High-resolution (19)F MAS NMR spectroscopy: structural disorder and unusual J couplings in a fluorinated hydroxy-silicate

High-resolution (19)F magic angle spinning (MAS) NMR spectroscopy is used to study disorder and bonding in a crystalline solid. (19)F MAS NMR reveals four distinct F sites in a 50% fluorine-substituted deuterated hydrous magnesium silicate (clinohumite, 4Mg(2)SiO(4)·Mg(OD(1-x)F(x))(2) with x = 0.5), indicating extensive structural disorder. The four (19)F peaks can be assigned using density functional theory (DFT) calculations of NMR parameters for a number of structural models with a range of possible local F environments generated by F(-)/OH(-) substitution. These assignments are supported by two-dimensional (19)F double-quantum MAS NMR experiments that correlate F sites based on either spatial proximity (via dipolar couplings) or through-bond connectivity (via scalar, or J, couplings). The observation of (19)F-(19)F J couplings is unexpected as the fluorines coordinate Mg atoms and the Mg-F interaction is normally considered to be ionic in character (i.e., there is no formal F-Mg-F covalent bonding arrangement). However, DFT calculations predict significant (19)F-(19)F J couplings, and these are in good agreement with the splittings observed in a (19)F J-resolved MAS NMR experiment. The existence of these J couplings is discussed in relation to both the nature of bonding in the solid state and the occurrence of so-called "through-space" (19)F-(19)F J couplings in solution. Finally, we note that we have found similar structural disorder and spin-spin interactions in both synthetic and naturally occurring clinohumite samples.     

Recoupling in solid state NMR using γ prepared states and phase matching

The paper describes two-dimensional solid state NMR experiments that use powdered dephased antiphase coherence (γ preparation) to encode chemical shifts in the indirect dimension. Both components of this chemical shift encoded gamma-prepared states can be refocused into inphase coherence by a recoupling element. This helps to achieve sensitivity enhancement in 2D NMR experiments by quadrature detection. The powder dependence of the gamma-prepared states allows for manipulating them by suitable insertion of delays in the recoupling periods. This helps to design experiments that suppress diagonal peaks in 2D spectra, leading to improved resolution. We describe some new phase modulated heteronuclear and homonuclear recoupling pulse sequences that simplify the implementation of the described experiments based on γ prepared states. Recoupling in the heteronuclear spin system is achieved by matching the difference in the amplitude of the sine/cosine modulated phase on the two rf-channels to the spinning frequency while maintaining the same power on the two rf-channels.     

Dynamic nuclear polarization at 9T using a novel 250 GHz gyrotron microwave source. 2003

In this communication, we report enhancements of nuclear spin polarization by dynamic nuclear polarization (DNP) in static and spinning solids at a magnetic field strength of 9 T (250 GHz for g = 2 electrons, 380 MHz for ¹H). In these experiments, ¹H enhancements of up to 170 ± 50 have been observed in 1-¹³C-glycine dispersed in a 60:40 glycerol/water matrix at temperatures of 20 K; in addition, we have observed significant enhancements in ¹⁵N spectra of unoriented pf1-bacteriophage. Finally, enhancements of ∼17 have been obtained in two-dimensional ¹³C–¹³C chemical shift correlation spectra of the amino acid U–¹³C, ¹⁵N-proline during magic angle spinning (MAS), demonstrating the stability of the DNP experiment for sustained acquisition and for quantitative experiments incorporating dipolar recoupling. In all cases, we have exploited the thermal mixing DNP mechanism with the nitroxide radical 4-amino-TEMPO as the paramagnetic dopant. These are the highest frequency DNP experiments performed to date and indicate that significant signal enhancements can be realized using the thermal mixing mechanism even at elevated magnetic fields. In large measure, this is due to the high microwave power output of the 250 GHz gyrotron oscillator used in these experiments.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

Finite Element Analysis of Dynamically Loaded Homogeneous Viscous Beams

The paper is concerned with impulsively loaded beams in which the material is treated as homogeneous viscous as an approximation of a rigid-viscoplastic constitutive relation. As opposed to the standard displacement method finite element formulation, where interpolation functions describing the velocity field across elements is given, a mixed formulation is used in which nodal velocities and nodal moments are carried as parameters. At each instant the accelerations (by the Tamuzh principle) and the rates of change of moment (by a virtual velocities formulation) are found, and velocities and moments are integrated forward independently. The properties of the mode solution are also introduced, and the forward integration is carried through only for the difference between the mode solution and the actual solution. This leads to a very efficient scheme for the numerical solution of a cantilever beam problem shown as an illustration.