Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

Dynamic of binary molecular systems-Advantages and limitations of NMR relaxometry

1H spin-lattice relaxation studies have been performed for binary systems, including glycerol as the first component and alanine, glycine, and aspartic acid (with different levels of deuteration) as the second one. The relaxation studies have been performed in the frequency range from 10 kHz to 10 MHz vs temperature. A theoretical framework, including all relevant 1H-1H and 1H-2H relaxation pathways, has been formulated. The theory has been exploited for a thorough interpretation of a large set of the experimental data. The importance of the 1H-2H relaxation contributions has been discussed, and the possibility of revealing dynamical properties of individual liquid components in binary liquids has been carefully investigated. As far as the dynamical properties of the specific binary liquids, chosen as an example, are considered, it has been shown that in the presence of the second component (alanine, glycine, and aspartic acid), both molecular fractions undergo dynamics similar to that of glycerol in bulk.

Molecular Dynamics of Jelly Candies by Means of Nuclear Magnetic Resonance Relaxometry

¹H spin-lattice Nuclear Magnetic Resonance relaxation studies have been performed for different kinds of Haribo jelly and Vidal jelly in a very broad frequency range from about 10 kHz to 10 MHz to obtain insight into the dynamic and structural properties of jelly candies on the molecular level. This extensive data set has been thoroughly analyzed revealing three dynamic processes, referred to as slow, intermediate and fast dynamics occurring on the timescale of 10^-6 s, 10^-7 s and 10^-8 s, respectively. The parameters have been compared for different kinds of jelly for the purpose of revealing their characteristic dynamic and structural properties as well as to enquire into how increasing temperature affects these properties. It has been shown that dynamic processes in different kinds of Haribo jelly are similar (this can be treated as a sign of their quality and authenticity) and that the fraction of confined water molecules is reduced with increasing temperature. Two groups of Vidal jelly have been identified. For the first one, the parameters (dipolar relaxation constants and correlation times) match those for Haribo jelly. For the second group including cherry jelly, considerable differences in the parameters characterizing their dynamic properties have been revealed.

X-nuclei hyperpolarization for studying molecular dynamics by DNP-FFC

Dynamic Nuclear Polarization methods are used for improving the quality of the NMR data, opening new possibilities by increasing both the sensitivity and the selectivity in NMR relaxation experiments. Recently, Fast Field Cycling relaxometry combined with DNP was introduced, demonstrating that molecular dynamics studies in the presence of natural or artificial radicals are indeed feasible under conditions where the signal-to-noise ratio is frequently critical. In this work, the extension of NMR relaxation dispersion beyond ¹H NMR, by hyperpolarization of X-nuclei, is demonstrated. Overhauser effect via nitroxide radicals in simple (low viscous) liquids and saline solutions was observed for ²H, ⁷Li and ¹³C nuclei at ambient temperature. Substantial NMR signal enhancement up to several hundred was achieved for the studied samples. An advanced approach for reconstructing of the original relaxation dispersion of pure substances is used to eliminate the effect of the additional radical relaxivity of the X-nuclei.

Multi-quantum quadrupole relaxation enhancement effects in 209Bi compounds

¹H spin-lattice nuclear magnetic resonance relaxation experiments have been performed for triphenylbismuth dichloride (C₁₈H₁₅BiCl₂) and phenylbismuth dichloride (C₆H₅BiCl₂) in powder. The frequency range of 20-128 MHz has been covered. Due to ¹H-²⁰⁹Bi dipole-dipole interactions, a rich set of pronounced Quadrupole Relaxation Enhancement (QRE) peaks (quadrupole peaks) has been observed. The QRE patterns for both compounds have been explained in terms of single- and double-quantum transitions of the participating nuclei. The analysis has revealed a complex, quantum-mechanical mechanism of the QRE effects. The mechanism goes far beyond the simple explanation of the existence of three quadrupole peaks for ¹⁴N reported in literature. The analysis has been supported by nuclear quadrupole resonance results that independently provided the ²⁰⁹Bi quadrupole parameters (amplitude of the quadrupole coupling constant and asymmetry parameter).

Model - free approach to quadrupole spin relaxation in solid 209Bi-aryl compounds

Nuclear Quadrupole Resonance (NQR) experiments were performed for deuterated and non-deuterated triphenylbismuth (BiPh3) to inquire into 209Bi relaxation mechanisms. The studies are motivated by the idea of exploiting Quadrupole Relaxation Enhancement (QRE) as a novel contrast mechanism for Magnetic Resonance Imaging. From this perspective relaxation features of nuclei possessing quadrupole moment (quadrupole nuclei) are of primary importance for the contrast effect. Spin-spin relaxation rates associated with the NQR lines were described in terms of the Redfield relaxation theory assuming that the relaxation is caused by fluctuations of the electric field gradient tensor at the position of the quadrupole nucleus that are described by an exponential correlation function. The description referred to as a model-free approach is an analogy of the description used for paramagnetic contrast agents. It was demonstrated that for the deuterated compound this approach captures the essential features of 209Bi relaxation, but it should not be applied for non-deuterated compounds as dipolar interactions between neighbouring protons and the quadrupole nucleus considerably contribute to the relaxation of the last one. Thus, the relaxation scenario for species containing quadrupole nuclei is fundamentally different than for paramagnetic contrast agents and this fact has to be taken into account when predicting contrast effects based on QRE.

Dynamics of solid alanine by means of nuclear magnetic resonance relaxometry

¹H nuclear magnetic resonance relaxometry was applied to investigate the dynamics of l-alanine in the solid phase (powder). The experimental studies were carried out in a very broad frequency range, covering four orders of magnitude-from 4 kHz to 40 MHz (referring to the ¹H resonance frequency) in order to probe motional processes of much different time scales by a single experiment. To get access to the dynamics of different proton groups of alanine, the ¹H spin-lattice relaxation measurements were performed for non-deuterated and partially deuterated alanine. The experiments were carried out in the temperature range of 293 K-370 K (non-deuterated alanine) and 318 K-370 K (partially deuterated alanine). As a result of a thorough theoretical analysis of the extensive set of experimental results, three motional processes occurring on different time scales are identified and quantitatively described. The slowest process occurs on a time scale of μs and it is attributed to the collective dynamics of a 3D hydrogen bond network of alanine, while the intermediate, attributed to the dynamics of the NH₃ group, corresponds to the range of tenths of ns. The fast process describes the rotation of the CH₃ group.

209Bi quadrupole relaxation enhancement in solids as a step towards new contrast mechanisms in magnetic resonance imaging

²⁰⁹Bi containing species have the potential to become novel contrast agents for MRI.

Unprecedented transformation of [I−·I3−] to [I42−] polyiodides in the solid state: structures, phase transitions and characterization of dipyrazolium iodide triiodide

Dipyrazolium iodide triiodide, [C₃N₂H₅⁺]₂[I⁻·I₃⁻], has been synthesized and studied by means of X-ray diffraction, differential scanning calorimetry, dielectric measurements, and UV-Vis spectroscopy.

Solid state field-cycling NMR relaxometry: instrumental improvements and new applications

The paper reviews recent progress in field cycling (FC) NMR instrumentation and its application to solid state physics. Special emphasis is put on our own work during the last 15years on instrumentation, theory and applications. As far as instrumentation is concerned we report on our development of two types of electronical FC relaxometers, a mechanical FC relaxometer and a combination of FC and one-dimensional microimaging. Progress has been achieved with respect to several parameters such as the accessible field and temperature range as well as the incorporation of sample spinning. Since an appropriate analysis of FC data requires a careful consideration of relaxation theory, we include a theory section discussing the most relevant aspects of relaxation in solids which are related to residual dipolar and quadrupolar interactions. The most important limitations of relaxation theory are also discussed. With improved instrumentation and with the help of relaxation theory we get access to interesting new applications such as ionic motion in solid electrolytes, structure determination in molecular crystals, ultraslow polymer dynamics and rotational resonance phenomena.

Dynamics of ferroelectric bis(imidazolium) pentachloroantimonate(III) by means of nuclear magnetic resonance 1H relaxometry and dielectric spectroscopy

Some of haloantimonates(III) and halobismuthates(III) are ferroelectric. Bis(imidazolium) pentachloroantimonate(III), (C3N2H5)2SbCl5 (abbreviation: ICA) is the first example of such compounds with a one-dimensional anionic chain which exhibits ferroelectric properties. The relation between the ionic dynamics and network structure and the ferroelectric features is not clear. Here Nuclear Magnetic Resonance (NMR) (1)H spin-lattice relaxation experiments at 25 MHz are reported for ICA in the temperature range of 80 K-360 K, covering ferroelectric-paraelectric and structural phase transitions of the compound occurring at 180 and 342 K, respectively. The relaxation process is biexponential in the whole temperature range indicating two dynamically nonequivalent types of imidazolium cations. Temperature dependences of both relaxation contributions allow for identifying three motional processes. Two of them are cation-specific - i.e. they are attributed to the two types of imidazolium cations, respectively. The third process involves both types of cations, and it is characterized by much lower activation energy. Moreover, the relaxation data (combined with (1)H second moment measurements) show that the ferroelectric-paraelectric phase transition mechanism is governed, to a large extent, by the anionic network arrangement. The NMR studies are complemented by dielectric spectroscopy experiments performed in the vicinity of the Curie temperature, TC = 180 K, to get insight into the mechanism of the ferroelectric-paraelectric phase transition. The dielectric dispersion data show critical slowing down of the macroscopic relaxation time, τ, in ICA when approaching TC from the paraelectric side, indicating an order-disorder type of ferroelectrics.

Sensitivity of 2H NMR spectroscopy to motional models: proteins and highly viscous liquids as examples

In order to study to what extent mechanisms of molecular motion can be unambiguously revealed by (2)H NMR spectroscopy, (2)H spectra for proteins (chicken villin protein headpiece HP36, selectively methyl-deuterated at leucine-69, C(δ) D(3)) and binary systems of high viscosity (benzene-d(6) in tricresyl phosphate) have been carefully analyzed as illustrative examples (the spectra are taken from the literature). In the first case, a model of restricted diffusion mediated by jumps between rotameric orientations has been tested against jump- and free diffusion models which describe rotational motion combined with jump dynamics. It has been found that the set of (2)H spectra of methyl-deuterated at leucine-69 chicken villin protein headpiece HP36 can be consistently explained by different motional models as well as by a gaussian distribution of correlation times assuming isotropic rotation (simple brownian diffusion model). The last finding shows that when the possible distribution of correlation times is not very broad one might not be able to distinguish between heterogeneous and homogenous (but more complex) dynamics by analyzing (2)H lineshapes. For benzene-d(6) in tricresyl phosphate, the dynamics is heterogeneous and it has been demonstrated that a gaussian distribution of correlation times reproduces well the experimental lineshapes, while for a Cole-Davidson distribution the agreement is somewhat worse. For inquires into the sensitivity of quadrupolar NMR spectral analysis (by "quadrupolar NMR spectroscopy we understand NMR spectroscopy of nuclei possessing quadrupole moment), the recently presented theoretical approach [Kruk et al., J. Chem. Phys. 135, 224511 (2011)] has been used as it allows simulating quadrupolar spectra for arbitrary motional conditions by employing the stochastic Liouville equation.

Nuclear quadrupole resonance lineshape analysis for different motional models: stochastic Liouville approach

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000)] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

Quadrupole relaxation enhancement--application to molecular crystals

A general theory of field dependent spin-lattice relaxation for nuclei of the spin quantum number 1/2 (1H, 19F, 13C) caused by dipole-dipole interactions with neighboring quadrupolar nuclei (nuclei possessing a quadrupolar moment) is presented. The theory is valid for arbitrary motional conditions and should be treated as a quadrupolar counterpart of the paramagnetic relaxation enhancement theory. When the energy level splitting of the dipolar spin (I=1/2) matches one of the transition frequencies of the quadrupolar nuclei one can observe a local enhancement of the dipolar spin relaxation (referred to as "quadrupolar peaks"). To see such effects the dynamics modulating the spin interactions has to be relatively slow. This brings the system beyond the validity range of perturbation approaches and requires the stochastic Liouville equation to be applied. The presented theory describes the quadrupolar relaxation enhancement (QRE) for an arbitrary spin quantum number of the quadrupolar nuclei and includes the asymmetry of the quadrupolar coupling. It has been applied to interpret the shape of magnetization curves (amplitude of 1H magnetization versus magnetic field) for the molecular crystal [C3N2H5]6[Bi4Br18] ([C3N2H5]-imidazolium). The magnetization curves show several dips (local minima) attributed to 1H-14N quadrupolar relaxation enhancement effects. In addition, as a limiting case a perturbation approach to QRE has been presented and its validity conditions have been discussed.

Mechanism of 1H-14N cross-relaxation in immobilized proteins

A resonant enhancement of the water-1H relaxation rate at three distinct frequencies in the range 0.5-3 MHz has been observed in a variety of aqueous biological systems. These so-called quadrupole (Q) peaks have been linked to a dipolar flip-flop polarization transfer from 1H nuclei to rapidly relaxing amide 14N nuclei in rotationally immobilized proteins. While the Q-peak frequencies conform to the known amide 14N quadrupole coupling parameters, a molecular model that accounts for the intensity and shape of the Q peaks has not been available. Here, we present such a model and test it against an extensive set of Q-peak data from two fully hydrated crosslinked proteins under conditions of variable temperature, pH and H/D isotope composition. We propose that polarization transfer from bulk water to amide 14N occurs in three steps: from bulk water to a so-called intermediary proton via material diffusion/exchange, from intermediary to amide proton by cross-relaxation driven by exchange-mediated orientational randomization of their mutual dipole coupling, and from amide proton to 14N by resonant dipolar relaxation 'of the second kind', driven by 14N spin fluctuations, which, in turn, are induced by restricted rigid-body motions of the protein. An essentially equivalent description of the last step can be formulated in terms of coherent 1H-->14N polarization transfer followed by fast 14N relaxation. Using independent structural and kinetic information, we show that the Q peaks from these two proteins involve approximately 7 intermediary protons in internal water molecules and side-chain hydroxyl groups with residence times of order 10(-5) s. The model not only accounts quantitatively for the extensive data set, but also explains why Q peaks are hardly observed from gelatin gels.

Field cycling methods as a tool for dynamics investigations in solid state systems: recent theoretical progress

In this paper physical mechanisms and theoretical treatments of polarization transfer and field-dependent relaxation in solid state systems, containing mutually coupled spins of spin quantum numbers I=12 (spins 12) and S1 (quadrupolar spins), are presented. First, theoretical descriptions of these effects are given in detail for an illustrative, simple system. Next, it is shown how to generalize the theories to much more complex spin systems. The polarization transfer and relaxation effects are illustrated by several examples. Typical misunderstandings regarding their physical origins are clarified. This paper reviews recent theoretical descriptions of the polarization transfer and relaxation phenomena. Its goal is to popularize the proper theoretical treatments with the intention to establish them as standard tools for analyzing field cycling data.

Simultaneous effects of relaxation and polarization transfer in LaF3-type crystals as sources of dynamic information

Fluorine nuclear magnetic resonance (NMR) spin-lattice relaxation dispersion has been measured for pure LaF(3) and La(1-x)Sr(x)F(3-x) for admixture concentrations x ranging from 0.01% up to 16%. The relaxation dispersion experiments have been carried out in a wide frequency range (20 kHz-40 MHz) at temperatures between 300 and 1400 K. The data have been analyzed using the recently published [J. Magn. Res. 179 (2006) 250] relaxation model for multispin systems of mutually interacting quadrupolar and dipolar nuclei. Rate constants of the fluorine ionic jumps within and among distinct fluorine sublattices have been extracted. Characteristic effects of the polarization transfer between fluorine and lanthanum spins have been observed and attributed to slow dynamics within one of the fluorine sublattices.