Contains research objectives and reports on three research projects

Deutch, J. M.

Leonardi, A.

Macomber, J. D.

Newmark, R.

Riehl, J. W.

Rugheimer, J. H.

Stone, E. T.

Thompson, D. S.

Wade, C. G.

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VIII. MAGNETIC RESONANCEProf. J. S. Waugh J. W. Riehl D. S. ThompsonDr. J. Rugheimer C. G. Wade E. T. StoneDr. R. Newmark D. W. Schaefer A. LeonardiJ. D. Macomber E. L. WeiRESEARCH OBJECTIVESThe work of this group continues to be centered on the study of structure and atomicdynamics of solids and fluids through experiments on nuclear and electronic magnetism.Particular attention is given to intermolecular forces and the mechanisms through whichthey are reflected in nuclear magnetic relaxation. The following specific projects areunder way at the present time.1. Structure of Liquid DielectricsNuclear spin Hamiltonians of interest in magnetic-resonance experiments can beexpressed in terms of spherical tensors of rank 2, a circumstance that arises becausethe nuclear moments involved are magnetic dipole and electric quadrupole. The secularinteractions, which give rise to shifts and splittings of the nuclear Zeeman levels, thushave scalar parts and parts that depend on the orientation of molecules through Y m(',9).In ordinary liquids, rapid molecular reorientation makes the anisotropic terms unobserv-able, inasmuch as the average of Ym over a spherically symmetric probability distri-bution vanishes. In a polar liquid subjected to an electric field, however, the probabilitydistribution is no longer exactly spherical, and one expects to see small perturbations ofthe nuclear-resonance spectrum which depend on electric field intensity E and temper-ature T as (E/T) 2, and also on the local order in the liquid produced by intermolecularforces. For molecules of known properties it becomes possible to measure such aver-ages as Y2 0 through the nuclear-resonance spectrum. This information, together witha knowledge of Y10 obtained from dielectric studies, is expected - for the first time - toprovide detailed information about the degree and type of local order produced by molec-ular interaction in dielectric liquids. The present state of our experiments is describedin this report.J. D. Macomber, E. T. Stone2. Magnetic Relaxation in GasesNuclear relaxation in monatomic gases such as helium is exceedingly slow, a factthat has suggested the use of He 3 nuclear moments in navigational gyroscopes. We arestudying the mechanisms responsible for such relaxation by performing transientmagnetic-resonance experiments on gases at high pressures for which the relaxation israpid enough to be measurable. We are even more actively studying nuclear relaxationby similar methods in simple polyatomic gases, in which there are stronger mechanismsarising from the anisotropy of the forces between colliding molecules. Basically theseforces lead to rotational transitions of various kinds and the nuclear relaxation timesreflect the cross sections for such inelastic collision. Transitions between differentinitial and final rotational states reflect themselves differently in the nuclear relaxationtime according to the nature of the coupling between the nuclei and the molecular frame-work. Such couplings may include the angle-dependent dipolar coupling between nuclei,the spin-rotational interaction, anisotropy of the chemical shielding, etc. Each of thesehas its own characteristic dependence on temperature, magnetic field, and isotopic sub-stitution. By varying such parameters we are attempting to sort out the role played bydifferent rotational states and thereby to get a clearer understanding of the nature of theintermolecular forces involved.J. H. Rugheimer, J. W. RiehlQPR No. 76(VIII. MAGNETIC RESONANCE)3. Transport Properties of Dense FluidsFor a long time, a great deal of theoretical attention has been devoted to the generalproblem of the nonequilibrium properties of liquids and dense gases. Despite the factthat diffusion, viscosity, thermal conductivity, and so forth, are among the most clas-sical subjects of experimental physical chemistry, almost none of the work that has beendone is of direct use in testing transport theory. This is because of the necessity of lowtemperatures and/or high pressures for obtaining high densities of fluids composed ofsingle atoms or small molecules. Also, one would like experimental values of transportcoefficients over wide ranges of temperature and density, since one would expect trans-port theories to do a better job of predicting the form of temperature and density depend-ences than of giving numerical values of the transport coefficients. Fortunately theexperimental difficulties of the classical methods are largely obviated, in the case of dif-fusion, by the spin-echo technique of nuclear resonance. We have already used thismethod to study the temperature dependence of self-diffusion in liquid ethane over anextremely wide temperature range (see Quarterly Progress Report No. 64, pages 37-39).We have now completed and tested a system for extending the same type of measurementsto high pressures. It has been used initially to complete the earlier investigation ofliquid C2H 6 and will now be turned to the study of simpler liquids.C. G. Wade4. Atomic Motion in SolidsThermal relaxation of nuclei in solids typically occurs through the agency of mag-netic dipole-dipole interactions, randomly modulated by the motions of nuclei with respectto one another. In general, it is assumed that the time autocorrelation function G(T)describing the statistical fluctuation of these interactions X(t) is an exponential,described by a correlation time Tc:G(T) H <(t) C'(t+T)= 2(t) exp(-T/tc).This assumption, applied to solids whose atomic motions are thermally activated so thatT = T co exp(E/kT), has been very successful in identifying the atomic motions that occurand determining the energetic barriers E that hinder them. An example from our recentwork is described in this report.In general, where correlations exist between the motions of neighboring nuclei orwhere the motion is complex in character, the assumption that a single correlation timeexists is certainly not correct. The nuclear relaxation time is still a measure of thecorrelation function, being directly related to its Fourier transform evaluated at theexperimental resonance frequency. We are beginning a series of studies of relaxationin various solids with the object of mapping out the correlation function experimentallyand finding out what sorts of departures from exponential behavior do occur typically.Such work requires observing the relaxation of nuclear magnetization toward equilibriumin an applied magnetic field whose strength is variable from a few to many thousandoersteds. The usual procedure is to polarize the sample in a strong field and then reducethe field quickly to the desired value. After a time, the field is restored to a large valueand the remaining magnetization is measured by means of a free-induction decay or anadiabatic fast passage. Alternatively, the desired low magnetic fields can be obtainedin the rotating frame by means of Solomon's "spin-locking" procedure.R. Newmark, A. Leonardi5. Electron Spin ResonanceA good deal of interest exists in the properties of magnetically dilute solutions oftransition metal ions in diamagnetic crystals, partly because of the applications of suchQPR No. 76(VIII. MAGNETIC RESONANCE)systems to optical masers. We are carrying out some optical and X-band electron spin-resonance studies on the d4 ion Cr +2 in CaF 2 and SrF 2 single crystals. The object of thiswork is to obtain an analysis of the Jahn-Teller effect through its influence on the F 1 9hyperfine interaction at low temperatures. We are also carrying on some electron spin-resonance work on solutions of rare-earth metals in liquid ammonia in the hope ofthrowing some further light on the structure of these peculiar conducting liquids.D. S. ThompsonA. STATUS OF CURRENT PROJECTS1. NUCLEAR MAGNETIC RESONANCE OF POLAR LIQUIDS IN ELECTRIC FIELDSOur attempts to observe the quadratic electric field effect in liquid CH 3 NO2 and othersubstances has so far not been entirely successful. We are now attempting to observethe quadrupole splitting of the deuterium resonance in heavy chloroform and other sub-stances, which is induced by the alignment of the molecule in an electric field. Thesesplittings are expected to be an order of magnitude larger than the dipolar splittingswhich we have heretofore been looking for.While this experiment is being set up we have been working on two associated theo-retical problems. One has to do with the sideband phenomena which are produced whenthe electric field is modulated (see Quarterly Progress Report No. 72, pages 61-63;No. 75, pages 37-38). The other has to do with the manner in which intermolecularforces and local order in the liquid are reflected in the results of the electric fieldexperiment as opposed to experiments in which the static dielectric constant is measured.A result of Kirkwood's theory1 of dielectrics can be expressed for the case of pure ori-entation polarization bycos Oi 1 E 1+(N-1) cosy i (1)The quantity -on the left is essentially what is experimentally measured when the dielec-tric constant is determined in an electric field E, 0. being the direction of the i'th dipole1with respect to the electric field. The average on the right is over the equilibrium dis-tribution of the liquid in the absence of a field, yij being the angle between dipoles i andj. In the NMR electric field experiment one measures the alignment rather than thepolarization of the liquid, which turns out to be expressible in a form analogous toKirkwood's result above, asP2(cos 0i))E = + (N- 1) P 2 (cos yij -N cos y3(N-2)+ 2 cosy .Cos ik i (2)QPR No. 76(VIII. MAGNETIC RESONANCE)This expression exhibits the fact that, regardless of the type of intermolecular forcespresent, the NMR electric field effect is quadratic in (E/T). Also it displays the typesof intermolecular correlations that can contribute. In the limit of vanishing intermolec-ular forces both of these results correspond to Debye's theory for dilute gases. Whenintermolecular forces are important the local order they produce is reflected quite dif-ferently in the results of the two experiments. A detailed discussion of this work,together with calculations based on equation (2) above, will be submitted for publicationin the near future.J. M. Deutch, J. D. Macomber, E. T. StoneReferences1. J. G. Kirkwood, J. Chem. Phys. 7, 911 (1939).2. SELF-DIFFUSION IN LIQUID ETHANEThe work of Gaven I on diffusion in ethane between the triple point and the criticalpoint has been extended to pressures above 2000 atmospheres. In order to determinethe dependence of diffusion constant on density, approximate measurements were alsomade of the equation of state, taking the density at a given pressure as proportional tothe amplitude of the observed free induction decay. Gaven had found that his results onthe temperature dependence of diffusion could be fitted satisfactorily into the frameworkof the free volume theory of liquids, either with or without an intrinsic dependence ofT on T1/2. Our new results on the density dependence show that these simple theoriesare in fact untenable, as might have been expected. A description of this work willappear in the author's doctoral thesis and also be submitted for publication.C. G. WadeReferences1. J. V. Gaven, Jr., Spin-Echo Studies of Diffusion in Liquids, Ph.D. Thesis,Department of Chemistry, M. I. T., November 1961.QPR No. 76

Magnetic Resonance

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Magnetic Resonance

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