2556
J . Phys. Chem. 1985,89, 2556-2560
Anisotropic Rotational Reorientation of Perdeuterated 2,2,6,6-Tetramethyl-4-piperidone N-Oxide in Jojoba Oil: An ESR Line Shape Study Anson S . W. Li and James S . Hwang* University of Petroleum and Minerals, Department of Chemistry, Dhahran, Saudi Arabia (Received: August 6, 1984)
A detailed ESR line shape study of perdeuterated 2,2,6,6-tetramethyl-4-piperidone N-oxide (PD-Tempone) in jojoba oil has been performed on desktop computer utilizing on-screen simulation. A detailed description of the procedure is presented. The uniqueness of such computer fitting is demonstrated. An analysis employing anisotropic rotational diffusion at the fast motional narrowing region (Q Ilo-" s) suggests that PD-Tempone exhibits asymmetric rotational diffusion with N = 3.3 at an axis z' = Y in the plane of the molecule and perpendicular to the N-0 bond direction. The anisotropic interaction parameter K has been determined to be 0.018. The t parameter for correction to the nonsecular Debye spectral densities is found to correlate with the ansiotropic interaction parameter K . Larger t value seems to correlate with smaller K value. Both observations are interpreted as small solute experiencing steric hindrance in large solvent molecules which results in preferential orientation. The precision of the parameters N and t and the uniqueness of the simulation are discussed.
Introduction An imDortant area of research in chemisrv has been to seek structur; information about the system at the molecular level. In ESR, this can be achieved by introducing stable nitroxide radicals into the system and studying its dynamic interaction with the system.' The location or the motional effect of the nitroxide spin probes usually provides valuable information about its local environment and many other useful physical p r o p e r t i e ~ l - ~ Nitroxide spin probe studies have been performed in poly(phen~lacetylene),~ poly(viny1 alcohol) gels: liquid crystal^,^ micelles: and phospholipids or synthetic vesicle^.^ In order to obtain information concerning the motion of the probes or its local en~ i r o n m e n t , ' - ~ J @one l ~ needs to determine the half-width at half-height, or the intrinsic line width w ,of the ESR lines and
(1) Berliner, L. J., Ed. 'Spin Labeling: Theory and Applications"; Academic Press: New York, 1976. (2) Goldman, S. A,; Bruno, G. V.; Freed, J. H. J . Chem. Phys. 1972,56, 716. (3) Goldman, S. A,; Bruno, G. V.; Freed, J. H. J . Chem. Phys. 1973.59, 3071. (4) Hwang, J. S.;Mason, R. P.; Hwang, L.-P.; Freed, J. H. J. Phys. Chem. 1975, 79, 489. ( 5 ) (a) Hwang, J. S.; Tsonis, C. P. Macromolecules 1983, 16, 736. (b) Hwang, J. S.;Saleem, M. M.; Tsonis, C. P. Macromolecules, accepted for publication. (6) Watanabe, T.; Yahagi, T.; Fujiwara, S. J . A m . Chem. SOC.1980, 102, 5187. (7) (a) Broido, M. S.; Belsky, I.; Meirovitch, E. J. Phys. Chem. 1982,86, 4197. (b) Broido, M. S.; Meirovitch, E. J . Phys. Chem. 1983, 87, 1635. (8) (a) Spague, E. D.; Duecker, D. C.; Larrabee, Jr., C. E. J . A m . Chem. SOC.1981, 103,6797. (b) Pyter, R. A,; Ramachandran, C.; Mukerjee, P. J . Phys. Chem. 1982, 86, 3206. (c) Mukerjee, P. In "Solution Chemistry of Surfactant"; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 1, p 153. (d) Ottaviani, M. F.; Baglioni, P.; Martini, G. J . Phys. Chem. 1983.87, 3146. (e) Isshiki, S . ; Uzu, Y. Bull. Chem. SOC.Jpn. 1981, 54, 3205. (9) (a) Kusumi, A,; Singh, M.; Tirrell, D. A. Oehme, G.; Singh, A.; Samuel, N. K. P.; Hyde, J. S . ; Regen, S . L. J . Am. Chem. SOC.1983, 105, 2975. (b) Lim, Y. Y.; Fendler, J. H. J . A m . Chem. SOC.1979, 101, 4023. (c) Polnaszek, C. F.; Schreier, S.; Butler, K. W.; Smith, I. C. P. J . Am. Chem. SOC.1978, ZOO, 8223. (d) Schreier, S.; Polnaszek, C. F.; Smith, I. C. P. Biochim. Biophys. Acta 1978, 515, 375. (10) Kivelson, D. J. Chem. Phys. 1960, 33, 1094. (11) Freed, J. H.; Fraenkel, G. K. J. Chem. Phys. 1963, 39, 326. (b) Freed, J. H.; Fraenkel, G.K. J . Chem. Phys. 1964, 40, 1815. (12) (a) Ahn, M.-K. J . Chem. Phys. 1976, 64, 134. (b) Bales, B. L. J . Magn. Reson. 1980, 38, 193. (13) Hudson, A,; Luckhurst, G.R. Chem. Reu. 1969, 69, 191. (14) Jolicoeur, C.; Friedman, H. L. J. Solution Chem. 1978, 7, 813. (15) Stillman, A. E.; Schwartz, R. N. J . Magn. Reson. 1976, 22, 269. (16) Lim, Y. Y.; Smith, E. A.; Symons, M. C. R. J . Chem. SOC.,Faraday Trans. 1 1976, 72, 2876.
its isotropic hyperfine coupling constant Ai,. Unfortunately these two parameters are not directly measurable from the ESR spectra because of the unresolved multiplets generated from the 12 or more protons (or deuterons). The unresolved structure can lead to large error in the determination of T2I7if ignored. One of the many methods in obtaining intrinsic line widths is to perform a line shape study and resort to computer simulation. There are large volumes of literature that either discuss or employ this technique. But few of them provide detailed description about the method except but it lacks details on the uniqueness of the simulation. Recently, we performed a detailed line shape study for PD-Tempone in jojoba oil utilizing a desktop computerla and employed procedures developed previously by Hwang et aL4 We discussed in detail all the steps involved, investigated the uniqueness of the simulation, and analyzed the precision of such extracted parameters. Jojoba oil is a liquid wax which is collected from the seeds of jojoba tree, a tree which adapts itself well to semiarid regions. The oil has superior lubricating properties which makes it a good lubricant to replace depleting fossil fuel reserves and is a substitute for sperm whale oil. It also has many important industrial application~.'~-*' In this study, we investigate the molecular dyN-oxide namics of perdeuterated 2,2,6,6-tetramethyl-4-piperidone (PD-Tempone) in jojoba oil. We seek to obtain microscopic information on the anisotropy of molecular reorientation (N) and the anisotropic interaction parameter K . ~K is~ a ratio of the mean square intermolecular torques to the mean square intermolecular forces, and N is the ratio R I I / R , . R I lis the rotational diffusion constant along the molecular Z axis and R , is the rotational diffusion constant along the X and Y axis. The rotation is assumed to be axially symmetric.
Experimental Section ESR measurements were performed with a Varian E-109 spectrometer with either 10- or 100-kHz field modulation in conjunction with a Varian rectangular cavity. The spectrometer is interfaced with the E-935 data acquisition system which employs the HP-9835 desktop computer for data processing. Recorded (17) Poggi, G.; Johnson, C. S. Jr., J . Magn. Reson. 1970, 3, 436. (18) Li, A. S . W.; Hwang, J. S. Arabian J . Sci. Eng. 1984, 9, 233. (19) Jojoba oil is used in shampoos, cosmetics, motor oil, and medicine and is an excellent substitute for sperm whale oil. (20) Yermanos, D. M. Cal$ Agric. 1979, 33, 4. (21) "Jojoba Feasibility for Cultivation on Indian Reservations in the Sonoran Desert Region"; National Academy of Sciences National Research Council: Washington, DC, 1977. (22) Hwang, J. S.; Kivelson, D.; Plachy, W. Z. J . Chem. Phys. 1973, 58, 1753.
0022-3654/85/2089-2556$01.50/0Q 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 12, 1985 2557
Tempone in Jojoba Oil spectra were digitized and stored on cassette tapes. Software we have written provides on-screen simulations. Some of the hardcopies are obtained from the plotter of the ESR spectrometer. Other hardcopies which require X-Y plotter are obtained from an IBM 370/158 mainframe computer. The temperature was controlled by a Varian E-257 variable temperature unit to within f0.5 “C. The absolute temperature was checked at the geometric center of the cavity with a copper-constantan thermocouple and found to be accurate to f l “C. The microwave frequency was measured with a Hewlett-Packard Model 5342A digital frequency counter. The magnetic field sweep was calibrated with a Varian E-500-2 self-tracking N M R gaussmeter with an accuracy of fO.OOO1 mT. Both microwave power and modulation amplitude were verified experimentally to be at least 10 times below the onset of broadening. Scan speed and time constant were also carefully chosen so as not to introduce any artifact from scanning. Samples were prepared in 2-mm i.d. X 3-mm 0.d. Pyrex sample tubes. Dissolved oxygen was removed by several cycles of freeze-pump-thaw. The concentration of the nitroxide was 0.3 f 0.1 mM and was checked experimentally to be absent of exchange broadening. After the addition of the nitroxide probes, the mixtures were agitated and left at room temperature for more than 1 h to reach equilibrium. PD-Tempone was obtained from Stohler Isotope. Jojoba oil was a gift from Hobex, Sacremento, CA.
Calculation and Results The ESR spectra of PD-Tempone at room temperature consists of three hyperfine lines due to the interaction of the unpaired electron with the I4N nuclei ( I = 1). The spectrum was found to vary continuously from a typical three-line spectrum in the fast rotational or motional narrowing region to a rigid limit spectrum at T 5 -80 “C. The sharpest spectra showed up at 15 f 1 “C. Sharper lines have steeper decay gradient and are more sensitive to simulation. The sharpest manifold among the three was digitized into 4096 points and recorded on tapes. In a scan range of 0.4 mT, the digitization was accurate to fO.OOO1 mT. The simulated curves were displayed side by side with the experimental curve on video for visual comparison. The parameters N , t, and e‘ and rotational diffusion axes along X , Y, and 2 could be adjusted a t leisure through keyboard input. Simulated curves appeared on screen within minutes. The particular simulation could be recorded on tape immediately. The simulations utilizing desktop computers provide onscreen simulations, visual comparison, and storage on external peripherals. This greatly reduces the time wasted on guessing the initial parameters by trial and error, and is convenient and efficient to work with. We have demonstrated earlier1*that a simulation of the decay is necessary in determining a unique pair of w and Ab The unique simulation gives the parameters w equal to 0.0170 mT and the corresponding deuteron hyperfine coupling constant 0.0022 mT. Motion Narrowing Analysis. We have adapted the motion narrowing analysis of Freed et a1.24 Equation 5 in ref 2 has been rearranged with the same symbols for easy comprehension. We have also incorporated experimentally adjustable factors c and e’ for non-Debye type spectral density, as suggested in the later version of their improved models! Table I gives all the parameters needed for the calculation which was carried out by using eq 1-3.
co = 8 / 3 - [ I
(W,~O)~€’]-I
c2 = 8 / 3 - [1 4- ( W , T ~ ) ~ € ’ ] - ’
- 1/(3[1
(Wo70)~€])
- 1/(3[1 -t ( W 0 7 2 ) ~ € ] )
C = (2/3’/2y)(0.8*2)(D,2~0C0 + ~DZ’T~C,)
Bo = 16/3 B2 = 16/3
(1)
(2)
+ 4/[1 + ( w ~ T ~ ) ~ ~ ] + 4/[1 + ( W O T ~ ) ~ ~ ]
The magnetic parameters 8’s and A’s were obtained from a computer simulation of rigid limit spectrum recorded at 77 K. This will be discussed elsewhere.23 Figure 1 shows the C vs. B
TABLE I ge = 2.00232 gx = 2.0096 g, = 2.0064 gz = 2.0022 BN = ( 8 x + By + &)/3 Bo = ($,, - B N ) ( 3 / W 2 $2 = (gx, - &)/2 A, = 4.12 G A, = 5.28 G A, = 33.32 G AN = (A, A, A,)/3 G y = 1.764097 X lo7 rad s-l G-’
+ +
- BS *
I -2.0
LOG(B)
I -1.0
EXPT
I 0.0
Figure 1. C vs. E plot. Points shown are experimental points. Curve shown is the best simulation (BS). Simulation parameters are Z‘ = Y, N = 3.3, and t = t’ = 7.
-1
N 0.3
0-1.0
2.8
0
3.8 6.3 3.3
-I
-2.0j /// I
-2.0
LOG(B)
I -10
I 00
Figure 2. Effect of varying N. Curves are simulated similar to the BS but with different N. Simulation parameters are z’ = Y , c = e’ = 7, and N equal to 0.3, 2.8, 3.8, 6.3, and 3.3 for curves a, b, c, d, and BS.
plot of jojoba oil at different temperatures. Both C and B are shown in logarithmic scale. Points shown are experimentally observed points. The curve marked BS is the best fit obtained by simulation. The curve overlaps with most number of points. The simulation suggests an anisotropic rotation of N = 3.3 with an axis equal to Y. Upper axis shows T~ (s) in log scale. In the region of faster motion, T~ I s and t = e’ = 7 give the best fit. In order to demonstrate that Figure 1 is a unique fit, we also simulate the curves with different N values and different e’s. Figure 2 shows simulation with z’ = Y , e = e’ = 7. N is shown to vary from 0.3 to 6.30. As shown in the figure, curves generated with different N values are parallel to each other. Higher N values have an upward shift. The uniqueness of N is partly dependent on the uncertainty of the experimental points. On the basis of (23) Hwang, J. S.;AI-Rashid, W. A,; to be published.
2558
The Journal of Physical Chemistry, Vol. 89, No. 12, 1985
Li and Hwang
O’Ol
O.O
1
*.Ol -210
-2:o
0.0
LOG(B)-l:O
Figure 3. Effect of varying e’s. Simulations similar to the BS Except with e’s varying, Le., z’= Y,N = 3.3, c = c’ = 1, 5 , 9, 12, BS for curves a, b, c, d, and BS.
N
h
0
3.3 0.8 3.3 8.3 33
v
0-
s
&ge
a 3.3 1 b 3.3 12 c 0.3 7 d 3.3 7 e 8.3 7 0 s 3.3 7
,
,
LOG(B)
- 110
0.0
Figure 5. Simulation with z’ = Z. BS is shown for comparison: curve a, N = 3.3 and c = c’ = 1; curve b, N = 3.3 and c = t’ = 12; curve c, N = 0.3 and c = t’ = 7; curve d, N = 3.3 and c = e’ = 7; curve e, N = 8.3 and t = c’ = 7; and curve BS, z’ = Y .
E:E‘ 1 7
7 7 7
I
0 .o
Rs
Figure 4. Simulations with z’ = X. BS is shown for comparison. Simulation parameters are as follows: curve a, N = 3.3, and c = t’ = 1; curve b, N = 0.8 and c = e’ = 7; curve c, N = 3.3 and c = c’ = 7; curve d, N = 8.3 and c = c’ = 7; and curve BS, z’ = Y.
the precision of our experiment, Nvalues of 2.8,3.3(BS),and 3.8 are clearly seen separating from each other. N thus determined has a precision better than f 0.5. Figure 3 shows the effect of changing e’s. Simulations are obtained with z’ = Y and N = 3.3. e’s from 1 to 12 were attempted. As expected from eq 2, e’s do not affect the slower portion of the motion narrowing region. e’s are observed to have effect only for T~ 5 lo-” s. As shown in Figure 3, e’s shift the lower portion of the curve at a definite direction. Large e’s shift the curve upward. The curves of e’s equal to 9 and 12 are seen to separate from each other whereas those of e equal to 5, 7, and 9 do not. Actually in the curves for e equal to 6 and 7 we cannot even tell which is which. Thus the simulation is not very sensitive to changes in e’s and the determination is probably good to f l . Next we look at axes z‘ = X and z‘ = 2. Figure 4 shows simulation with z’ = X . The top curve marked BS is the best simulation, i.e., with z’ = Y , N = 3.3 and e = e’ = 7. The rest of the curves are simulated with 9 = X . Simulations with N varied from 0.8 to 8.3 and E’S varied from 1 to 7 were attempted. It is observed that the effect of N is opposite to z’ = Y. Here larger N shift curves downward. All these curves are well below BS. Figure 4 also shows that the simulation is able to determine the axis of rotation unambiguously. e’s are observed to have similar effects as with i = Y, shifting the faster portion of the curve down. Figure 5 shows simulations with z’ = 2. The simulation is very insensitive to changes in N . The curve that lies below BS is actually a mixture of three curves with N equal to 0.3, 3.3, and 8.3. Changes in N are not able to bring the curves to approach BS. e’s are observed to have similar effects as in other axis. Small value of t brings the faster portion of the curve down. The best simulation as shown in Figure 6 suggests z’ = Y , N = 3.3, and t = t‘ = 7. Finally, we would like to look at the anisotropic interaction parameter K. For spherical top or linear molecules, correlation time T~ is related to K as TR
= [47Vo3q/(3kT)]K
1 Figure 6. Molecular axis of PD-Tempone and its proposed orientation within the jojoba oil. The two zig-zag’s above and below the probe are two jojoba molecules. The oil is composed of mainly long, straight-chain molpules of over 22 carbon atoms. Figure show only six carbon atoms. The molecules are many times larger than the probe.
in K, q the coefficient of shear viscosity of the solvent, and r, the effective radius of the solute. PD-Tempone is nearly a prolate with the long axis a, = 0.42 nm and the short axis a, = 0.285 nm.24 Substituting these parameters into the Stokes-Einstein model
Ri = kT/(8aqa,3ui), i =
(1 or I
where 0 1 1
6,
= (2/3)X2(1 - X2)(1 - ( 1 - X2)X-l In [(l = (2/3)X2(2 - Xz){(l
+ X2)X-’
In [(l
+ X)/(l
+ X)/(1
- X2)1/2]]-1
- X2)1/2] - l)-I
with X = (all2-
and 0
