Jeener Broekaert Research Articles

NMR dipolar constants of motion in liquid crystals: Jeener–Broekaert, double quantum coherence experiments and numerical calculation on a 10-spin cluster

Two proton quasi-equilibrium states were previously observed in nematic liquid crystals, namely the S and W quasi-invariants. Even though the experimental evidence suggested that they originate in a partition of the spin dipolar energy into a strong and a weak part, respectively, from a theoretical viewpoint, the existence of an appropriate energy scale which allows such energy separation remains to be confirmed and a representation of the quasi-invariants is still to be given. We compare the dipolar NMR signals yielded both by the Jeener–Broekaert (JB) experiment as a function of the preparation time and the free evolution of the double quantum coherence (DQC) spectra excited from the S state, with numerical calculations carried out from first principles under different models for the dipolar quasi-invariants, in a 10-spin cluster which represents the 5CB ( 4 ′ -pentyl-4-biphenyl-carbonitrile) molecule. The calculated signals qualitatively agree with the experiments and the DQC spectra as a function of the single-quantum detection time are sensible enough to the different models to allow both to probe the physical nature of the initial dipolar-ordered state and to assign a subset of dipolar interactions to each constant of motion, which are compatible with the experiments. As a criterion for selecting a suitable quasi-equilibrium model of the 5CB molecule, we impose on the time evolution operator consistency with the occurrence of two dipolar quasi-invariants, that is, the calculated spectra must be unaffected by truncation of non-secular terms of the weaker dipolar energy. We find that defining the S quasi-invariant as the subset of the dipolar interactions of each proton with its two nearest neighbours yields a realistic characterization of the dipolar constants of motion in 5CB. We conclude that the proton-spin system of the 5CB molecule admits a partition of the dipolar energy into a bilinear strong and a multiple-spin weak contributions therefore providing two orthogonal constants of motion, which can be prepared and observed by means of the JB experiment. This feature, which implies the existence of two timescales of very different nature in the proton-spin dynamics, is ultimately dictated by the topology of the spin distribution in the dipole network and can be expected in other liquid crystals. Knowledge of the nature of the dipolar quasi-invariants will be useful in studies of dipolar-order relaxation, decoherence and multiple quantum NMR experiments where the initial state is a dipolar-ordered one.

Quasiequilibrium states in thermotropic liquid crystals studied by multiple-quantum NMR

Previous work showed that by means of the Jeener-Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in LC the two spin reservoirs, into which the Zeeman order is transferred, originate in the dipolar energy and that they are associated with a separation in energy scales: A constant of motion related to the stronger dipolar interactions (S), and a second one (W) corresponding to the secular part of the weaker dipolar interactions with regard to the Zeeman and the strong dipolar part. We study the nature of these quasi-invariants in nematic 5CB (4(')-pentyl-4-biphenyl-carbonitrile) and measure their relaxation times by encoding the multiple-quantum coherences of the states following the JB pulse pair on two orthogonal bases, Z and X. The experiments were also performed in powder adamantane at 301 K which is used as a reference compound having only one dipolar quasi-invariant. We show that the evolution of the quantum states during the buildup of the quasiequilibrium state in 5CB prepared under the S condition is similar to the case of powder adamantane and that their quasiequilibrium density operators have the same tensor structure. In contrast, the second constant of motion, whose explicit operator form is not known, involves a richer composition of multiple-quantum coherences of even order on the X basis, in consistency with the truncation inherent in its definition. We exploited the exclusive presence of coherences of +/-4,+/-6,+/-8, besides 0 and +/-2 under the W condition to measure the spin-lattice relaxation time T(W) accurately, so avoiding experimental difficulties that usually impair dipolar order relaxation measurement such as Zeeman contamination at high fields and also superposition of the different quasi-invariants. This procedure opens the possibility of measuring the spin-lattice relaxation of a quasi-invariant independent of the Zeeman and S reservoirs, so incorporating a new relaxation parameter useful for studying the complex molecular dynamics in mesophases. In fact, we report the first measurement of T(W) in a LC at high magnetic fields. Comparison of the obtained value with the one corresponding to a lower field (16 MHz) points out that the relaxation of the W-order strongly depends on the intensity of the external magnetic field, similarly to the case of the S reservoir, indicating that the relaxation of the W-quasi-invariant is also governed by the cooperative molecular motions.

Constants of motion in NMR spectroscopy

We present a general method for constructing a subset of the constants of motion in terms of products of spin operators. These operators are then used to give insight into the multi-spin orders comprising the quasi-equilibrium state formed under a Jeener–Broekaert sequence in small, dipolar-coupled, spin systems. We further show that constants of motion that represent single-quantum coherences are present due to the symmetry of the dipolar Hamiltonian under 180° spin rotations, and that such coherences contribute a DC component to the FID which vanishes in the absence of the flip-flop terms and is only present for spin clusters with an odd number of spins.

Simple modeling of dipolar coupled 7Li spins and stimulated-echo spectroscopy of single-crystalline β-eucryptite

Stimulated-echo spectroscopy has recently been applied to study the ultra-slow dynamics of nuclear spin-3/2 probes such as 7Li and 9Be in solids. Apart from the dominant first-order quadrupolar interaction in the present article also the impact of the homonuclear dipolar interactions is considered in a simple way: the time evolution of a dipole coupled pair of spins with I=3/2 is calculated in an approximation, which takes into account that the satellite transitions usually do not overlap. Explicit analytical expressions describing various aspects of a coupled quadrupolar pair subjected to a Jeener–Broekaert pulse sequence are derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor.

Spin counting experiments in the dipolar-ordered state

The dipolar-ordered state (ρ∝Hd) can be prepared from a state of Zeeman equilibrium at high field by adiabatically removing the Zeeman field. It is also possible to produce dipolar-ordered states in the rotating frame using two well-known methods—adiabatic demagnetization in the rotating frame and the Jeener–Broekaert (JB) pulse pair. Using multiple quantum nuclear magnetic resonance techniques, we illustrate the transient dynamics of the spin system following the JB pulse pair and its evolution to a dipolar-ordered state over a period of approximately 60 μs in a single crystal of CaF2 oriented along the [100] direction, and approximately 100 μs when the crystal is oriented along the [110] direction. By encoding the coherence numbers in an orthogonal basis (the x basis) to the Zeeman basis, we show that the dipolar-ordered state is a two spin correlated state. The observed ratio between double quantum and zero quantum coherences in the x basis confirms the presence of the Ii+Ij−+Ii−Ij+ (flip–flop) terms in the experimentally prepared dipolar-ordered state.

NMR second moment imaging using Jeener–Broekaert dipolar signals

It is demonstrated that imaging of the 1H NMR second moment can be achieved by using the Jeener–Broekaert (JB) dipolar signal instead of the Zeeman FID signal commonly employed. The JB dipolar signal can be induced by applying a JB pulse sequence, 90° x – τ−45° y – τ ′−45° y , which is followed by the time-suspension magic echo sequence, TREV-16TS, for imaging detection. Scanning the imaging detection to cover the whole evolution of the JB dipolar signal finally results in producing spatially resolved JB dipolar signals. The local value of the quantity called the “JB second moment,” M 2(JB), is then estimated from the initial slope of each resolved JB dipolar signal. The M 2(JB) can be regarded as the “weighted” powder average of the usual second moment. The “weighting” effect due to the JB sequence leads to the τ dependent M 2(JB) value. The τ dependence is potentially useful for characterizing the second moment distribution resulting from the crystal orientation dependence: For example, in addition to the usual powder average, an approximate distribution range can be deduced by a simple analysis of the τ dependence, serving as a new contrast for materials imaging. This is illustrated by preliminary experiments performed on test samples.

Dipolar spectroscopy and spin alignment in electron paramagnetic resonance

Two single-frequency techniques for refocusing (SIFTER) dipolar couplings between electron spins are introduced. The experiments are based on the solid-echo and Jeener–Broekaert sequences, well established in dipolar NMR spectroscopy of solids, and open up new routes to high-resolution two-dimensional EPR spectroscopy with only moderate requirements on the spectrometer. For distances between paramagnetic centres larger than 3 nm, SIFTER provides better resolution than double electron–electron resonance (DEER). Good agreement between distances from SIFTER measurements and force-field computations is found for shape-persistent biradicals with distances up to 5.1 nm corresponding to a dipolar frequency of 390 kHz.

Molecular hydrogen in amorphous silicon revisited

We measured the concentration of molecular hydrogen (H 2) in hydrogenated amorphous silicon (a-Si:H) by nuclear magnetic resonance (NMR) using a Jeener–Broekaert three-pulse sequence. For samples prepared by both plasma enhanced chemical vapor deposition (PECVD) and hot-wire chemical vapor deposition (HWCVD), the concentrations measured by this method are one order of magnitude larger than that inferred from the spin–lattice relaxation time ( T 1) of hydrogen bonded to silicon. For the sample prepared by PECVD, we found two different environments for molecular hydrogen, where the relaxation mechanisms differ. Molecular hydrogen in the samples prepared by HWCVD is motionally narrowed even at 8 K, while in the sample prepared by PECVD the molecular hydrogen is almost completely `frozen in' at 8 K. This difference is attributed to the effect of the host silicon structure.

Ortho-molecular hydrogen in hydrogenated amorphous silicon

Using a Jeener–Broekaert three-pulse sequence to measure directly the concentration of o-H2 by H1 nuclear magnetic resonance (NMR), we find that this concentration is one order of magnitude larger than that previously inferred from spin-lattice relaxation time (T1) measurements. At 300 K, this concentration of o-H2 contributes at most 30% to the narrow H1 NMR line attributed to hydrogen bonded to silicon. For a plasma-enhanced-chemical-vapor-deposition (PECVD) sample, two distinct values of T1 for o-H2 are found, only one of which contributes to the T1 for bonded hydrogen. In hot-wire-chemical-vapor-deposition samples, the line shape of o-H2 exhibits motional narrowing at lower temperatures, suggesting a more ordered structure than in a typical PECVD sample.

Sodium Ions in Ordered Environments in Biological Systems: Analysis of 23Na NMR Spectra

Experimentsthat selectively excite I = 32 nuclei exhibiting residual quadrupolar splittings are used to acquire 23Na NMR spectra from a range of biologically relevant samples containing sodium in ordered environments. Three complementary approaches to the analysis of such spectra are described: (i) measurement of relaxation rates, (ii) extraction of homogeneous linewidths from two-dimensional Jeener–Broekaert spectra, and (iii) simultaneous fitting of detailed theoretical functions to a series of one-dimensional Jeener–Broekaert spectra. Analysis of relaxation rates provides evidence for compartmentation in bovine nasal cartilage. Each approach is used to demonstrate the presence of anisotropy in transverse relaxation in porcine tendon. For certain samples containing collagen, a good theoretical fit to the spectra was obtained using a model that allows for anisotropic relaxation by including the effects of slow lateral and radial diffusion.

Molecular motions in thermotropic liquid crystals studied by NMR spin-lattice relaxation

Nuclear magnetic resonance relaxation experiments with field cycling techniques proved to be a valuable tool for studying molecular motions in liquid crystals, allowing a very broad Larmor frequency variation, sufficient to separate the cooperative motions from the liquidlike molecular diffusion. In new experiments combining NMR field cycling with the Jeener Broekaert order-transfer pulse sequence, it is possible to measure the dipolar order relaxation time (T1D), in addition to the conventional Zeeman relaxation time (T1Z) in a frequency range of several decades. When applying this technique to nematic thermotropic liquid crystals, T1D showed to depend almost exclusively on the order fluctuation of the director mechanism in the whole frequency range. This unique characteristic of T1D makes dipolar order relaxation experiments specially useful for studying the frequency and temperature dependence of the spectral properties of the collective motions.

Order fluctuations of the director in nematic thermotropic liquid crystals studied by nuclear magnetic resonance dipolar relaxation

Larmor frequency dependent NMR studies of dipolar order relaxation in liquid crystals have seldom been tried in the past. Using conventional static magnetic field techniques, the experiment cannot be extended to the low Larmor frequency (νL) regime due to limitations in the signal-to-noise ratio of the dipolar echo. In this work, we present an experimental study of the dipolar relaxation time in the frequency range 103–7×107 Hz in nematic thermotropic liquid crystals. To extend the study to such low frequencies, we used the Jeener–Broekaert pulse sequence combined with fast field-cycling NMR technique. For frequencies higher than 105 Hz, the dipolar relaxation time T1D(νL) follows the νL1/2-law that is characteristic of order fluctuations of the director (OFD) in nematics. In contrast, the Zeeman relaxation is driven by faster and less correlated motions, specially in the MHz frequency range. The relaxation of dipolar energy was measured to be remarkably faster than the one predicted by the usual semiclassical model of isolated spin pairs. Conceivably, the failure of the usual two-spin model should be sought in the absence of multispin interactions and multispin correlations. We propose that the OFD are the dominant relaxation mechanism for the dipolar order, even in the MHz regime. This result turns T1D(νL) experiment in a useful NMR technique for the study of slow molecular dynamics in mesophases.

Alignment Echo of Spin-3/29Be Nuclei: Detection of Ultraslow Motion

It is demonstrated that the alignment echo of9Be is quite useful for detecting ultraslow atomic motions in the metallic glass Zr46.75Ti8.25Cu7.5Ni10Be27.5. The time scale of detectable atomic motion is betweenT2= 1.5 ms andT1of a few seconds. Similar to previous works of2H NMR, the Jeener–Broekaert sequence is used to create quadrupolar order for spin-32nuclei upon nonselective excitations. Since the chemical and Knight shift distributions are not negligible for9Be, the proper choice of the dephasing time between the first and the second pulses is essential for achieving pure quadrupolar order. It is demonstrated experimentally that slow atomic motions contribute significantly to the decay of the alignment echo near the glass transition temperature.

Multiple-quantum filtered 17O and 23Na NMR analysis of mitochondrial suspensions

The fraction of strongly- and weakly-bound water molecules within mitochondrial suspensions, determined using three-quantum filtered 17O NMR relaxation analysis, was found to be large in comparison with that in erythrocytes and concentrated solutions of bovine serum albumen. It is suggested that bound water, together with regulation of mitochondrial matrix volume, may be an important controlling factor in the modulation of enzymic activity in the matrix. A spin I=5/2 Jeener–Broekaert experiment and a four-quantum filtration experiment were used to demonstrate the absence of orientationally ordered water molecules within the mitochondrion. In contrast, the mitochondrial sodium environment was shown to be highly ordered using a spin I=3/2 Jeener–Broekaert experiment.

17O NMR of water in ordered environments

Two NMR experiments are designed for selective excitation of spin I=5/2 nuclei that exhibit residual quadrupolar splittings. The I=5/2 Jeener–Broekaert experiment is preferred to the four-quantum filtration experiment as it is shown to be a more sensitive technique in experimental practice. Both techniques are applied to 17O-enriched water in biological systems. The occurrence of water which displays a residual 17O quadrupolar splitting is demonstrated for the first time in a model biological system and an excised tissue sample. The resulting 17O NMR spectra are shown to have the characteristics predicted in computer-simulated I=5/2 NMR spectra.

Quantification of the Contribution of Extracellular Sodium to23Na Multiple-Quantum-Filtered NMR Spectra of Suspensions of Human Red Blood Cells

23Na double-quantum-filtered (DQF) NMR enables the detection of anisotropic motion of sodium ions due to their interaction with ordered structures in biological tissues. Using the technique, anisotropic motion was found for sodium ions in mammalian red blood cell suspensions (RBC) and the effect was shown to correlate with the integrity of membrane cytoskeleton. In the present study relative contributions to the DQF and triple-quantum-filtered (TQF) spectra of sodium bound to anisotropic and isotropic binding sites in the intra- and extracellular sodium pools (Na content being 15 and 150 mM, respectively) of human RBC were quantified for different hematocrits. DQF spectra were measured by a modified Jeener–Broekaert pulse sequence which enabled exclusive detection of anisotropically moving sodium ions. The relative contributions of the extracellular sodium to the TQF and DQF spectra decreased as the hematocrit increased, but their efficiency relative to the sodium content increased. The contribution of the extracellular sodium to the TQF signal was found to dominate the spectrum of the RBC suspension at all hematocrits studied. The contribution of the extracellular sodium to the DQF was significantly smaller than that to the TQF and was only 22% at a high hematocrit of about 90%.

Simultaneous Acquisition of Quadrupolar Order and Double-Quantum23Na Signals

Na+with both residual quadrupolar coupling and biexponential relaxation contributes to the signal acquired from DQF-4, while only Na+with residual quadrupolar coupling contributes to the signal acquired with the Jeener–Broekaert sequence. Since RF phases and flip angles for DQF-4 and Jeener-Broekaert sequences are identical, these different types of signals can be generated simultaneously. A phase-cycling scheme is developed to differentiate the signals corresponding to residual quadrupolar coupling and biexponential relaxation after the signals are acquired by use of the same RF sequences. This technique can maximize the attainable information from Na+in biological tissues in a given acquisition time.

Extraction of Homogeneous23Na NMR Linewidths from Two-Dimensional Jeener–Broekaert Spectra*

The Jeener–Broekaert experiment has recently been applied to heterogeneous biological systems for selective observation of spinI= 3/2 nuclei which exhibit residual quadrupolar splittings. This paper describes the use of a two-dimensional version of this experiment to extract the homogeneous linewidths of such nuclei. The powderlike spectra produced by the one-dimensional Jeener–Broekaert experiment have lineshapes which depend on both homogeneous and inhomogeneous quadrupolar broadening. In two-dimensional Jeener–Broekaert spectra, the inhomogeneous broadening appears along the ω1= ω2and ω1= −ω2diagonal axes, with the result that the two broadenings are separated. The homogeneous linewidth can then be extracted by fitting cross sections through analytically generated lineshapes to the experimental spectra. The reliability of this technique is evaluated by computer simulation, and23Na NMR linewidths are measured experimentally in disordered liquid crystalline and heterogeneous biological samples. The possibility of measuring frequency-dependent variations in the homogeneous linewidth is also discussed.

Deuteron relaxation and anisotropic reorientation of a nematic liquid crystal

2H-NMR relaxation experiments have been used to investigate molecular motion of the nematogen 2-fluorenyl-4′-tetradecycloxy benzoate-d9 (FLOC14-d9). The molecule is perdeuterated in the rigid fluorenyl moiety and in the magnetically oriented nematic phase gives spectra with seven quadrupole doublets. An inversion recovery experiment was used to measure Zeeman order relaxation times T1Z, and a separate broadband Jeener–Broekaert experiment was used to measure quadrupolar relaxation times T1Q. This combination yields spectral densities, J1i(ω0) and J2i(2ω0), for each site i, on the liquid crystal molecule. The spectral density data have been interpreted by fitting the experimental results with a composite diffusion model of molecular motion of nematic liquid crystal molecules. The temperature and frequency dependence of the rotational correlation times is examined and discussed. The rotational motion is found to be statistically correlated with fluctuations of the nematic director, in such a fashion that director fluctuations make negligible contribution to the observed spectral densities.

Angular anisotropy of 2H NMR spectral densities in phospholipid bilayers containing cholesterol

Spin—lattice ( R 1Z) and quadrupolar order ( R 1Q) relaxation rates were measured for bilayers of macroscopically oriented 1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC- d 54) containing cholesterol (1:1 molar ratio), using inversion recovery and broadband Jeener—Broekaert pulse sequences, respectively. Anisotropic deuterium ( 2H) NMR spin relaxation data were obtained for the first time along the entire flexible acyl chains of the phospholipid molecules in the liquid-crystalline state. Individual spectral densities J 1(ω 0) and J 2(2ω 0) were calculated from these relaxation rates, and a strong dependence on the angle θ between the macroscopic bilayer normal and the static magnetic field was observed. The spectral densities exhibited opposite angular anisotropies, which were explained in terms of a simple rotational diffusion model for the molecular dynamics of membrane lipid constituents.