Tritium and proton nuclear magnetic resonance study of the isotope effects on the molecular structure and the degree of order of partially oriented [3H1] benzene

JOURNAL

OF MAGNETIC

37,285291

RESONANCE

(1980)

Tritium and Proton Nuclear Magnetic Resonance Study of the Isotope Effects on the Molecular Structure and the Degree of Order of Partially Oriented [3H1]Benzene T. C. WONG Department

of Chemistry,

Tufts

University,

Medford,

Massachusetts

02155

AND LAWRENCE J. ALTMAN Department

of Chemistry,

SUNY

at Stony

Brook,

Stony

Brook,

New

York

11794

Received March 23, 1979 Tritium and proton nuclear magnetic resonance spectra of [3Hl]benzene partially oriented in a liquid crystal were studied. Isotope effects on the difference in the CH and C3H bond lengths and on the degree of order were deduced. The direction of the isotope effect on the ordering is consistent with the theory which attributes ordering to molecular shape and polarizabilities.

INTRODUCTION

NMR spectra of partially oriented molecules in liquid crystal solvents provide information on the molecular structure and ordering of the molecules (I). A recent study of benzene and several deuterated benzenes (2) has demonstrated the isotope effects on the degree of ordering and has shown that the direction of the isotope effect can test the models which describe the ordering process. In the present investigation we have analyzed the ‘H and 3H spectra of a mixture of benzene and [3H1]benzene from which the isotope effects on both the molecular structure and the degree of ordering were examined. This study is the first tritium NMR study of molecules partially oriented in liquid crystal. Tritium is a spin-$ nucleus and has the highest magnetogyric ratio of all known nuclei. Therefore tritium NMR enjoys the advantage of the highest sensitivity (3) (about 1.2 times higher than proton at the same magnetic field). EXPERIMENTAL

AND SPECTRAL

ANALYSIS

The tritiated benzene sample was obtained from New England Nuclear as a 4 : 1 mixture of benzene and [3H1]benzene. It was synthesized by catalytic exchange of benzene with tritiated water. In addition a small amount of ditritiated benzene was present. A simple 3H{‘H} spectrum of the sample in nematic crystals showed one dominating peak due to [3H1]benzene and two doublets with the ratio of the 285

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286

WONG

AND

ALTMAN

splittings equal to the expected ratio of the dipolar couplings due to the tritium nuclei in the ortho- and meta-ditritiated benzenes. A third doublet due to the paraditritiated benzene was not resolved but appeared as shoulders of the main peak. From the intensity measurement, the amount of each of the ditritiated species was approximately 4 to 5% of [3H1]benzene. This distribution is consistent with a completely random catalytic substitution mechanism. No spectral lines due to the ditritiated benzene were observed in spectra without ‘H decoupling. The liquid crystal sample was made up of about 14 mol% mixture of benzene and [3H1]benzene in Merck Nematic Phase IV sealed in a 5-mm tube. The spectra were recorded on a Bruker WP-200 spectrometer equipped with a 48K Aspect 2000 computer, and quadrature detection. Spectrometer frequencies were 200.13 and 213.47 MHz, respectively, for ‘H and 3H. All spectra were recorded with 16 or 32 K data points. The pulsewidth was 8 ysec (approximately 65” nutation angle), and the observed linewidths were 3 to 5 Hz. A ‘H spectrum was taken at 303 K with 36 scans and no line broadening. Resonances due both to benzene and to [3H1]benzene were observed and analyzed from this spectrum. Two 3H spectra were taken at a temperature about 0.5 K lower than that for the ‘H spectrum. They were recorded with 100 and 1000 scans, and line broadening of 0.3 and 1.0 Hz, respectively. The spectrum with 100 scans is shown in Fig. 1. All spectra were analyzed with the computer program LEQUOR (4). The rms in all cases, fitting to between 60 and 95 lines, was below 0.5 Hz, which agrees with the

FIG. 1. 3H NMR spectrum of [3H1]benzene partially oriented in Merck spectrum was accumulated with 100 scans and a line-broadening of 0.3 Hz.

Nematic

Phase

IV.

The

TRITIUM

ISOTOPE

EFFECT

ON BENZENE

ORDER

287

uncertainty in determining the line positions. The indirect spin-spin couplings, .Tii, were optimized in the case of benzene. The optimized values of JIHlw were used in the analysis of the [3HI]benzene spectra. Values of J,,,, were calculated by the relation JlH3"

[II

= (Y3HIY1H)J1H1H,

where the ratio of ~3~ and ylH is 1.6663975 (5). The dipolar couplings Djj, and Jjj are listed in Table 1. The effect of harmonic vibration was corrected as described previously (6). The harmonic vibrational force fields of Scherer (7) were used. A normal coordinate program MSAV (8) was used to calculate the parallel and perpendicular amplitudes of vibration. The correction for the effect of harmonic vibration was represented in the form

Da =fDexp,

El

where Da are dipolar couplings corresponding to the r, structure (9), and f is the correction factor relating the experimental dipolar couplings, Dexp, to D,. The values of f are given in Table 2. The values for the proton-proton pairs are equal, within their uncertainties, to those calculated for deuterated benzenes in Ref. (2).

TABLE

1

SPECXRALPARAMETERSFORBENZENEAND[~HJBENZENE~

012 013

014

Benzene

I

II

III

-398.64 f 0.03 -76.47 *0.04 -49.60 i 0.04

-429.1O~tO.13 -81.12*0.14 -52.2OkO.16 -391.81 kO.09 -75.58rt0.12 -49.97 * 0.07 -77.46kO.12 -401.22*0.08 -77.53*0.17

-432.95*0.10 -81.79iO.13 -52.49kO.14 -394.91 io.13 -76.10*0.18 -50.18iO.20 -77.76 + 0.20 -404.48 + 0.18 -78.13*0.25

-432.43*0.11 -81.9OkO.14 -52.46i0.16 -394.85*0.14 -76.24kO.20 -50.24 * 0.24 -77.88 f. 0.24 -404.59 k 0.16 -78.28 zt 0.28

96

64

61

65

0.46

0.40

0.44

0.49

023 024 025

026 034 D35 J1zC

J13 J 14

Lines assigned rms error (Hz)

7.47 f 0.05 1.41 kO.06 0.66*0.06

n Tritium in [3Hr]benzene is labeled as nucleus 1, Dii in hertz. b I was obtained from a ‘H spectrum of [‘Hilbenzene; II and III from 3H spectra with loo-scan, 0.3-Hz line broadening and lOOO-scan, l.O-Hz broadening, respectively. ’ The hi for [3HJbenzene are taken from the result for benzene. The JiHaH are modified by the difference in Y.

WONG

288

AND TABLE

ALTMAN 2

CORRECTION FACTOR f FOR HARMONIC VIBRATION FOR EXPERIMENTAL DIPOLAR COUPLINGS,& IN [3HI]B~~~~~~

f

ij

12 13 14 23 24 25 26 34 35

RESULTS

1.0120 1.0055 1.0030 1.0144 1.0074 1.0045 1.0073 1.0143 1.0073

AND

DISCUSSION

The isotope effect of the tritium substitution is more evident on the degree of order than on the molecular structure. If we define the molecular plane as the X2 plane, and the tritium nucleus is on the 2 axis, it is clear that two different order parameters, S,., and S,,, are necessary to describe the orientation of [3H1]benzene. However, the comparison of the order parameters of benzene and [‘Hilbenzene is complicated by the fact that the dipolar couplings obtained for benzene do not follow the relations expected for a regular hexagon. This was observed for several previous investigations (10, 11 ), as well as in the present study. The origin of this discrepancy is not clear, but vibrational corrections do not remove the discrepancy. Because of this complication, the best way to decipher the isotope effect on ordering, as was suggested in Ref. (2), is to compare directly the ratios of dipolar couplings in benzene and [3Hl]benzene. A direct comparison can be made by calculating the ratios of D23, D35, and Dz6 between the two species. These couplings correspond to pairs with the internuclear distance vectors parallel to either the X or the 2 axis. Assuming negligible distortion of the proton coordinates due to tritium substitution, which was shown to be true, these ratios will give the ratios for the order parameters S,, and S,, of benzene and [3H1]benzene. From these ratios, it can be deduced that S,,/S,, in [3H1]benzene, averaged over three measurements, is equal to 1.0298 f 0.0005; i.e., the effect of the tritium substitution along the 2 axis results in reducing the order parameter of the 2 axis by approximately 3% with respect to the X axis. The isotope effect on the ordering matrix is greater than that in [*HJ benzene, but less than that in 1,4[*H2]benzene, which give S,,/S,, values of 1.0201 and 1.0389, respectively (2). A more detailed comparison of the ratio of dipolar couplings in benzene and [3H1]benzene in the same manner as that in Ref. (2), is given in Table 3. Again, only the ratios of 026 and 023 and of D35 and 023 are significantly different from unity, indicating that the major isotope effect is in the difference of S,, and S,,. The result of these ratios gives the same value of S,,/S,, for [3H1]benzene. From the proton spectrum which contains both the spectra due to benzene and [3Hi]benzene, we

TRITIUM

ISOTOPE

EFFECT

ON BENZENE

ORDER

289

TABLE 3 RATIO OF D,, RESULTING RATIO OF S VALUES, AND THE DIFFERENCE IN C3H AND CH BOND LENGTHS DETERMINED FROM THE MIXTURE OF BENZENEAND[~HJBENZENE“" Nuclear pairs AB

CD

P

12 13 14 36 26 25 26 35

45 46 23 12 35 34 23 23

1.0004*0.0005 1.0048 i 0.0030 1.0008*0.0005 0.9981~0.0005 0.9963 k-o.0027 0.9985 f 0.0006 1.0279i 0.0006’ 1.0316*0.0007’

a 3H’H couplings are converted from the equivalent ‘H’H couplings by multiplication with (y3,/y1J= 1.06663975. [The ratio P is defined as P = (DAB/ DcD) in [3Hl]benzene/(DAn/DCo) in benzene]. The values are averaged over three spectra described in text. b SJS,, = 1.0298 * 0.0005; r&, - rCH (from 0,) = 0.001*0.003 A; r& - rCH (from D,,,) = 0.008 k 0.002 A. ’ Values used to evaluate S,,/S,, as described in text. The difference in their values is due to a small but discernible isotopic effect in the coordinates of protons 2,6 and 3,s.

observed that the sum of S,, and S,, for both species agrees to within 0.2%. This means that S,, for these two species remains unchanged, as was the case for the deuterated benzenes (2). The various isotopic species of benzene provide unique tests for theories of the ordering of solute molecules in liquid crystals. Anderson’s model (12) attributes the asymmetry of the ordering matrix, qs = (S,, - S,.,)/S,, to the asymmetry of the inertial tensor, TjT = (T,, - TX,)/ Tyy, where Tii is the principal moment of inertia with respect to the ith axis. An approximate linear relationship between 7, and nT with a positive slope was obtained by fitting to a series of substituted benzenes. This model would then predict that S,., < S,,, because the 2 axis is the axis with the smallest principal moment of inertia. This is opposite to what was deduced experimentally in the present study, in which it was determined that S,, > S,, and v5 - - 0.25 VT. The other theory on ordering processes, which is more generally accepted, is based on the dispersion forces (13). Gilson et al. (14) used a simplified treatment and related the asymmetry of the ordering matrix to the anisotropies of the molecular dimensions (L), (L, -L,)/(L, -LY). Since the tritium substitution gives a shorter C3H bond, reducing the molecular dimension in the 2 axis, this theory gives the right direction of the isotope effects on ordering. Therefore, the results of both this study

290

WONG

AND

ALTMAN

and the study of deuterated benzenes (2) suggest that the dispersion forces largely govern the ordering of solutes in liquid crystals. The shortening of the C3H bond compared with the CH bond was determined by fitting the dipolar couplings with the computer program SHAPE (4). Assuming there is a negligible isotope effect on the coordinates of the protons, the origin of the axis was located symmetrically with respect to the coordinates 2,3,5, and 6. Therefore, the difference in the magnitude of the 2 coordinates of the tritium and proton 4 represents the difference between the CH and C3H bond lengths. From the average of three measurements, it was found that the r, distance of the C3H bond is shorter than the CH bond by 0.001 f 0.003 A. The difference in r, distances observed for various isotopic species can be estimated by the use of the calculated parallel and perpendicular amplitudes of vibration and the Morse anharmonicity parameters (15), which was assumed to be 2.0 A-’ (16). The calculated r, difference between the CH and C3H bonds in benzene is -0.0008 A, and 0.0002 8, between the CH and C*H bonds (17). While the experimental difference for the C3H and CH bond lengths obtained from this study is small compared with experimental uncertainties, the magnitude is in good agreement with the calculations based on the vibrational force field. The structure obtained from the dipolar couplings without correction for harmonic vibrations gives a much larger difference in the bond lengths of the CH and C3H bonds, as expected. The average difference of rc3H - rcn is 0.008 f 0.002 A, which is smaller than the value of -0.016 A calculated from the formalism developed by Diehl and Niederberger based on the parallel and perpendicular amplitudes of vibration (6~). No definite structural effect beyond the primary isotope effect of the tritium substitution was observed, although 026 was consistently smaller than D35 from the analysis of all three spectra. This difference implies that r26 may be slightly longer than r3s. The average ratio of D&D35 is 0.9963*0.0027, corresponding to a difference between r3s and r26 of about 0.016 f 0.012 A. While this is of interest for observing the isotope effect due to the nonbonded interaction of the tritium atom, the difference is too marginal to make any definite conclusions at this time.

ACKNOWLEDGMENTS Acknowledgment American Chemical

is made to the Donors of the Petroleum Research Fund, administered by the Society, and to New England Nuclear for partial financial support for this research.

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