NOTES
3688 the effect of two cationic surfactants, octadecyltrimethylammonium bromide and eicosanyltrimethylammonium bromide. The ordinates have been normalized with respect to the rate constant with no surfactant present. I n both cases studied, the rate constant appeared to be unaffected below the critical micelle concentration, suggesting that substrate-induced micelles are not formed in these cases. The probable existence of substrate-induced micelles has been noted by Behme, Fullington, Noel, and Cordes in the hydrolysis of ortho esters in the presence of micelle^.^ The drop in reaction rate at high concentrations of cationic surfactant is probably due to saturation of the benzaldehyde with surfactant; i.e., all of the reactant is solubilized and its intramicellar concentration begins to decrease. Acknowledgment. The authors acknowledge the financial assistance of the Graduate Research Fund of the University of Washington.
Nuclear Magnetic Resonance Dynamic Determination of Boron-Fluorine Internuclear Distances in Alkali Metal Fluoroborates
by H. J. C . Yeh and J. L. Ragle’ Department of Chemistry, University of ivassachusetts, Amherst, Massachusetts 01003 (Received June 3, 1968)
As a result of a detailed investigation2 of lgF spinlattice relaxation in NaBF4, KBF,, RbBF4, and CsBF4, we have obtained estimates of the B-F internuclear separations. Since very few data are available in the literature on the structures of these salts, we believe the results to be of sufficient interest to report below (our results are shown in Table I). Although the method is not new, it is also somewhat novel and is described qualitatively.
Table I : Estimated B-F Bond Lengths
Compd
NaBF4
KBFa RbBF4 CsBF4
tnuu (min), msec
Frequency, MHZ
6.45 6.60 7.10 7.80
23.15 23.90 23.36 24.28
R (B-I?) (i.0.015),“’b
A
1.412 1.410 1.432 1.445
Cala Mean values, assuming a rigid regular tetrahedron. culations assumed the following values for nuclear gyromagnetic ratios: YF = 2.51673 X lo4 sec-’ G-l, r ~ ( 1 ’ B )= 8.58283 x 10s sec-1 (3-1, y~(’0B) = 2.87456 X 10s sec-1 G-1. The Journal of Physical Chemistry
I n tetrafluoroborate salts, the anion undergoes rotational diffusion. This random motion modulates the dipolar interactions between the various magnetic nuclei present and leads to a particularly effective means for the exchange of energy between the nuclear-spin system and the remaining degrees of freedom of the solid. When the mean frequency of the motion is near the Zeeman splitting of the I9Fnuclei in the nmr experiment, this spin-lattice coupling is at its maximum and leads therefore to a maximum in the relaxation rate for ”F. The theoretical description of this process is well knownas4and leads to a dependence of the maximum relaxation rate on the sixth power of the relevant internuclear separations. This technique is closely related to the ((second-moment’’ technique of Pake, differing principally in its sensitivity to the $uctuating part of the dipolar local field rather than to the static part. As used here, it also depends for its success on the existence of a single dominant relaxation process, which, from 19F line-width measurements,2 we may take to be an isotropic anion rotation. The most important assumptions on which a computation of internuclear distances from relaxation data on this series of compounds rests are: (a) the ad hoc assumption that the anion is a rigid regular tetrahedron (despite the fact that the site symmetry is known to be only m or mm) and (b) the neglect of interionic dipole-dipole coupling. Under assumption a accordingly, the bond lengths reported are average bond lengths. The reasonableness of the second assumption hinges upon the sixth power distance dependence mentioned above, upon the relatively innocuous magnetic character of the cation species (especially K+), and upon the fact that relaxation measurements sample the dynamic rather than static local field components. Thus the changes of internuclear vectors between a l9F nucleus and a second nucleus (alkali metal ion or interionic l9F) outside the itineary of the motion will be negligibly small. Furthermore, one may estimate from the potential hindering the motion what fraction of the anions possesses kinetic energy sufficient to undergo rotation; this fraction is very small in all cases at the temperatures of interest, ca. l O . O l % . The immediate surroundings of any particular anion rotor are therefore essentially static. We estimate at most a 1% contribution of interionic coupling to the bond distances reported below. This contribution will be least for KBF4, greatest for NaRF4, and always in such a direction that the apparent (Le,, experimentally determined) length is shorter than the actual length. (1) Author to whom correspondenoe should be addressed. (2) D. J. Huettner, J. L. Ragle, L. Sherk, T. R. Stengle, and H. J. C. Yeh, J. Chem. Phz/s.?48, 1739 (1968). (3) A. Abragam, “The Principles of Nuclear Magnetism,” Clarendon Press, Oxford, 1961, pp 290-295, 457-458. (4) A detailed development of the specific case at hand is to be found in H. J. C. Yeh, Ph.D. Thesis, University of Massachusetts, Amherst, Mass., 1968.
3689
NOTES
9
i
1.35
1.45 R(B-F),
1.55
d.
Figure 1. Solid lines illustrate theoretical dependence of tnu1l(min)on B-F bond length a t two frequencies (see Table I). Circles correspond to experimental values of tnull(min).
The process by which the bond length is abstracted from the relaxation data is arithmetically complex. The longitudinal magnetimtion of the fluorine spin system decays as the weighted sum of four exponentials. If the spin ensemble is prepared by use of a 180" pulse at the 19FLarmor frequency, the simplest observable characteristic of this decay is the time, tnull, at which the magnetization passes through zero during the evolution toward thermal equilibrium at the lattice temperature. This null time is dependent upon the correlation time of the local field fluctuation (hence the lattice temperature) and upon the B-F and F-F bond lengths in a complex but known way. At a particular temperature, the value of which is irrelevant, the null time is a minimum. We have simply calculated t n u l l as a function of correlation time at a fixed bond length and a t the experimental frequency. The minimum values of t n u l l , tnull(min), at various bond lengths were then plotted and compared with experimental data. A typical result is shown in Figure 1, and the results are summarized in Table I. The mean of these measurements is R(B-F) = 1.425 f 0.015 8, very close to the assumed value of 1.43 8 used by Hoard and Blair in an early refinement of the structures of NH4BF4 and RbBF4.' The data offer weak support for the idea that the B-F bond length increases as the cation radius increases. This is in accord with the concomitant increase in cation polarizability and the unit cell free volume, but is is also in accord with the expected decrease in interanionic dipolar coupling. We are therefore not willing to assign reality to the apparent trend in bond length. Recent X-ray work by Weiss, et al.,6 on NaBF4 yields a value R(B-F(1)) = R(B-F(11)) = 1.377 8 and implies a minimum value of tnull about 18% shorter t h t n our measurements yield. The distance of 1.377 A, not reported by Weiss, is calculated from his coordinates, is not corrected for thermal motion, and is in substantial agreement owwith the average uncorrected length of 1.382 f 0.006 A obtained by Caron, et aZ.,' for NH4BF4 at room temper-
ature. Since our measurements yield internuclear separations and since they are not influenced by anion liberation, one may estimate a mean liberation halfamplitude of ca. 10" from the ratio of the X-ray and nmr results.* Anisotropic refinement of the NH4BF4 structure followed by a rigid-body analysis of the anion liberation yields liberation half-amplitudes of 9.5, 7.2, and 5.0°, as well as an average B-F bond length of 1.406 8, corrected for thermal motion. Acknowledgment. The financial support of the National Science Foundation is gratefully acknowledged. (5) J. L.Hoard and V. Blair, J . Amer. Chem. Soc., 5 7 , 1985 (1935). (6) A. Weiss and K. Zohner, Phys. Status Solidi, 21, 257 (1967). (7) A. P. Caron and J. L. Ragle, to be submitted for publication. (8) D. W. J. Cruickshank, Acta Crystallogr., 9, 757 (1956).
Interruption and Evaporation Effects for the Reaction of Atomic Hydrogen with Solid Olefins at 7 7 O K
by R. L. Espino, J. P. Jones, R. C. Reid, and M. W. P. Strandberg Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received June IO, 1968)
The hydrogenation of thin films of solid, low molecular weight olefins has been investigated in recent years by Klein and Scheer,1--5Hughes and P ~ r n e l land , ~ Hill.5 Various models have been proposed to interpret experimental rate data and product distributions. The two best known models differ rather drastically. I n hydrogen atoms are assumed to be capable of diffusing into the solid olefin film where they either react with the olefin or recombine to form molecular hydrogen. The olefin and olefin radicals are endowed with very low diffusivities; ie., they are, for all practical purposes, immobile. The other model6 assumes that hydrogen atoms cannot penetrate any appreciable distance into the olefin and all of the reaction occurs in a thin surface layer. As the olefin is consumed, olefin radicals (and saturated hydrocarbon products) diffuse into the bulk of the film and fresh olefin counterdiffuses to the surface. (1) R. Klein and M. D. Scheer, J . Amer. Chem. SOC.,80, 1007 (1958). (2) R. Klein and M. D. Scheer, J . Phys. Chem., 62, 1011 (1958). (3) R. Klein, M. D. Scheer, and J. G. Waller, ibid., 64, 1247 (1960). (4) A. N.Hughes and J. H. Purnell, Trans. Faraday SOC.,61, 2710 (1965). (5) C. G.Hill, Jr., R. C. Reid, and M. W. P. Strandberg, J . Chem. Phys., 42, 4170 (1965). (6) R. Klein and M. D. Scheer, ibid., 66, 2677 (1962). Volume 72,Number IO October I968
