Solid-state 13C and 1H spin diffusion NMR analyses of the microfibril structure for bacterial cellulose

To obtain further information about the cause for the rather large splitting of the C4 resonance line into the downfield (C4D) and upfield (C4U) lines in CP/MAS ¹³C NMR spectra for native cellulose, ¹³C and ¹H spin diffusion measurements have been conducted by using different types of bacterial cellulose samples. In ¹³C spin diffusion measurements, the C4D resonance line is selectively inverted by the Dante π pulse sequence and the ¹³C spin diffusion is allowed to proceed from the C4D carbons to other carbons including the C4U carbons with use of the ¹³C4-enriched bacterial cellulose sample. The analysis based on the simple spin diffusion theory for the process experimentally observed reveals that the C4U carbons may be located at distances less than about 1 nm from the C4D carbons. In ¹H spin diffusion measurements, poly(vinyl alcohol) (PVA) films in which ribbon assemblies of bacterial cellulose are dispersed are employed and the ¹H spin diffusion process is examined from the water-swollen PVA continuous phase to the dispersed ribbon assemblies by the ¹³C detection through the ¹H–¹³C CP technique. As a result, it is found that the C4D and C4U carbons are almost equally subjected to the ¹H spin diffusion from the PVA phase, indicating that the C4U carbons are not localized in some limited area, e.g. in the surfacial region, but are distributed in the whole area in the microfibrils. These experimental results suggest that the C4U carbons may exist as structural defects probably due to conformational irregularity associated with disordered hydrogen bonding of the CH₂OH groups in the microfibrils.     

Apparent diffusion behaviour of intermolecular double-quantum coherence modulated by a distant dipolar field in solution NMR

A modified correlated spectroscopy (COSY) revamped with asymmetric Z-gradient echo detection sequence was designed to investigate the influence of diffusion behaviour on intermolecular double-quantum coherence signal attenuation during the pre-acquisition period. Theoretical formulas were deduced and experimental measurements and simulations were performed. It is found that the diffusion behaviour of intermolecular double-quantum coherence in the pre-acquisition period may be different from that of conventional single-quantum coherence, depending on the relative orientation of diffusion weighting gradients to coherence selection gradients. When the orientation of the diffusion weighting gradients is parallel or anti-parallel to the orientation of the coherence selection gradients, the diffusion is modulated by the distant dipolar field. This study is helpful for understanding the signal properties in intermolecular double-quantum coherence magnetic resonance imaging.     

Apparent diffusion behaviors of spins in the presence of distant dipolar field in two-component solution NMR

The diffusion behaviors of spins in the presence of distant dipolar field in two-component spin systems during the second evolution period of a modified CRAZED sequence before acquisition were investigated. Theoretical formulas were deduced based on the distant dipolar field model. The simulation results and experimental observations are consistent with the theoretical predictions. This study shows that the relative intensities of signals from intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) have the same diffusion attenuation characteristic under the combined effect of diffusion weighting gradients and distant dipolar field during the second evolution period. This diffusion attenuation may be different from that of conventional single-quantum coherence signal, depending on the relative orientation of the diffusion weighting gradients to the coherence selection gradients. The results presented herein are helpful for understanding the effect of distant dipolar field from a spin system on the diffusion behavior of other spin system and the signal properties in the iZQC or iDQC magnetic resonance imaging.     

Correction of spin diffusion during iterative automated NOE assignment

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus beta-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.     

Photon energy dependence of the spin polarization

Spin polarization in semiconductors was investigated by pump-probe measurements, where the transmissions of the samples were monitored with probe pulses with same and opposite circular polarizations. The spin polarization as a function of the pump-probe delay was estimated, and the polarization was found to decay in a sub-ns timescale. It was also found that the polarization depends strongly on photon energy of the pump beam. The pumping energy dependence of the spin polarization was discussed based on the inter-band transition probabilities.     

Spin diffusion and nuclear spin-lattice relaxation in irradiated solids: a multiple-pulse NQR study

We present a detailed theoretical and experimental NQR multiple-pulse spin-locking study of spin-lattice relaxation and spin diffusion processes in the presence of paramagnetic impurities in solids. The relaxation function of the nuclear spin system at the beginning of the relaxation process is given by exp , where T_1ρ is spin-lattice relaxation time in rotating frame and =d/6, d is the sample dimensionality. Then the relaxation proceeds asymptotically to an exponential function of time, which was attributed to the spin-diffusion regime. Using the experimental data obtained from the analysis of those two relaxation regimes in γ-irradiated powdered NaClO₃, spin diffusion coefficient has been determined and the radius of the diffusion barrier has been estimated.     

Multi-scale NMR characterisation of mesostructured materials using 1H-->13C through-bond polarisation transfer,fast MAS,and 1H spin diffusion

A NMR method for the characterisation of materials at different length scales, robust and simple to implement, is presented. It combines selection of 1H-13C pairs by a through-bond polarisation transfer (INEPT here) and exploration of larger distances by the introduction of 1H spin diffusion. This characterisation method is well adapted to the highest MAS rates and takes benefits of it. The effect of 1H dephasing on the efficiency of the 1H-->13C through-bond polarisation transfer is determined. This allows consecutively the quantification of signals. Mesostructured spherical silica-based particles containing CTA+ cations were studied by this multi-scale characterisation method. Contrasted spin diffusion curves were found and qualitatively explained by differences in terms of mobility and spatial distributions.     

Proton NMR T 1 Studies in Methylammonium TrichlorO Stannate(II) (CH 3 NH 3 SnCl 3 )

Proton spin lattice relaxation time ( T 1 ) measurements have been carried out in methylammonium trichloro stannate(II) (CH 3 NH 3 SnCl 3 ) as a function of temperature in the range 317-5 K at a Larmor frequency of 10 MHz. The temperature dependence of T 1 shows a phase transition around 220 K and four T 1 minima (294 K, 62 K, 32 K and 12 K). The results are discussed in terms of proton dynamics, namely, uncorrelated reorientation of NH 3 and CH 3 groups at high temperatures and tunnelling of NH 3 and CH 3 protons at low temperatures.     

13C NMR Studies on 3-Aryl-4-Cyanosydnones (II). NMR Spectroscopy and the Chain-Conjugated Structure of Sydnones

Carbon-13 NMR spectra of 3-aryl-4-cyanosydnones have been analyzed to serve as an electronic structure probe of sydnones. 2-Dimensional INADEQUATE experiments and spin-lattice relaxation time measurements were employed to ascertain exact assignments. Deshielding of the phenyl carbon para to the sydnone ring manifests that N(3) bears positive charge. The electronic-rich property of C(4) is confirmed by shift data of cyano carbons, which have been found by far the most shielded cyano carbons in nitrile-containing compounds yet reported. Shift variations of C(5) resulting from the substitution at C(4) and supplementary oxygen-17 chemical shift data provide evidence in favor of the chain-conjugated structure.     

Versatility of the dipolar filter selection: from 1H nuclear spin diffusion experiment to the measurement of nuclear Overhauser effect in homopolymer melts

Dipolar filters select ¹H magnetization according to local dipolar dephasing, which corresponds to site mobility in systems with heterogeneous molecular mobility. Combined with a conventional exchange experiment, it is usually applied to polymeric samples exhibiting structures on the nanometer length scale associated with a strong dynamic contrast. There, the resulting ¹H nuclear spin diffusion experiment yields the size of the structure. When the same experiment is applied to homopolymer melts exhibiting a weak dynamic contrast and dynamic heterogeneities on significant shorter length scales, the recorded magnetization decay is in agreement with decays expected from a heterogeneous nanostructure. However, dipolar filters actually can also select mobile parts of the repeat unit, e.g. the end of the alkyl side chains and the subsequent magnetization transfer then can occur via cross relaxation due to non coherent zero-quantum transitions (nuclear Overhauser effect, NOE). The difficulties of distinguishing these two cases are examined and it is demonstrated that NOE experiments exploiting magnetization selection via the dipolar filter allow quantifying the local dynamics of the side chains. This opens new possibilities for measurements of local dynamics in non isotopically labeled homopolymer melts.     

Correlations between electronic energy bands spin splitting and magnetic profile symmetry of magnetic superlattice

We have theoretically investigated the energy band structures of two typical magnetic superlattices formed by perpendicular or parallel magnetization ferromagnetic stripes periodically deposited on a two-dimensional electron gas (2DEG), where the magnetic profile in the perpendicular magnetization is of inversion anti-symmetry, but of inversion symmetry in parallel magnetization, respectively. We have shown that the energy bands of perpendicular magnetization display the spin-splitting and transverse wave-vector symmetry, while the energy bands of the parallel magnetization exhibit spin degeneration and transverse wave-vector asymmetry. These distinguishing spin-dependent and transverse wave-vector asymmetry features are essential for future spintronics devices applications.     

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.     

Spin-orbit torques induced by spin Hall and spin swapping currents of a separate ferromagnet in a magnetic trilayer

Spin-orbit torques (SOTs) have been investigated most widely in normal metal/ferromagnet bilayers where the spin Hall effect of normal metal is a main source of spin currents. Recently, ferromagnets are found to also serve as spin-current sources through spin-orbit coupling. In this work, we theoretically investigate SOT acting on ferromagnet₂ in ferromagnet₁/normal metal/ferromagnet₂ trilayers, which is caused by the spin Hall and spin swapping effects of ferromagnet₁. Our result provides an analytical expression of SOT in the trilayers, which may be useful for quantifying the spin Hall and spin swapping effects of ferromagnets and also for designing and interpreting SOT experiments where a ferromagnet is used as a spin-current source instead of a normal metal.     

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in one-dimensional hard-point model. For diatom model, we find an anomalous energy diffusion as $\langle x^2 \rangle\sim t^\beta$ with $\beta=1.33$, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be $\alpha=0.33$, which is confirmed by a simple numerical calculation.     

Long-lived nuclear spin states in the solution NMR of four-spin systems

The existence of long-lived nuclear spin states in four-spin systems is explored by solution-state NMR experiments. Long-lived states are proved to exist in three different natural product molecules, each containing either a AA'BB' or a AA'XX' proton spin system. The measured state lifetimes are between four and eight times the spin-lattice relaxation time constants.     

Assessing the quantitative reliability of solid-state 13C NMR spectra of kerogens across a gradient of thermal maturity

Five type II kerogens, shown by elemental analysis and Rock-Eval pyrolysis to represent a gradient of thermal maturity, were further characterized using a range of solid-state ¹³C NMR spectroscopic techniques. ¹³C cross polarization (CP) NMR spectra of the kerogens confirmed the well-established pattern of increasing aromaticity with increasing thermal maturity. Spin counting showed that CP observability was around 50% for the immature kerogens, and only 14–25% for the mature kerogens. Spin counting also showed that the direct polarization (DP) observabilities were >80% for all but one of the kerogens. Despite the large differences in observability between the two techniques, aromaticities derived from corresponding CP and DP spectra differed by only 1–15%. The RESTORE technique showed that the low CP observability of the immature kerogens was due mostly to rapid T_1ρH relaxation, whereas both rapid T_1ρH relaxation and slow polarization transfer contributed to the low CP observability of the mature kerogens.     

The Ising spin glass in finite dimensions: A perturbative study of the free energy

Replica field theory is used to study the n  -dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian, independently of the special structure of the order parameter. The free energy difference between the replica symmetric and (infinite level) replica symmetry broken phases is studied in details: the line n(T)$n(T)$ where it is zero coincides with the Almeida–Thouless line for d>8$d>8$. The dimensional domain 6<d<8$6<d<8$ is more complicated, and several scenarios are possible.     

Separation and characterization of different signals from intermolecular three-spin orders in solution NMR

In this paper, signals originating from a pure specific coherence of intermolecular three-spin orders were separated and characterized experimentally in highly polarized two-component spin systems. A modified CRAZED sequence with selective radio-frequency excitation was designed to separate the small signals from the strong conventional single-spin single-quantum signals. General theoretical expressions of the pulse sequence with arbitrary flip angle pulses were derived using dipolar field treatment. The expressions were used to predict the relaxation and diffusion properties and optimal experimental parameters such as flip angles. For the first time, relaxation and diffusion properties of pure intermolecular single-quantum, double-quantum, and triple-quantum coherences of three-spin orders were characterized and analyzed in one-dimensional experiments. All experimental observations are in excellent agreement with the theoretical predictions. The theoretical results show that the quantum-mechanical treatment leads to exactly the same predictions as the dipolar field treatment. The quantitative study of intermolecular multiple-quantum coherences of three-spin orders presented herein provides a better understanding of their mechanisms.