1170
J. Phys. Chem. 1981, 85,1170-1172
determined previously by Long et a1.l1 The order tensor elements have been computed by setting r23 to a value of 2.4785 the microwave value for fluorobenzene and 2.481 for the remaining halobenzenes. Our recent determination of the signs of the order parameters of the laurate amphiphile by carbon-13 shielding anisotropy measurements indicates that the long axis of the surfactant is perpendicular to the applied field direction (see ref 25). These results are not consistent with a cylindrical superstructure for the potassium laurate type I1 nematic phase oriented perpendicular to the applied field. The order tensor elements for the halobenzenes show that the CZvsymmetry axis is also on the average perpendicular to the applied field and coincident with the long (25)R.C.Long, Jr., and J. H. Goldstein, “Liquid Crystals and Ordered Fluids”, Vol. 3,J. F. Johnson and R. S. Porter, Ed., Plenum Press, New York, 1978.
axis of the surfactant. The results in Table IX indicate that SzrDincreases progressively on going from H < F < C1< Br < I. This phenomenon has previously been observed by Tracey12for the halobenzenes oriented in the decyl sulfate and decylammonium meosphases and by Spearman and Goldstein in p-halofluorobenzenes in the potassium laurate mesophase? In the case of the laurate data the order of the z axis increases with the length of the molecule. It is possible that the interaction between the surfadant alkyl chains is one of anisotropic dispersion forces which appear dominant for thermotropic solvents. A reasonable picture is one in which the aromatic ring and substitutent interact with the packed alkyl chains of the amphiphile. The order parameters indicate that the Czu axis tends to be parallel to the interface normal, parallel to the long axis of the surfactant. Due to the hydrophobic nature of the halobenzenes intercalation into the hydrocarbon region near the interface is most reasonable.
The Influence of Anisotropic Motion on the Barrier to Methyl Rotation in p-Toluenes Joseph B. Lambert,* Ronald J. Nlenhuis, and Rodney B. Flnzel Department of Chemistry, Northwestern Universlty, Evanston, Illlnois 6020 1 (Recelved November 3, 1980)
The barrier to rotation about the methyl-ring bond in toluene and its para-substituted derivatives has been examined by the Woessner approach. Whereas the isotropic model (Dl = DZ)gives a barrier of about 0.51 kcal/mol for unsubstituted toluene, the anisotropic model, for which the optimized u (= D1/D2)is 2.2, gives a barrier of 0.0 kcal/mol, in essential agreement with the microwave result. The para-substitutedtoluenes do not possess enough independent C-H vectors to define both D1 and D2. From assumed values of u, it is apparent that these barriers also become smaller as u increases. Thus a barrier calculated from the isotropic Woessner model (u = 1.0) may be an upper limit.
Introduction In 1962, Woessnerl introduced a method for the determination of methyl rotational barriers from the dipoledipole spin-lattice relaxation time T1(DD). The intramolecular motion of the methyl group is superimposed upon the overall diffusion of the molecule, so that both motions contribute to the dipolar process that normally dominates 13Crelaxation. If rotation of the methyl group occurs by a series of 120’ jumps, eq 1 provides the rela-
Because of the difficulty in obtaining a separate measurement of two diffusion rates (Dl and D2),most authors have chosen to assume that the overall motion of the molecule is isotropic (Dl = D2 = D). Under this condition, eq 1reduces to eq 2 (n = 3 for CHs). When there is no r
internal rotation, as for a rigid CH group, the term Di goes to zero, and eq 2 becomes eq 3 ( A B C = 1.0) (n = 1
+ +
tionship between the dipolar relaxation and the various diffusion constants ( n is the number of protons attached to the relaxing carbon, h is Planck’s constant over 27, the y’s are gyromagnetic ratios, Di is the methyl jump rate, D1 is the molecular diffusion rate along the principal axis of the imagined ellipsoid that represents the molecule, D2 is the diffusion rate perpendicular to the axis, and A (= 1/4(3 cos2 A - 1)2), B (= 3 sin2 A cos2 A), and C (= 3/4 sin4 A) are geometrical constants depending on the angle A between the C-H bond and the major axis). (1)D. E. Woessner, J. Chem. Phys., 37,647 (1962). 0022-3654/81/2085-1170$01.25/0
for CH). The usual procedure for determining the methyl jump rate is to use the dipolar relaxation of a rigid CH group (or the average for all such CH groups) to determine the isotropic diffusion rate D from the measured T1(DD) in eq 3 ( n = l ) , and then calculate Di from eq 2 (n = 3).2 The barrier to methyl rotation (Vo)can be obtained from an Arrhenius expression such as eq 4, in which Diois the (2)K. F.KuhLnann and D. M. Grant, J. Chem. Phys., 55,2998(1971); J. R.Lyerla, Jr., and D. M. Grant, J. Phys. Chem., 76,3213 (1972);T. D.Alger, D. M. Grant, and R. K . Jarris, ibid., 76,281(1972);S . W.Collins, T. D. Alger, D. M. Grant, K. F. Kuhlmann, and J. C. Smith, ibid., 79,2031 (1975);J. W. ApSimon, H. Beierbeck, and J. K. Saunders, Can. J. Chem., 53,338(1975);D.E.Axelson and C. E. Holloway, ibid., 54,2820 (1976); J. W. Blunt and J. B. Stothers, J. Magn. Reson., 27,515 (1977).
0 1981 American Chemical Soclety
Methyl Rotation in p-Toluenes
The Journal of Physical Chemistry, Vol. 85, No. 9, 198 1 1171
Di = Dioe-V0/RT
(4)
rate of a freely rotating methyl group. In the absence of relaxation data a t multiple temperatures, Dio can be equated to (KT/1)1/2 = 0.89 X 1013s-l (Iis the moment of inertia of the methyl group) a t 40 'C. To date, few studies have reported an anisotropic analysis of methyl rotation in any detaiL3p4 Platzer calculated the barriers from the isotropic equation for 24 methyl groups in 12 substituted ben~ofurans.~ In addition, she attempted to calculate barriers from the anisotropic equation for five of these methyl groups. Actual barrier heights were obtained in the anisotropic analysis for 2methylbenzofuran and the 2 methyl group of 2,5-dimethylbenzofuran. The isotropic barriers for these two cases were, respectively, 0.2 and 0.5 kcal/mol higher than the anisotropic barriers (1.96 and 1.75 kcal/mol for 2methylbenzofuran; 2.11 and 1.60 for 2,5-dimeth~lfuran).~ Because of the widespread use of the isotropic approximation, we felt that it is important to analyze further systems by an anisotropic model. Using Platzer's approach, we have examined the barriers to methyl rotation in para-substituted toluenes. These molecules contain methyl groups whose CH3-C bond lies on the symmetry axis of the molecule, thereby simplifying some of the mathematics not alluded to above. Each of the three molecular axes is quite distinct, so that anisotropy of motion might be expected.
Results The anisotropic analysis of methyl rotational motion requires the evaluation of three diffusion constants (Dl, D2,and Di in eq 1)instead of two (D and Di in eq 2):s We used the method of Platzel.3 for the evaluation of these rate constants in the toluenes 1-3. For the ring carbons (Di y3
l,X=Cl 2, X = H 3, X = NH,
= 0 ) ,rearrangement of eq 1yields the expression given in eq 5. Thus T1-l(DD) is proportional to the quantity in
n
1
the brackets, which depends only on the anisotropy ratio, u = D1/D2. This ratio can be adjusted to give the best agreement between the observed relaxation times of all the (3) N. Platzer, Org. Magn. Reson., 11, 350 (1978). (4) H. Beierbeck, R. Martino, and J. K. Saunders, Can. J. Chem., 58, 102 (1980). (5) A complete anisotropic analysis would necessitate the evaluation of four diffusion constants (Dl, Dz,Di,and DJ,since the two axes perpendicular to the major axis are not identical. Because toluene does not supply enough variables for a complete anisotropic analysis, we must use the symmetrical top approximation. (6) We have neglected cross correlation between the methyl carbons and protons. So long as internal diffusion is no more than about 20 times the overall diffusion (Di/D < 20), this approximation is g ~ o d Our . ~ ~ ~ measurements show that toluene is well within this limit. (7) K. H. Ladner, D. K. Dalling, and D. M. Grant, J.Pbys. Chem., 80, 1783 (1976). (8) D. E. Woessner and B. S. Snowden, Jr., Adu. Mol. Relaxation Processes, 3, 181 (1972).
TABLE I: Methyl Rotational Barrier as a Function of Motional Anisotropy for p-Aminotoluene ( 3)a
v,,
10-'0D,, o
S -I
1.0 1.3 1.7 2.1
2.11 1.87 1.68 1.52
TIf, 5 5.90 5.23 4.70 4.27
10-'2Di, s -' kcal/mol 1.85 0.96 2.91 0.68 6.64 0.18 large free
T,(CH,)= 8.5, T,(DD)(CH,) = 13.1, T,"(CH) = 4.4, TI"(DD)( CH) = 5.75 s. TABLE 11: Methyl Rotational Barriers as a Function of Motional Anisotropy for Toluene (2)= 1O-10Dz, 0
1.0 2.0 2.2 3.6
S-I
8.77 5.75 5.38 4.27
lo-lzq,
v,,
TIf, s
s- l
kcal /mol
24.5 16.1 15.0 11.9
2.95 8.02 11.95 large
0.66 0.06 0.0 free
a T,(CH,) = 14.1, T,(DD)(CH,) = 39.7, T,"(CH) = 16.2, TILY(DD)(CH) = 21.3 s. See footnote 10 and the Experimental Section.
TABLE 111: Methyl Rotational Barrier as a Function of Motional Anisotropy for p-Chlorotoluene ( l)a
10-loD,, lO-'zDi, vo, s TIf, 5 S kcal/mol 4.27 11.94 1.25 1.0 1.20 1.7 3.40 9.50 1.76 0.99 2.5 2.82 7.89 2.91 0.69 3.4 2.4 2 6.75 6.83 0.16 3.8 2.11 5.90 large free a T,(CH,) = 10.9, T,(DD)(CH,) = 18.3, T,"(CH) = 10.2, T,"(DD)(CH) = 11.65 s. 0
rigid carbons and the bracketed quantity? The constants A , B , and C are defined in our series (A = 109.5'). From Dl/D2 calculated in this fashion and from the measured values of Tl(DD) (ortho, 21.7 s; meta, 20.9 s; para, 14.8 s),l0 eq 5 gives an independent measure of D2 (outside the brackets) and hence of D1. We found that this procedure gives a well-defined Q = 2.2 for unsubstituted toluene, which contains three distinct C-H vectors. For the para-substituted toluenes and for 1-substituted propenes (CH,CH=CHX)," however, the availability of only two symmetry related C-H vectors fails to define a unique value of u. When both D1 and D2 are known, it is more convenient to use the ratio of the relaxation time of a rigid carbon to that of methyl for determining Di, as in eq 6. In isotropic systems (Dl = D2),the average dipolar relaxation time for all rigid carbons (Tla(DD))is used for TICH(DD)in eq 6. TICH(DD)= TlCH8(DD)
+ +A
B + 5 + (D1/D2) + (3Di/2D2) C (6) 2 + ( ~ D I / D J+ (3Di/2D2) For use of eq 6 in the anisotropic analysis, the rigid carbon must have its CH vector lined up with the principal axis of the ellipsoid, and hence in these toluenes with the CH3-C bond. No such rigid carbon exists here. For cases
]
(9) We have written a Fortran program ANISOP to carry out this calculation. Copies are available from the authors. (10) These values come from the measured values of T1(16.4,15.9, and 12.2 S) a d = NOE - 1 (1.5, 1.5, 1.64). (11) The isotropic barriers were calculated as part of an earlier study; see J. B. Lambert and R. J. Nienhuis, J. Am. Chem. Soc., 102, 6669 (1980).
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The Journal of Physical Chernistty, Vol. 85, No. 9, 1981
of this sort, Platzer invented a fictitious carbon, whose relaxation time T:(DD) would be obtained by multiplying the average Tla(DD) for all the rigid methinyl carbons by the ratio D 2 / D (the average D comes from eq 3 and D2 from eq 5). The methyl rotational jump rates thus can be evaluated most easily from eq 6. The quantity TICHs(DD)is measured; D1 and D2 come from optimization of the proportionality in eq 5; TICH(DD)= T,f(DD) comes from the average Tl"(DD) multiplied by D2/D. This procedure works only for toluene (2) itself. From u = 2.2 and eq 6, the barrier to methyl rotation in toluene was found to be essentially 0.0 kcal/mol. For the para-substituted toluenes (1,3), we calculated the barriers Vofor a series of assumed values of u. In this fashion considerable insight can be gained concerning the dependence of the barrier on the anisotropy of motion. These values, along with an analogous set for toluene, are given in Tables I-III.ll The tables also contain the original Tldata and the intermediate figures (D2,Tlf,D J .
Discussion Although comparisons between Woessner barriers and those measured by other methods have generally been quite good,12 toluene has been a conspicuous exception. The earliest barrier determination for toluene was by Woessner and Snowden, who used quadrupolar rather than dipolar relaxation in perdeuterated toluene, a procedure essentially equivalent to ours.* They obtained a barrier of 0.93 kcal/mol for methyl rotation. Using the dipolar relaxation and an isotropic model, we obtained a barrier of 0.51 kcal/mol.l' Both of these results are appreciably larger than the microwave barrier of 0.014 kcal/mol.13 The barrier for CF3-C rotation in perfluorotoluene was found to be 1.41 kcal/mol.14 These authors14 suggested that intermolecular effects may serve to raise the Woessner barrier in toluene. Our results demonstrate that the NMR and the microwave barriers are essentially identical when the anisotropic Woessner model is used. Toluene possesses a sufficient number of C-H vectors to define both D1and Dz. Using the Platzer procedure, we found that the optimal ratio of the diffusion rates (a = D 1 / D z )is about 2.2 and that the corresponding barrier is essentially 0.0 kcal/mol. Although we cannot exclude the presence of intermolecular effects, it appears that use of the anisotropic model is sufficient to bring the Woessner and the microwave barriers into close agreement. Hence it is not necessary to invoke intermolecular effects to explain the previous discrepancy. Table I1 shows that the barrier height for toluene decreases as the anisotropy factor increases. In this case we know the optimal value of the u. The para-substituted toluenes do not possess enough independent C-H vectors to define u, but from a series of assumed values of u we can still observe the relationship between the anisotropy factor and the barrier height. From Tables I and 111it can be seen that the pattern is-similarto that for toluene. The barrier falls off rapidly as the diffusion rates diverge. At sufficiently large (I,in each case the free rotor extreme is reached. It is interesting that this point differs for the various molecules. Thus p-chlorotoluene would be a free (12) For a review, see J. B. Lambert, R. J. Nienhuis, and J. W. Keepers, Angew. Chen., in press. (13) H. D. Rudolph, A. Jaeschke, and P. Wendirg, Ber. Bunsenges. Phys. Chem., 70, 1162 (1966); H. D. Rudolph, H. Dreizler, A. Jaeschke, and P. Wendling, 2.Naturforsch. A , 22, 940 (1967). (14) J. Kowalewski and A. Ericsson, J.Phys. Chern., 83, 2044 (1979).
Lambert et al.
rotor if u were about 3.8, but p-aminotoluene would be a free rotor at about 2.1. I t is unfortunate that Q could not be independently defined for these systems. For two substituted benzofurans, Platzer also found that the anisotropically calculated barrier was smaller than the barrier from the isotropic model (see a b ~ v e ) For . ~ three other substituted benzofurans, the anisotropic calculation indicated a free rotor, whereas the isotropic calculation gave a barrier in the vicinity of 1kcal/mol. Although few cases have been examined to date, from our results and those of Platzer it seems that the isotropic Woessner calculation provides an upper limit to the barrier. A full anisotropic calculation appears to be necessary in order to obtain the most reliable result. Experimental Section All the toluenes were commercially available. The 13C spectra were recorded at 20 MHz on a Varian CFT-20 spectrometer,16equipped with a Sykes 120 Compu/Corder. The spin-lattice relaxation times were measured by the inversion recovery pulse sequence, 18Oo-7-9O0, and were calculated from program RNTlCAL, a locally written least-squares exponential fit to both T1and Mo.Each T point was the result of 20 or more accumulated pulse sequences, with a pulse delay of at least 5T1. Each Tlwas the average of four or more separate experimental measurements (3% average deviation). The dipolar relaxation T1(DD) was calculated in the standard fashion from the observed Tl and the nuclear Overhauser enhancement factors (71 = NOE - l)(Tl(DD) = 1.988T1/71). The NOE factors were measured by the NOE-suppress gated decoupling technique. At least eight measurements of 9 were obtained in each case (3% average deviation). To improve accuracy for the NOE factors, a spectral width of only lo00 Hz was used. Temperature measurements showed that no significant probe heating occurred during the NOE experiment. All measurements were carried out at ambient temperatures, 27 f 0.5 OC. The intensities were measured as peak heights. All samples were prepared as 80% v/v solutions in C6D6, which provided an internal deuterium lock. At least five freeze-thaw cycles were carried out with a Sargent-Welch Model 1302 oil diffusion vacuum pump (typically mmHg). Samples were sealed while under vacuum to exclude subsequent oxygen diffusion into the sample. Anisotropic Analysis. Program ANIS02 was written in Fortran to compute D1/D2,D2, and Sumdif (the sum of the differences between the observed and calculated values of Tl(DD) according to eq 5) from dipolar relaxation times for rigid CH carbons. Knowledge of these quantities permits calculation of Di from eq 6. Although the program was written for the general case in which the CH,-C bond subtends any angle with the principal axis of the molecule, these axes are collinear for the toluenes. Input consists of the observed values of T1(DD) for all rigid carbons, the angle A between the C-H bonds and the principal axes, and the range of values of D1/Dzand D2 to be considered. Only the quantity within the brackets of eq 5 is optimized to give D1/D2. In the use of eq 6, the average TICH(DD) included only ortho and meta carbons, so that the calculations would be analogous down the series. Acknowledgment. This work was supported by the National Science Foundation (Grant No. CHE79-05542). (15) This instrument was purchased by a departmental grant from the National Science Foundation.
