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In this work, several exact and approximate analytical solutions to the quantum master equation are derived using both classical and non-classical coupling models to describe the kinetics of Hartmann-Hahn cross-polarization (HHCP) and multiple-contact CP (MCCP). Moreover, the analytical solution originally obtained by Naito and McDowell [J. Chem. Phys. 84 (1986) 4181.] is shown to be incorrect and the different regimes of spin diffusion and T1ρ relaxation are characterized by the amplitude of the second stage of the HHCP dynamics and the HHCP/MCCP crossing time. The analysis of the 1H–13C HHCP and MCCP dynamics together with (Lee-Goldburg) 1H T1ρ relaxation experimental data provides a consistent picture of spin dynamics in solid alanine and explains the apparent discrepancies previously observed between T1ρ and T1 relaxation measurements. The CH and CH3 protons relax as expected via spin diffusion towards the NH3 protons but the assumption of common proton spin temperature, in which the bottleneck of relaxation is at the NH3 sites, generally valid for T1 relaxation breaks down for T1ρ relaxation. A diffusion-limited situation in which nuclear Zeeman energy is transferred to the lattice faster than can be supplied by spin diffusion is observed instead.

Dust particles and sand storms can cause attenuation and cross-polarization of electromagnetic wave propagation, especially at high frequencies above 10 GHz. Dust attenuation has been the focus of many research works, mainly with the deployment of a 5G wireless network in the FR-2 band (mmWave band, 23–53 GHz with TDD). This has led to the development of novel models to accurately predict and estimate attenuation. However, the existing review works have not adequately provided extensive taxonomies for these models to show the state-of-art and future research directions. This paper aims to bridge this gap by providing a comprehensive review of all electromagnetic scattering models in terms of their strengths, weaknesses, and applications. Lessons learned from the detailed survey have been stated and discussed extensively. Key findings from this review indicate that all the models developed were limited to the region where they were developed, with frequency and visibility levels as the two main parameters. The survey across regions showed no model was developed for Region 2, including the Americas, Greenland, and some of the eastern Pacific Islands. Among the dry regions of the globe, where dust and sand storms can occur either occasionally or frequently, it can be seen that only a few parts of these desert regions of Africa (Region 1) and Asia (Region 3) have been considered by authors for the development of prediction models for attenuation due to dust storms. Thus, this also shows the limitations of the overall deterministic models and presents the crucial need to develop new models or modify existing models to accurately predict dust attenuation in other regions, particularly in Africa.

Deuterium rotating frame solid-state NMR relaxation measurements ( 2 H R 1ρ ) are important tools in quantitative studies of molecular dynamics. We demonstrate how 2 H to 13 C cross-polarization (CP) approaches under 10-40 kHz magic angle spinning rates can be combined with the 2 H R 1ρ blocks to allow for extension of deuterium rotating frame relaxation studies to methyl groups in biomolecules. This extension permits detection on the 13 C nuclei and, hence, for the achievement of site-specific resolution. The measurements are demonstrated using a nine-residue low complexity peptide with the sequence GGKGMGFGL, in which a single selective - 13 CD 3 label is placed at the methionine residue. Carbon-detected measurements are compared with the deuterium direct-detection results, which allows for fine-tuning of experimental approaches. In particular, we show how the adiabatic respiration CP scheme and the double adiabatic sweep on the 2 H and 13 C channels can be combined with the 2 H R 1ρ relaxation rates measurement. Off-resonance 2 H R 1ρ measurements are investigated in addition to the on-resonance condition, as they extent the range of effective spin-locking field., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

The proton-phosphorus (H-P) cross-polarization (CP) is effective in Sn(HPO 4 ) 2 ·H 2 O despite of the presence of paramagnetic ion impurities. Polarization constants T H-P and 1 H T 1ρ times are measured in static Sn(HPO 4 ) 2 ·H 2 O by the kinetic variable-temperature H-P CP experiments. The temperature dependence of the 1 H T 1ρ times is interpreted in terms of proton movements in the interlayer space occurring between the phosphate groups without participation of the water molecules. The process requires an activation energy of 8.7 ± 0.7 kcal/mol. The MAS effect on the 1 H T 1ρ times is shown and discussed., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Static satellite-transitions (ST) NMR line shapes from half-integer quadrupolar nuclei could be very informative: they can deliver insight about local motions over a wide range of timescales, and can report on small changes in the local electronic environments as reflected by variations in the quadrupolar parameters. Satellite transitions, however, are typically "invisible" for half-integer quadrupolar nuclei due to their sheer breadth, leading to low signal-to-noise ratio -especially for unreceptive low-gamma or dilute quadrupolar nuclei. Very recently we have introduced a method for enhancing the NMR sensitivity of unreceptive X nuclei in static solids dubbed PROgressive Saturation of the Proton Reservoir (PROSPR), which opens the possibility of magnifying the signals from such spins by repeatedly imprinting frequency-selective X-driven depolarizations on the much more sensitive 1 H NMR signal. Here, we show that PROSPR's efficacy is high enough for enabling the detection of static ST NMR for challenging species like 35 Cl, 33 S and even 17 O -all at natural-abundance. The ensuing ST-PROSPR NMR experiment thus opens new approaches to probe ultra-wideline (6-8 MHz wide) spectra. These highly pronounced anisotropies can in turn deliver new vistas about dynamic changes in solids, as here illustrated by tracking ST line shapes as a function of temperature during thermally-driven events., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Double-cross polarization to the satellite-transitions (STs) of half-integer quadrupolar nuclei is demonstrated using proton-detected heteronuclear correlation (HETCOR) under fast magic-angle spinning (MAS). By placing the rf frequency away from the central-transition (CT) and selective to the STs, average Hamiltonian theory shows a scaled effective rf field with a phase equal to the complex ST spinning sideband being irradiated. Such an effective rf field can excite and spinlock STs but the phase spread usually leads to signal cancellation in one-step excitation or cross polarization experiments. The cancellation does not occur for two-step double cross-polarization (DCP) HETCOR experiments, therefore high efficiencies can be obtained. With careful magic-angle calibration, ST and double-quantum ST (DQST) HETCOR experiments are demonstrated with the 35 Cl nuclei in histidine·HCl·H 2 O. These experiments provide additional information over the commonly observed CT spectra and near isotropic resolution in the case of DQST of spin S = 3/2 quadrupolar nuclei., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023. Published by Elsevier Inc.)

Dynamic nuclear polarization (DNP) build-up times at low temperature for low-gamma nuclei can be unfavorably long and can be accelerated by transfer of polarization from protons. The efficiency of the cross polarization (CP) depends on the B 1 -field strengths, the pulse sequence chosen for cross polarization and the sample composition. CP experiments rely on high B 1 -fields, which typically lead to electrical discharge and breakdown in the circuit. This problem is particularly severe in the low pressure helium atmosphere due to easily ionized helium atoms. The purpose of this study is to identify strategies to minimize voltages across components in a tuning and matching circuit of the coil to avoid electrical discharge during CP experiments. Design equations for three tuning and matching network configurations are derived. The results of the study are then used in the design of a single coil double resonance DNP probe operating at 71.8 MHz ( 13 C frequency) and 285.5 MHz ( 1 H frequency). In the current setup we achieve 28% polarization on 13 C in urea with a build-up time of 11.6 min with CP compared to 14% and 53 min by direct polarization using TEMPOL as the radical. Different cross polarization sequences are compared., (Copyright © 2019 Elsevier Inc. All rights reserved.)

High magnetic field can dramatically increase the spectral resolution and sensitivity of quadrupole nuclei S > 1/2 by the reduction of the second-order quadrupole broadening. A brief overview and outlook on spectral acquisition, the importance of high magnetic field, inter-nuclei distance measurement, various 2D separation and correlation methods of quadrupole nuclei are presented. The complications and consequences of spin dynamics under rf irradiation for the (2S + 1) level system and level-crossing with the satellite transition frequencies under magic-angle spinning are discussed. There is a scaling down of (S + 1/2) to the efficiency of many experiments in comparison with a spin-1/2 due to the fact that only two central transition spin states out of the (2S + 1) levels contribute to polarization transfer and spin correlation., (Copyright © 2019. Published by Elsevier Inc.)

It has recently been shown how dynamic nuclear polarization can be used to hyperpolarize the bulk of proton-free solids. This is achieved by generating the polarization in a wetting phase, transferring it to nuclei near the surface and relaying it towards the bulk through homonuclear spin diffusion between weakly magnetic nuclei. Pulse cooling is a strategy to achieve this that uses a multiple contact cross-polarization sequence for bulk hyperpolarization. Here, we show how to maximize sensitivity using the pulse cooling method by experimentally optimizing pulse parameters and delays on a sample of powdered SnO 2 . To maximize sensitivity we introduce an approach where the magic angle spinning rate is modulated during the experiment: the CP contacts are carried out at a slow spin rate to benefit from faster spin diffusion, and the spin rate is then accelerated before detection to improve line narrowing. This method can improve the sensitivity of pulse cooling for 119 Sn spectra of SnO 2 by an additional factor of 3.5., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Polarization-inversion (PI) has been applied to proton magic angle spinning (MAS) NMR spectra recorded under fast MAS conditions. The combination of cross-polarization (CP) from carbon to proton and subsequent polarization-inversion produces strong oscillatory behavior in the proton signal intensities at high MAS speeds of 60 kHz. It is observed that by a suitable choice of the polarization-inversion time, a proton spectrum free of methylene and methine protons can be obtained. Such a spectrum, on the one hand, increases the resolution of the crowded proton spectrum and on the other hand provides exclusively chemical shifts of protons such as NH, OH and SH which might otherwise overlap with carbon attached protons. The oscillations observed during PI can also be used to estimate the dipolar coupling between proton and carbon by Fourier transformation of data acquired at equally incremented time periods. The utility of the above ideas has been demonstrated on a set of molecules with both 13 C labeled and 13 C in natural abundance., (Copyright © 2018 Elsevier Inc. All rights reserved.)

DNP methods can provide significant sensitivity enhancements in magic angle spinning solid-state NMR, but in systems with long polarization build up times long recycling periods are required to optimize sensitivity. We show how the sensitivity of such experiments can be improved by the classic flip-back method to recover bulk proton magnetization following continuous wave proton heteronuclear decoupling. Experiments were performed on formulations with characteristic build-up times spanning two orders of magnitude: a bulk BDPA radical doped o-terphenyl glass and microcrystalline samples of theophylline, l-histidine monohydrochloride monohydrate, and salicylic acid impregnated by incipient wetness. For these systems, addition of flip-back is simple, improves the sensitivity beyond that provided by modern heteronuclear decoupling methods such as SPINAL-64, and provides optimal sensitivity at shorter recycle delays. We show how to acquire DNP enhanced 2D refocused CP-INADEQUATE spectra with flip-back recovery, and demonstrate that the flip-back recovery method is particularly useful in rapid recycling regimes. We also report Overhauser effect DNP enhancements of over 70 at 592.6 GHz/900 MHz., (Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.)

We present a detailed analysis of the radiofrequency (RF) field over full volume of a rotor that is generated in a solenoid coil. On top of the usually considered static distribution of amplitudes along the coil axis we describe dynamic radial RF inhomogeneities induced by sample rotation. During magic angle spinning (MAS), the mechanical rotation of the sample about the magic angle, a spin packet travels through areas of different RF fields and experiences periodical modulations of both the RF amplitude and the phase. These modulations become particularly severe at the end regions of the coil where the relative RF amplitude varies up to ±25% and the RF phase changes within ±30°. Using extensive numerical simulations we demonstrate effects of RF inhomogeneity on pulse calibration and for the ramped CP experiment performed at a wide range of MAS rates. In addition, we review various methods to map RF fields using a B 0 gradient along the sample (rotor axis) for imaging purposes. Under such a gradient, a nutation experiment provides directly the RF amplitude distribution, a cross polarization experiment images the correlation of the RF fields on the two channels according to the Hartmann-Hahn matching condition, while a spin-lock experiment allows to calibrate the RF amplitude employing the rotary resonance recoupling condition. Knowledge of the RF field distribution in a coil provides key to understand its effects on performance of a pulse sequence at the spectrometer and enables to set robustness requirements in the experimental design., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Multiple-contact cross-polarization (MC-CP) is applied to powder samples of ferrocene and l-alanine under magic-angle spinning (MAS) conditions. The method is described analytically through the density matrix formalism. The combination of a two-step memory function approach and the Anderson-Weiss approximation is found to be particularly useful to derive approximate analytical solutions for single-contact Hartmann-Hahn CP (HHCP) and MC-CP dynamics under MAS. We show that the MC-CP sequence requiring no pulse-shape optimization yields higher polarizations at short contact times than optimized adiabatic passage through the HH condition CP (APHH-CP) when the MAS frequency is comparable to the heteronuclear dipolar coupling, i.e., when APHH-CP through a single sideband matching condition is impossible or difficult to perform. It is also shown that the MC-CP sideband HH conditions are generally much broader than for single-contact HHCP and that efficient polarization transfer at the centerband HH condition can be reintroduced by rotor-asynchronous multiple equilibrations-re-equilibrations with the proton spin bath. Boundary conditions for the successful use of the MC-CP experiment when relying on spin-lattice relaxation for repolarization are also examined., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Combined use of cross-polarization and magic-angle spinning in the middle of the seventies has opened a new era of high-resolution solid-state NMR spectroscopy. Cross-polarization procedure is commonly used to obtain a shorter measuring time and to investigate or exploit one nucleous by means of the other nucleous involved in the polarization transfer. An extended family of cross-polarization experiments including constant time cross-polarization approach, cross-polarization inversion and indirect observation of proton spin system is reviewed and illustrated with applications to a large range of solids., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Spin-locking and cross-polarization under magic-angle spinning are investigated for uniformly (13)C and (15)N labeled solids. In particular, the interferences from chemical shift anisotropy, and (1)H heteronuclear and (13)C homonuclear dipolar couplings are identified. The physical origin of these interferences provides guidelines for selecting the best (13)C and (15)N polarization transfer rf fields. Optimal settings for both the zero- and double-quantum cross-polarization transfer mechanisms are recommended., (Copyright © 2015 Elsevier Inc. All rights reserved.)

We show that Cross-Polarization with Variable Contact-time (CP-VC) allows an accurate determination of C-H dipolar interactions, which permits an easy detailed analysis of bond lengths and local dynamics, e.g. in biomolecules. The method presents a large dipolar scaling factor of 1/√2, leading to a better determination of dipolar interactions, especially for long C-H distances, and it allows the observation of very small local details such as those related either to CH(2) three spin systems, or even to hydrogen bonds. CP-VC is very simple to set up and very robust with respect to most experimental parameters, such as: rf-offsets, chemical-shift anisotropies, imperfect Hartmann-Hahn setting, and rf-inhomogeneity. The only required condition is the use of a sufficiently fast MAS spinning speed of at least ca. 60 kHz., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Objectives: The aim of this study was to test the hypothesis that cross-polarization optical coherence tomography (CP-OCT) can be used to longitudinally monitor demineralization peripheral to orthodontic brackets in an extended clinical study., Methods: A high-speed CP-OCT system was used to acquire 3D volumetric images of the area at the base of orthodontic brackets over a period of 12 months after placement. The reflectivity was measured at 3-month intervals for 12 months to determine if there was increased demineralization. Two teeth were monitored on 20 test subjects and the brackets were bonded using two types of adhesives. This was a randomized controlled clinical study with a split mouth design such that each subject served as his or her own control. On one side, the control premolar was bonded with a bonding agent (Adper Scotchbond from 3M ESPE, St. Paul, MN) and composite (Transbond XT from 3M Unitek, Monrovia, CA) that lacked fluoride. On the other side, the experimental premolar was bonded with a fluoride releasing glass ionomer cement (GC Fuji Ortho LC from GC America, Alsip, IL)., Results: There was a small but significant increase in the calculated lesion depth and integrated reflectivity over that depth (ΔR) for both adhesive types (p<0.0001) indicating increasing demineralization with time. There was no significant difference in the lesion depth (p=0.22) and ΔR (p=0.91) between the groups with the fluoride releasing glass ionomer cement and the conventional composite., Conclusions: CP-OCT was able to measure a significant increase in demineralization (p<0.0001) at the base of orthodontic brackets over a period of 12 months., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

We demonstrate that a very simple experiment, Cross-Polarization with Variable Contact-time (CP-VC), is very efficient at ultra-fast MAS (νR ≥ 60 kHz) to measure accurately the C-H and N-H distances, and to analyze the dynamics of bio-molecules. This experiment can be performed with samples that are either (13)C or (15)N labeled or without any labeling. The method is very robust experimentally with respect to imperfect Hartman-Hahn setting, and presents a large scaling factor allowing a better dipolar determination, especially for long C-H or N-H distances, or for CH3 or NH3 moieties with three-site hopping. At ultra-fast MAS, it can be used quantitatively in a 2D way, because its scaling factor is then little dependent on the offsets. This robustness with respect to offset is related to the ultra-fast spinning speed, and hence to the related small rotor diameter. Indeed, these two specifications lead to efficient n = ±1 zero-quantum Hartman-Hahn CP-transfers with large RF-fields on proton and carbon or nitrogen channels, and large dipolar scaling factor., (Copyright © 2013 Elsevier Inc. All rights reserved.)