Philip J. Grandinetti

Two-dimensional magic-angle spinning isotropic reconstruction sequences for quadrupolar nuclei.

Two-dimensional magic-angle spinning (triple quantum, single quantum) correlation pulse sequences and phase cycles based on the technique of Frydman and Harwood for the reconstruction of the isotropic spectrum of half-integer spin quadrupolar nuclei broadened to second-order are described. These sequences provide pure absorption mode two-dimensional lineshapes and increased sensitivity. Experimental examples on spin I = 3/2 (87Rb in RbNO3) and I = 5/2 (27Al in NaSi3AlO8) are presented. The isotropic chemical shift and quadrupolar coupling parameters could be obtained from a simple analysis of the triple quantum filtered single quantum magic-angle spinning cross-sections.

Sensitivity enhancement of the central transition NMR signal of quadrupolar nuclei under magic-angle spinning

An approach for enhancing the NMR sensitivity of the central transition of spin-3/2 nuclei is presented. Through selective excitation of the satellite transitions using a fast 180 degrees phase alternating pulse train during magic-angle spinning a selectively excited state is prepared where the populations of all eigenstates textbackslash m > with the same sign of m are equal, resulting in an enhanced central m = -1/2 --> 1/2 transition polarization. Numerical simulations predict enhancements up to a factor of 2 and values of 1.7 and 1.9 have been obtained experimentally for Na-23 in Na2C2O4 and Rb-87 in RbClO4, respectively. We observe no significant anisotropic lineshape distortion. The conditions for optimum enhancement are discussed

Anionic Species Determination in CaSiO3Glass Using Two-Dimensional29Si NMR

The structure of the alkaline earth silicate glass CaSiO 3 has been investigated using a two-dimensional 29 Si NMR experiment that correlates the isotropic magic-angle-spinning (MAS) spectrum with an anisotropic off-magic-angle-spinning spectrum. Although the one-dimensional magic-angle-spinning (MAS) spectrum is completely unresolved, all five types of SiO 4 tetrahedra (represented by the notation Q (n) , where n ) 0-4 representing the number of bridging oxygen) can be resolved and quantified on the basis of the separated anisotropic line shapes in the 2D spectrum. The distribution of isotropic chemical shifts derived from the 2D spectrum suggests that in the case of CaSiO3 glass the conventional approach of fitting the one-dimensional MAS spectrum with overlapping Gaussian line shapes would lead to significant errors in Q (n) quantification. The equilibrium constants for the disproportionation reaction Q (n) h Q (n-1) + Q (n+1) with n ) 1, 2, and 3 were determined from the 2D spectrum to be 0.105 ( 0.019, 0.156 ( 0.005, and 0.106 ( 0.022, respectively. These results clearly indicate a significantly greater deviation from a binary model of Q (n) species disproportionation in alkaline earth silicate melts when compared to alkali silicate melts and thus suggest a relatively more disordered structure.

Variable‐angle correlation spectroscopy in solid‐state nuclear magnetic resonancea)

We describe here a new solid‐state nuclear‐magnetic‐resonance (NMR) experiment for correlating anisotropic and isotropic chemical shifts of inequivalent nuclei in powdered samples. Spectra are obtained by processing signals arising from a spinning sample, acquired in independent experiments as a function of the angle between the axis of macroscopic rotation and the external magnetic field. This is in contrast to previously proposed techniques, which were based on sudden mechanical flippings or multiple‐pulse sequences. We show that the time evolution of variable‐angle‐spinning signals is determined by a distribution relating the isotropic frequencies of the spins with their corresponding chemical shift anisotropies. Fourier transformation of these data therefore affords a two‐dimensional NMR spectrum, in which line shapes of isotropic and anisotropic interactions are correlated. Theoretical and experimental considerations involved in the extraction of this spectral information are discussed, and the techn...

Theoretical aspects of higher‐order truncations in solid‐state nuclear magnetic resonance

Recent experimental developments of high‐resolution NMR in solids (for example, double rotation and dynamic‐angle spinning) address the reduction of second‐order line broadening effects, particularly in systems involving quadrupolar nuclei such as 23Na, 17O, 27Al, and 14N. However, some aspects of the theoretical description of these systems have not been clearly understood; in particular, the various procedures available to truncate the interactions give incompatible results. We present a general framework, based on static perturbative methods, which provides a natural procedure to derive the correct Hamiltonian for higher‐order effects in irreducible tensor form. Applications of this method to coherent averaging techniques (sample motion or radio‐frequency irradiation) are described and compared to previous treatments based on average Hamiltonian theory.

Silicon site distributions in an alkali silicate glass derived by two-dimensional 29Si nuclear magnetic resonance

A common approach to quantify Q(n) species in silicate glasses is to use 29Si magic-angle spinning (MAS) nuclear magnetic resonance (NMR) and assume that the overlapping isotropic chemical shift distributions of Q(n) species are Gaussian. We have shown that a two-dimensional isotropic/anisotropic 29Si NMR experiment can not only determine the distributions of Q(n) species without any a priori assumptions about the distribution, but can also provide over an order of magnitude improvement in the precision of Q(n) species quantification in silicate glasses. Using this approach we have investigated an alkali silicate glass of composition 2Na2O · 3SiO2 and have observed a small concentration of Q(4) in a sample mainly having Q(2) and Q(3). We have found that the distribution of isotropic chemical shifts for each of the Q(n) is approximately Gaussian. The relative populations of Q(2), Q(3), and Q(4) obtained from these separated distributions give an equilibrium constant of 0.0129 ± 0.0001 for the disproportionation reaction 2 Q(3) ⇌ Q(2) + Q(4). This value is slightly higher than what is obtained from analyzing the one-dimensional MAS spectrum alone, thus revealing a higher degree of disorder in speciation and configurational entropy for the glass.

Enhancing sensitivity of quadrupolar nuclei in solid-state NMR with multiple rotor assisted population transfers

Rotor-assisted population transfer (RAPT) was developed as a method for enhancing MAS NMR sensitivity of quadrupolar nuclei by transferring polarization associated with satellite transitions to the central m=12-->-12 transition. After a single RAPT transfer, there still remains polarization in the satellite transitions that can be transferred to the central transition. This polarization is available without having to wait for the spin system to return to thermal equilibrium. We describe a new RAPT scheme that uses the remaining polarization of the satellites to obtain a further enhancement of the central transition by performing RAPT-enhanced experiments multiple times before waiting for re-equilibration of the spin system. For 27Al (I=5/2) in albite we obtain a multiple RAPT enhancement of 3.02, a 48% increase over single RAPT. For 93Nb (I=9/2) in NaNbO(3) we obtain a multiple RAPT enhancement of 5.76, an 89% increase over single RAPT. We also describe a data processing procedure for obtaining the maximum possible signal-to-noise ratio.

Multiple quantum magic-angle spinning using rotary resonance excitation

We have discovered rotary resonances between rf field strength, ω1, and magic-angle spinning (MAS) frequency, ωR, which dramatically enhance the sensitivity of triple quantum preparation and mixing in the multiple-quantum MAS experiment, particularly for quadrupolar nuclei having low gyromagnetic ratios or experiencing strong quadrupole couplings. Triple quantum excitation efficiency minima occur when 2ω1=nωR, where n is an integer, with significant maxima occurring between these minima. For triple quantum mixing we observe maxima when ω1=nωR. In both preparation and mixing the pulse lengths required to reach maxima exceed one rotor period. We have combined these rotary resonance conditions into a new experiment called FASTER MQ-MAS, and have experimentally demonstrated a factor of 3 enhancement in sensitivity in comparison to conventional MQ-MAS.

Relationships between bridging oxygen 17O quadrupolar coupling parameters and structure in alkali silicates

We have performed ab initio calculations on the model cluster (OH)3Si–O–Si(OH)3 with lithium or sodium cations coordinated to the central oxygen in order to refine the relationships between 17O quadrupolar coupling parameters and the local structure around the bridging oxygen in the case of alkali silicates. We have also used a point charge model to derive approximate expressions to describe the dependence of the 17O electric field gradient tensor on the orientation of the alkali cation-bridging oxygen internuclear vector(s). From these calculations we predict that the previously established trend in 17O quadrupolar coupling constant, Cq, with Si–O–Si angle is systematically shifted to lower magnitudes with increasing number and field strength of coordinating alkali cations and that Cq will be relatively insensitive to variations in the alkali cation-bridging oxygen internuclear vector orientation. The previously established trend in 17O quadrupolar coupling asymmetry parameter, ηq, with Si–O–Si angle is ...

Dependence of bridging oxygen 17O quadrupolar coupling parameters on Si–O distance and Si–O–Si angle

Ab initio quantum chemistry calculations and comparisons with experimental 17 Os o lid-state nuclear magnetic resonance (NMR) investigations were used to determine the dependence of the 17 O quadrupolar coupling constant and asymmetry parameter on the first-coordination-sphere structure around bridging oxygen. The quadrupolar asymmetry parameter was found to be dependent on the Si–O–Si angle, in agreement with previous studies, and independent of the Si–O distance. In contrast, the quadrupolar coupling constant was found to have as tr ong dependence on Si–O distance as well as Si–O–Si angle. Analytical expressions describing these dependences were proposed and used to develop an approach for relating measured 17 O quadrupolar coupling constant and asymmetry parameter values for bridging oxygen to their Si–O–Si angle and average Si–O distance. Examples of this approach were given using 17 ON MR results from the crystalline silica polymorphs, coesite, α-quartz, cristobalite, and ferrierite. (Some figures in this article are in colour only in the electronic version)