Publications

Many linear inversion problems involving Fredholm integrals of the first kind are frequently encountered in the field of magnetic resonance. One important application is the direct inversion of a solid-state NMR spectrum containing multiple overlapping anisotropic subspectra to obtain a distribution of the tensor parameters. Because of the ill-conditioned nature of this inverse problem, we investigate the use of the TSVD-S-LASSO based regularization method, which (a) stabilizes the solution and (b) promotes sparsity and smoothness in the solution. We also propose a unambiguous representation for the anisotropy parameters using a piecewise polar coordinate system to minimize rank deficiency in the inversion kernel. To obtain the optimum tensor parameter distribution, we implement the k-fold cross-validation, a statistical learning method, to determine the hyperparameters of the regularized inverse problem. In this article, we provide the details of the linear- inversion method along with numerous illustrative applications on purely anisotropic NMR spectra, both synthetic as well as experimental two-dimensional spectra correlating the isotropic and anisotropic frequencies.

The Core Scientific Dataset (CSD) model with JavaScript Object Notation (JSON) serialization is presented as a lightweight, portable, and versatile standard for intra- and interdisciplinary scientific data exchange. This model supports datasets with a p-component dependent variable, {U0, …, Uq, …, Up−1}, discretely sampled at M unique points in a d-dimensional independent variable (X0, …, Xk, …, Xd−1) space. Moreover, this sampling is over an orthogonal grid, regular or rectilinear, where the principal coordinate axes of the grid are the independent variables. It can also hold correlated datasets assuming the different physical quantities (dependent variables) are sampled on the same orthogonal grid of independent variables. The model encapsulates the dependent variables’ sampled data values and the minimum metadata needed to accurately represent this data in an appropriate coordinate system of independent variables. The CSD model can serve as a re-usable building block in the development of more sophisticated portable scientific dataset file standards.

A two-dimensional (2D) $J$-resolved magic-angle spinning nuclear magnetic resonance (NMR) spectrum of silica glass at $^{29}$Si natural abundance levels, 4.7%, was measured using the shifted-echo phase-incremented echo train acquisition (SE-PIETA) pulse sequence. At $^{29}$Si natural abundance levels the $J_\text{Si-O-Si}$ coupling splittings appear as overlapping doublet patterns arising from isolated $^{29}$Si−O−$^{29}$Si linkages. The experimental 2D J-resolved spectrum is analyzed to obtain a bivariate probability distribution correlating the central Si-O-Si angle of a Q4−Q4 linkage to its mean Si-O-Si angle (seven angles) using relationships between $^{29}$Si isotropic chemical shifts and geminal $J$ SiO-Si coupling of a Q4−Q4 to its local structure. To obtain a self-consistent bivariate probability distribution it was necessary to introduce an additional dependence of the $^{29}$Si chemical shift of a Q4 on mean Si-O distance as well as mean Si-O-Si angle. The implication of this necessary modification is a positive correlation between Si-O-Si angle and Si-O distance in the silica glass, consistent with recent $^{17}$O NMR measurements on ambient and densified silica glasses but running opposite to the trend generally found in crystalline silica polymorphs. From the analysis of the $^{29}$Si 2D J-resolved spectrum we determine a Si-O-Si bond angle distribution in silica glass as having a mean at $147.8^\circ$, a mode at $147^\circ$, and a standard deviation of $10.7^\circ$. Our statistical model for analyzing the experimental $^{29}$Si 2D $J$-resolved spectrum also indicates that the individual Si-O-Si bond angle distributions are relatively uncorrelated.

The dependence of a $^{29}$Si geminal J coupling across the inter-tetrahedral linkage on local structure was examined using first-principles DFT calculations. The two main influences on $^2J_\mathrm{Si–O–Si}$ were found to be a primary dependence on the linkage Si–O–Si angle and a secondary dependence on mean Si–O–Si linkage of the two coupled $^{29}$Si nuclei. An analytical expression describing these dependencies was proposed and used to develop an approach for relating the correlated pair of $^2J$ Si-O-Si coupling and mean $^{29}$Si isotropic chemical shift to the linkage Si–O–Si angle and the mean Si–O–Si angle of the two coupled $^{29}$Si nuclei. An example of this analysis is given using $^{29}$Si NMR results from the siliceous zeolite Sigma-2.

There is considerable interest in using zeolite membranes for gas separations. For CO2 and N2 separation, much research has focused on faujasitic (FAU) membranes. Simulations suggest that chabazite (CHA) membranes can also be good at CO2 and N2 separation. In this study, we have focused on CHA membranes grown on porous polymeric polyethersulfone (PES) supports. Recently, we have reported on a dehydration rehydration hydrothermal (DRHT) process for FAU membrane growth on PES supports, which results in rapid crystallization. It is well known that FAU can be converted to CHA by an interzeolite conversion method, and is our choice for CHA synthesis in this study. A synthesis method for isolated CHA nanocrystals with size of 50–100 nm is reported. Rapid DRHT-based CHA powder synthesis and CHA/PES membrane growth are also being reported, all made by the interzeolite conversion of FAU. The CHA/PES membranes of ∼4 μm thickness were coated with polydimethylsiloxane (PDMS), and at 25 °C, CO2 permeance of 1243 GPU with CO2/N2 selectivity of 19 was observed. The porosity of the PES support was critical to enhancing the formation and stability of the CHA membrane, since the CHA membrane on the PES surface was bonded to interconnected CHA crystals that grew within the PES from the seed crystals.

In this article, a simple heuristic approach that is in agreement with the density operator formalism is presented for understanding the mechanism of multi-quantum (MQ) excitation in half-integral quadrupolar systems. Employing the population level diagram of the nuclear spin states, the effect of radio-frequency (RF) pulses on multi-level systems is described. Based on this approach, alternate schemes that involve non-equilibrium spin states are proposed for improving the sensitivity of MQ experiments in spin 3/2 and 5/2 systems. Additionally, the utility of frequency sweep techniques in the excitation of MQ transitions is discussed. The results obtained from the analytic theory are substantiated through numerical simulations.

With the development of technology and improved understanding of nuclear spin–spin interactions and their behavior in static/oscillating magnetic fields, NMR spectroscopy has emerged as a powerful tool for characterizing molecular structure in a wide range of systems of chemical, physical and biological relevance. Here in this article, we revisit the important connection between “Secular-Approximation” (a well-known fundamental concept) and NMR spectroscopy. Employing recent experimental results as the background, an alternate interpretation of the secular approximation is presented for describing and understanding the nuances of Multi-Quantum (MQ) NMR spectroscopy of quadrupolar nuclei. Since MQ NMR spectroscopy of quadrupolar nuclei forms the basis of the structural characterization of inorganic solids and clusters, we believe that the analytic theory presented herein would be beneficial both in the understanding and design of MQ NMR experiments. Additionally, the analytic results are corroborated with rigorous numerical simulations and could be employed in the quantitative interpretation of experimental results.

Employing the concept of effective Hamiltonians, an analytical theory is introduced to describe transitions in a multi-level system in nuclear magnetic resonance (NMR) spectroscopy. Specifically, the discussion is centered towards the treatment of selective and non-selective excitations in static quadrupolar spin (I > 1/2) systems. To this end, effective radiofrequency (RF) Hamiltonians based on the spherical tensor formalism are proposed for describing transitions in both integral (I = 1, 2 and 3) and half-integral (I = 3/2, 5/2 and 7/2) quadrupolar spins. The optimum conditions desired for selective excitation in a multi-level system are derived pedagogically from first principles and presented through analytical expressions. Employing suitable model systems, the derived optimum conditions are substantiated through rigorous numerical simulations based on the spherical tensor formalism. The theory presented provides a framework for describing selective and non-selective RF pulses and could improve our understanding of multiple-pulse experiments involving quadrupolar nuclei.