Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

Stability of Zernike coefficients solved by the covariance matrix method in the analysis of the wave front aberration

The deduction of Zernike coefficients is usually influenced by the finite number of sampling dots on interferogram and their inherited measurement errors. In this paper, a simplified Gram-Schmidt method for solving the Zernike polynomial with the higher fitting precision is presented and used to analyze the wave front aberrations for the circle interference fringe of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We find the stability of the Zernike coefficients changes with changing the Zernike term, which has lead to the wrong expression for the wave front aberration. By analyzing the condition number of the coefficients matrix and the fitting precision of the method, it is indicated that the instability can be avoided when the Zernike term is lower than 14. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis in optical testing.     

Application of High-Resolution NMR Spectroscopy in Analyzing Ionites

The ¹H and ¹³C NMR spectra of granulated carboxylic cationite MAC-3 and fibrous anionites FIBAN (A-5, A-7, and A-9) have been investigated. The dependence of the chemical shifts and times of spin–spin relaxation of the water protons and carbon nuclei of MAC-3 on the water content in a sample has been investigated. A comparison of the carbon spectra of polyelectolytes and FIBAN fibrous anionites swollen in water has been made. It is shown that the carbon spectra of the ionites swollen in water represent fairly narrow lines practically for all groups of the skeleton, and therefore the structure of the ionites can be analyzed using a high-resolution NMR.     

On-line coupling of high temperature GPC and 1H NMR for the analysis of polymers

The on-line coupling of gel permeation chromatography (GPC) and 1H NMR operating at temperatures up to 130 degrees C is presented. A NMR flow probe with a cell volume of 120 microL and a stop-flow valve are developed for on-flow and stop-flow NMR measurements at high temperatures. To maintain high and constant temperatures through the whole probe, the flow probe contains two separate heating circuits. A modified stop-flow valve is developed as a control device for enabling on-flow and stop-flow experiments at high temperature conditions. Heated transfer lines connect the flow probe with the high temperature GPC system. Due to their semicrystalline nature, polyolefins can be studied by liquid chromatography only at temperatures above 100 degrees C. The novel high temperature GPC-NMR system is used for the separation of complex polyolefins regarding their molar mass and for the analysis of different chemical structures. Blends of polyethylene, poly(methyl methacrylate), and ethylene-methyl methacrylate copolymers are separated according to the molar masses of the components. The compositions of the components are directly studied by on-line NMR. Moreover, the chemical composition distribution of an ethylene-methyl methacrylate copolymer sample is analysed. Differences between results of on-flow and stop-flow measurements are discussed.     

Measurement of dipolar couplings in partially oriented molecules by local field NMR spectroscopy with low-power decoupling

Low-power phase-modulated Lee–Goldburg homonuclear decoupling was used to record PDLF spectra of fluorine-substituted benzene derivatives dissolved in nematic thermotropic liquid crystalline solvents. The low-power decoupling minimizes sample heating during RF irradiation while still achieving highly resolved PDLF spectra. The method is illustrated by recording spectra for 1,3-dichloro-4-fluoro-5-nitrobenzene, 1,3-dichloro-4-fluorobenzene, and 1,2-difluorobenzene dissolved in different nematic solvents.     

Measurement of J-couplings between spin-(1/2) and quadrupolar nuclei by frequency selective solid-state NMR

We report a REDOR-based scheme for the measurement of heteronuclear J-couplings in solid samples with well defined structure, containing spin-12 and quadrupolar nuclei, which can be used with selective RF irradiation to target a specific spin pair, and which provides direct information about the number of coupled spins.     

Implications of using approximate Bloch-McConnell equations in NMR analyses of chemically exchanging systems: application to the electron self-exchange of plastocyanin

The validity of a series of approximate solutions of the Bloch-McConnell equations normally applied in the analyses of chemically exchanging systems is evaluated, using the electron self-exchange (ESE) in the blue copper protein plastocyanin from Anabaena variabilis as an example. The evaluation is based on a comparison with the results of a complete analysis of the NMR signals of chemically exchanging nuclei that allows an independent and accurate determination of all the involved parameters. The complete analysis is based on the general solution of the Bloch-McConnell equations. It includes a simultaneous analysis of the chemical shift, and the transverse and longitudinal relaxation rates of the observed nuclei as well as the variation of these parameters with the molar fractions of the exchanging species and the rate of the chemical exchange process. The linear prediction model method was used in the data analysis to achieve the highest possible precision. Surprisingly, it is found that the fast exchange condition may not be fulfilled even in cases where a single exchange-averaged NMR signal is observed, and the Larmor frequency and relaxation rates depend linearly on the molar fractions of the exchanging species. In such cases the use of approximate solutions in the analysis of the transverse relaxation rates and the pseudo-contact shifts can lead to erroneous results. In limiting cases close to the fast exchange and slow exchange regimes correct values of some of the parameters can be obtained using the second order approximate solution of the Bloch-McConnell equations. In contrast, the complete analysis of the NMR signals results in an accurate determination of the exchange rates and the NMR parameters of the exchanging sites. This, in turn, can provide information about the structure and function of a protein undergoing chemically exchange. For the investigated plastocyanin the complete analysis results in an accurate determination of the paramagnetic enhancement of the nuclear relaxation rates, the paramagnetic chemical shift, the electron relaxation rate, the electron self-exchange rate, and the distances between the nuclei and the paramagnetic metal ion, viz. the Cu2+ ion.     

An investigation of the structure and bond rotational potential of some fluorinated ethanes by NMR spectroscopy of solutions in nematic liquid crystalline solvents

NMR spectra of 1,2-dibromo-1,1-difluoroethane and 1-bromo-2-iodo-tetrafluoroethane dissolved in nematic liquid crystalline solvents have been analysed to yield the magnitudes and signs of the scalar couplings, J(ij), and total anisotropic couplings, T(ij), between all the (1)H, (19)F, and (13)C nuclei, except for those between two (13)C nuclei. The values obtained for T(ij) in principle contain a contribution from J(ij)(aniso), the component along the static applied magnetic field of the anisotropic part of the electron-mediated spin-spin coupling. Neglecting this contribution allows partially averaged dipolar couplings, D(ij), to be extracted from the T(ij), and these were used to determine the structure, orientational order, and the conformational distribution generated by rotation about the C-C bond. The values obtained are compared with the results of calculations by ab initio and density functional methods. The differences found are no greater than those obtained for similar compounds which do not contain fluorine, so that there is no definitive evidence for significant contributions from J(CF)(aniso) or J(FF)(aniso) in the two compounds studied.     

An analysis of the size distribution of Italian firms by age

In this paper we analyze the size distribution of Italian firms by age. In other words, we want to establish whether the way that the size of firms is distributed varies as firms become old. As a proxy of size we use capital. In [L.M.B. Cabral, J. Mata, On the evolution of the firm size distribution: Facts and theory, American Economic Review 93 (2003) 1075–1090], the authors study the distribution of Portuguese firms and they find out that, while the size distribution of all firms is fairly stable over time, the distributions of firms by age groups are appreciably different. In particular, as the age of the firms increases, their size distribution on the log scale shifts to the right, the left tails becomes thinner and the right tail thicker, with a clear decrease of the skewness. In this paper, we perform a similar analysis with Italian firms using the CEBI database, also considering firms’ growth rates. Although there are several papers dealing with Italian firms and their size distribution, to our knowledge a similar study concerning size and age has not been performed yet for Italy, especially with such a big panel.     

Theoretical and experimental investigation of (13)C relayed (2)H-(2)H-COSY 2D experiments: application to the analysis of weakly aligned solutes

We describe new NMR 2D experiments denoted DECADENCY for DEuterium CArbon DEuterium Nuclear Correlation spectroscopY dedicated to the analysis of anisotropic deuterium spectra. They belong to the class of X-relayed Y,Y-COSY 2D experiments that was initially explored in the case of a (1)H-X-(1)H fragment (I(X)=1/2) in isotropic medium. DECADENCY 2D experiments permit to correlate the quadrupolar doublets associated with two inequivalent deuterium nuclei in an oriented CD(2) fragment through heteronuclear polarization transfers. Two kinds of pulse sequences are described here using either a double INEPT-type or DEPT-type process. DECADENCY 2D experiments provide an interesting alternative to (2)H-(2)H COSY experiments when the geminal (2)H-(2)H total coupling (scalar and dipolar) is null or too small to provide visible cross-correlation peaks. Such a situation is typically observed for geminal deuteriums in prochiral or chiral molecules dissolved in chiral liquid crystals. The efficiency of these techniques is illustrated using dideuterated prochiral molecules, the phenyl[(2)H(2)]methanol and the 1-chloro[1-(2)H(2)]nonane, both dissolved in organic solutions of poly-gamma-benzyl-l-glutamate. The advantages of each sequence are presented and discussed. It is shown that the relative sign of the quadrupolar doublets can be determined.     

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

Concerted double proton transfer in the hydrogen bonds of a carboxylic acid dimer has been studied using 13C field-cycling NMR relaxometry. Heteronuclear 13C-1H dipolar interactions dominate the 13C spin-lattice relaxation which is significantly influenced by the polarisation state of the 1H Zeeman reservoir. The methodology of field-cycling experiments for such heteronuclear spin-coupled systems is studied experimentally and theoretically, including an investigation of various saturation-recovery and polarisation-recovery pulse sequence schemes. A theoretical model of the spin-lattice relaxation of this coupled system is presented which is corroborated by experiment. Spectral density components with frequencies omega(C), omega(C) + omega(H), and omega(C) - omega(H) are mapped out experimentally from the magnetic field dependence of the 13C and 1H spin-lattice relaxation and the proton transfer rate at low temperature is determined from their widths. Any dynamic isotope effect on the proton tunnelling in the hydrogen bond arising from 13C enrichment in the skeletal framework of the dimer is found to be smaller than experimental uncertainties (approximately 5%).     

Analysis of the mechanism of photolysis of acetylpropionyl peroxide in acetone-d<Subscript>6</Subscript> by the NMR pectroscopy data

The photolysis of acetylpropionyl peroxide solutions in acetone at different temperatures has been investigated by the NMR method with consideration for the effects of chemical polarization of nuclei and the yields of the photolysis products. Acetylpropionyl peroxide decomposes when it is found in the binding or loosening triplet electron states. In the process of photolysis, acetone not only serves as the triplet sensitizer, but also effectively homologizes with the formation of methyl and acetyl radicals; however, it practically does not participate in the photoreduction.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 732–739, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials

A systematic and intuitive approach for the separation of variables of the three-dimensional Dirac equation in spherical coordinates is presented. Using this approach, we consider coupling of the Dirac spinor to electromagnetic four-vector potential that satisfies the Lorentz gauge. The space components of the potential have angular (non-central) dependence such that the Dirac equation becomes separable in all coordinates. We obtain exact solutions for a class of three-parameter static electromagnetic potential whose time component is the Coulomb potential. The relativistic energy spectrum and corresponding spinor wave functions are obtained. The Aharonov–Bohm and magnetic monopole potentials are included in these solutions.     

Improved quantification of alite and belite in anhydrous Portland cements by Si MAS NMR: Effects of paramagnetic ions

The applicability, reliability, and repeatability of ²⁹Si MAS NMR for determination of the quantities of alite (Ca₃SiO₅) and belite (Ca₂SiO₄) in anhydrous Portland cement was investigated in detail for 11 commercial Portland cements and the results compared with phase quantifications based on powder X-ray diffraction combined with Rietveld analysis and with Taylor–Bogue calculations. The effects from paramagnetic ions (Fe³⁺) on the spinning sideband intensities, originating from dipolar couplings between ²⁹Si and the spins of the paramagnetic electrons, were considered and analyzed in spectra recorded at four magnetic fields (4.7–14.1 T) and this has led to an improved quantification of alite and belite from ²⁹Si MAS NMR spectra recorded at “high” spinning speeds of ν_R=12.0–13.0 kHz using 4 or 5 mm rotors. Furthermore, the impact of Fe³⁺ ions on the spin-lattice relaxation was studied by inversion-recovery experiments and it was found that the relaxation is overwhelmingly dominated by the Fe³⁺ ions incorporated as guest-ions in alite and belite rather than the Fe³⁺ sites present in the intimately mixed ferrite phase (Ca₂Al_xFe_2−xO₅).     

Double quantum transition as the origin of the central dip in the z-spectrum of HDO in variably stretched gel

The ²H NMR spectrum of HDO in gelatin gel, that is stretched inside silicone rubber tubing, displays a well resolved doublet. Spectra were obtained with a range of offset frequencies of partially saturating radio-frequency (RF) radiation. The resulting steady-state irradiation envelope (also referred to as a ‘z-spectrum’) has the peculiar feature that maximal suppression of the doublet occurs when the irradiation is applied exactly at the centre frequency, between the two HDO peaks. We present a quantum mechanical explanation for this phenomenon. It is shown that the phenomenon is the result of double quantum transitions. The analysis is extendable to more complex quadrupolar and dipolar-coupled systems of other nuclides. It has implications for enhancement of contrast in magnetic resonance imaging of heterogeneous systems using dipolar and quadrupolar interactions.