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

Water Dynamics in Dextran-Based Hydrogel Micro/Nanoparticles Studied by NMR Diffusometry and Relaxometry

Water dynamics in mesoporous dextran hydrogel micro/nanoparticles was investigated by means of nuclear magnetic resonance (NMR) techniques. High-resolution 1H NMR spectra and pulsed field gradient (PFG) NMR diffusometry measurements obtained on swollen state dextran micro/nanogel revealed the existence of different fractions of water molecules based on their interaction with the gel matrix. In addition to the translational diffusion of bulk water, two more diffusion processes characterized with self-diffusion coefficients 1 and 2 orders of magnitude smaller than that of bulk water were identified. 1H spin-lattice relaxation dispersion profiles obtained for a broad range of Larmor frequencies using fast field cycling (FFC) and conventional NMR relaxometry techniques allowed us to further clarify the mechanisms of molecular motion. According to the water proton pool fractions and associated self-diffusion coefficients, it is shown that the relaxation contribution associated with reorientation-mediated translational motions (RMTDs) dominates the relaxation dispersion observed at intermediate frequencies. At very low frequencies, the spin-lattice relaxation rate is dominated by the slow solid-gel dynamics probed by the water molecules interacting with the pores' surface hydroxyl groups due to the rapid chemical exchange between surface hydroxyl groups and free water. The correlation time for the thumbling-like motion of the dextran gel was found to be in the submillisecond range. The values of the self-diffusion and coherence lengths associated with motion of water molecules interacting with the solid-gel particles are consistent with the particle size and pore size distributions obtained for the studied dextran gels.

Dynamical Susceptibilities of Confined Water from Room Temperature to the Glass Transition

We confine water to narrow silica pores, where crystallization is suppressed, and determine the dynamical susceptibilities of the liquid from room temperature down to the glass transition by combining broadband dielectric spectroscopy (BDS) with ¹H and ²H nuclear magnetic resonance (NMR), in particular, by establishing NMR field-cycling relaxometry. For the correlation times, derivative analysis reveals Vogel-Fulcher-Tammann and Arrhenius regimes at T ≥ 215 K and T ≤ 160 K, respectively, which are separated by a broad crossover region. The continuous transition in the temperature dependence is accompanied by a gradual change from asymmetric high-temperature shapes of the dynamical susceptibilities to symmetric low-temperature ones and by a steady decrease of the dielectric relaxation strength. In the Arrhenius regime (E_a = 0.48 eV) at T ≤ 160 K, 2D ²H NMR spectra reveal quasi-isotropic water reorientation. We rationalize these results in terms of a crossover to an interface-affected, noncooperative relaxation involving both rotational and translational motions.

NMR Relaxometry Accessing the Relaxation Spectrum in Molecular Glass Formers

It is a longstanding question whether universality or specificity characterize the molecular dynamics underlying the glass transition of liquids. In particular, there is an ongoing debate to what degree the shape of dynamical susceptibilities is common to various molecular glass formers. Traditionally, results from dielectric spectroscopy and light scattering have dominated the discussion. Here, we show that nuclear magnetic resonance (NMR), primarily field-cycling relaxometry, has evolved into a valuable method, which provides access to both translational and rotational motions, depending on the probe nucleus. A comparison of ¹H NMR results indicates that translation is more retarded with respect to rotation for liquids with fully established hydrogen-bond networks; however, the effect is not related to the slow Debye process of, for example, monohydroxy alcohols. As for the reorientation dynamics, the NMR susceptibilities of the structural (α) relaxation usually resemble those of light scattering, while the dielectric spectra of especially polar liquids have a different broadening, likely due to contributions from cross correlations between different molecules. Moreover, NMR relaxometry confirms that the excess wing on the high-frequency flank of the α-process is a generic relaxation feature of liquids approaching the glass transition. However, the relevance of this feature generally differs between various methods, possibly because of their different sensitivities to small-amplitude motions. As a major advantage, NMR is isotope specific; hence, it enables selective studies on a particular molecular entity or a particular component of a liquid mixture. Exploiting these possibilities, we show that the characteristic Cole-Davidson shape of the α-relaxation is retained in various ionic liquids and salt solutions, but the width parameter may differ for the components. In contrast, the low-frequency flank of the α-relaxation can be notably broadened for liquids in nanoscopic confinements. This effect also occurs in liquid mixtures with a prominent dynamical disparity in their components.

Recent advances in NMR spectroscopy of ionic liquids

This review presents recent developments in the application of NMR spectroscopic techniques in the study of ionic liquids. NMR has been the primary tool not only for the structural characterization of ionic liquids, but also for the study of dynamics. The presence of a host of NMR active nuclei in ionic liquids permits widespread use of multinuclear NMR experiments. Chemical shifts and multinuclear coupling constants are used routinely for the structure elucidation of ionic liquids and of products formed by their covalent interactions with other materials. Also, the availability of a multitude of NMR techniques has facilitated the study of dynamical processes in them. These include the use of NOESY to study inter-ionic interactions, pulsed-field gradient techniques for probing transport properties, and relaxation measurements to elucidate rotational dynamics. This review will focus on the application of each of these techniques to investigate ionic liquids.

Nuclear Spin Relaxation in Viscous Liquids: Relaxation Stretching of Single-Particle Probes

Spin-lattice relaxation rates R₁(ω,T), probed via high-field and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency-temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R₁(T) vs the spin-spin relaxation rate R₂(T) and (ii) a plot of R₁(T) vs an independently measured reference time τ_ref(T). Using single-frequency scans, (i) allows one to extract the relaxation stretching as well as the NMR coupling constant. Surveying 26 data sets, we find Kohlrausch functions with exponents 0.39 < β_K ≤ 0.67. Plots of the spin-spin relaxation rate R₂─rescaled by the NMR coupling constant─as a function of temperature allow one to test how well site-specific NMR relaxations couple to a given reference process. Upon cooling of flexible molecule liquids, the site-specific dynamics is found to merge, suggesting that near T_g the molecules reorient essentially as a rigid entity. This presents a possible resolution for the much lower stretching parameters reported here at high temperatures that contrast with the ones that were reported to be universal in a recent DLS study close to T_g. Our analysis underlines that deuteron relaxation is a uniquely powerful tool to probe single-particle reorientation.

Dynamics in the plastic crystalline phase of cyanocyclohexane and isocyanocyclohexane probed by 1H field cycling NMR relaxometry

Proton Field-Cycling (FC) nuclear magnetic resonance (NMR) relaxometry is applied over a wide frequency and temperature range to get insight into the dynamic processes occurring in the plastically crystalline phase of the two isomers cyanocyclohexane (CNCH) and isocyanocyclohexane. The spin-lattice relaxation rate, R₁(ω), is measured in the 0.01-30 MHz frequency range and transformed into the susceptibility representation χ_NMR ^″ω=ωR₁ω. Three relaxation processes are identified, namely, a main (α-) relaxation, a fast secondary (β-) relaxation, and a slow relaxation; they are very similar for the two isomers. Exploiting frequency-temperature superposition, master curves of χ_NMR ^″ωτ are constructed and analyzed for different processes. The α-relaxation displays a pronounced non-Lorentzian susceptibility with a temperature independent width parameter, and the correlation times display a non-Arrhenius temperature dependence-features indicating cooperative dynamics of the overall reorientation of the molecules. The β-relaxation shows high similarity with secondary relaxations in structural glasses. The extracted correlation times well agree with those reported by other techniques. A direct comparison of FC NMR and dielectric master curves for CNCH yields pronounced difference regarding the non-Lorentzian spectral shape as well as the relative relaxation strength of α- and β-relaxation. The correlation times of the slow relaxation follow an Arrhenius temperature dependence with a comparatively high activation energy. As the α-process involves liquid-like isotropic molecular reorientation, the slow process has to be attributed to vacancy diffusion, which modulates intermolecular dipole-dipole interactions, possibly accompanied by chair-chair interconversion of the cyclohexane ring. However, the low frequency relaxation features characteristic of vacancy diffusion cannot be detected due to experimental limitations.

Molecular dynamics simulations vs field-cycling NMR relaxometry: Structural relaxation mechanisms in the glass-former glycerol revisited

We combine field-cycling (FC) relaxometry and molecular dynamics (MD) simulations to study the rotational and translational dynamics associated with the glassy slowdown of glycerol. The ¹H NMR spin-lattice relaxation rates R₁(ω) probed in the FC measurements for different isotope-labelled compounds are computed from the MD trajectories for broad frequency and temperature ranges. We find high correspondence between experiment and simulation. Concerning the rotational motion, we observe that the aliphatic and hydroxyl groups show similar correlation times but different stretching parameters, while the overall reorientation associated with the structural relaxation remains largely isotropic. Additional analysis of the simulation results reveals that transitions between different molecular configurations are slow on the time scale of the structural relaxation at least at sufficiently high temperatures, indicating that glycerol rotates at a rigid entity, but the reorientation is slower for elongated than for compact conformers. The translational contribution to R₁(ω) is well described by the force-free hard sphere model. At sufficiently low frequencies, universal square-root laws provide access to the molecular diffusion coefficients. In both experiment and simulation, the time scales of the rotational and translational motions show an unusually large separation, which is at variance with the Stokes-Einstein-Debye relation. To further explore this effect, we investigate the structure and dynamics on various length scales in the simulations. We observe that a prepeak in the static structure factor S(q), which is related to a local segregation of aliphatic and hydroxyl groups, is accompanied by a peak in the correlation times τ(q) from coherent scattering functions.

Self-diffusion micromechanism in Nafion studied by 2H NMR relaxation dispersion

Field Cycling (FC) ²H nuclear magnetic resonance (NMR) relaxometry was applied to study dynamics in Nafion NR 212 in the temperature range from 300 K to 190 K and water content of λ = 8.2. The sensitive time window of FC was extended up to eight decades using the temperature-frequency superposition principle and master curve. The rotational correlation times obtained from ²H FC NMR coincide with translational correlation times gained from static field ²H NMR diffusometry in the temperature range applied. This fact means that a long-range mass transport in Nafion is coupled to molecular rotations. It is assumed that confined water in Nafion has more ordered oxygen sublattices as compared with bulk water, on a short range is similar to ice. We discuss the possible role of D and L defects, typical for the ordered ice structure and using this concept to describe the processes of self-diffusion of confined water in Nafion, as well as the similarity of temperature and humidity dependence of self-diffusion and proton conductivity.

Dielectric relaxation and proton field-cycling NMR relaxometry study of dimethyl sulfoxide/glycerol mixtures down to glass-forming temperatures

Mixtures of glycerol and dimethyl sulfoxide (DMSO) are studied by dielectric spectroscopy (DS) and by 1H field-cycling (FC) NMR relaxometry in the entire concentration range and down to glass-forming temperatures (170-323 K). Molecular dynamics is accessed for 0 < xDMSO ≤ 0.64, at higher concentration phase separation occurs. The FC technique provides the frequency dependence of the spin-lattice relaxation rate which is transformed to the susceptibility representation and thus allows comparing NMR and DS results. The DS spectra virtually do not change with xDMSO and T, only the relaxation times become shorter. This is in contrast to the non-associated mixture toluene/quinaldine for which strong spectral changes occur. The FC relaxation spectra of glycerol in solution with DMSO or (deuterated) DMSO-d6 display a bimodal structure with a high-frequency part reflecting rotational and a low-frequency part reflecting translational dynamics. Regarding the rotational contribution in the glycerol/DMSO-d6 mixtures, no spectral change with xDMSO and T is observed. Yet, the non-deuterated mixture reveals a broader relaxation spectrum. Time constants τrot(T) probed by the two techniques complement each, a range 10-11 s < τ < 10 s is covered. The glass transition temperature Tg(xDMSO) is determined, yielding Tg = 149.5 ± 1 K of pure DMSO by extrapolation. Analysing the low-frequency FC NMR spectra allows to determine the diffusion coefficient Dtrans. Its logarithm shows a linear xDMSO-dependence as does lg τrot. The ratio Dtrans/Drot is independent of xDMSO and its low value indicates large separation of translation and rotation. The corresponding unphysically small hydrodynamic radius indicates strong failure of Stokes-Einstein-Debye relation. Such anomaly is taken as characteristics of a 3d hydrogen-bonded network. We conclude, although DMSO is an aprotic liquid the molecule is continuously incorporated in the hydrogen network of glycerol. Both molecules display common dynamics, i.e., no decoupling of the component dynamics is found in contrast to quinaldine/toluene with a similar Tg difference of its components.

The dynamics of the plastically crystalline phase of cyanoadamantane revisited by NMR line shape analysis and field-cycling relaxometry

The dynamics of cyanoadamantane (CN-ADA) in its plastically crystalline phase encompasses three processes: overall tumbling of the rigid molecule, rotation around the molecular symmetry axis, and vacancy diffusion. This makes CN-ADA a prototypical case to be studied by field-cycling as well as by conventional NMR relaxometry. Data are collected from 430 K down to about 4 K and frequencies in the range of 10 kHz-56 MHz are covered. The overall tumbling is interpreted as a cooperative jump process preceding along the orthogonal axis of the cubic lattice and exhibiting a temperature independent non-Lorentzian spectral density. Consequently, a master curve is constructed, which yields model-independent correlation times, which agree well with those reported in the literature. It can be interpolated by a Cole-Davidson function with a width parameter β_CD = 0.83. The uniaxial rotation persisting in the glassy crystal (T < T_g = 170 K) is governed by a broad distribution of activation energies, g(E). In this case, the standard master curve construction applied for the overall tumbling, for example, fails, as the actually probed distribution of correlation times G(ln τ) strongly changes with temperature. We suggest a scaling method that generally applies for the case that a relaxation process is determined by a distribution of thermally activated processes. Frequency as well as temperature dependence of the relaxation rate can be used to reconstruct g(E). In addition, g(E) is extracted from the proton line-shape, which was measured down to 4 K. Vacancy diffusion governs the relaxation dispersion at highest temperatures; yet, a quantitative analysis is not possible due to instrumental limitations.

Application of proton field-cycling NMR relaxometry for studying translational diffusion in simple liquids and polymer melts

With the availability of commercial field-cycling relaxometers together with progress of home-built instruments nuclear magnetic resonance relaxometry has gained new momentum as a method of investigating the dynamics in viscous liquids and polymer melts. The method provides the frequency dependence of the spin-lattice relaxation rate. In the case of protons, one distinguishes intramolecular and intermolecular relaxation pathways. Whereas the intramolecular contribution prevails at high frequencies and reflects rotational dynamics, the often ignored intermolecular relaxation contribution dominates at low-frequency and provides access to translational dynamics. A universal low-frequencies dispersion law holds which in pure systems allows determining the diffusion coefficient in a straightforward way. In addition, the rotational time constant is extracted from the high-frequency relaxation contribution. This is demonstrated for simple and ionic liquids and for polymer melts.

Dynamics of Dimethylbutanols in Plastic Crystalline Phases by Field Cycling 1H NMR Relaxometry

2,2-Dimethylbutan-1-ol (2,2-DM-1-B), 3,3-dimethylbutan-1-ol (3,3-DM-1-B), and 3,3-dimethylbutan-2-ol (3,3-DM-2-B) show a rich solid-state polymorphism, which includes one or more plastic crystalline phases (also referred to as orientationally disordered crystalline (ODIC) phases) and glass of the liquid or ODIC phases. In this work, the dynamics of the three isomeric alcohols was investigated in the liquid and plastic crystalline phases by fast field cycling ¹H NMR relaxometry in the temperature range between 213 and 303 K. The analysis of the nuclear magnetic relaxation dispersion curves (i.e., longitudinal relaxation rate R₁ vs ¹H Larmor frequency) acquired for the different alcohols at different temperatures gave quantitative information on internal motions, overall molecular reorientations, and molecular self-diffusion. Self-diffusion coefficients were also determined in the liquid phase and in some ODIC phases of the samples from the trends of ¹H R₁ as a function of the frequency square root at low frequencies. Remarkable changes in the temperature trends of correlation times and self-diffusion coefficients were found at the transition between the liquid and the ODIC phase for 2,2-DM-1-B and 3,3-DM-1-B, and between ODIC phases for 3,3-DM-2-B, the latter sample showing a markedly different dynamic and phase behavior.

Field-cycling NMR experiments in an ultra-wide magnetic field range: relaxation and coherent polarization transfer

An experimental method is described allowing fast field-cycling Nuclear Magnetic Resonance (NMR) experiments over a wide range of magnetic fields from 5 nT to 10 T. The method makes use of a hybrid technique: the high field range is covered by positioning the sample in the inhomogeneous stray field of the NMR spectrometer magnet. For fields below 2 mT a magnetic shield is mounted on top of the spectrometer; inside the shield the magnetic field is controlled by a specially designed coil system. This combination allows us to measure T1-relaxation times and nuclear Overhauser effect parameters over the full range in a routine way. For coupled proton-carbon spin systems relaxation with a common T1 is found at low fields, where the spins are "strongly coupled". In some cases, experiments at ultralow fields provide access to heteronuclear long-lived spin states. Efficient coherent polarization transfer is seen for proton-carbon spin systems at ultralow fields as follows from the observation of quantum oscillations in the polarization evolution. Applications to analysis and the manipulation of heteronuclear spin systems are discussed.

Multiscale nuclear magnetic relaxation dispersion of complex liquids in bulk and confinement

The nuclear magnetic relaxation dispersion (NMRD) technique consists of measurement of the magnetic-field dependence of the longitudinal nuclear-spin-lattice relaxation rate 1/T₁. Usually, the acquisition of the NMRD profiles is made using a fast field cycling (FFC) NMR technique that varies the magnetic field and explores a very large range of Larmor frequencies (10 kHz < ω₀/(2π) <40 MHz). This allows extensive explorations of the fluctuations to which nuclear spin relaxation is sensitive. The FFC technique thus offers opportunities on multiple scales of both time and distance for characterizing the molecular dynamics and transport properties of complex liquids in bulk or embedded in confined environments. This review presents the principles, theories and applications of NMRD for characterizing fundamental properties such as surface correlation times, diffusion coefficients and dynamical surface affinity (NMR wettability) for various confined liquids. The basic longitudinal and transverse relaxation equations are outlined for bulk liquids. The nuclear relaxation of a liquid confined in pores is considered in detail in order to find the biphasic fast exchange relations for a liquid at proximity of a solid surface. The physical-chemistry of liquids at solid surfaces induces striking differences between NMRD profiles of aprotic and protic (water) liquids embedded in calibrated porous disordered materials. A particular emphasis of this review concerns the extension of FFC NMR relaxation to industrial applications. For instance, it is shown that the FFC technique is sufficiently rapid for following the progressive setting of cement-based materials (plasters, cement pastes, concretes). The technique also allows studies of the dynamics of hydrocarbons in proximity of asphaltene nano-aggregates and macro-aggregates in heavy crude oils as a function of the concentration of asphaltenes. It also gives new information on the wettability of petroleum fluids (brine and oil) embedded in shale oil rocks. It is useful for understanding the relations and correlations between NMR relaxation times T₁ and T₂, diffusion coefficients D, and viscosity η of heavy crude oils. This is of particular importance for interpreting T₁, T₂, 2D T₁-T₂ and D-T₂ correlation spectra that could be obtained down-hole, thus giving a valuable tool for investigating in situ the molecular dynamics of petroleum fluids. Another domain of interest concerns biological applications. This is of particular importance for studying the complex dynamical spectrum of a folded polymeric structure that may span many decades in frequency or time. A direct NMRD characterization of water diffusional dynamics is presented at the protein interface. NMR experiments using a shuttle technique give results well above the frequency range accessible via the FFC technique; examples of this show protein dynamics over a range from fast and localized motions to slow and delocalized collective motions involving the whole protein. This review ends by an interpretation of the origin of the proton magnetic field dependence of T₁ for different biological tissues of animals; this includes a proposal for interpreting in vivo MRI data from human brain at variable magnetic fields, where the FFC relaxation analysis suggests that brain white-matter is distinct from grey-matter, in agreement with diffusion-weighted MRI imaging.

Dynamics of poly(vinyl butyral) studied using dielectric spectroscopy and 1H NMR relaxometry

Dielectric Spectroscopy (DS) and ¹H Fast Field-Cycling (FFC) NMR relaxometry were applied for understanding the dynamic behavior of the amorphous ter-polymer poly(vinyl butyral) (PVB) across the glass transition temperature (T_g = 70 °C by Differential Scanning Calorimetry). Above T_g, main chain segmental motions (α relaxation) were detected and characterized using both DS and FFC NMR relaxometry. The correlation times extracted by the analysis of DS and FFC NMR relaxometry data agreed within a factor of three and showed a Vogel-Fulcher-Tammann temperature dependence, with an associated T_g of 69 °C and a fragility of 155 for PVB glass. Below T_g, a secondary process (β relaxation) was revealed by DS, and was ascribed to reorientations of the vinyl alcohol dipoles due to local twisting motions with an associated activation barrier of 11 kcal mol^-1. The β process was also found to contribute to ¹H NMR relaxation above T_g.

Correction of environmental magnetic fields for the acquisition of Nuclear magnetic relaxation dispersion profiles below Earth's field

T₁ relaxation times can be measured at a range of magnetic field strengths by Fast Field-Cycling (FFC) NMR relaxometry to provide T₁-dispersion curves. These are valuable tools for the investigation of material properties as they provide information about molecular dynamics non-invasively. However, accessing information at fields below 230 μT (10kHz proton Larmor frequency) requires careful correction of unwanted environmental magnetic fields. In this work a novel method is proposed that compensates for the environmental fields on a FFC-NMR relaxometer and extends the acquisition of Nuclear Magnetic Relaxation Dispersion profiles to 2.3μT (extremely low field region), with direct application in the study of slow molecular motions. Our method is an improvement of an existing technique, reported by Anoardo and Ferrante in 2003, which exploits the non-adiabatic behaviour of the magnetisation in rapidly-varying magnetic fields and makes use of the oscillation of the signal amplitude to estimate the field strength. This increases the accuracy in measuring the environmental fields and allows predicting the optimal correction values by applying simple equations to fit the data acquired. Validation of the method is performed by comparisons with well-known dispersion curves obtained from polymers and benzene.

13C-Decoupled J-Coupling Spectroscopy Using Two-Dimensional Nuclear Magnetic Resonance at Zero-Field

We present a two-dimensional method for obtaining ¹³C-decoupled, ¹H-coupled nuclear magnetic resonance (NMR) spectra in zero magnetic field using coherent spin-decoupling. The result is a spectrum determined only by the proton-proton J-coupling network. Detection of NMR signals in zero magnetic field requires at least two different nuclear spin species, but the proton J-spectrum is independent of isotopomer, thus potentially simplifying spectra and thereby improving the analytical capabilities of zero-field NMR. The protocol does not rely on a difference in Larmor frequency between the coupled nuclei, allowing for the direct determination of J-coupling constants between chemically equivalent spins. We obtain the ¹³C-decoupled zero-field spectrum of [1-¹³C]-propionic acid and identify conserved quantum numbers governing the appearance of cross peaks in the two-dimensional spectrum.