1H NMR at Larmor frequencies down to 3Hz by means of Field-Cycling techniques.

Field-Cycling (FC) NMR experiments were carried out at 1H Larmor frequencies down to about 3Hz. This could be achieved by fast switching a high polarizing magnetic field down to a low evolution field which is tilted with respect to the polarization field. Then, the low frequency Larmor precession of the nuclear spin magnetization about this evolution field is registered by means of FIDs in a high detection field. The crucial technical point of the experiment is the stabilization of the evolution field, which is achieved by compensating for temporal magnetic field fluctuations of all three spatial components. The paper reports on some other basic low field experiments such as the simultaneous measurement of the Larmor frequency and the spin-lattice relaxation time in such small fields as well as the irradiation of oscillating transversal magnetic field pulses at very low frequencies as a novel method for field calibration in low field FC NMR. The potential of low field FC is exemplified by the 1H relaxation dispersion of water at frequencies below about 2kHz stemming from the slow proton exchange process.

Perspectives of Deuteron Field-Cycling NMR Relaxometry for Probing Molecular Dynamics in Soft Matter.

Due to the single-particle character of the quadrupolar interaction in molecular systems, (2)H NMR poses a unique method for probing reorientational dynamics. Spin-lattice relaxation gives access to the spectral density, and its frequency dependency can be monitored by field-cycling (FC) techniques. However, most FC NMR studies employ (1)H; the use of (2)H is still rare. We report on the application of (2)H FC NMR for investigating the dynamics in molecular liquids and polymers. Commercial as well as home-built relaxometers are employed accessing a frequency range from 30 Hz to 6 MHz. Due to low gyromagnetic ratio, high coupling constants, and finite FC switching times, current (2)H FC NMR does not reach the dispersion region in liquids (toluene and glycerol), yet good agreement with the results from conventional high-field (HF) relaxation studies is demonstrated. The pronounced difference at low frequencies between (2)H and (1)H FC NMR data shows the relevance of intermolecular relaxation in the case of (1)H NMR. In the case of the polymers polybutadiene and poly(ethylene-alt-propylene), very similar relaxation dispersion is observed and attributed to Rouse and entanglement dynamics. Combination with HF (2)H relaxation data via applying frequency-temperature superposition allows the reconstruction of the full spectral density reflecting both polymer as well as glassy dynamics. Transformation into the time domain yields the reorientational correlation function C2(t) extending over nine decades in time with a long-time power law, C2(t) ∝ t(-0.45±0.05), which does not conform to the prediction of the tube-reptation model, for which ∝ t(-0.25) is expected. Entanglement sets in below C2(t = τe) ≅ S(2) = 0.001, where τe is the entanglement time and S the corresponding order parameter. Finally, we discuss the future prospects of the (2)H FC NMR technique.

Dynamics of [C3H5N2]6[Bi4Br18] by means of (1)H NMR relaxometry and quadrupole relaxation enhancement.

(1)H spin-lattice field cycling relaxation dispersion experiments in the intermediate phase II of the solid [C3H5N2]6[Bi4Br18] are presented. Two motional processes have been identified from the (1)H spin-lattice relaxation dispersion profiles and quantitatively described. It has been concluded that these processes are associated with anisotropic reorientations of the imidazolium ring, characterized by correlation times of the order of 10(-8) s-10(-9) s and of about 10(-5) s. Moreover, quadrupole relaxation enhancement (QRE) effects originating from slowly fluctuating (1)H-(14)N dipolar interactions have been observed. From the positions of the relaxation maxima, the quadrupole coupling parameters for the (14)N nuclei in [C3H5N2]6[Bi4Br18] have been determined. The (1)H-(14)N relaxation contribution associated with the slow dynamics has been described in terms of a theory of QRE [Kruk et al., Solid State Nucl. Magn. Reson. 40, 114 (2011)] based on the stochastic Liouville equation. The shape of the QRE maxima (often referred to as "quadrupole peaks") has been consistently reproduced for the correlation time describing the slow dynamics and the determined quadrupole coupling parameters.

Simultaneous measurement of very small magnetic fields and spin-lattice relaxation.

A field cycling (FC) NMR experiment is presented which allows for the simultaneous determination of very small magnetic fields down to about 3 µT and the concomitant measurement of nuclear spin-lattice relaxation times in these fields. The technique will enable broadband spin-lattice relaxation dispersion experiments down to about 100 Hz (1)H Larmor frequency. Limitations of its applicability are discussed.

Long-Time Diffusion in Polymer Melts Revealed by 1H NMR Relaxometry.

We demonstrate that field-cycling 1H NMR relaxometry can be used as a straightforward method of determining translational diffusion coefficient D = D(M) in polymer systems. The 1H spin-lattice relaxation dispersion for polybutadiene of different molecular masses M (446 < M/(g mol-1) < 9470) is measured at several temperatures (233 < T/K < 408) in a broad frequency range. The diffusion coefficient D(T) is determined from the intermolecular contribution to the overall spin-lattice relaxation rate R1(ω), which dominates in the low-frequency range and follows a universal dispersion law linear in √ω. The extracted diffusion coefficients are in good agreement with the values obtained previously by field gradient NMR. The molecular mass dependence D = D(M) exhibits two power laws: D ∝ M-1.3±0.1 and ∝M-2.3±0.1. They show a crossover for M = 2300, a value that is close to the entanglement molecular mass Me of polybutadiene. The corresponding power-law exponents are close to the prediction of the tube-reptation model.

Rotational Resonance in milli-tesla fields detected by Field Cycling NMR.

Rotational Resonance (R(2)) between different spin Zeeman levels in samples of adamantane C(10)H(16) (homonuclear R(2)) and a mixture of C(10)H(16) and C(10)D(16) (both homonuclear and heteronuclear R(2)) has been studied. A Field Cycling NMR instrument was used to match the external field frequency ν(0) to a fixed frequency of sample rotation ν(r) at ν(r) = 40, 50 or 60 kHz. Rotational Resonance is observed at rational frequency ratios of ν(0)/ν(r), such as 12, 23, 32 and 1. The method may prove to become a useful tool for the determination of spin-spin distances in condensed matter.

NMR field-cycling at ultralow magnetic fields.

The paper describes some significant technical improvements of a home built NMR field cycling relaxometer [O. Lips, A. Privalov, S. Dvinskikh, F. Fujara, J. Magn. Reson. 149 (2001) 22-28] now allowing for fast switching of polarization fields (up to more than 1T) to evolution fields down to the sub-µT range. The most important instrumental details such as the description of an involved 3-dimensional resistive coil setup are given. Fields below about 5 µT can only be stabilized by incorporation of an active field drift and fluctuation compensation tool. In this way, the smallest 1H Larmor frequency obtained and measured so far has been 12 Hz.

Combining one-dimensional stray-field micro-imaging with mechanical field-cycling NMR: a new spectrometer design.

A new spectrometer design combining stray-field micro-imaging with mechanical field-cycling Nuclear Magnetic Resonance (FC-NMR), allowing for one dimensional spatial resolution in the order of 10 µm is described. The field-cycle is implemented by moving the probe in the stray-field of a superconducting gradient magnet. In this way a field range between 10 mT and 6.3 T is covered. The maximum transfer time is less than 5 s. Further, methods to correct for some of the imaging artefacts found in previous studies are implemented. The main objective of this design is a depth- and field-dependent investigation of the defect structure caused by heavy-ion irradiation of ionic crystals.

Spatially resolved nuclear spin relaxation, electron spin relaxation and light absorption in swift heavy ion irradiated LiF crystals.

Spatially resolved (19)F and (7)Li spin-lattice relaxation rates are measured for LiF single crystals after irradiation with two kinds of swift heavy ions ((12)C of 133 MeV and (208)Pb of 1.78 GeV incident energy). Like in earlier studies on (130)Xe and (238)U irradiated LiF crystals, we found a strong enhancement of the nuclear spin-lattice relaxation rate within the ion penetration depth and a slight--but still significant--enhancement beyond. By evaluating the nuclear relaxation rate enhancement within the ion range after irradiation with different projectiles, a universal relationship between the spin-lattice relaxation rate and the dose is deduced. The results of accompanying X-band electron paramagnetic resonance relaxation measurements and optical absorption spectroscopy are included in a physical interpretation of this relationship. Also the reason for the enhanced relaxation rate beyond the ion range is further discussed.

Flat RF coils in static field gradient nuclear magnetic resonance.

The use of flat RF coils allows considerable gains in the sensitivity of static field gradient (SFG) nuclear magnetic resonance (NMR) experiments. In this article, this effect is studied theoretically as well as experimentally. Additionally, the flat coil geometry has been studied theoretically depending on magnetic field gradient, pulse sequence and amplifier power. Moreover, detecting the signal directly from the free induction decay (FID) turned out to be quite attractive for STRAFI-like microimaging experiments, especially when using flat coils. In addition to wound rectangular flat coils also spiral flat coils have been developed which can be manufactured by photolithography from printed circuit boards.

Fluorine dynamics in BaF2 crystal lattice as an example of complex motion in a simple system.

Fluorine relaxation profiles for a BaF(2) single crystal collected at several temperatures have been analyzed in terms of essentially different motional models: free rotational and free translational diffusion. The analysis has been performed to critically review the sensitivity of field dependent relaxation studies to mechanisms of molecular motions. The tested motional models do not realistically describe the fluorine dynamics within the crystal lattice. They have been chosen to attempt to answer quite fundamental questions regarding the feasibility of the field dependent nuclear spin relaxation studies to provide unique information on dynamic processes: 1. Is it possible to get information about the motional mechanisms by analyzing relaxation profiles collected in a broad frequency range? 2. To what extent is it possible to reasonably reproduce relaxation profiles in terms of unrealistic motional models? It has been concluded from the analysis that the rotational model leading to a single exponential correlation function explains the experimental data much better than the translational one. Validity regimes of the second order perturbation theory have been discussed in the context of the investigated system and the applied models.

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.

Deuteron spectra, spin-lattice relaxation, and stimulated echoes in ice II.

(2)H NMR spectra, spin-lattice relaxation, and stimulated echoes have been measured in polycrystalline ice II in the temperature range of 84-145 K at ambient pressure. From the spectra we obtain the quadrupole coupling constant in ice II, e(2)qQ/h = (225.7+/-1.2) kHz, and the asymmetry parameter, eta = 0.118+/-0.006. At 145 K, a phase transition of ice II into ice I(c) is observed by a change of both, its spectral and relaxation behavior. The spin-lattice relaxation in ice II is bimodal, showing two components of approximately the same weight. The fast relaxing part of the recovery curve progresses monoexponentially and the temperature dependence of its mean relaxation time corresponds to an unusually low activation energy of 2.3 kJ mol(-1). The slowly relaxing part, displaying average relaxation times of about 4000 s, is significantly stretched with a Kohlrausch parameter of 0.6 and shows no temperature dependence. The stimulated echo experiments show a temperature independent correlation decay. The analysis of intermediate states indicates that no small-angle motions are involved in the underlying process. Both findings exclude an interpretation in terms of molecular motion. Instead, spin diffusion in the deuteron system has to be considered as the origin of the phenomena observed in the stimulated echo experiments.

On the nature of the high-frequency relaxation in a molecular glass former: a joint study of glycerol by field cycling NMR, dielectric spectroscopy, and light scattering.

Fast field cycling (1)H NMR relaxometry is applied to determine the dispersion of spin-lattice relaxation time T(1)(omega) of the glass former glycerol in broad temperature (75-360 K) and frequency (10 kHz-30 MHz) ranges. The relaxation data are analyzed in terms of a susceptibility chi(")(omega) proportional, variantomegaT(1)(omega), related to the second rank (l=2) molecular orientational correlation function. Broadband dielectric spectroscopic results suggest the validity of frequency temperature superposition above the glass transition temperature T(g). This allows to combine NMR data of different temperatures into a single master curve chi(")(omegatau(alpha)) that extends over 15 decades in reduced frequency omegatau(alpha), where tau(alpha) is the structural alpha-relaxation time. This master curve is compared with the corresponding ones from dielectric spectroscopy (l=1) and depolarized light scattering (l=2). At omegatau(alpha)<1, NMR susceptibility is significantly different from both the dielectric and light scattering results. At omegatau(alpha)>1, there rather appears a difference between the susceptibilities of rank l=1 and l=2. Specifically, at omegatau(alpha)>>1, where the susceptibility is dominated by the so-called excess wing, the NMR and light scattering spectra (both l=2) rather coincide with each other and are about three times more intense than the dielectric (l=1) spectrum. This is explained by assuming that the high frequency dynamics correspond to only small-angle excursions. Below T(g), dielectric and NMR susceptibility compare well and exhibit an exponential temperature dependence.

High temperature mechanical field-cycling setup.

A new design of a mechanical field-cycling setup, operating in the wide temperature range up to 1200 K has been implemented. The sample is moved by a stepping motor in the stray field of a superconducting magnet inside a furnace of homogeneous temperature profile. For a field range from 0.75 to 7 T (transfer length 24 cm), the transfer time is less than 100 ms. The temperature profile is homogenized to better than 1% of the absolute set temperature. The main objective of this design is to extend the T1 relaxation dispersion range covered by electronic field-cycling to higher frequencies.

Spatially resolved characterization of Xe ion irradiated LiF crystals using static field gradient NMR.

Spatially resolved (19)F and (7)Li nuclear magnetic resonance (NMR) spin-lattice relaxation rates have been measured in LiF crystals irradiated with 1.44 GeV Xe ions at fluences from 10(10) to 10(12) ions cm(-2). In addition, the F-centre concentration has been measured by optical absorption spectroscopy and the concentration of paramagnetic centres by electron paramagnetic resonance (EPR). Within the ion range, the relaxation rate turns out to increase linearly with the concentration of paramagnetic centres but super-linearly with the F-centre concentration. Beyond the ion range, the relaxation rate is still significantly enhanced compared to non-irradiated LiF.

Spatially resolved characterization of heavy ion irradiated crystals using static field gradient nuclear magnetic resonance.

Static magnetic field gradient NMR has been used for one-dimensional spatial (19)F spin-lattice relaxation profile studies (resolution of the order of 10 µm) in a LiF crystal irradiated with U ions. Technical aspects of the use of large static magnetic field gradients are discussed as well as a special data acquisition mode allowing for effectively measuring spatially resolved spin-lattice relaxation rates as low as 10(-3) s(-1). In addition to the expected enhanced spin-lattice relaxation rate within the ion range, also an enhanced rate beyond the ion range has been found.

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.

Deuteron spin lattice relaxation in amorphous ices.

Temperature-dependent deuteron spin lattice relaxation times T(1) have been obtained from water in its three amorphous states at ambient pressure: low density amorphous (LDA), high density amorphous (HDA), and very high density amorphous (VHDA). It is found that in all of these states the magnetization recovery is essentially monoexponential and that T(1) of LDA is significantly longer than that of the higher density forms. Thus, T(1) can be used as a monitor parameter to study the kinetics of the transitions from HDA to LDA and from VHDA to LDA. During the transformation of VHDA to LDA an intermediate state is formed, which, according to its T(1) at low temperature, is clearly determined to be HDA-like. However, and most significantly, the transition from VHDA to this HDA-like state and further on to LDA occurs at temperatures significantly above the kinetic stability limit of native HDA produced at 77 K. These findings contribute to the current discussion on the nature of HDA and VHDA by strengthening the view that the annealing of VHDA at ambient pressure produces a relaxed HDA-like state.

Magnet design with high B(0) homogeneity for fast-field-cycling NMR applications.

The design, construction, and performance of a low-inductance solenoidal coil with high B(0) homogeneity for fast-field-cycling NMR is presented. It consists of six concentric layers. The conductor width is varied to minimize the B(0) inhomogeneity in the volume of the sample. This is done using an algorithm which takes the real shape of the conductor directly into account. The calculated coil geometry can be manufactured easily using standard computerized numeric control equipment, which keeps the costs low. The coil is liquid cooled and produces a B(0) field of 0.95 T at 800 A. The field inhomogeneity in a cylindrical volume (diameter 5 mm, length 10 mm) is about 10 ppm, and the inductance is 190 microH. Switching times below 200 micros can be achieved. During 6 months of operation the coil has shown good stability and reliability.