Progress in spin dynamics solid-state nuclear magnetic resonance with the application of Floquet–Magnus expansion to chemical shift anisotropy

The purpose of this article is to present an historical overview of theoretical approaches used for describing spin dynamics under static or rotating experiments in solid state nuclear magnetic resonance. The article gives a brief historical overview for major theories in nuclear magnetic resonance and the promising theories. We present the first application of Floquet–Magnus expansion to chemical shift anisotropy when irradiated by BABA pulse sequence.     

Heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance under ultra-high magic-angle spinning

We compare in this communication several heteronuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance experiments under a magic-angle spinning frequency of 60 kHz. The decoupling radiofrequency field amplitudes considered are 190 and 10 kHz. No substantial difference was found among the sequences considered here in performance barring the difference in the optimisation protocol of the various schemes, an aspect that favours the use of swept-frequency two pulse phase modulation (SW(f)-TPPM).     

Applications of Floquet–Magnus expansion,average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence

This work presents the possibility of applying the Floquet–Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented.     

A theoretical perspective on the accuracy of rotational resonance (R 2)-based distance measurements in solid-state NMR

The application of solid-state NMR methodology for bio-molecular structure determination requires the measurement of constraints in the form of ¹³C–¹³C and ¹³C–¹⁵N distances, torsion angles and, in some cases, correlation of the anisotropic interactions. Since the availability of structurally important constraints in the solid state is limited due to lack of sufficient spectral resolution, the accuracy of the measured constraints become vital in studies relating the three-dimensional structure of proteins to its biological functions. Consequently, the theoretical methods employed to quantify the experimental data become important. To accentuate this aspect, we re-examine analytical two-spin models currently employed in the estimation of ¹³C–¹³C distances based on the rotational resonance (R ²) phenomenon. Although the error bars for the estimated distances tend to be in the range 0.5–1.0 Å, R ² experiments are routinely employed in a variety of systems ranging from simple peptides to more complex amyloidogenic proteins. In this article we address this aspect by highlighting the systematic errors introduced by analytical models employing phenomenological damping terms to describe multi-spin effects. Specifically, the spin dynamics in R ² experiments is described using Floquet theory employing two different operator formalisms. The systematic errors introduced by the phenomenological damping terms and their limitations are elucidated in two analytical models and analysed by comparing the results with rigorous numerical simulations.     

Experimental aspect of solid-state nuclear magnetic resonance studies of biomaterials such as bones

Solid-state nuclear magnetic resonance (SSNMR) spectroscopy is increasingly becoming a popular technique to probe micro-structural details of biomaterial such as bone with pico-meter resolution. Due to high-resolution structural details probed by SSNMR methods, handling of bone samples and experimental protocol are very crucial aspects of study. We present here first report of the effect of various experimental protocols and handling methods of bone samples on measured SSNMR parameters. Various popular SSNMR experiments were performed on intact cortical bone sample collected from fresh animal, immediately after removal from animal systems, and results were compared with bone samples preserved in different conditions. We find that the best experimental conditions for SSNMR parameters of bones correspond to preservation at −20 °C and in 70% ethanol solution. Various other SSNMR parameters were compared corresponding to different experimental conditions. Our study has helped in finding best experimental protocol for SSNMR studies of bone. This study will be of further help in the application of SSNMR studies on large bone disease related animal model systems for statistically significant results.     

Characterization of polyalkylvinyl ether phases by solid-state and suspended-state nuclear magnetic resonance investigations

Pure organic polyalkylvinyl ether phases were synthesized by suspension polymerization using different ratios and compositions of n-butylvinyl ether (C₄VE) and n-octadecylvinyl ether (C₁₈VE) with triethylene glycol divinyl ether or divinylbenzene as crosslinkers, respectively. These phases were investigated by means of solid-state ¹³C cross-polarization magic angle spinning nuclear magnetic resonance (NMR) spectroscopy and ¹H high-resolution magic angle spinning (HR MAS) NMR spectroscopy in suspended-state. A comparison of these two methods showed the substantial advantages of ¹H HR MAS NMR measurements. Structure elucidation was achieved using a 2D H,H-COSY NMR experiment performed under MAS conditions enabling full peak assignment of the ¹H NMR spectra of these phases. The dynamic behavior of the polyalkylvinyl ether phases was determined by employing temperature-dependent measurements of spin–lattice relaxation times (T₁) as well as accumulation of a 2D wide line separation NMR spectrum.     

Dynamic H nuclear magnetic resonance of rotating solids

The sensitivity of one-dimensional dynamic magic-angle spinning (MAS) and off-MAS ²H nuclear magnetic resonance spectra to changes in the parameters of jump-type molecular motions is studied. The Floquet theory approach is used to simulate spectra of spins with I = 1, which are involved in exchange processes in rotating solids. The solution of the Bloch-McConnell equations for rotating samples are derived and some simulated frequency spectra are shown. The dependence of the lineshapes of the center and sidebands of the MAS and off-MAS spectra on the exchange parameters are discussed. Experimental results of ²H spectra of perdeuterated dimethyl sulfone, obtained in the temperature range 20–55 °C, are demonstrated. The methyl groups in this molecule undergo π flips at rates that can be detected by MAS and off-MAS NMR. The shapes of the experimental sidebands are compared with simulated results.     

Analytical theory of gamma-encoded double-quantum recoupling sequences in solid-state nuclear magnetic resonance

Many important double-quantum recoupling techniques in solid-state NMR are classified as being gamma-encoded. This means that the phase of the double-quantum effective Hamiltonian, but not its amplitude, depends on the third Euler angle defining the orientation of the molecular spin system in the frame of the magic-angle-spinning rotor. In this paper, we provide closed analytical solutions for the dependence of the powder-average double-quantum-filtered signal on the recoupling times, within the average Hamiltonian approximation for gamma-encoded pulse sequences. The validity of the analytical solutions is tested by numerical simulations. The internuclear distance in a (13)C(2)-labelled retinal is estimated by fitting the analytical curves to experimental double-quantum data.     

An analysis of phase-modulated heteronuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance

The design of variants of the swept-frequency two-pulse phase modulation sequence for heteronuclear dipolar decoupling in solid-state NMR is reported, their performance evaluated, and compared with other established sequences like TPPM and SPINAL. Simulations performed to probe the role of the homonuclear (1)H-(1)H bath show that the robustness of the decoupling schemes improves with the size of the bath. In addition, these simulations reveal that the homonuclear (1)H-(1)H bath also leads to broad baselines at high MAS rates. Results from a study of the SPINAL decoupling scheme indicate that optimisation of the starting phase and phase increment improves its performance and efficiency at high MAS rates. Additionally, experiments performed on a liquid crystal display the role of the initial phase in SPINAL-64 and sequences in the SW(f)-TPPM family.     

170 nm nuclear magnetic resonance imaging using magnetic resonance force microscopy

We demonstrate one-dimensional nuclear magnetic resonance imaging of the semiconductor GaAs with 170 nm slice separation and resolve two regions of reduced nuclear spin polarization density separated by only 500 nm. This was achieved by force detection of the magnetic resonance, magnetic resonance force microscopy (MRFM), in combination with optical pumping to increase the nuclear spin polarization. Optical pumping of the GaAs created spin polarization up to 12 times larger than the thermal nuclear spin polarization at 5K and 4T. The experiment was sensitive to sample volumes of 50 microm(3) containing approximately 4 x 10(11)71 Ga/Hz. These results demonstrate the ability of force-detected magnetic resonance to apply magnetic resonance imaging to semiconductor devices and other nanostructures.     

Supercycled SW(f)-TPPM sequence for heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance

The performance of a supercycled SW(f)-TPPM sequence for heteronuclear dipolar decoupling in solid-state NMR is analyzed here. The decoupling performance of this sequence with respect to experimental parameters, such as, the phase angle, proton offset and MAS frequency is studied. A comparison is made with two other commonly used decoupling schemes in solid-state NMR namely, SPINAL-64 and SW(f)-TPPM, on a sample of U-13C-labeled tyrosine. Our results show that supercycled SW(f)-TPPM performs better than the former sequences. Also, numerical spin dynamics studies are presented which support the experimentally observed efficiency in the decoupling.     

Crossed-coil detection of two-photon excited nuclear quadrupole resonance

Applying a recently developed theoretical framework for determining two-photon excitation Hamiltonians using average Hamiltonian theory, we calculate the excitation produced by half-resonant irradiation of the pure quadrupole resonance of a spin-3/2 system. This formalism provides expressions for the single-quantum and double-quantum mutation frequencies as well as the Bloch-Siegert shift. The dependence of the excitation strength on RF field orientation and the appearance of the free-induction signal along an axis perpendicular to the excitation field provide an unmistakable signature of two-photon excitation. We demonstrate single- and double-quantum excitation in an axially symmetric system using 35Cl in a single crystal of potassium chlorate (omega(Q) = 28 MHz) with crossed-coil detection. A rotation plot verifies the orientation dependence of the two-photon excitation, and double-quantum coherences are observed directly with the application of a static external magnetic field.     

Period-doubling bifurcation in two-stage power factor correction converters using the method of incremental harmonic balance and Floquet theory

In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated post-regulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.     

Why does PMLG proton decoupling work at 65 kHz MAS?

Schemes such as phase-modulated Lee–Goldburg (PMLG) for homonuclear dipolar decoupling have been shown to yield high-resolution ¹H spectra at high magic-angle spinning (MAS) frequencies of 50–70 kHz. This is at variance to the commonly held notion that these methods require MAS frequencies not comparable to the cycle frequencies of the pulse schemes. Here, a theoretical argument, based on bimodal Floquet theory, is presented to explain this aspect together with conditions where PMLG type of schemes may be successful at high MAS frequencies.     

Criteria to average out the chemical shift anisotropy in solid-state NMR when irradiated with BABA I,BABA II,and C7 radiofrequency pulse sequences

Floquet–Magnus expansion is used to study the effect of chemical shift anisotropy in solid-state NMR of rotating solids. The chemical shift interaction is irradiated with two types of radiofrequency pulse sequences: BABA and C7. The criteria for the chemical shift anisotropy to be averaged out in each rotor period are obtained.     

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.     

High-pressure magic angle spinning nuclear magnetic resonance

A high-pressure magic angle spinning (MAS) NMR capability, consisting of a reusable high-pressure MAS rotor, a high-pressure rotor loading/reaction chamber for in situ sealing and re-opening of the high-pressure MAS rotor, and a MAS probe with a localized RF coil for background signal suppression, is reported. The unusual technical challenges associated with development of a reusable high-pressure MAS rotor are addressed in part by modifying standard ceramics for the rotor sleeve by abrading the internal surface at both ends of the cylinder. In this way, not only is the advantage of ceramic cylinders for withstanding very high-pressure utilized, but also plastic bushings can be glued tightly in place so that other removable plastic sealing mechanisms/components and O-rings can be mounted to create the desired high-pressure seal. Using this strategy, sealed internal pressures exceeding 150 bars have been achieved and sustained under ambient external pressure with minimal loss of pressure for 72 h. As an application example, in situ¹³C MAS NMR studies of mineral carbonation reaction intermediates and final products of forsterite (Mg₂SiO₄) reacted with supercritical CO₂ and H₂O at 150 bar and 50 °C are reported, with relevance to geological sequestration of carbon dioxide.     

Information processing in nuclear magnetic resonance imaging

An extended image analysis and classification system is presented to discuss the principal composition of the components as well as the methods of its realization in the field of reference based NMR diagnostics and tissue characterization.