Statistical characterization of residual noise in the low-rank approximation filter framework, general theory and application to hyperpolarized tracer spectroscopy

The use of low-rank approximation filters in the field of NMR is increasing due to their flexibility and effectiveness. Despite their ability to reduce the Mean Square Error between the processed signal and the true signal is well known, the statistical distribution of the residual noise is still undescribed. In this article, we show that low-rank approximation filters are equivalent to linear filters, and we calculate the mean and the covariance matrix of the processed data. We also show how to use this knowledge to build a maximum likelihood estimator, and we test the estimator's performance with a Montecarlo simulation of a 13C pyruvate metabolic tracer. While the article focuses on NMR spectroscopy experiment with hyperpolarized tracer, we also show that the results can be applied to tensorial data (e.g. using HOSVD) or 1D data (e.g. Cadzow filter).Comment: 26 pages, 7 figure

Anisotropy and NMR spectroscopy

Abstract: In this paper, different aspects concerning anisotropy in Nuclear Magnetic Resonance (NMR) spectroscopy have been reviewed. In particular, the relevant theory has been presented, showing how anisotropy stems from the dependence of internal nuclear spin interactions on the molecular orientation with respect to the external magnetic field direction. The consequences of anisotropy in the use of NMR spectroscopy have been critically discussed: on one side, the availability of very detailed structural and dynamic information, and on the other side, the loss of spectral resolution. The experiments used to measure the anisotropic properties in solid and soft materials, where, in contrast to liquids, such properties are not averaged out by the molecular tumbling, have been described. Such experiments can be based either on static low-resolution techniques or on one- and two-dimensional pulse sequences exploiting Magic Angle Spinning (MAS). Examples of applications of NMR spectroscopy have been shown, which exploit anisotropy to obtain important physico-chemical information on several categories of systems, including pharmaceuticals, inorganic materials, polymers, liquid crystals, and self-assembling amphiphiles in water. Solid-state NMR spectroscopy can be considered, nowadays, one of the most powerful characterization techniques for all kinds of solid, either amorphous or crystalline, and semi-solid systems for the obtainment of both structural and dynamic properties on a molecular and supra-molecular scale. Graphic abstract: [Figure not available: see fulltext.

Effect of phosphate additives on the hydration process of magnesium silicate cements: Thermal and spectroscopic characterization

The role of phosphate additives on the hydration process of magnesium silicate cement pastes was investigated through a multi-technique approach. A MgO/SiO2 mixture was hydrated for 28 days either in the absence or in the presence of sodium hexametaphosphate, trimetaphosphate or orthophosphate. Information on the kinetics of the hydration reaction was acquired by monitoring the free water index by means of differential scanning calorimetry, while the hydration products were thoroughly investigated by X-ray diffraction, thermogravimetric analysis, Fourier transform infrared spectroscopy, scanning electron microscopy and 29Si solid-state nuclear magnetic resonance spectroscopy. The overall results provide new insight into the effect of phosphates on the hydration reaction and on the structure of magnesium silicate hydrate cements. All additives showed a plasticizing effect and promoted the formation of the binding phase magnesium silicate hydrate (M–S–H), without significantly altering its structure. Sodium orthophosphate was found to be by far the best-performing additive, even better than sodium hexametaphosphate, which is commonly used in these cementitious formulations. For the first time, 31P solid-state NMR investigation allowed orthophosphate ion to be identified as the effective species

Titanium-Based Tetrakis-2,3-[5,6-di(Substituted)pyrazino]porphyrazine: Synthesis and Characterization

Tetrapyrazinoporphyrazine (TPysPz) ligands and metal complexes find, generally, application as electronic materials and catalysts. Considering the limited application of Titanium (Ti), we prepared and characterized a family of ligands and Ti-based complexes of tetrakis-2,3-[5,6-di-R8-pyrazino]porphyrazine (R = H, 2-Py, Ph). UV/Vis measurements in different solvents confirm molecular aggregation, which results more pronounced in the presence of 2-pyridil and phenyl substituents on the macrocycle edge. Because of low solubility, solid state NMR was applied for structure characterization. Additional IR and MALDI-TOF were carried out to complete the characterization. Cyclic voltammetry in DMSO/Bu4NBF4 0.1 m unveiled that our Ti complexes can take part in up to five redox events. The first two quasi-reversible reductions involve Ti(IV), whereas the further to or three occur at the expense of the TPysPz macrocycle. To test the applicability of our compounds as catalytic materials, we performed a preliminary cyclic voltammetry investigation in the solid-state, which showed typical peaks of hydrogen redox reactions

Modification of Amorphous Mesoporous Zirconia Nanoparticles with Bisphosphonic Acids: A Straightforward Approach for Tailoring the Surface Properties of the Nanoparticles

The use of readily prepared bisphosphonic acids obtained in few steps through a thio-Michael addition of commercially available thiols on tetraethyl vinylidenebisphosphonate enables the straightforward surface modification of amorphous mesoporous zirconia nanoparticles. Simple stirring of the zirconia nanoparticles in a buffered aqueous solution of the proper bisphosphonic acid leads to the surface functionalization of the nanoparticles with different kinds of functional groups, charge and hydrophobic properties. Formation of both chemisorbed and physisorbed layers of the bisphosphonic acid take place, observing after extensive washing a grafting density of 1.1 molecules/nm2 with negligible release in neutral or acidic pH conditions, demonstrating stronger loading compared to monophosphonate derivatives. The modified nanoparticles were characterized by IR, XPS, ζ-potential analysis to investigate the loading of the bisphosphonic acid, FE-SEM to investigate the size and morphologies of the nanoparticles and 31P and 1H MAS NMR to investigate the coordination motif of the phosphonate units on the surface. All these analytical techniques demonstrated the strong affinity of the bisphosphonic moiety for the Zr(IV) metal centers. The functionalization with bisphosphonic acids represents a straightforward covalent approach for tailoring the superficial properties of zirconia nanoparticles, much straightforward compared the classic use of trisalkoxysilane or trichlorosilane reagents typically employed for the functionalization of silica and metal oxide nanoparticles. Extension of the use of bisphosphonates to other metal oxide nanoparticles is advisable

The SPORT-NMR software: A tool for determining relaxation times in unresolved NMR spectra

A software package which allows the correct determination of individual relaxation times for all the nonequivalent nuclei in poorly resolved NMR spectra is described. The procedure used, based on the fitting of each spectrum in the series recorded in the relaxation experiment, should improve the analysis of relaxation data in terms of quantitative dynamic information, especially in anisotropic phases. Tests on simulated data and experimental examples concerning 1H and 13C T1 measurement in a solid copolymer and 2H T1Z and T1Q measurement in a liquid crystal are shown and discussed