Two-dimensional2H NMR exchange spectroscopy on conducting ionic crystals

The two-dimensional (2-D) deuterium nuclear magnetic resonance (NMR) exchange spectroscopy is applied to two types of conducting ionic crystals for the study of hydrogen mobility and conductivity, viz. partially deuterated ammonium hydrogen selenate, NH₄HSO₄ (AHSe), and partially deuterated mixed crystals of betaine phosphate (DBP) and betaine phosphite (DBPI), DBP_1?x DBPI_x. In both crystals chemical exchange processes of deuterons between different hydrogen bridges occur which are studied by the 2-D-₂H-NMR technique over a wide temperature range in the slow-exchange regime. For AHSe exchange only occurs between two sites which are involved in hydrogen bonds. Two Arrhenius-like exchange processes were found the activation energies of which could be determined. For the case of DBP_1?x DBPI_x, with several deuteron sites taking part in the exchange, the analysis of the quantitative exchange behavior required a combination of time-domain analysis of our 2-D NMR data with mixing-time- and temperature-dependent measurements. Different exchange rates for each two-site exchange, all showing Arrhenius behavior, were obtained for DBP_0.3, DBPI_0.7. For crystals with different phosphite concentrationx the differences towards DBP_0.3, DBPI_0.3 were established. With the help of conductivity data from dielectric measurements quantitative relations between the exchange and conductivity processes are obtained for AHSe as well as for DBP_1?x DBPI_x. Finally, an estimation of effective charge carrier densities is discussed in view of possible conductivity models for both crystals.     

Two-dimensional PFG NMR for encoding correlations of position, velocity, and acceleration in fluid transport

A generalized approach to obtain two-dimensional maps of spatial particle coordinates and their derivatives with respect to time by PFG-NMR employing multiple gradient pulses is presented. A sequence of n magnetic field gradient pulses makes it possible, after independent stepping of each pulse and subsequent Fourier transformation, to plot the spin density distribution in coordinate space at n times and along the respective directions of the gradient pulses. In particular, two gradient pulses of effective area k(1) and k(2) separated by a time interval Delta lead to a plot of the combined two-time probability density, W(2)(r(1), 0; r(2), Delta), to find a particle at a coordinate r(1) at t = 0 and at r(2) at t = Delta. A conventional experiment for measuring transport properties by simultaneous stepping of the gradients under the condition k(1) = -k(2) is equivalent to a projection onto the secondary diagonal in the [r(1), r(2)] plot. The main diagonal represents an average position between the two timepoints t = 0 and t = Delta, so that a rotation of the coordinate plot by an angle of 45 degrees allows one to correlate the displacement R = r(2) - r(1) with the averaged position r parallel to the gradient direction. While an average velocity during the time interval Delta can be defined as &vmacr; = R/Delta, an extension toward acceleration and higher order derivatives is straightforward by modification of the pulse sequence. We discuss this concept by application to flow through a circular and a narrowing pipe (confusor), respectively, the experimental results of which are compared to numerical simulations. Copyright 2000 Academic Press.     

Two-dimensional measurements of velocity using two rotating gratings

A two-dimensional vector velocimeter is proposed on the basis of the time-varying spatial filtering method using a rotating disk with two transmission gratings. The filtering characteristics of the spatial filter used in the velocimeter were studied theoretically. A preliminary experiment was performed to measure the velocity vector of a rotating random pattern. The experimental results show the usefulness of the present velocimeter for measurements of the velocity.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

Two-dimensional nutation exchange NQR spectroscopy: direct determination of rotational angles

A new method for the direct determination of rotational angles based on 2-dimensional nutation exchange NQR spectroscopy is proposed. The method involves the detection of exchange processes through NQR nutation spectra recorded after the mixing interval. The response is analysed of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence with incrementing pulse widths. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively. It is shown that the 2D nutation exchange NQR spectrum exhibits characteristic ridges, which reveal the motional mechanism in a model-independent fashion. The angles through which the molecule rotates can be read directly from elliptical ridges in the 2D spectrum, which are also sensitive to the value of asymmetry parameter of the electric field gradient tensor.     

Two-dimensional NMR spectroscopy in Earth's magnetic field

We demonstrate the first two-dimensional correlation NMR (COSY) spectra obtained at ultra low frequencies (ULF) using the Earth's magnetic field. Using a specially developed spectrometer with multiple audio-frequency pulses under controlled pulse phase, we observe magnetisation transfer arising from heteronuclear J-couplings in trifluoroethanol and para-difluorobenzene. The 2D COSY spectra exhibit all diagonal and off-diagonal multiplets consistent with known J-couplings in these molecules.     

Two-dimensional imaging with a single-sided NMR probe

A new low field unilateral NMR sensor equipped with a two-dimensional gradient coil system was built. A new NMR-MOUSE concept using a simple bar magnet instead of the classical U-shaped geometry was used to produce magnetic field profiles comparatively homogeneous in extended lateral planes defining a suitable field of view for 2D spatial localization. Slice selection along the depth direction is obtained by means of the highly constant static magnetic field gradient produced by this magnet geometry. Implementing a two-dimensional phase-encoding imaging method 2D cross sections of objects were obtained with high spatial resolution. By retuning the probe it was possible to change the depth of the selected slice obtaining a 3D imaging method. The details of the construction of the new device are presented together with imaging tests to show the quality of space encoding.     

Two-dimensional ion velocity diffusion due to ion-acoustic turbulence

The diffusion of an ion beam caused by ion-acoustic turbulence is demonstrated experimentally by measuring the two-dimensional velocity distribution function f_b(v_⊥, v_⌈). The obtained ratio between the perpendicular and the parallel diffusion coefficient D_⊥/D_⌈ ≈ 21 is in reasonable agreement with three-dimensional quasi-linear theory.     

Two-dimensional organic superconductors studied by NMR under pressure

The (BEDT)₂X family of layered superconductors is one of the largest among nearly 50 organic superconductors currently known. One of the advantages of the organic compounds as prototype materials for studying the mechanisms of superconductivity is their relatively high sensitivity to hydrostatic pressure. We review recent NMR studies of these compounds using NMR under liquid and gas pressure. We focus on the low temperature part of the phase diagram where the physics is controlled by electronic correlations leading to a competition between magnetism and superconductivity. This interplay between different ground states is shown by the observation of a pseudo-gap and antiferromagnetic fluctuations and can be finely tuned by the application of pressure. Using a gas pressure system gives the unique possibility of sweeping the pressure at low temperature. Recently we used this technique to study the AF-SC boundary and established the existence of a first order transition line between the superconducting and antiferromagnetic states. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two-dimensional NMR correlation experiments in the gas phase

The application of common two-dimensional NMR correlation experiments to gaseous analytes for structural elucidation is reported. Standard sequences such as COSY, HSQC, and HMBC are readily applied to volatile hydrocarbons and fluorocarbons. In experiments using (19)F or (13)C as the observed nucleus, it is possible to take advantage of efficient spin-rotation relaxation to perform common experiments swiftly (a (19)F COSY acquired in 6s is shown) or to render insensitive experiments possible on a practical timescale (e.g. a gas phase INADEQUATE at natural isotopic abundance in 14h). NOE-based experiments were not successful on the gaseous systems studied.     

Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled time domain and thus allows for analysis of high dimensionality spectra acquired in a short time. The proposed method is not limited to radial sampling, it requires only to fulfill the Nyquist theorem considering two or more time domains at the same time. We show the application of new approach to the 3D HNCO spectrum acquired for protein sample with radial and spiral time domain sampling.     

Separation of velocity distribution and diffusion using PFG NMR

Pulsed field gradient (PFG) NMR is applied to investigate flow processes. In this case the NMR signal experiences phase modulation due to flow and signal attenuation due to the distribution of velocities. The velocity distribution consists of one part originating from diffusion and of a second part, the distribution of the directed motion. The usual PFG-experiment in which the gradient strength is incremented cannot distinguish between both. Incrementing velocity at constant gradient strength keeps the contribution from diffusion constant but changes the absolute width of the velocity distribution. So the signal is attenuated again, but only due to the distribution of the directed motion. The phase modulation as a signature of flow is not affected by this strategy, because velocity and gradient strength are Fourier conjugated. The key advantage of this approach is the possibility of measuring very low velocities, which only cause a very slight phase modulation that is easily covered by diffusion. The method is discussed here for very slow flow in a rheometer cell.     

Two-dimensional exchange nuclear quadrupole resonance spectroscopy of molecular crystals

A theoretical treatment of the 2D exchange NQR pulse sequence is presented and applied to the quantitative study of exchange processes in molecular crystals. It takes into account the off-resonance irradiation, which critically influences the spin dynamics. The response of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence is analysed. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. The mixing dynamics by exchange and the expected cross-peak intensities as a function of the frequency offset have been derived. The theory is illustrated by a study of the optimization procedure, which is of crucial importance for the detection of the cross- and diagonalpeaks in a 2D exchange spectrum. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively.     

Spin relaxation and chemical exchange in NMR simulations

Theory for describing the density matrix of a spin system experiencing chemical exchange and relaxation during the steps of an NMR experiment is presented in a form suitable for computation. Features in the theory that arise from exchange are discussed in detail, and comparisons to the exchange-free situation are made. A general computer program to carry out simulations of NMR experiments is described, and several examples of its performance are presented.     

Spectrally resolved velocity exchange spectroscopy of two-phase flow

The Velocity EXchange SpectroscopY (VEXSY) technique, which provides a means to correlate macroscopic molecular displacements measured during two intervals separated by a variable mixing period, has been applied for the first time to a system of two-phase flow. The chemical shift difference between water and methyl protons has been exploited to simultaneously determine the probability of displacements, or propagator, of both components in a water/silicone oil mixture flowing through a glass bead pack. The joint two-time probability densities as well as the conditional probabilities of velocities show a clearly distinct dispersion behaviour of both fluids which is a consequence of the different wetting properties of the fluids with respect to the glass surface of the bead pack.