J. S. Waugh

Proton‐enhanced NMR of dilute spins in solids

The NMR signals of isotopically or chemically dilute nuclear spins S in solids can be enhanced by repeatedly transferring polarization from a more abundant species I of high abundance (usually protons) to which they are coupled. The gain in power sensitivity as compared with conventional observation of the rare spins approaches NII(I+1)γI2/NSS(S+1)γS2, or ∼ 103 for S = 13C, I = 1H in organic solids. The transfer of polarization is accomplished by any of a number of double resonance methods. High‐frequency resolution of the S ‐spin signal is obtained by decoupling of the abundant spins. The experimental requirements of the technique are discussed and a brief comparison of its sensitivity with other procedures is made. Representative applications and experimental results are mentioned.

NMR in rotating solids

The NMR free induction decay from a spinning sample having inhomogeneous anisotropic interactions (chemical shifts, first order quadrupole couplings) takes the form of a train of rotational spin echoes. The Fourier transform of the echo envelope is a sharp spectrum from which the effects of anisotropy have been removed. The Fourier transform of the echo shape contains information concerning the anisotropies: This information can be extracted by a moment analysis. The effects of localized homonuclear spin–spin interactions are to convert the ’’isotropic’’ spectrum into a characteristic powder pattern. Second order quadrupole coupling produces a similar effect. It is shown in this case that the usual second‐order level shifts cannot be used to calculated this pattern, which must be described by a proper average Hamiltonian theory. Finally it is shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τc≲1 sec).

Magic-angle spinning and polarization transfer in proton-enhanced NMR

Abstract High-speed spinning at the magic angle can significantly modify the rate of polarization transfer from abundant to rare spins in proton-enhanced NMR experiments on solids, if the spinning speed is greater than or comparable to the static dipole-dipole interaction among abundant spins in the rotating frame. In adamantane, this fact can be strikingly demonstrated experimentally. When the spinning speed is much less than dipolar coupling among abundant spins, the effect of spinning on polarization transfer is not dramatic, regardless of the nature of the static dipolar coupling between rare and abundant spins. A semiquantitative theoretical analysis is presented which describes the principal features of these phenomena in terms of the amplitude and frequency modulation of the dipolar interactions between and among the two spin systems. This analysis of the effect of coherent motion (spinning) on polarization transfer also provides some qualitative insight into how incoherent random molecular motion affects transfer in cross-polarization experiments.

Transverse relaxation of dipolar coupled spin systems under rf irradiation: Detecting motions in solids

The spin–spin relaxation time T2 for an S spin dipolar coupled to an unlike I spin under conditions of random isotropic rotational motion and I spin rf decoupling is calculated. The results of the analysis form the basis for a method to detect and analyze rotational motions in solids. The technique is sensitive to motions which occur on the time scale of the rotating‐frame Larmor frequency of the applied rf field and is presented in the context of a variable temperature magic‐angle sample‐spinning experiment where the S spins are observed and the I spins are decoupled. The previously well characterized molecules hexamethylbenzene, hexamethylethane, and adamantane are studied (S=13C and I=1H), and the resulting motional parameters are found to be in good agreement with previous results. As well, the theoretically predicted dependence of T2 on the strength of the decoupling field is experimentally borne out. Finally, the question of resolution of heteronuclear coupled spin systems and the role of decoupling...

Proton-enhanced nuclear induction spectroscopy 13C chemical shielding anisotropy in some organic solids

Abstract Using the recently introduced technique of proton-enchanced nuclear induction spectroscopy, 13 C chemical shielding parameters are reported for a number of simple organic compounds, and some exemplary spectra are shown. The 13 C chemical shielding parameters are sensitive to the functional character of the carbon and to molecular structure. Several interesting aspects of these experiments, including molecular motion and cross-relaxation effects, are mentioned briefly.

Slow molecular motion detected in the NMR spectra of rotating solids

We present an approach for detecting and analyzing slow molecular motions in solids based on changes in the zero order sideband of an inhomogeneously broadened spin system under magic angle spinning conditions. The effect is discussed theoretically from the standpoint of second order perturbation theory and the stochastic Liouville equation of Kubo, both for the case where the chemical shift is the main interaction. Experimental investigations of decamethylferrocene (resulting in Ea=3.3 kcal/mole) and hexamethyl benzene support the predicted trends. A five site jump model is used to interpret the results for decamethyl ferrocene, while the interpretation of the hexamethyl‐ benzene data is obfuscated by the presence of a chemical shift inequivalency presumably caused by a distortion of the aromatic ring above the phase transition (Tc=116 K).

Theory of broadband spin decoupling

Abstract The NMR spectrum of a spin S coupled to another spin I which is undergoing an arbitrary time-dependent irradiation is analyzed. The efficacies of various schemes for spin decoupling are compared using the average Hamiltonian method, and the limitations of this method are pointed out. A procedure for exact numerical analysis is outlined. This analysis leads to a very simple criterion, namely: decoupling will be effective over a bandwidth δ o if the net precessional angle φ of a spin is insensitive to offset δ for 0 δ δ 0 . The application of this criterion in quantitative form permits us to exhibit decoupling sequences which are somewhat superior to any previously described.

Two‐dimensional 13C NMR of highly oriented polyethylene

The two‐dimensional NMR procedure of separated local field spectroscopy [J. S. Waugh, Proc. Natl. Acad. Sci. USA 73, 1394 (1976)] is applied to fibers of highly oriented polyethylene. The 1H decoupled 13C chemical shift spectrum of the fiber oriented parallel to the external magnetic field is a single line, while a distinctive powder pattern results from the perpendicular orientation that is in excellent agreement with calculations. The 13C–1H dipolar splitting is 45 kHz at σ33 and nonexistent at σ22 consistent with perfectly aligned methylene groups with C–H bond length of 1.10 a.u. The splitting at σ11 is somewhat reduced from the predicted value; this finding, along with the temperature invariance of parameters, is discussed in terms of the molecular disorder and motion of the polymer.

Single Crystal Study of the 19F Shielding Tensors of a Trifluoromethyl Group

Coherent averaging techniques are used to examine the 19F shielding tensors of the trifluoromethyl group in single crystals of silver trifluoroacetate. At room temperature, where the CF3 groups are rotating rapidly, the spectrum consists of a single line whose orientation dependence allows a determination of the orientation of the CF3 groups in the unit cell. The rigid lattice (40°K) spectra exhibit the six lines expected on the basis of the x‐ray crystal structure, also determined in this work, and allow a determination of all six independent elements of each of the three incongruent chemical shift tensors.

19F Shielding Tensors from Coherently Narrowed NMR Powder Spectra

Coherent line‐narrowing methods are used to reduce the dipolar width of the 19F resonance in a number of powdered solids, disclosing the powder patterns arising from chemical shift anisotropy. The principal elements of the shielding tensors are reported and compared with previous experimental and theoretical results. In certain cases it has been possible to use the averaging induced by high‐temperature restricted rotation to assign the principal elements of the shielding tensor to directions in the molecular framework. In C6F6 the shielding tensor is axially symmetric within experimental error; σ‖–σ⊥ = 155 ppm, with the unique (‖) axis parallel to the molecular sixfold symmetry axis. In CF3CO>2−Ag+ we find σXX = − 3 ppm, σYY = − 67 ppm, σZZ = + 70 ppm, and 〈σ〉 = − 96 ppm referred to liquid C6F6. Here the Z axis is approximately along the C–F bond and the Y axis lies in the CCF plane.