Effect of the frequency of intramolecular motions on the NMR relaxation in liquid state temperature regime

Equations for the spectral densities of complex motion of a spin pair undergoing internal motion and isotropic/anisotropic overall rotation have been considered. The fluctuations of the interproton distances, caused by internal motion, have been taken into account in the theoretical equations. A method allowing a distinction between the isotropic and the anisotropic overall rotation of molecules has been proposed. The effect of the activation parameters of internal motions (known from the solid state study) on the measured T ₁ relaxation of the ¹³C and ¹H–¹H cross-relaxation rates has been analysed for methyl-β-D-galactopyranoside in DMSO-d6 solution. The conformational trans-gauche jumps of the methylene group are not fast enough to affect the T ₁ value of carbon C6 in the liquid state temperatures regime. Only the methyl group rotation is a very fast internal motion. This motion influences the carbon C7 relaxation and methyl protons–anomeric proton cross-relaxation. The values of interatomic distances between anomeric H(C1) and H(C5) as well as the three methyl protons H(C7) have been calculated from the cross-relaxation rates. The distance H(C1)–H(C7) fluctuates due to the rotation of methyl group. The application of the ‘model-free approach’ to study molecular dynamics in solutions is discussed.     

Spin relaxation of the photoexcited electron system in P-type InSb

By means of far-infrared (84 μm) laser cyclotron resonance, it is found that the photoexcited electron system in p-type InSb can enter a spin-hot state. The spin temperature cools down from ∽60 K with a time constant of several microseconds at the lattice temperature 4.2 K. Crude calculation for spin-flipping between 0^- and 0⁺ Landau subbands by electron- impurity scattering yields a reasonable time constant quite comparable with experimental observation.     

Two-dimensional envelope localized waves in the anomalous dispersion regime

Narrowband localized wave packets that are nondispersing and nondiffracting in one transverse dimension are characterized in anomalously dispersive media by means of a Fourier approach. Depending on the group velocity, waves with a dispersion relationship characterized by real wavenumbers can be O or X waves, while we also find waves with evanescent wavenumbers.     

The determination of the electron spin relaxation time in InSb in high magnetic fields

We report a direct observation of electron spin lattice relaxation time in n-InSb. This time is deduced from a time-resolved observation of electrical conductivity following a stimulated spin-flip Raman pulse in a material having a carrier concentration of 1.57 × 10¹⁶ cm⁻³. In addition, we present the matrix elements for the transition between |0,k_x,k_z, −> and |0,k′_x,k′_z, + > states for ionized impurity, acoustic phonon (longitudinal and transverse modes), and optic phonon (polar and non-polar modes) scattering, respectively.     

Sodium NMR relaxation in porous materials

The NMR relaxation of hydrogen nuclei of a fluid in a porous material is generally interpreted in terms of the Brownstein-Tarr model, in which the relaxation rate of the signal is inversely proportional to the pore size. We have investigated whether this model can be applied to the relaxation of Na nuclei in a NaCl solution in a porous material. The results indicate that the ion distribution over the pores can be obtained from an analysis of the Na NMR signal decay, if the pore sizes are roughly below 1 microm. This information is very useful for studies of combined moisture and ion transport in porous building materials.     

NMR of localized magnetic states in graphene

The NMR relaxation rate is studied on the magnetic states of an impurity in bilayer graphene within a tight-binding scenario. The dependencies of the relaxation rate on temperature, interlayer interaction and also the chemical potential have been considered. Although for low temperatures we observe the usual Korringa relation, a characteristic of the conventional fermions, the rate increases with the increase in temperature and tends to saturate for high temperatures. For small interlayer interactions (t_⊥) the system can be either magnetic or non-magnetic. However for higher t_⊥ we observe the existence of only a pure magnetic state. In graphene this transition is also observed with two cusps related to the magnetic to non-magnetic transition, which modifies to a single hump for higher t_⊥, where the system is purely magnetic for any value of chemical potential.     

On the regime of localized excitations for disordered oscillator systems

Letters in Mathematical Physics - We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle...     

Spin dynamics of the potassium magnetometer in spin-exchange relaxation free regime

The laser-pumped potassium spin-exchange relaxation free(SERF) magnetometer is the most sensitive detector of magnetic field and has many important applications. We present the experimental results of our potassium SERF magnetometer. A pump–probe approach is used to identify the unique spin dynamics of the atomic ensemble in the SERF regime.A single channel sensitivity of 8 f·THz-1/2is achieved with our SERF magnetometer.     

Energy relaxation of two-dimensional electrons in the quantum Hall effect regime

The mm-wave spectroscopy with high temporal resolution is used to measure the energy relaxation times τ_e of 2D electrons in GaAs/AlGaAs heterostructures in magnetic fields B=0–4 T under quasi-equilibrium conditions at T=4.2 K. With increasing B, a considerable increase in τe from 0.9 to 25 ns is observed. For high B and low values of the filling factor ν, the energy relaxation rate τ _e ^?1 oscillates. The depth of these oscillations and the positions of maxima depend on the filling factor ν. For ν>5, the relaxation rate τ _e ^?1 is maximum when the Fermi level lies in the region of the localized states between the Landau levels. For lower values of ν, the relaxation rate is maximum at half-integer values of τ _e ^?1 when the Fermi level is coincident with the Landau level. The characteristic features of the dependence τ _e ^?1 (B) are explained by different contributions of the intralevel and interlevel electron-phonon transitions to the process of the energy relaxation of 2D electrons.     

Spectral estimation of NMR relaxation

In this paper, spectral estimation of NMR relaxation is constructed as an extension of Fourier Transform (FT) theory as it is practiced in NMR or MRI, where multidimensional FT theory is used. nD NMR strives to separate overlapping resonances, so the treatment given here deals primarily with monoexponential decay. In the domain of real error, it is shown how optimal estimation based on prior knowledge can be derived. Assuming small Gaussian error, the estimation variance and bias are derived. Minimum bias and minimum variance are shown to be contradictory experimental design objectives. The analytical continuation of spectral estimation is constructed in an optimal manner. An important property of spectral estimation is that it is phase invariant. Hence, hypercomplex data storage is unnecessary. It is shown that, under reasonable assumptions, spectral estimation is unbiased in the context of complex error and its variance is reduced because the modulus of the whole signal is used. Because of phase invariance, the labor of phasing and any error due to imperfect phase can be avoided. A comparison of spectral estimation with nonlinear least squares (NLS) estimation is made analytically and with numerical examples. Compared to conventional sampling for NLS estimation, spectral estimation would typically provide estimation values of comparable precision in one-quarter to one-tenth of the spectrometer time when S/N is high. When S/N is low, the time saved can be used for signal averaging at the sampled points to give better precision. NLS typically provides one estimate at a time, whereas spectral estimation is inherently parallel. The frequency dimensions of conventional nD FT NMR may be denoted D₁, D₂, etc. As an extension of nD FT NMR, one can view spectral estimation of NMR relaxation as an extension into the zeroth dimension. In nD NMR, the information content of a spectrum can be extracted as a set of n-tuples (ω₁, … ω_n), corresponding to the peak maxima. Spectral estimation of NMR relaxation allows this information content to be extended to a set of (n + 1)-tuples (λ, ω₁, … ω_n), where λ is the relaxation rate.     

NMR relaxation and NMR imaging of elastomers in the course of thermal aging

A complex aging regime occurs in the course of thermal aging of elastomers. Depending on the type and the content of the rubber filler materials, temperature, chemical environment (normally air), and time, a different aging process can be observed also by nuclear magnetic resonance (NMR) [1–6]. The methods used are the common spin-echo ¹H-NMR, including variable echo times and parameter-selective NMR-¹H-imaging (material properties imaging). The decay of the echo-magnetization is discussed on the basis of a single-chain model with a distribution of dipolar interactions. This model is based on the influence of a very fast, but anisotropic, local motion, as well as larger and slower motions, which are able to diminish the residual dipolar interaction. Carbon-black-filled natural rubber, as well as silica and carbon-black-filled E-SBR (emulsion-polymerized styrene butadiene rubber) and S-SBR (solution-polymerized SBR) are the systems under investigation, with the results showing some characteristic features of the course of aging observable by NMR.     

Assigning uncertainties in the inversion of NMR relaxation data

Recovering the relaxation-time density function (or distribution) from NMR decay records requires inverting a Laplace transform based on noisy data, an ill-posed inverse problem. An important objective in the face of the consequent ambiguity in the solutions is to establish what reliable information is contained in the measurements. To this end we describe how upper and lower bounds on linear functionals of the density function, and ratios of linear functionals, can be calculated using optimization theory. Those bounded quantities cover most of those commonly used in the geophysical NMR, such as porosity, T(2) log-mean, and bound fluid volume fraction, and include averages over any finite interval of the density function itself. In the theory presented statistical considerations enter to account for the presence of significant noise in the signal, but not in a prior characterization of density models. Our characterization of the uncertainties is conservative and informative; it will have wide application in geophysical NMR and elsewhere.     

NMR relaxation rate in metallic carbon nanotubes

NMR relaxation rate, T₁⁻¹, of the metallic carbon nanotube is discussed based on Tomonaga–Luttinger-liquid theory. It is found that the Coulomb interaction leads to increase of (T₁T)⁻¹ by a power law with decreasing temperature, T. The dependence on temperature of (T₁T)⁻¹ in the multi-wall nanotube (MWNT) is shown to be strongly suppressed by existence of the metallic shells in the MWNTs.     

Transverse NMR relaxation in magnetically heterogeneous media

We consider the NMR signal from a permeable medium with a heterogeneous Larmor frequency component that varies on a scale comparable to the spin-carrier diffusion length. We focus on the mesoscopic part of the transverse relaxation, that occurs due to dispersion of precession phases of spins accumulated during diffusive motion. By relating the spectral lineshape to correlation functions of the spatially varying Larmor frequency, we demonstrate how the correlation length and the variance of the Larmor frequency distribution can be determined from the NMR spectrum. We corroborate our results by numerical simulations, and apply them to quantify human blood spectra.     

Rectifying system-specific errors in NMR relaxation measurements

15N spin relaxation parameters provide a powerful tool for probing the internal dynamics and thermodynamics of proteins. The biological insight provided by these experiments often involves interpretation of small changes in relaxation parameters. This, in turn, requires careful data analysis, especially in the identification and treatment of systematic error. While progress continues on reduction of experiment-specific errors associated with pulse sequences, system-specific sources of error have received far less attention. The impact of these errors varies between facilities, spectrometers, and biological samples. We demonstrate that performing a series of control experiments along with relaxation measurements can help identify, quantify, and isolate sources of system-specific error, and, in some cases, correct for systematic changes. We further demonstrate that control experiments can be performed without significant loss of spectrometer time, and lead to more accurate relaxation parameter values.