6852
J. Phys. Chem. 1992,96,6852-6853
intermediate spectra at 308 and 318 K can be fit with a sum of both slow and fast tumbling components as shown in Figure 7 for 308 K. Discussion The major results of these ESR spectral simulations are shown in Figure 8, which is a plot of the parameters S and R, versus the x-doxy1 position in the x-DSA/DODAC vesicle system. As x increasa,the order parameter Sdccreases in the range x = 5-12. This is consistent with more flexibility of the alkyl chain carbon to which the doxyl group is attached as the distance from the vesicle interface increases. However, at x = 16, S increases consistent with a U-shaped bending of the alkyl chain of x-DSA. The bending is likely a consequence of the doxyl group polarity and its position near the end of the stearic acid alkyl chain. This trend for liquid vesicle solutions is remarkably consistent with the trend of the xdoxyl position deduced infrozen DODAC vesicle systems from an analysis of deuterium modulation depths determined by electron spin echo spectroscopy.28 The inset to Figure 8 shows these data. These data were also interpreted as indicating a U-shaped bending of the 16-DSA alkyl chain. The trend of the R, parameter is also consistent with the S parameter trend. RL is slower in a more ordered environment and faster in a less ordered one. The decrease in R , for x = 16 is indicative of a U-shaped bend in the 16-DSA alkyl chain to put the doxyl group into a more ordered environment. The temperature dependence of the 16-DSA probe versus that of the 5-DSA and 7-DSA probes shows that the environment of the 16-doxy1 group is not quite the same as that of the 5-doxy1 and 7-doxy1 groups. This difference is not shown by the 298 K spectra alone or by the S and R , parameters at 298 K. Since the 16-doxy1group is near the end of the stearic acid alkyl chain, one expects it to have greater motional fluctuation than a 5-doxy1 or 7-doxy1 group even if they are both near the same average distance from the vesicle interface. This difference becomes more detectable in the ESR spectra as the temperature increases above 298 K. Conclusions This study demonstrates that the ESR line shape of an xdoxylstearic acid spin probe located within DODAC vesicles between 298 and 328 K can be satisfactorily simulated with the microscopic order-macroscopic disorder model of Freed and coworkers. The simulated spectra were most sensitive to changes in the order parameter and the perpendicular component of the rotational diffusion rate R,. The trend in the order parameter with the x-doxy1 position approximately correlates with the deuterium electron spin echo modulation depths previously observed for frozen solutions of the x-DSAIDODAC system. It is concluded that the alkyl chain of 16-DSA is U-shaped in DODAC vesicles in both liquid and frozen solutions.
Acknowledgment. This research was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, US.Department of Energy. Regbtry No. 5-Doxylstearic acid, 29545-48-0; 7-doxylstearic acid, 40951-82-4; 10-dtoxylstearic acid, 50613-98-4; 12-doxylstearic acid, 29545-47-9; 16-doxylstearic acid, 53034-38-1; dioctadecyldimethylammonium chloride, 107-64-2.
References a d Notes (1) Fendler, J. H. Acc. Chem. Res. 1980, 13, 7. (2) Kalyanasudaram, K. Photochemistry in Microheterogeneous Systems; Academic: New York, 1987. (3) Hurley, J. K.; Tollin, G. Sol. Energy 1982, 28, 187. (4) Kevan, L. In Photoinduced Electron Transfer, Part B Fox, M., Chanon, M.. Eds.; Elsevier: Amsterdam, 1988; pp 329-384. (5) Freed, J. H. In Spin Labeling, Berliner, L. J., Ed.; Academic: New York, 1976; Chapter 3. (6) Fendler, J. H.; Fendler, E.J. Catalysis in Micelles and Macromolecular Systems; Academic: New York, 1975. (7) Marsh, D. In Membrane Spectroscopy; Grell, E., Ed.; Springer-Verlag: Berlin, 1981; Chapter 2. (8) Seelig, J.; Limacher, H.; Bader, P. J . Am. Chem. Soc. 1972,94,6364. (9) Waggoner, A. S.; Keith, A. D.; Griffith, 0. H. J . Phys. Chem. 1968, 72, 4129. (10) Povich, M. J.; Mann, J. A.; Kawamoto, A. J. J . Colloid Interface Sci. 1972, 41, 145. (1 1) Esposito, G.; Giglio, E.; Pavel, N. V.; Zanobi, A. J. Phys. Chem. 1987, 91, 356. (12) Hearing, G.; Luisi, P. L.; Hauser, H. J. Phys. Chem. 1988,92, 3574. (13) Emandes, J. R.; Schrier, S.; Chaimovich, H. Chem. Phys. Lipids 1976, 16, 19. (14) Yoshioka, H. Chem. Lorr. (Jpn.) 1977, 1477. (15) Baglioni, P.; Ottaviani, M. F.; Martini, G. J. Phys. Chem. 1986, 90, 5878. (16) Lasic, D. D.; Hauser, D. J. Phys. Chem. 1985, 89, 2648. (17) Schrier, S.; Polnaszek, C. F.; Smith, I. C. P. Biochim. Biophys. Acta 1978,515, 395. (18) Gaffney, B. J.; McConnell, H. M. J . Magn. Reson. 1974, 16. 1. (19) Berliner, L. J., Ed. Spin Labeling, Academic: New York, 1976. (20) Seelig, J. J . Am. Chem. SOC.1970, 92, 3881. (21) Hubbel, W. L.; McConnell, H. M.J . Am. Chem. Soc. 1971,93,314. (22) Moro, G.; Freed, J. H. J . Phys. Chem. 1980,84, 2837. (23) Moro, G.; Freed, J. H. J . Chem. Phys. 1981, 74, 3757. (24) Meirovitch, E.; Igner, D.; Igner, E.; Moro, G.; Freed, J. H. J. Chem. Phys. 1980, 84, 2459. (25) Meirovitch, E.; Freed, J. H. J . Phys. Chem. 1982, 77, 3915. (26) Meirovitch, E.; Nayeem, A.; Freed, J. H. J . Phys. Chem. 1984,88, 3454. (27) Schneider, D. J.; Freed, J. H. In Biological Magnetic Resonance; Berliner, L. J., Reuben, J., as. Plenum: ; New York, 1989; Vol. 8, Chapter 1. (28) Hiff. T.: Kevan. L.J . Phvs. Chem. 1989. 93. 1572. (29) Bratt, P. J.; Kang, Y. S.(Kevan, L.; Nakamura, H.; Matsuo, T. J . Phys. Chem. 1991,95,6399. (30) Seelig, J. In Spin Labeling, Berliner, L. J., Ed.; Academic: New York, 1976; Chapter 10. (31) Wikander, G.; Eriksson, P. 0.;Burnell, E. E.; Lindblom, G. J . Phys. Chem. 1990,94, 5964. (32) Mason, R. P.; Polnaszek, C. F.; Freed, J. H. J . Phys. Chem. 1974, 78, 1324. (33) Meirovitch, E.; Freed, J. H. J . Phys. Chem. 1980, 84, 3281.
COMMENTS
The Zeno Llne and the Radlal Dktrlbutlon Functlon at Contact Sir: Xu and Herschbach' have pointed out that the Zeno line, which is the locus of points in the T-p plane for which 2 = p / p k T = 1, is nearly linear for most normal fluids and that this linearity furnishes a constraint on equations of state for supercritical fluids and compressed liquids. They point out that the Song-Mason2 0022-3654/92/2096-6852$03.00/0
equation of state (EOS)for molecular fluids does not give a straight &no line, using C02as an example. In fact, neither does the simpler Song-Mason EOS for simple fluids, such as the noble gases.3 The Song-Mason equation contains a new strong principle of corresponding states in which an entire p v - T surface can be collapsed to a single curve: and the resulting EOS is appreciably more accurate than the original Song-Mason EOS. 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6853
Comments
t
t
TBto well below the critical temperature. This relation is suggested by considering the van der Waals model, for which a = 6 and B2 = b - (a/kT), but numerical calculation^^^^ show that it also holds approximately for more realistic potential models. The corresponding-states result is that G' is linear in bp, which from eq 2 gives the Zen0 contour to be given by
\a
1 - Xbp
\
\j
, , ,
I , , , ,
T/TB
(3)
where X is the slope of G-l vs bp. Thus, the linearity of G1vs bp is reflected in the linearity of the Zen0 contour. The third comment follows directly from eq 2. Since a( T ) is the contribution of the repulsive forces to B2(T),the quantity a - B2 must represent the (absolute value of the) contribution of just the attractive forces to B2(7). Hence, eq 2 can be interpreted as implying the following relation along the Zen0 contour: radial distribution function at contact c attractive contribution to B2 repulsive contribution to B2 (4)
i
This conclusion in itself does not require that the Zen0 contour be linear, nor even that it have the same functional form for all normal fluids. However, the apparent universal empirical linearity of the Zen0 contour puts a strong constraint on G(bp), in particular on how the radial distribution function at contact must scale with temperature and distance (through b) and with density p. The fourth comment is less precise than the other three. There is no indication from the Zen0 line concerning the significance of many-body forces, since the Zen0 contour for the pairwise additive (12,6) potential seems to be just as linear as those for real fluids. However, the G1vs bp plot for the (12,6) potential covers a much greater range of temperature (about 30-fold) and of density (about 3-fold) than does the Zen0 line, and this plot does show curvature-in fact, the points scatter around the Carnahan-Starling curve for hard spheres. The G-' vs bp plots for real fluids are nevertheless straight lines, and these deviations from the expected curves for hard convex bodies have been interpreted as caused by many-body forces? In other words, there may be some evidence for many-body forces in the linear G-' vs bp plots, but the ranges of temperature and density covered by the Zen0 lines are too limited to either confm or refute this result. In conclusion, it remains a mystery why the Zen0 contour is linear and not some other shape, and the associated linearity of G-' vs bp is also still a mystery, but it appears that the two mysteries are connected. 1 + 6bp
\-I
where B2 is the second virial coefficient, a is the contribution to B2 of just the repulsive forces, and b = a + T(da/dT) is the covolume. The repulsive forces are defined according to the Wecks-Chandler-Andersen decomposition of the intermolecular p~tential.~ The term involving the constant 6 is a small correction, and other quantities are as previously defined. The full calculations shown in Figure 1 demonstrate that the Zen0 line from this EOS are indeed nearly linear, but we can extract this result in a simple mathematical form with the aid of three approximations. We first neglect the correction term involving 6 and the weak temperature dependence of b and then set 2 = 1 and solve eq 1 for G(bp)
G ( ~ P=) (a (2) It happens that (a- B 2 ) / ac TB/Tfrom the Boyle temperature
Acknowledgmenr. We thank Professor Dudley R. Herschbach for several interesting conversationsand helpful comments. This work was supported in part by NSF Grant CHE 88-19370.
References and Notes (1) (2) (3) (4) (5) 5231.
Xu, J.; Herschbach, D. R. J. Phys. Chem. 1992, 96, 2307. Song, Y . ;Mason, E. A. Phys. Rev. A 1990,42,4743,4749. Song, Y . ;Mason, E. A. J . Chem. Phys. 1989, 91, 7840. Ihm, G.; Song, Y . ; Mason, E. A. J . Chem. Phys. 1991, 93, 3839. Weeks,J. D.; Chandler, D.; Andersen, H. C. J . Chem. Phys. 1971,54,
Department of Chemistry Brown University Providence, Rhode Island 02912 Received: May 11, 1992
Yubua Song
E.A. Mason*
