Allen N. Garroway

Resolution in 13C NMR of organic solids using high-power proton decoupling and magic-angle sample spinning

Abstract The 13C NMR linewidths observed in organic solids by means of high-power proton decoupling and magic-angle sample spinning are roughly 10 to 100 times broader than resonances in the liquid phase. This paper investigates important 13C line-broadening mechanisms in organic solids and their dependences on experimental parameters, notably static and rf magnetic field strength. The discussion is limited to glassy (disordered, partially mobile) and crystalline (ordered, rigid) organics at natural isotopic abundance. Excluded are elastomers and systems with a third dipolar coupled nuclear species. Experimental data, primarily at 1.4 T, for glassy and semi-crystalline polymers as well as crystalline materials, illustrate and confirm the linebroadening mechanisms identified. For some specimens, 13C linewidths are compared at 1.4 and 4.7 T. It is found that a substantial linebroadening (0.5 to 6 ppm) corresponding to a dispersion of isotropic chemical shifts can arise from distributions of anisotropic sources of magnetic susceptibility, bond angles, or frozen molecular conformations; in other cases, the resonance lines may be split into many distinct lines by magnetic inequivalences present in the solid but not the liquid phase. For crystalline materials, methods for reducing the broadening from anisotropic bulk susceptibility are discussed. Other broadening mechanisms considered are: insufficient proton-decoupling fields, off-resonance decoupling, imperfections in magic-angle sample spinning, and motional modulation of both the carbon-proton dipolar coupling and the carbon chemical shift anisotropy. On consideration of these mechanisms, it is anticipated (and shown experimentally in limited cases) that no significant gain in resolution will be enjoyed at high magnetic fields, especially when variable-temperature operation is available. In some instances, degradation of resolution may occur at high field if large rf field strengths or high spinning rates cannot be achieved.

NMR images of solids

Abstract A way of obtaining two-dimensional NMR images of solids using multiple-pulse line narrowing is demonstrated. The method is adaptable to any fast recovery solid-state spectrometer having 2D FT NMR software and provisions for applying magnetic gradients. The use of molecular mobility as an NMR image contrast mechanism is demonstrated.

Zero quantum NMR in the rotating frame: J cross polarization in AXN systems

An analysis of liquid state cross polarization in AXN spin systems is presented. A two‐level geometrical formalism derived from symmetry considerations provides a closed form description of the quantum dynamics for arbitrary N. A parallel discussion using a classical vector model explains the significance of the quantum mechanical solutions and illustrates the nature of the spin–spin correlations accompanying magnetization transfer. General expressions for the J cross polarization A signal with and without X decoupling are given. A discussion of RJCP and PCJCP pulse sequences introduced previously shows how manipulation of Hartmann–Hahn mismatch can advantageously modify cross‐polarization dynamics. The quantum formalism demonstrates that efficient polarization transfer is equivalent to population inversion of an ensemble of fictitious spins subjected to different rf field intensities, and that pulse sequences for cross polarization can be constructed by analogy with conventional spin inversion techniques.

Time-suspension multiple-pulse sequences : applications to solid-state imaging

In this Communication, we introduce a 48-pulse homonuclear dipolar decoupling cycle which also refocuses chemical shifts and other resonance offsets. When applied by itself to a system of spins then it appears that the spin system does not evolve in the absence of irreversible effects. By carefully combining this multiple-pulse sequence with a time-dependent magnetic field gradient, the gradient-induced evolution can be preserved without destroying the line-narrowing benefits of the cycle. With this method we hope to obtain liquid-like images of solid samples. One approach to solid-state imaging, then, is to combine a multiple-pulse cycle which averages time-independent linear and bilinear Z, Hamiltonians with a temporally and spatially dependent linear Z, Hamiltonian in such a manner that this spatially dependent Hamiltonian does not interfere (I ) with the multiple-pulse averaging of the time-independent Hamiltonians. This approach allows high-resolution solid-state images to be obtained with modest magnetic field gradient strengths thereby avoiding the sensitivity cost associated with large detection bandwidths (2,3). In addition, the resulting images have nearly uniform spatial resolution unlike solid-state images that are acquired with multiple-pulse sequences in a time-independent magnetic field gradient. These “time-suspension” cycles average both linear and bilinear Z, Hamiltonians by toggling Z, and Z,Z: operators through a variety of states the temporal average of which is zero. We use time suspension here to connote setting to zero the time evolution of a propagator rather than the equivalent picture in which the spin-dependent part of the Hamiltonian is set to zero: this phrase is chosen in analogy to “time-reversal” sequences which change the sign of the spin Hamiltonian. Such discussions are only useful when one remembers that irreversible effects are excluded, and spin-lattice relaxation and molecular motions place a limit on the interval over which manipulations of the Hamiltonian may be equated to manipulations of time. Naturally, timesuspension only refers to the sampling point for the cycle, and spin evolution during the cycle is much more complicated. Time-suspension sequences are well known in solid-state imaging: an eight-pulse version was the basis of an early imaging scheme suggested by Mansfield and Grannel (4); Weitekamp et al. have used this approach for radio frequency gradient solid-state imaging (5, 6), and we have employed this approach for solid-state imaging with

Determination of aromatic hydrocarbon fraction in oil shale by 13C n.m.r. with magic-angle spinning

Abstract A method for estimation of aromatic content in oil shales is demonstrated. Magic-angle spinning at 2 kHz is shown to remove chemical shift anisotropy to a sufficient degree to resolve aromatic and aliphatic 13 C n.m.r. spectral regions for a lithic oil shale specimen. The proton and carbon n.m.r. relaxation parameters are such as to allow room-temperature use of this proton-enhanced 13 C n.m.r. technique as a quantitative analytical tool. Cross polarization times of a millisecond or less and experiment repetition periods of 0.5 s or less are optimum. The specimen examined is represented by an aromatic carbon fraction 0.264 ± 0.007; this determination is quite insensitive to the proton-carbon cross polarization time. Spectra for kerogen, shale oil, and dawsonite are also presented. Dawsonite may interfere in the determination of the aromatic fraction.

NQR detection using a meanderline surface coil

14N pure NQR detection in a thin-layer sample using a meanderline, or zig-zag, surface coil is reported. The RF magnetic field of the meanderline drops off approximately as exp−πhb), where b is the conductor spacing and h is the distance from the plane of the coil, and therefore is ideally suited for NQR detection in thin, planar samples. A meanderline with 11 conducting strips of 4 cm spacing was used to observe the 14N ν-resonance line in sodium nitrite at sample distances up to 1.6 cm, where the RF field has dropped to less than 1e. The meanderline results are compared with those obtained using a solenoid of comparable dimensions. It is also shown that the sensitivity of NQR detection using surface coils is greatly enhanced by using fast-pulsing techniques such as the strong off resonance comb, which can produce an order-of-magnitude or better improvement in the signal-to-noise ratio over more conventional (T1-limited) techniques.

Homogeneous and inhomogeneous nuclear spin echoes in organic solids: Adamantane

Abstract Under conditions of proton dipolar decoupling, the 13C magnetization in adamantane has been further subjected to the following separate coherent averaging procedures: magic angle mechanical spinning, Carr-Purcell, Carr-Purcell-Meiboom-Gill, and multiple-pulse (solid echo) sequences. A comparison of the respective widths of the 13C NMR response demonstrates that in adamantane the 13C13C intermolecular dipolar coupling is approximately 40 Hz; all but the Carr-Purcell sequence reduced this, albeit with varying efficiencies. It is suggested that in an organic solid with substantial molecular motion in the kilohertz range, the 13C13C dipolar coupling can limit spectral resolution even under magic angle sample spinning.

Three-frequency nuclear quadrupole resonance of spin-1 nuclei

Abstract We introduce a new nuclear quadrupole resonance (NQR) method for the detection of spin-1 nuclei, where the transition excited and directly detected is not irradiated at all. It is demonstrated, theoretically and experimentally, that the irradiation of a powder sample containing spin-1 nuclei by two of the three characteristic NQR frequencies can result in free induction decay (FID) and echo signals at the third NQR frequency. We present the optimal conditions for such three-frequency NQR experiments and compare theory with experiment using 14 N ( I =1) in a powder sample of sodium nitrite.

Pulsed field gradient NMR imaging of solids

Abstract The use of multiple pulse line narrowing for NMR imaging of solids is hampered because large magnetic field gradients can place some spins sufficiently far from resonance so that the local line narrowing efficiency is reduced. We propose that this interference can be modeled as a phase error of the rf pulses and can be reduced by applying the gradient only during selected windows in the pulse cycle. We demonstrate this interference with the use of a digital phase and compare one-dimensional images obtained with the standard static gradient technique and this new pulse gradient method.

Homogeneous and inhomogeneous distributions of correlation times. Lineshapes for chemical exchange

Abstract Molecular motions, especially in polymers, can be described in terms of a broad distribution of correlation times. In principle, these distributions can arise in two fundamentally different ways. There may be an inhomogeneous spatial distribution of processes individually characterized by a single correlation time and each with an exponentially decaying autocorrelation function. Alternatively one can imagine an autocorrelation function identical for all common molecular processes but one which is inherently nonexponential. This nonexponential autocorrelation function can also be expressed mathematically as a probability distribution of exponential autocorrelation functions. The latter is called a homogeneous distribution. It is shown that NMR lineshape analysis can distinguish between the two forms of distributions. For simplicity the lineshape expected for two-site chemical exchange driven by homogeneous and inhomogeneous distributions is treated theoretically. Computer simulations of the expected lineshapes are presented for a distribution whose autocorrelation function is exp[ −( t τ p ) α ], where 0