Pake Doublet Research Articles

Spin relaxation in six-pulse double-quantum coherence (DQC) signal: stretched exponential approach for a polycrystalline average

Using the Redfield equation, the effect of electron-spin relaxation is taken into account on six-pulse double-quantum coherence (DQC) signal for coupled nitroxide radicals, each characterized by the electron spin $$S = 1/2 $$ and nuclear spin $$I = 1$$ . It is found that a two-dimensional time-domain ( $$t_{\rm dip}$$ , $$ t_{\rm echo} )$$ signal for a single orientation of the external magnetic field with respect to the dipolar axis becomes multiplied by the decaying exponential factor: $$\exp\left( { - \left( {2t_{\max} + t_{\rm echo} } \right)/T_{2}^{S} - 2t_{DQ} /T_{2}^{D} } \right) , $$ where T2S and T2D are the spin–spin relaxation times for that orientation of the magnetic field along the $$p = \pm 1 $$ and $$p = \pm 2$$ coherence pathways, respectively; here $$p $$ is the coherence order, which represents the transverse magnetization, equal to $$\pm 1$$ for the single-quantum states and $$\pm 2$$ for the double-quantum states, $$t_{DQ}$$ is the time interval over which the two electrons are on a double-quantum $$p = \pm 2$$ coherence pathway, and $$t_{\max} $$ is the time between the first and the sixth pulse, which is kept constant in the six-pulse DQC sequence considered. To calculate the average effect of the orientation-dependent relaxation times on the signal for a polycrystalline sample, an overall stretched-exponential relaxation time is used. Several illustrative examples are included for chosen values of ( $$T_{2}^{S}$$ , $$T_{2}^{D} ,{\beta }$$ ), where $${\beta }$$ is the exponent characterizing the stretched exponential, exhibiting the effect of relaxation on the intensity and width of the DQC signal along the echo-axis. However, there is absolutely no effect of relaxation on the shape of the Fourier transform of the signal along the dipolar axis, other than reducing its intensity, implying that six-pulse DQC experiment is a superior technique over other pulse arrangements, e.g. 2-pulse COSY/SECSY, 2-pulse DQ, 5-pulse double-quantum modulation (DQM), whose Pake doublets are broadened by relaxation, to use the splitting of the Pake doublet to determine the distance between the two nitroxide radicals. The Fourier transform of the polycrystalline six-pulse DQC signal shows very prominent Pake doublet at $$\pm d$$ , with $$d$$ being 2D/3, where D is the dipolar interaction. This spacing can be used to estimate distances between the nitroxide radicals directly using the relationship $$r\left[ {A^{ \circ } } \right] = 10\left( {51.9/D\left[ {{\text{MHz}}} \right]} \right)^{1/3}$$ .

In situ NMR Investigation of the Photoresponse of Perovskite Crystal

Summary Hybrid perovskites are outstanding candidates for use in optoelectronic devices. Nonetheless, hybrid perovskites present numerous fundamental issues that are not yet fully understood. This study seeks to address this problem by reporting on the occurrence of ultraslow dynamic orientation changes in the methylammonium (MA) cations and the corresponding changes in the inorganic lattice of MAPbI3 perovskite crystals occurring over a time scale of 100 s under continuous illumination based on in situ single-crystal 2H nuclear magnetic resonance and in situ X-ray diffraction results. The demonstrated ultraslow dynamic changes in MAPbI3 are far slower than elementary molecular motions typically having time scales of femtoseconds and picoseconds and have never been reported previously. The ultraslow dynamic changes have been correlated with the reduction of band gap and the increase of absorption coefficient of MAPbI3, providing the molecular origins of the stabilization process in the photoresponse of the MAPbI3 device.

Enhanced tensor polarization in solid-state targets

We report measurements of enhanced tensor polarization on solid-state targets. The results here represent an increase in tensor polarization over that previously achieved in high energy and nuclear scattering experiments that focused on the measurement of tensor polarized observables. Enhancement techniques are used which require RF produced close to the Larmor frequency of the target spins and use selective semi-saturation resulting from two sources of irradiation, microwave for the DNP process and the additional RF used to manipulate the population of the energy levels in the target material. The spin dynamics of the solid target are used to align the spins enhancing the ensemble average to improve the figure of merit of the scattering experiment. Target rotation at an optimized rate can lead to additional enhancement by applying selective semi-saturation in polycrystalline materials that possess a Pake doublet in their NMR signal.

NMR study of microscopic mechanism of water molecules diffusion in natrolite

The mineral natrolite is a good object for studying the features of the molecular mobility of water molecules in spatially restricted structures by NMR techniques. The microscopic mechanisms of water molecule mobility in channels of monocrystal natural zeolite natrolite (Na16Al16Si24O80·16H2O) have been investigated by broad-line (CW) NMR method. The CW NMR method, which accurately reproduces the shape of a Pake doublets of water molecules, has made it possible to trace diffusion of individual water molecules between specific positions in the crystal lattice as a function of temperature, which is important in understanding diffusion mechanisms in narrow channels of natrolite, where a diameter of the channel is smaller than the diameter of the water molecule. It has been shown that at temperatures higher than 250 K the regular diffusion of water molecules along the Schottky defects located along channels parallel to the c-crystal axis is a main kind of water molecules mobility. At temperature higher than 350 K the diffusion of water molecules in transversal channels of natrolite was observed also. Using the structural data the possible pathways of water molecules diffusion in natrolite channels have been discussed. The relationship between diffusion of water molecules and the dynamics of the zeolite framework and sodium cations is discussed on the basis of the assumption non-Markovian characte of diffusion in natrolite.

Oscillating Free Induction Decay in Polymer Systems: Theoretical Analysis

It is shown that during the Anderson-Weiss transformation derivation, as applied to a reptating polymer chain, the spin system can be divided into two sub-systems: an ergodic fluctuating one and a nonergodic quasi-static one. Consequently, the free induction decay (FID) expression is factorized. The factor with a fluctuating dipole-dipole interaction for an arbitrary correlation time is transformed into the generalized Anderson-Weiss exponential, and the factor with a quasi-static dipole-dipole interaction in an isotropic polymer melt is transformed into the oscillating Fourier image of the Pake doublet. The final expression permits both describing the FID shape of a polymer melt as a function of the molecular mass and temperature below the temperature of the primitive segment quasi-static state and forecasting the temperature range in which oscillating FIDs have been observed for poly(isoprene) melt. The new approach is applicable to qualitatively describe the oscillating FID in semi-crystalline poly(ethylene).

Electronic and Magnetic Properties of Black Phosphorus

Black phosphorus (bP) has emerged as the next member in the graphene inspired two‐dimensional materials family. Its electronic and magnetic properties are studied herein using electron and nuclear magnetic resonance techniques (ESR and NMR) and microwave conductivity measurement. The latter is a unique technique to study conductivity on air sensitive samples. The ESR study indicates the absence of free charge carriers and no sign of paramagnetic defects are found. 31P NMR shows the presence of a characteristic Pake doublet structure due to the interaction between I = 1/2 nuclei. Microwave conductivity shows, in accordance with the ESR results, that black phosphorus behaves as a semiconductor and we identify extrinsic and intrinsic charge carrier contributions to the conductivity and extracted the sizes of the gaps. ESR measurement also yields that bP might find applications as a microwave absorbent.

Simulation of Pake doublet with classical spins and correspondence between the quantum and classical approaches

Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used to model spin systems. In this paper we show that a classical spins based approach can be used to describe the phenomena essentially quantum in nature such as of the Pake doublet.

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. The posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

Molecular motion of alcohols adsorbed in ACF hydrophobic nanoslits as studied by solid-state NMR

The molecular motion and local structure of methanol-d1 (CH3OD) and ethanol-d1 (C2H5OD) in activated carbon fiber (ACF) with a slit width of 0.7 and 1.1 nm have been investigated by solid-state 1H and 2H NMR. 2H NMR spectra for alcohols confined in ACF gave a so-called Pake doublet below 140 K, which were characterized by the 2H quadrupole coupling constant (QCC) of 185 kHz and the asymmetric parameter of the electric-field-gradient tensor (η) of 0.1. The QCC value of the deuteron was indicative of the hydrogen bond formation with the O···O distance of ca. 0.27 nm, suggesting the solid-like feature of alcohols in ACFs. The quadrupole broadening vanished on heating and the single isotropic resonance line was observed. Alcohol molecules were undergoing a rapid motion like as in the bulk liquid, indicating a transition from solid to liquid in ACFs. Temperature-dependent 1H NMR spectra were used for evaluating the Ea value for reorientation in solid-like alcohols, whereas the 2H NMR spectra were used for obtaining the translation accompanying reorientation in liquid-like alcohols. Alcohols with a bilayered structure in ACF with a slit width of 1.1 nm gave similar Ea values, whereas C2H5OD in ACF with a slit width of 0.7 nm, in which a monolayered structure is expected, exhibited a cross-over of two activation processes at 172 K. The variation in Ea was probably caused by the structural relaxation concerning with the hydrogen bonding formation and/or excitation of the large amplitude local motion. The competition of the directionality of hydrogen bonds and a freedom of molecular orientation plays an important role to characterize the intermolecular structure as well as the physicochemical properties in amphipathic molecules in confinement.

Deformation Defects Supporting Quantum Readout of 29 Si Nuclear Spins in Si: P Deformed Crystals

High temperature (950 °C) plastic deformation of the 29Si enriched silicon crystals generates ˜10 15 cm−3 paramagnetic defects of the new type. The multiline spectrum of electron paramagnetic resonance (EPR) of the defects corresponds to S = 1 electronic spin of the clusters containing oxygen. Strong anisotropy and large linewidth of the EPR spectra (˜1 kOe) were observed. The Pake doublet split by spin-spin nuclear dipole interaction was analyzed in the nuclear magnetic resonance (NMR) spectra of the crystals. Contribution of the electron-nuclear interaction to the EPR linewidth is negligibly small, while the NMR linewidth is controlled by the dipole-dipole nuclear relaxation.

Deformation paramagnetic defects in Fz-29Si:P crystals

A new type of paramagnetic defects generated under plastic deformation (at 1223 K) in isotopically enriched floating-zone-grown silicon crystals Fz-Si:P (76% 29Si) are found. The anisotropic spectra of the electron-spin resonance of these defects testify that they are of doping origin and have the spin S = 1. The spectra of nuclear magnetic resonance are Pake doublets split by the spin-spin nuclear interaction and broadened by electron-nuclear dipole-dipole relaxation.

Electron and nuclear spin dynamics in plastically deformed silicon crystals enriched in isotope 29Si

Paramagnetic defects of a new type with a concentration of about 1015 cm−3 are shown to be generated during the plastic deformation of isotope-rich (72%, 76% 29Si) silicon crystals at a temperature of 950°C. The electron paramagnetic resonance (EPR) spectra of these defects are anisotropic and have a significant width (up to 1 kOe). The nonuniform broadening of the EPR lines is caused by the variation of the internal magnetic field in correlated defect clusters. The nuclear magnetic resonance (NMR) spectra of the deformed crystals consist of Pake doublets split by nuclear spin-spin interaction. The broadening of the NMR spectra is caused by nuclear dipole-dipole relaxation.

Vibrations and reorientations of H2O molecules in [Sr(H2O)6]Cl2 studied by Raman light scattering, incoherent inelastic neutron scattering and proton magnetic resonance

Vibrational–reorientational dynamics of H2O ligands in the high- and low-temperature phases of [Sr(H2O)6]Cl2 was investigated by Raman Spectroscopy (RS), proton magnetic resonance (1H NMR), quasielastic and inelastic incoherent Neutron Scattering (QENS and IINS) methods. Neutron powder diffraction (NPD) measurements, performed simultaneously with QENS, did not indicated a change of the crystal structure at the phase transition (detected earlier by differential scanning calorimetry (DSC) at TCh=252.9K (on heating) and at TCc=226.5K (on cooling)). Temperature dependence of the full-width at half-maximum (FWHM) of νs(OH) band at ca. 3248cm−1 in the RS spectra indicated small discontinuity in the vicinity of phase transition temperature, what suggests that the observed phase transition may be associated with a change of the H2O reorientational dynamics. However, an activation energy value (Ea) for the reorientational motions of H2O ligands in both phases is nearly the same and equals to ca. 8 kJmol−1. The QENS peaks, registered for low temperature phase do not show any broadening. However, in the high temperature phase a small QENS broadening is clearly visible, what implies that the reorientational dynamics of H2O ligands undergoes a change at the phase transition. 1H NMR line is a superposition of two powder Pake doublets, differentiated by a dipolar broadening, suggesting that there are two types of the water molecules in the crystal lattice of [Sr(H2O)6]Cl2 which are structurally not equivalent average distances between the interacting protons are: 1.39 and 1.18Å. However, their reorientational dynamics is very similar (τc=3.3⋅10−10s). Activation energies for the reorientational motion of these both kinds of H2O ligands have nearly the same values in an experimental error limit: and equal to ca. 40kJmole−1. The phase transition is not seen in the 1H NMR spectra temperature dependencies. Infrared (IR), Raman (RS) and inelastic incoherent neutron scattering (IINS) spectra were calculated by the DFT method and quite a good agreement with the experimental data was obtained.

Area Per Lipid of Membranes from Natural Abundance Solid-State 13C NMR Spectroscopy

The properties of liquid-crystalline membranes vary according to the molecular composition of the lipid bilayer [1]. Structural investigations of lipid membranes using NMR spectroscopy generally require isotopic labeling of the lipids, thereby precluding investigations of complex lipid systems. Combining natural-abundance solid-state 13C magic-angle-spinning (MAS) NMR with a statistical mean torque (MT) model [2] enabled us to obtain the average area per lipid and volumetric bilayer thickness DB for lipid bilayers. The 2D separated local field (SLF) NMR experiment DROSS gives isotropic chemical shifts in the F2 frequency dimension and site-specific dipolar Pake doublets in the F1 dimension [1]. By analyzing the Pake patterns we extracted 13C-1H residual dipolar couplings (RDCs) and calculated segmental |SCH| order parameters. The |SCH| order parameters carry the structural information that aid calculation of and DB using the MT model. Experiments were conducted with DMPC, POPC, and EYSM lipids as single component (liquid-disordered, ld) lipid bilayers as well as with cholesterol. EYSM is more ordered in the ld phase and hence experiences less structural perturbation upon adding cholesterol to form the liquid-ordered (lo) phase relative to POPC. We infer that the cholesterol stiffening effect on lipid bilayers is limited by the maximum volumetric hydrocarbon thickness [2]. Knowledge of structural parameters like and DB is important for molecular dynamics (MD) simulations and provides information about the balance of forces in membrane lipid bilayers [3]. Our studies demonstrate the applicability of solid-state 13C NMR spectroscopy to site-specific structural investigations of complex lipids, where isotope labeling may be prohibitive, allowing structural studies of biologically relevant membrane systems. [1] A. Leftin et al.(2013) JMB425 2973-2987. [2] H. I. Petrache et al.(2000) BJ.79 3172-3192. [3] A. Leftin et al.(2011) BBA1808 818-839.

Nuclear magnetic resonance study of superprotonic conductor Rb4LiH3(SO4)4 single crystals

To investigate the molecular dynamics of a Rb4LiH3(SO4)4 crystal below superionic phase transitions, we examined the temperature dependences of the NMR spectra and the spin-lattice relaxation time, T1, of the 1H, 7Li, and 87Rb nuclei. The symmetry of 1H signals resembles the Pake doublet containing a pair of dipolar-coupled protons. From the temperature dependence of T1, the activation energy of proton at high temperature is twice of those of 7Li and 87Rb. A striking feature was the formation of the weak hydrogen bond creating a significant influence of proton at high temperatures due to the mobility of the hydrogen-bond protons. And, we compared these data with 1H and 7Li results for (NH4)4LiH3(SO4)4 and K4LiH3(SO4)4 crystals, which have similar structures.

Magnetic and Electric Properties of Organic Conductors Probed by 13C-NMR Using Selective-Site Substituted Molecules

Quasi-One and quasi-two dimensional organic conductors consisting of TTF derivatives such as BEDT-TTF (bis-(ethylene-dithio)-tetra-thia-fulvalene) and TMTCF (C = S; TMTTF: tetra-methyl-tetra-thia-fulvalene, C = Se; TMTSF: tetra-methyl-tetra-selena-fulvalene) have been well investigated in condensed matter physics because of interest in the emerging electric and magnetic properties, such as the spin density wave, charge order, superconductivity, anti-ferromagnetism, and so on. To probe the electronic state, nuclear magnetic resonance (NMR) is one of the most powerful tools as the microscopic magnetometer. A number of 13C-NMR studies have been performed of the double-site central 13C=13C bond substituted molecules. However, problems with the coupled spin system of 13C=13C complicated the interpretation for observations on NMR. Therefore, single-site 13C-enriched molecules are desired. We summarize the problem of Pake doublet and the preparation of the single-site 13C-susbstituted BEDT-TTF and TMTCF molecules. We also demonstrate the superiority of 13C-NMR of the single-site 13C-susbstituted molecule utilizing the hyperfine coupling tensor.

Pulsed EPR Analysis of the Photo-Induced Triplet Radical Pair in the BLUF Protein SyPixD: Determination of the Protein–Protein Distance and Orientation in the Oligomeric Protein

A photo-induced radical pair of FADH· and Y8· and in BLUF protein SyPixD was studied by pulsed electron paramagnetic resonance (EPR) spectroscopy. Blue light illumination at 150 K for 30 min followed by cooling to 50 K during illumination induced the stable radical pair. The EPR signal has been characterized by a Pake doublet signal with complete S = 1 spin state. The radical pair was utilized as a probe to analyze the oligomer of SyPixD. The relative arrangement of PixD proteins in the complex was investigated by pulsed electron–electron double resonance (PELDOR) with the orientation selection. Based on the decameric structure in the crystal, the possible structure for the PELDOR results was discussed.

Water Structure and Dynamics at a Silica Surface: Pake Doublets in 1H NMR Spectra

Detailed knowledge about the dynamics and structure of liquids in the vicinity of a solid surface is important in several fields of research. In this study a homogeneous model system of colloidal and nonporous silica particles with a narrow particle size distribution was used to examine such properties of adsorbed water and 1-heptanol. Doublet (1)H water resonances ("Pake doublets") indicate a preferred spatial orientation for the water molecules, as well as a lower molecular density in the surface-induced water structures compared to bulk water. These surface-induced structures are found to extend at least 8 nm from the silica surface. T(1) relaxation measurements at several temperatures indicate weaker H-bonding in the adsorbed water compared to bulk water. T(2) relaxation measurements at several temperatures reveal the presence of two water phases and give quantitative information on the mobility of water molecules and proton exchange processes. The presence of 1-heptanol changes the water characteristics, primarily in the water phase closer to the surface, where water molecules experience decreased translational and increased rotational freedom. In the absence of water, adsorbed 1-heptanol forms surface aggregates encompassing several molecular layers, where the first adsorbed layer shows severe restrictions in mobility and subsequent layers are more mobile.

Calculation of Double-Quantum-Coherence Two-dimensional Spectra: Distance Measurements and Orientational Correlations

The double quantum coherence (DQC) echo signal for two coupled nitroxides separated by distances ≳10 Å, is calculated rigorously for the six-pulse sequence. Successive application of six pulses on the initial density matrix, with appropriate inter-pulse time evolution and coherence pathway selection leaves only the coherent pathways of interest. The amplitude of the echo signal following the last π pulse can be used to obtain a one-dimensional dipolar spectrum (Pake doublet), and the echo envelope can be used to construct the two-dimensional DQC spectrum. The calculations are carried out using the product space spanned by the two electron-spin magnetic quantum numbers m(1), m(2) and the two nuclear-spin magnetic quantum numbers M(1), M(2), describing e.g. two coupled nitroxides in bilabeled proteins. The density matrix is subjected to a cascade of unitary transformations taking into account dipolar and electron exchange interactions during each pulse and during the evolution in the absence of a pulse. The unitary transformations use the eigensystem of the effective spin-Hamiltonians obtained by numerical matrix diagonalization. Simulations are carried out for a range of dipolar interactions, D, and microwave magnetic field strength B for both fixed and random orientations of the two (14)N (and (15)N) nitroxides. Relaxation effects were not included. Several examples of one- and two-dimensional Fourier transforms of the time domain signals vs. dipolar evolution and spin-echo envelope time variables are shown for illustration. Comparisons are made between 1D rigorous simulations and analytical approximations. The rigorous simulations presented here provide insights into DQC ESR spectroscopy, they serve as a standard to evaluate the results of approximate theories, and they can be employed to plan future DQC experiments.

Decomposition of a NMR signal comprising a single resonance in exchange with a Pake doublet: Application to the analysis of 1H NMR spectra of water molecules embedded in synthetic clays

Conventional 1H NMR spectra of water in clays generally consist of several broad overlapping resonances. However, when a type of water is partially oriented, it leads to a Pake doublet superposed to the resonances corresponding to different types of non-oriented water. With the help of a recent method based on nutation experiments, the proportions of the different kinds of water could be determined. Thus, we are able to determine interesting NMR parameters like dipolar couplings, exchange rate, and line broadening. These determinations are complemented by spin relaxation times and self-diffusion measurements which bring additional information about the dynamical behavior of water.