On substitution of the a* parameter for the SPPE term, eq 1 becomes
-
XYZ = XYZo
+ aa + bo + sa*
-
(2)
where s is the susceptibility of XYZ to changing SPPE and is characteristic of a given solute. Our work has aimed at investigating the solvent-solute interactions in the supercritical fluid (dense gas) regime and comparing supercritical fluids to conventional liquid solvents. We utilize the shift in UV-visible position of maximum absorbance with density, for pure and mixed supercritical fluids, of a solute probe which has been characterized by Kamlet, Taft, and c o - w ~ r k e r s . ~ With supercritical fluid solvents, one would expect a* to be a function of density; therefore, both pressure and temperature should have an effect on peak position. The supercritical fluid systems and solute in this work were chosen to minimize hydrogen-bonding interaction^,'^ and therefore eq 2 could in many instances be reduced to urnax= Yo
+ sa*
(3)
where,,,Y is the wavenumber of maximum absorbance in the UV-visible spectrum and v0 is the reference wavenumber of absorbance maximum determined for a standard solvent (cyclohexane). A change in position of maximum absorbance can be related to changes in the supercritical fluid's polarity-polarizability as a function of density. Thus, we have used this technique to probe the solute organized cybotactic region (Le., the region around the solute where the structural order of the solvent molecules has been influenced by the s01ute)~and to explore the solvating properties of pure and mixed supercritical fluid solvents and the effect of fluid density.
Experimental Section The solvatochromic probe molecule chosen for this work was 2-nitroanisole (Aldrich Chemical Co.). The s value reported in the literature for 2-nitroanisole is -2.428 f 0.195.5 This value was representative of a series of solvents: HBA, amphiprotic hydrogen-bond acceptor-donor, and non-hydrogen-bond acceptor-donor solvents (NHB) (ref 5 and references therein). A known s value for the solute allows one to calculate the change in the (5) Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J . Am. Chem. SOC.1977, 99, 6027. (6) Abboud, J. L.; Kamlet, M. J.; Taft, R. W. J . Am. Chem. SOC.1977, 99, 8325. (7) Kamlet, M. J.; Hall, T. N.; Boykin, T.; Taft, R. W. J . Org. Chem. 1979, 44, 2599. (8) Kamlet, M. J.; Carr, P. W.; Taft, R. W.; Abraham, M. H. J . Am. Chem. SOC.1981.103. 6062. (9) Kamlet, M. J.; Abboud, J. L.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983, 48, 2877. (10) Taft, R. W.; Abboud, J. M.; Kamlet, M. J. J . Am. Chem. Soc. 1981, ? I -i n- -, - -O-R-.O (11) Abboud, J. M.; Guihenuef, G.; Essfar, M.; Taft, R. W.; Kamlet, M. J. J . Phys. Chem. 1984,88, 4414. (12) Taft, R. W.; Kamlet, M. J. Inorg. Chem. 1983, 22, 250. (13) Sigman, M. E.; Lindley, S. M.; Leffler, J. E. J. Am. Chem. Soc. 1985, 107, 1471.
A
Freon-13
I
304
I/
X
?
4
292
290
1 ' ~ ' ' ~ ' ' ' ' ' ~ ~ ' ~' I " ' ~ " ~ ' 500
1000
1500
2000
2500
3000
Pressure (psi)
Figure 1. Wavelength of maximum absorbance (Amax) vs. pressure (psi) for 2-nitroanisole with C02 and Freonl13.
supercritical fluid solvents' a* value using eq 3 as temperature
or pressure change. The reference absorption maximum for 2nitroanisole is 32.56 X lo3 cm-' ( y o ) in cyclohe~ane.~ Absorption spectra of 2-nitroanisole in supercritical C02,N 2 0 , Freon-13, ammonia, and C02-methanol were obtained with a Cary Model 1605 spectrophotometer used in the dual-beam mode. The gases used as supercritical solvents were of the highest purity available from the supplier (Matheson) and were further filtered prior to use. The mixed solvent system of C02-methanol was obtained from Scott Speciality Gases (1 5.4 wt 5% methanol), and other mixtures were made in the laboratory. Liquid solvent spectra of 2-nitroanisole in n-pentane, methanol, tetrahydrofuran, and acetonitrile (Burdick & Jackson) were obtained by using quartz cells with a 1-cm light path and with a pure solvent in the reference beam. Vapor-phase and supercritical fluid spectra were obtained with an air reference. The high-pressure cell was constructed from stainless steel (SS 304) and had dimensions of 1 in. in diameter by 2 in. long, with a 3/16-in. diameter hole drilled along the axis. High-pressure 1/ 16-in.-0.d. stainless steel inlet and outlet connections were silver-soldered into the cell, which allowed for supercritical fluid to flow through and purge the cell. Each end of the cell had a seat for a l/4-in.-o.d., '/&.-thick quartz window and was threaded to accept a brass compression nut. A '/4-in.-o.d. Teflon O-ring was placed on each side of each window to provide cushioning and make a gas-tight seal. The optical path length of the assembled cell was approximately 1.5 cm with a total volume of 350 pL. The absorption cell was wrapped with heating tape, insulated, and temperature monitored with a thermocouple. For the mixed fluid solvent systems a similar but larger volume high-pressure cell was used. Either assembly could be placed in the sample compartment of the spectrophotometer, and a single-mode temperture controller (West) provided temperature regulation to within f0.5 OC. The supercritical solvent was delivered to the cell by a high-pressure syringe pump (High Pressure Equipment) and was connected to the cell via a high-pressure liquid chromatographic sampling valve (Rheodyne Inc.). The sampling valve contained a 10-pL sample loop; this allowed for easy introduction of 2-nitroanisole into the absorption cell. A pressure transducer (Model 204, Setra Systems) provided pressure measurement (f10 psi). The experiments were conducted as follows: the sample was loaded into the sample loop, and a shut-off valve at the cell outlet was opened to allow fluid from the pump to flow through the cell. The sample loop was then switched in line, and the absorbance at a predetermined wavelength was monitored to detect the appearance of the sample in the cell. The solute (probe) concentration was diluted by introduction of additional solvent to obtain the desired concentration (and absorbance). The outlet valve was then closed, and the absorption spectrum of the 2-nitroanisole was recorded. Subsequent scans at different pressures or temperatures
3024
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
TABLE I:
T*
Yonker et ai.
Solubility Scale Parameters and the Peak Position of Absorbance Maximum for 2-Nitroanisole 10' cm-I
Y,,,,
solvent
T, K
P, atm
303 296 323 298 323 296 296 413 298 298 298 296
90 270 180 1 180 270 270 170
P,
gm/cm3
vapor
CCIF3' CCIF3e N,O'
pentane CO,' N2O' C02' NHA' tetrahydrofuran methanol acetonitrile "3'
0.87f 1.15, 0.6Sf 0.626 0.64' 0.95, 0.9sf 0.3@ 0.888 0.791 0.777 0.621
1
I 1 270
obsd
calcd'
T*
34.97 33.26 f 0.07 33.07 f 0.10 33.85 f 0.09 32.89 33.73 f 0.10 32.63 f 0.05 32.47 f 0.05 31.75 f 0.25 31.45 3 1.06 30.86 30.63 f 0.04
35.13
-1.06b -0.29 f 0.03 -0.21 f 0.04 -0.12 f 0.03 -0.08d -0.07 f 0.04 -0.03 f 0.02 0.04 0.03 0.34 0.07 0.58b O.6Ob O.7Sb 0.80 f 0.02
32.75
* *
31.15 31.10 30.74
ov,Bx values calculated based on vo = 32.56 X IO3 cm-'. b ~ values * from ref 9. CSupercriticalfluid, pr = 1.5. dEstimate K * vmax determined for subcritical liquid. fEstimated from: Gas Encyclopedia; Elsevier: Amsterdam, 1976.
value for pentane from
ref 9.
TABLE 11: Critical Parameters
supercritical fluid
co2 N 20
CCIF, 3"
T,, K
Pc,atm
pC, d c m 3
304.2 309.6 302.0 405.6
72.8 71.7 38.1 111.3
0.46 0.45 0.58 0.24
I
2
34
-
33
-
x
-
IT
E
5
32
31
310
I:
t
A co2 A Freon 13
-
3 05
10
20
1 5
2 5
Pr
Figure 3. vml (lo3cm-') vs. reduced density ( p , ) for 2-nitroanisole with CO,, N,O. Freon-13, and NH3.
1
I
302
X
COi , ? C h a n g e #
A
C 0 2 i T Change,
A
Freon 1 3
0
NiO
0
NU;
0 2
npi P -
2Jc I 2901 0 c c
1500
2000
25'20
3000
Pressure (psi)
Figure 2. Wavelength of maximum absorbance (Amax) vs. pressure (psi) for 2-nitroanisole with N,O and NH,.
:
:
were made after appropriate equilibration periods. In all cases the pure fluid spectra were also recorded to ensure that there were no interferences.
Results and Discussion Pure Fluids. The wavelengths of maximum absorption of 2-nitroanisole in liquid methanol, tetrahydrofuran, acetonitrile, and pentane are given in Table I. These results can be compared with the data obtained from the vapor-phase spectra and in supercritical fluids at a reduced density ( p r ) of 1.5. Table I also compares the a* parameters of the subcritical liquids with the supercritical fluids. Table I1 contains the critical parameters for the gases studied. Figures 1 and 2 depict the dependence of the wavelength of the absorbance maximum (A,) upon pressure for 2-nitroanisole in C 0 2 , CC1F3 (Freon-13), N 2 0 , and NH3, respectively. These studies provide a direct probe of the effect of pressure (density) on the cybotactic region. Figure 3 compares plots of vmaX ( lo3 cm-') against reduced density for the four supercritical fluid solvents investigated. Above a reduced density of 0.5, Figure 3 shows an approximately linear relationship between wavelength of maximum absorbance and reduced density. Freon- 13 shows a very small change in peak position of absorbance maximum with
1 23
0 2
0 4
06
0 8
10
1 2
1 4
16
I 8
20
Pr
reduced density ( p , ) for 2-nitroanisolewith C02, N20, Freon-13,and NH3. Gas-phase, dilute vapor of the indicator (ref 11).
Figure 4.
T* vs.
density. Carbon dioxide and N 2 0 behave similarly as a function of density. Supercritical NH, shows the largest shift in position of absorbance maximum for the four supercritical fluid solvents. Nitrous oxide and C 0 2 are very similar in physicochemical behavior and have nearly identical critical points.14 Therefore, similar behavior in the shift of the maximum absorption peak seen in Figure 3 is not unexpected. Freon-13 is the poorest solvent examined for 2-nitroanisole, which is consistent with the minimal density effect observed. Ammonia being the most polar of the four fluids should solvate 2-nitroanisole to the greatest extent, and therefore a change in density for ammonia was expected to have a large impact on the cybotactic region of 2-nitroanisole, as observed. On the basis of the present work, we cannot exclude (14) Gas Encyclopedia; Elsevier: Amsterdam, 1972;pp 334, 1053.
Supercritical Fluid Solvents
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 3025
contribution to specific chemical contributions ( H bonding) to the solvatochromic shifts observed for ammonia. The A* scale of solvent polarities can be used to qualitatively interpret the relative polarities of these four supercritical fluid solvents as a function of pressure or density, as shown in Figure 4 for reduced density. This figure gives data for CO, obtained by varying both pressure (X) and temperature (A);A* is to a first approximation only a function of solvent density in these fluids within the limited range of pressure and temperature studied. As for the absorbance shifts, the A* parameter was observed to undergo the greatest change for NH3 as a function of density; the minimum change for Freon-13, C02, and N 2 0 shows roughly similar intermediate behavior with density. It can be predicted from Figure 4 that ammonia will be the best solvent for 2nitroanisole, Freon-13 the poorest, and COz and N20 will show intermediate behavior. The large solvatochromic shift seen for ammonia as a function of density could be due to increased self-association of ammonia at higher concentrations. This can lead to higher A* values than expected as seen in water and alcohols for the ?r*/dipole moment correlation reported by Abboud et aL6 The A* values for C 0 2of -0.52 to -0.60 reported by HyattI5 compare favorably with our A* value for 2-nitroanisole in CO, of -0.55 at a reduced density of 0.43. Leffler et al.I3 reported an average A* values for CO, at three different fluid densities of 0.86,0.68, and 0.46 g/cm3 using ten indicator solutes. Their A* values at these densities are -0.12, -0.22, and -0.45, respectively. The A* values determined here a t similar densities are approximately -0.05, -0.10, and -0.25. These values are equal within experimental error at higher density values; the reason for the discrepancy seen at the low density is unknown. Ammonia’s A* value ranges from below that of n-heptane to approximately that of ethyl acetate and tetrahydrofuran as a function of density.” Carbon dioxide and N 2 0 range from a polarity similar to that of the perfluoroalkanes (perfluoro-n-octane, perfluoro-n-heptane, perfluoro-n-hexane) to that of the n-alkanes (n-heptane, etc.).” Freon- 13 is similar to the perfluoroalkanes at the densities studied. I I The increase in A* polarity-polarizability parameter with density is not unreasonable when compared to the increase in / ~ , fluid density as demsolubility parameter, 6 ( c a l / ~ m ~ ) ’with onstrated by Allada.I6 All of the solvent polarity ranges could be extended to greater fluid densities, and solvating properties more comparable to liquids are a n t i ~ i p a t e d . ’ ~ The Kamlet-Taft A* solvent polarity-polarizability scale is based on a linear solvation energy relationship between the solvent ’ ~ A* parameter and the solutes’ FA* transition e n e r g i e ~ . ~ -The has been shown to be related to the solvents dipole moment through linear correlations using the Block-Walker reaction field function under specified condition^.^' For any nonpolar liquid or supercritical fluid solvent, the solutes’ transition energy might be expected to have a linear dependence on the Onsager reaction field function.” Carbon dioxide, having no permanent dipole moment, should behave similarly to a nonpolar liquid in the supercritical fluid state but with density-dependent solvating properties. Therefore, one expects a linear relationship between A* and the Onsager reaction field function. The Onsager reaction field function (L(n2))is a function of solvent refractive index (n): L(n2) = (n2 - 1)/(2n2 1) (4)
+
The refractive index for supercritical COzas a function of temperature and pressure can be determined from the specific Lorentz-Lorenz refraction equation with respect to density ( p )
where AR and BR(nare the first and second refractometric viral (15) Hyatt, J. A. J . Org. Chem. 1984, 49, 5097. (16) Allada, S . R. Ind. Eng. Chem. Process Des. Deu. 1984, 23, 344. (17) Brady, J. E.; Carr, P. W. J . Phys. Chem. 1985, 89, 1813.
TABLE 111: Onsager Reaction Field Function ( L ( n * ) )for C02 at 50
OC for 2-Nitroanisole absorbance peak
P,atm
p , g/cm3
n
?r*
73.5 73.7 73.8 75.4 76.3 11.6 78.9 81.8 83.0 84.3 85.7 87.1 88.2 88.4 88.6 90.5 93.6 94.2 97.1 97.2 105.1 156.5 204.0 342.8
0.197 0.198 0.198 0.206 0.21 1 0.217 0.225 0.24 1 0.249 0.257 0.266 0.276 0.284 0.286 0.287 0.302 0.329 0.334 0.361 0.361 0.435 0.679 0.773 0.917
1.0454 1.0456 1.0456 1.0475 1.0487 1.0500 1.0519 1.0557 1.0576 1.0590 1.0616 1.0639 1.0660 1.0663 1.0665 1.0700 1.0760 1.0776 1.084 1 .OS4 1.1017 1.1615 1.1852 1.2222
-0.48 -0.48 -0.55 -0.46 -0.46 -0.42 -0.50 -0.39 -0.39 -0.33 -0.35 -0.3 1 -0.25 -0.28 -0.28 -0.32 -0.27 -0.27 -0.22 -0.22 -0.23 -0.09 -0.05 -0.00
=*
L(n2) 0.0291 0.0293 0.0293 0.0304 0.03 12 0.0320 0.0332 0.0354 0.0366 0.0377 0.0390 0.0404 0.0415 0.0418 0.0420 0.0441 0.0477 0.0485 0.0520 0.0520 0.0624 0.0944 0.1062 0.1238
max, nm 296.5 296.5 295.0 297.0 297.0 297.8 296.0 298.5 298.5 299.7 299.3 300.3 301.5 300.8 300.8 300.0 301.0 301.0 302.0 302.0 302.5 305.0 306.0 307.0
-0’5r/” L (n2)
Figure 5.
T*
vs. Onsager reaction field function ( L ( n 2 ) )for CO,at 50
OC.
coefficient^.'^^^^ The density for C 0 2 as a function of pressure and temperature can be calculated from a two-parameter, cubic equation of state (e.g., Peng-Robinson equation of state).20 The refractometric viral coefficients for CO, have been reported by Kholodov, Timoshenko, and Yaminovl* and Bose and S t - A r n a ~ d . ’ ~ Values for the two refractometric viral coefficients can be substituted into eq 5 to estimate the refractive index of supercritical CO,. A plot of the Onsager reaction field function vs. K* for CO, is shown in Figure 5, and the data are given in Table 111. A qualitative change in the dependence of K* as a function of the Onsager reaction field function is observed at a density of -0.29 g/mL. This likely is due to the enhanced solvation of the 2nitroanisole as the density of the CO, increases. At low L(n2) values (low density of CO,) one expects poor solvation of the 2-nitroanisole by CO,. The cybotactic region of 2-nitroanisole is deplete of CO, molecules, and one would expect an extrapolation of this regime of the curve to intercept with the vapor-phase limit of the probe molecule. Least-squares analysis of these experimental points in Figure 5 yields an intercept value of -1.02. The gas-phase limit reported by Essfar, Guihenuef, and Abboud of A * ~ is -1.06 f 0.10,21in excellent agreement. As the density of COz increases (larger L(n2)values), the cybotactic region of the solute becomes enriched with CO, molecules and begins to affect (18) Kholodov, E. P. Timosheko, N. I.; Yaminov, A. L. Therm. Eng. (Engl. Transl.) 1972, 19, 126. (19) Bose, T. K.; St-Arnaud, J. M. J . Chem. Phys. 1979, 71, 4951. (20) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, I S , 59. (21) Essfar, M.; Guiheneuf, G.; Abboud, J.-L. M. J. Am. Chem. SOC.1982, 104, 6786.
J . Phys. Chem. 1986, 90, 3026-3030
3026 34 \
1
I
0
100% c02
c
9.5% MeOH
I
the energy levels of the absorbance spectrum. Therefore, the absorbance spectrum shifts from a "gas-phase-like" region to a regime where the probe molecule becomes effectively solvated by C 0 2 . The precise density where the qualitative change observed in Figure 5 takes place is less readily explained but may correspond to the beginning of some ordering of adjacent molecules in the cybotactic region. Mixed Fluids. Methanol was added to C 0 2at 5.6 and 9.5 wt %, and the spectral shift of 2-nitroanisole was determined. Figure 6 shows the effect of methanol on the absorbance maxima with pressure. At low percentages of methanol in COz the spectra are red-shifted toward the value seen for pure methanol (see Table I). At 9.5% methanol i n , C 0 2 , pressure has no effect on the absorbance maximum. One can hypothesize that the cybotactic region of 2-nitroanisole experiences an effective enrichment in methanol at small percentages of methanol in C 0 2 that leads to an environment similar to that in pure methanol. Once this methanol cybotactic environment is established, then pressure would have a small effect on this region and hence on the energy of the P A * transition for 2-nitroanisole. Further studies are in
progress to better understand the effects in mixed fluid systems. Conclusion The A* solvent polarity-polarizability scale has been applied to four supercritical fluids based on the solvatochromic shift of the absorption peak maximum. Measurement of the solvatochromic shift in position of the absorption maximum directly probes the cybotactic region of the solute, providing information on the solute-solvent intermolecular interactions in the solvation
reaction field function is effective in relating the state of the cybotactic region of the solute as one progresses from gas-phase densities to liquidlike densities for the supercritical fluid. A significant effect of a solvent modifier in the fluid on the cybotactic region was observed. The cybotactic region can apparently become enriched with the solvent modifier under conditions of relatively small modifier concentrations. Extension of these studies is expected to lead to a more fundamental understanding of the intermolecular interactions occurring during supercritical fluid extraction or supercritical fluid chromatography and solutesolvent interactions relevant to reaction processes in supercritical fluid media. In the broader sense, these studies allow an enhanced understanding of solvation phenomena by probing the continuous range of interactions between the gas- and liquid-phase limits.
Acknowledgment. This work has been supported by the U S . Department of Energy, Office of Basic Energy Sciences, under Contract DE-AC06-76RLO 1830. Registry NO. CClF,, 75-72-9; N20, 10024-97-2;CO,, 124-38-9;"3, 7664-41-7;2-nitroanisole, 91-23-6;pentane, 109-66-0;tetrahydrofuran, 109-99-9;methanol, 67-56-1; acetonitrile, 75-05-8.
Is the Walden Product Useful? M. Nakahara* and K. Ibuki Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606, Japan (Received: November 19, 1985)
The invalidity of the use of the Walden (conductance-viscosity) product in the interpretation of the limiting ionic conductance Xo has been elucidated by comparing the experimental result and the prediction made for the relatively small alkali metal ions as a function of temperature, solvent, and pressure by the Hubbardansager dielectric friction theory. It is recommended to transform Xo into a more meaningful quantity such as the residual friction coefficient A{ which is defined as the overall friction coefficient subtracted by the Stokes friction coefficient for slip. Taking the residual friction coefficient comes from the dielectric friction theory, while taking the Walden product is based on the Stokes law where the effect of the charge on ion is not taken into account. It turns out that, contrary to what has so far been believed, the contribution of the viscosity qo to ion mobility is not eliminated by the multiplication of Xo by 7' but remains in the "corrected" quantity.
Introduction The limiting ionic conductance Xo has been determined in an exhaustive manner for a variety of ions in aqueous and nonaqueous solvents and used for a long time as a probe for getting insight into the dynamic aspects of ionsolvent interactions. Interpretation of this useful quantity is, of course, influenced by the form into which it is transformed for the discussion; any undesirable transformation obscures or distorts the original physical meaning. Unfortunately, however, it continues to take the Walden product, where Xo is multiplied by the solvent viscosity qo, in order to shed light on factors determining ion migration in solution even after the Walden rule1 was recognized to be invalid in the rigorous 0022-3654/86/2090-3026$01.50/0
sense;2 the afterglow of the Walden rule is too strong in view of the fact that the contribution of the dielectric f r i ~ t i o nas ~ .well ~ as the hydrodynamic one to the overall friction coefficient for moving ion was noticed a long time ago. This kind of transformation is seen in almost every paper on ion mobility whether it is theoretical or experimental. This prolonged convention will not (1) Walden, P. 2.Phys. Chem. 1906, 55, 207. (2) Fuoss, R. M.; Accascina, F. Electrolytic Conductance; Interscience: New York, 1959. (3) Wolynes, P. G. Annu. Rev. Phys. Chem. 1980, 31, 345. (4) (a) Hubbard, J.; Onsager, L. J . Chem. Phys. 1977, 67, 4850. (b) Hubbard, J. J . Chem. Phys. 1978, 68, 1649.
0 1986 American Chemical Society
