Dynamics of molecular reorientations: Analogies between quasielastic neutron scattering and deuteron NMR spin alignment

Reorientational dynamics in highly asymmetric binary low-molecular mixtures-A quantitative comparison of dielectric and NMR spectroscopy results

Previously, we scrutinized the dielectric spectra of a binary glass former made by a low-molecular high-T_g component 2-(m-tertbutylphenyl)-2'-tertbutyl-9,9'-spirobi[9H]fluorene (m-TPTS; T_g = 350 K) and low-T_g tripropyl phosphate (TPP; T_g = 134 K) [Körber et al., Phys. Chem. Chem. Phys. 23, 7200 (2021)]. Here, we analyze nuclear magnetic resonance (NMR) spectra and stimulated echo decays of deuterated m-TPTS-d₄ (²H) and TPP (³¹P) and attempt to understand the dielectric spectra in terms of component specific dynamics. The high-T_g component (α₁) shows relaxation similar to that of neat systems, yet with some broadening upon mixing. This correlates with high-frequency broadening of the dielectric spectra. The low-T_g component (α₂) exhibits highly stretched relaxations and strong dynamic heterogeneities indicated by "two-phase" spectra, reflecting varying fractions of fast and slow liquid-like reorienting molecules. Missing for the high-T_g component, such two-phase spectra are identified down to w_TPP = 0.04, indicating that isotropic reorientation prevails in the rigid high-T_g matrix stretching from close to T_g ^TPP to T_g1 w_TPP. This correlates with low-frequency broadening of the dielectric spectra. Two T_g values are defined: T_g1 (w_TPP) displays a plasticizer effect, whereas T_g2 (w_TPP) passes through a maximum, signaling extreme separation of the component dynamics at low w_TPP. We suggest understanding the latter counter-intuitive feature by referring to a crossover from "single glass" to "double glass" scenario revealed by recent MD simulations. Analyses reveal that a second population of TPP molecules exists, which is associated with the dynamics of the high-T_g component. However, the fractions are lower than suggested by the dielectric spectra. We discuss this discrepancy considering the role of collective dynamics probed by dielectric but not by NMR spectroscopy.

Small Molecules, Non-Covalent Interactions, and Confinement

This review gives an overview of current trends in the investigation of small guest molecules, confined in neat and functionalized mesoporous silica materials by a combination of solid-state NMR and relaxometry with other physico-chemical techniques. The reported guest molecules are water, small alcohols, and carbonic acids, small aromatic and heteroaromatic molecules, ionic liquids, and surfactants. They are taken as characteristic role-models, which are representatives for the typical classes of organic molecules. It is shown that this combination delivers unique insights into the structure, arrangement, dynamics, guest-host interactions, and the binding sites in these confined systems, and is probably the most powerful analytical technique to probe these systems.

Dynamically asymmetric binary glass formers studied by dielectric and NMR spectroscopy

We investigate the component dynamics in asymmetric binary glass formers. Focusing on the dielectric spectra of the high-T_g components m-tricresyl phosphate and quinaldine mixed with toluene as low-T_g component, the broadend spectra cannot be described by Kohlrausch or Cole-Davidson (CD) functions. Instead, we apply a generalized CD function which allows to control the width of the susceptibility independently of its high-frequency flank. The spectra show a common broadening and failure of the frequency-temperature superposition with increasing toluene concentration. This is confirmed by stimulated echo experiments showing an increased stretching of the probed orientational correlation function. In analogy to the definition of T_g, we consider "isodynamic points". For each component, a different but linear concentration dependence of 1/T_iso is revealed, indicating different time scales. Qualitativly, we do not find significant differences for the present mixtures with T_g-contrasts of 63-89K compared to those with larger T_g-contrast ( [Formula: see text] K): Whereas the high-T_g component shows relaxation features similar to those of neat glass formers, yet, with "atypical" weak relaxation broadening, the faster low-T_g component displays pronounced dynamic heterogeneities. This is supported by scrutinizing NMR relaxation data of several mixtures investigated previously as a function of concentration. A universal evolution of the dynamics of the high-T_g as well as the low-T_g component is suggested for mixtures with high [Formula: see text]T_g .

Two-site jumps in dimethyl sulfone studied by one- and two-dimensional 17O NMR spectroscopy

Polycrystalline dimethyl sulfone is studied using central-transition oxygen-17 exchange NMR. The quadrupolar and chemical shift tensors are determined by combining quantum chemical calculations with line shape analyses of rigid-lattice spectra measured for stationary and rotating samples at several external magnetic fields. Quantum chemical computations predict that the largest principal axes of the chemical shift anisotropy and electrical field gradient tensors enclose an angle of about 73°. This prediction is successfully tested by comparison with absorption spectra recorded at three different external magnetic fields. The experimental one-dimensional motionally narrowed spectra and the two-dimensional exchange spectrum are compatible with model calculations involving jumps of the molecules about their two-fold symmetry axis. This motion is additionally investigated by means of two-time stimulated-echo spectroscopy which allows for a determination of motional correlation functions over a wider temperature range than previously reported using carbon and deuteron NMR. On the basis of suitable second-order quadrupolar frequency distributions, sin-sin stimulated-echo amplitudes are calculated for a two-site model in the limit of vanishing evolution time and compared with experimental findings. The present study thus establishes oxygen-17 NMR as a powerful method that will be particularly useful for the study of solids and liquids devoid of nuclei governed by first-order anisotropies.

Quadrupolar transients, cosine correlation functions, and two-dimensional exchange spectra of non-selectively excited spin-3/2 nuclei: A (7)Li NMR study of the superionic conductor lithium indium phosphate

Cos-cos stimulated echoes of non-selectively excited spin-3/2 nuclei were not exploited in studies of slow motional processes in solids and solid-like samples, so far. Based on a theoretical analysis of the quadrupolar transients which hitherto obviously precluded the application of such echoes, their utility is demonstrated for the example of (7)Li NMR on the polycrystalline fast ion conductor lithium indium phosphate. Quadrupolar transients can adversely affect the shape of two- and three-pulse echo spectra and strategies are successfully tested that mitigate their impact. Furthermore, by means of suitably adapted cos-cos echo sequences an effective suppression of central-line contributions to the NMR spectra is achieved. By combining cos-cos and sin-sin datasets static two-dimensional exchange spectra were recorded that display quadrupolarly modulated off-diagonal intensity indicative of ionic motion.

Local-field approximation of homonuclear dipolar interactions in ⁷Li-NMR: density-matrix calculations and random-walk simulations tested by echo experiments on borate glasses

NMR echo techniques have proven to be important to study dynamics in ion conductors and other solid materials. Using the spin-3/2 nucleus (7)Li as a probe, both the quadrupolar and the often neglected homonuclear dipolar interactions modulate the NMR frequency as the ion performs jump processes. Retaining only the local-field term of the many-body Hamiltonian, the impact of the dipolar interaction on various echo experiments was studied using spin dynamics calculations yielding products of dipolar and quadrupolar correlation functions. Using a simple stochastic model these functions were simulated with particular emphasis on the impact of ionic motions and on the conditions under which the dipolar and quadrupolar contributions factorize. The results of the computations and of the random-walk simulations are compared with experimental data obtained for various lithium borate and lithium borophosphate glasses. It is concluded that the local-field approximation is a useful means of treating the Li-Li dipole interactions and that the simple model that we introduce is capable of describing many experimentally observed features. Furthermore, because the dipolar and quadrupolar contributions essentially factorize, a selective determination of the corresponding correlation functions becomes possible.

NMR studies on the temperature-dependent dynamics of confined water

NMR studies of water in nanoscopic confinements of various sizes reveal two dynamical crossovers related to a partial solidification of internal molecules and a glass transition of interfacial molecules, respectively.

Primary and secondary relaxation process in plastically crystalline cyanocyclohexane studied by 2H nuclear magnetic resonance. I

We study the main (α-) and secondary (β-) relaxation in the plastically crystalline (PC) phase of cyanocyclohexane by various 2H nuclear magnetic resonance (NMR) methods (line-shape, spin-lattice relaxation, stimulated echo, and two-dimensional spectra) above and below the glass transition temperature T(g) = 134 K. Our results regarding the α-process demonstrate that molecular motion is not governed by the symmetry of the lattice. Rather it is similar to the one reported for structural glass formers and can be modeled by a reorientation proceeding via a distribution of small and large angular jumps. A solid-echo line-shape analysis regarding the β-process below T(g) yields again very similar results when compared to those of the structural glass formers ethanol and toluene. Hence we cannot confirm an intramolecular origin for the β-process in cyanocyclohexane. The fast β-process in the PC phase allows for the first time a detailed 2H NMR study of the process also at T > T(g): an additional minimum in the spin-lattice relaxation time reflecting the β-process is found. Furthermore the solid-echo spectra show a distinct deviation from the rigid limit Pake pattern, which allows a direct determination of the temperature dependent spatial restriction of the process. In Part II of this work, a quantitative analysis is carried out, where we demonstrate that within the model of a "wobbling in a cone" the mean cone angle increases above T(g) and the corresponding relaxation strength is compared to dielectric results.

Reorientational Dynamics of Organophosphate Glass Formers – a Joint Study by 31P NMR, Dielectric Spectroscopy and Light Scattering

We study molecular reorientation in the glass formers triethyl-, tripropyl-, and m-tricresyl phosphate by measuring 31P NMR spectra, relaxation (T 1 and T 2), stimulated echo decays and two-dimensional spectra over a large temperature range (130–370 K). The results are compared to those from dielectric spectroscopy (DS) and depolarized light scattering (LS). While the time constants τ α of the primary (α-) process in the range  × 10−11–100 s well agree, the stretching of the reorientational correlation function is probe dependent, i.e., the rank-two functions (NMR and LS) essentially agree whereas the rank-one function (DS) is less stretched. The very similar 2D spectra recorded as a function of mixing time demonstrate that the reorientational mechanism does not significantly vary among the super-cooled liquids. A model of combining large- and small-angle reorientation allows for reproducing the 2D spectra and may be taken as generic for the dynamics in viscous molecular liquids. Pronounced secondary (β-) processes do not only effect the NMR relaxation but can be identified directly in the time domain by the stimulated echo technique. This becomes possible due to its broad time window (10 μs–100 s). Thus, applying the different 1D and 2D techniques makes 31P NMR well suited to probe molecular reorientation over a wide dynamic range.

Extremely slow Li ion dynamics in monoclinic Li2TiO3--probing macroscopic jump diffusion via 7Li NMR stimulated echoes

A thorough understanding of ion dynamics in solids, which is a vital topic in modern materials and energy research, requires the investigation of diffusion properties on a preferably large dynamic range by complementary techniques. Here, a polycrystalline sample of Li(2)TiO(3) was used as a model substance to study Li motion by both (7)Li spin-alignment echo (SAE) nuclear magnetic resonance (NMR) and ac-conductivity measurements. Although the two methods do probe Li dynamics in quite different ways, good agreement was found so that the Li diffusion parameters, such as jump rates and the activation energy, could be precisely determined over a dynamic range of approximately eleven decades. For example, Li solid-state diffusion coefficients D(σ) deduced from impedance spectroscopy range from 10(-23) m(2) s(-1) to 10(-12) m(2) s(-1) (240-835 K). These values are in perfect agreement with the coefficients D(SAE) deduced from SAE NMR spectroscopy. As an example, D(SAE) = 2 × 10(-17) m(2) s(-1) at 433 K and the corresponding activation energy determined by NMR amounts to 0.77(2) eV (400-600 K). At room temperature D(σ) takes a value of 3 × 10(-21) m(2) s(-1).

Studying Li Dynamics in a Gas-Phase Synthesized Amorphous Oxide by NMR and Impedance Spectroscopy

Li diffusion parameters of a structurally disordered Li-Al-Si-oxide prepared by gas-phase synthesis were complementarily investigated by both time-domain NMR techniques and impedance spectroscopy. The first include 7Li NMR spin-lattice relaxation (SLR) measurements in the laboratory as well as in the rotating frame of reference. An analysis of variable-temperature NMR line widths point to an activation energy Ea of approximately 0.6 eV. The value is confirmed by rotating-frame SLR NMR data recorded at approximately 11 kHz. Above room temperature the low-temperature flank of a diffusion-induced rate peak shows up which can be approximated by an Arrhenius law yielding Ea=0.56(1) eV. This is in very good agreement with the result obtained from 7Li spin-alignment echo (SAE) NMR being sensitive to even slower Li dynamics. For comparison, dc-conductivity measurements, probing long-range motions, yield Ea=0.8 eV. Interestingly, low-temperature SAE NMR decay rates point to localized Li motions being characterized with a very small activation energy of only 0.09 eV.

Single molecule probing of dynamics in supercooled polymers

Fluorescence experiments with single BODIPY molecules embedded in a poly(methyl acrylate) matrix have been performed at various temperatures in the supercooled regime. By using pulsed excitation, fluorescence lifetime and linear dichroism time trajectories were accessible at the same time. Both observables have been analyzed without data binning. While the linear dichroism solely reflects single particle dynamics, the fluorescence lifetime observable depends on the molecular environment, so that the dynamics from the polymer host surrounding a chromophore contributes to this quantity. We observe that the lifetime correlation decays slightly faster than polarization correlation, indicating the occurrence of large angular reorientations. Additionally, dichroism time trajectories have been adducted to reveal directly the geometry of rotational dynamics. We identify small but also significantly larger rotational jumps being responsible for the overall molecular reorientation.

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.

Nonexponential polymer segmental motion in the presence and absence of ions: H2 NMR multitime correlation functions for polymer electrolytes poly(propylene glycol)-LiClO4

The authors measure 2H NMR multitime correlation functions to investigate the segmental motion of poly(propylene glycol) containing various amounts of the salt LiClO4. 2H NMR two-time correlation functions indicate that addition of salt affects not only the time scale of the segmental motion, but also the degree of the nonexponential relaxation behavior. To quantify the origin of the nonexponential segmental motion, the authors analyze 2H NMR three-time correlation functions. In general, nonexponential relaxation can result from homogeneous dynamics, i.e., intrinsic nonexponentiality, and from heterogeneous dynamics, i.e., existence of a distribution of correlation times G(ln tau). For the studied high and low salt concentrations, including neat poly(propylene glycol), the analysis shows that both homogeneous and heterogeneous contributions are important. 2H NMR four-time correlation functions allow the authors to measure the lifetime of the dynamical heterogeneities. For the studied salt concentrations, the rate exchange occurs on the same time scale as the segmental motion, indicating short-lived dynamical heterogeneities. To arrive at these results, the authors reconsider the interpretation of (2)H NMR three-time correlation functions. Results of analytical calculations and computer simulations show that it is necessary to extend the previous way of analysis so as to include effects due to correlated back-and-forth jumps.

Geometry of phenylene motion in polycarbonate from NMR spectroscopy and neutron scattering

In view of the importance of molecular dynamics in condensed matter both time scale and geometry of such processes should be determined experimentally. Whereas many techniques are available for the former, only NMR spectroscopy and neutron scattering can provide detailed information on the latter. Because of the different time scales of the dynamics, which the two techniques can detect best, direct comparisons of probing the geometry of the dynamics in the same system are scarce. Here we present such a comparison for the complex rotational motion of the phenylene groups in amorphous polycarbonate based on published (2)H NMR and newly recorded (13)C NMR data covering a wide temperature range, and recent quasielastic neutron scattering (QENS) data. We show that the results of the two techniques are in remarkable agreement, provided the data are consistently analyzed. No evidence is found for additional motions characterized by 90 degrees flips recently deduced from QENS data alone. Instead, the phenylene motion in the glassy state displays a broad heterogeneous distribution of rotational angles, about 80 degrees in width, centered at a flip angle of 180 degrees , which stays essentially constant over a wide temperature range. Thus, the phenylene motion that can consistently be observed in NMR and neutron scattering experiments is sensitive to the local packing.

Ion and polymer dynamics in polymer electrolytes PPO–LiClO4.II. H2 and Li7 NMR stimulated-echo experiments

We use 2H NMR stimulated-echo spectroscopy to measure two-time correlation functions characterizing the polymer segmental motion in polymer electrolytes PPO-LiClO4 near the glass transition temperature Tg. To investigate effects of the salt on the polymer dynamics, we compare results for different ether oxygen to lithium ratios, namely, 6:1, 15:1, 30:1, and infinity. For all compositions, we find nonexponential correlation functions, which can be described by a Kohlrausch function. The mean correlation times show quantitatively that an increase of the salt concentration results in a strong slowing down of the segmental motion. Consistently, for the high 6:1 salt concentration, a high apparent activation energy Ea=4.1 eV characterizes the temperature dependence of the mean correlation times at Tg<T<or approximately 1.1Tg, while smaller values Ea approximately 2.5 eV are observed for moderate salt contents. The correlation functions are most nonexponential for 15:1 PPO-LiClO4 whereas the stretching is reduced for higher and lower salt concentrations. This finding implies that the local environments of the polymer segments are most diverse for intermediate salt contents, and, hence, the spatial distribution of the salt is most heterogeneous. To study the mechanisms of the segmental reorientation, we exploit that the angular resolution of 2H NMR stimulated-echo experiments depends on the length of the evolution time tp. A similar dependence of the correlation functions on the value of tp in the presence and in the absence of ions indicates that addition of salt hardly affects the reorientational mechanism. For all compositions, mean jump angles of about 15 degrees characterize the segmental reorientation. In addition, comparison of results from 2H and 7Li NMR stimulated-echo experiments suggests a coupling of ion and polymer dynamics in 15:1 PPO-LiClO4.

Analysis of one-dimensional pure-exchange NMR experiments for studying dynamics with broad distributions of correlation times

One-dimensional (1D) exchange NMR experiments can elucidate the geometry, time scale, memory, and heterogeneity of slow molecular motions (1 ms-1 s) in solids. The one-dimensional version of pure-exchange (PUREX) solid-state exchange NMR, which is applied to static samples and uses the chemical shift anisotropy as a probe for molecular motion, is particularly promising and convenient in applications where site resolution is not a problem, i.e., in systems with few chemical sites. In this work, some important aspects of the 1D PUREX experiment applied to systems with complex molecular motions are analyzed. The influence of intermediate-regime (10 micros-1 ms) motions and of the distribution of reorientation angles on the pure-exchange intensity are discussed, together with a simple method for estimating the activation energy of motions occurring with a single correlation time. In addition, it is demonstrated that detailed information on the motional geometry can be obtained from 1D PUREX spectral line shapes. Experiments on a molecular crystal, dimethyl sulfone, confirm the analysis quantitatively. In two amorphous polymers, atactic polypropylene (aPP) and polyisobutylene (PIB), which differ only by one methyl group in the repeat unit, the height of the normalized exchange intensity clearly reveals a striking difference in the width of the distribution of correlation times slightly above the glass transition. The aPP shows the broad distribution and Williams-Landel-Ferry temperature dependence of correlation times typical of polymers and other "fragile" glass formers. In contrast, the dynamics in PIB occur essentially with a single correlation time and exhibits Arrhenius behavior, which is more typical of "strong" glass formers; this is somewhat surprising given the weak intermolecular forces in PIB.

Rotational motion in the molecular crystalsmeta- andortho-carborane studied by deuteron nuclear magnetic resonance

Spin-lattice and spin-spin-relaxation times, one- and two-dimensional spectra as well as two- and four-time correlation functions were measured for the molecular crystals ortho- and meta-carborane using deuteron nuclear magnetic resonance. It is found that in their noncubic phases these crystals exhibit highly anisotropic motions. In order to allow for a quantitative description of the motional geometry of the carboranes several stochastic models are formulated. By comparison of the model calculations with the experimental results it is found that the dynamics of these quasi-icosahedrally shaped molecules is governed by a composite reorientation process. Here the molecules perform threefold jumps around a molecule-fixed axis which itself can be tilted in four different directions with respect to a crystal-fixed axis. The tilt angle increases significantly with increasing temperature. On the basis of measurements of four-time stimulated-echo functions, implications for dynamic heterogeneity also in comparison with that of supercooled liquids are discussed.

Ultraslow Diffusion in Polycrystalline h-LiTiS2 Studied by 7Li Spin-Alignment Echo NMR Spectroscopy

Multiple-time spin-alignment echo (SAE) NMR spectroscopy of spin- 3 2 nuclei is used to study ultraslow diffusion in the hexagonal layered Li ion conductor LixTiS2 (x 1). Two-time correlation functions were monitored by recording (Jeener-Broekaert) echo amplitudes for constant evolution and variable mixing times. Echo decay rates t

2H nuclear magnetic resonance study of the molecular motion in cyanoadamantane. I. Supercooled plastically crystalline phase

The supercooled plastically crystalline phase (glassy crystal) of cyanoadamantane was investigated by multidimensional 2H NMR (T>Tg). Although the orientationally disordered crystalline phase always coexisted with the orientationally ordered crystalline phase, we were able to single out the signal from the glassy crystal by selective excitation and it was possible to carry out line shape measurements and two-dimensional (2D) experiments (in frequency and time domain). The latter directly reveal sixfold jumps with an reorientation of the molecular C3 axis via 90 degrees angles, thus reflecting the symmetry of the lattice. The motion around the C3 axis is found to be always fast. We can reproduce the line shape by random walk simulations properly taking into account these molecular motions. Both methods (line shape and 2D experiments) yield time constants which agree with those reported by other techniques. Refining the analysis a narrow distribution of correlation times is introduced to account for a weak stretching of the correlation function. We did not find any indication of a small angle process usually found in structural glasses. Thus, the motional process in the glassy crystal appears to be simple and quite different from that in structural glasses.

Microscopic origin of the nonexponential dynamics in a glassy crystal

The origin of the slow relaxation and of the dynamic heterogeneity is studied for an orientation-ally disordered crystal, orthocarborane, composed of quasi-icosahedrally shaped molecules. Multidimensional deuteron magnetic resonance reveals that large jump angles dominate their complex, anisotropic reorientational motion. It involves a sequence of small-angle tilts about locally preferred axes as well as symmetry adapted threefold jumps. The intrinsic dynamics of this glassy crystal is nonexponential and can be fully accounted for in terms of the tilt and jump motion.

Effects of various types of molecular dynamics on 1D and 2D (2)H NMR studied by random walk simulations

By carrying out random walk simulations we systematically study the effects of various types of complex molecular dynamics on (2)H NMR experiments in solids. More precisely, we calculate one-dimensional (1D) (2)H NMR spectra and the results of two dimensional (2D) (2)H NMR experiments in time domain, taking into account isotropic as well as highly restricted motions which involve rotational jumps about different finite angles. Although the dynamical models are chosen to mimic the primary and secondary relaxation in supercooled liquids and glasses, we do not intend to describe experimental results quantitatively but rather to show general effects appearing for complex reorientations. We carefully investigate whether 2D (2)H NMR in time domain, which was originally designed to measure correlation times of ultraslow motions (tau >/= 1 ms), can be used to obtain shorter tau, too. It is demonstrated that an extension of the time window to tau >/= 10 &mgr;s is possible when dealing with exponential relaxation, but that it will fail if there is a distribution of correlation times G(lgtau). Vice versa, we show that 1D (2)H NMR spectra, usually recorded to look at dynamics with tau in the microsecond regime, are also applicable for studying ultraslow motions provided that the loss of correlation is achieved step by step. Therefore, it is useful to carry out 1D and 2D NMR experiments simultaneously in order to reveal the mechanism of complex molecular motions. In addition, we demonstrate that highly restricted dynamics can be clearly observed in 1D spectra and in 2D NMR in time domain if long solid-echo delays and large evolution times are applied, respectively. Finally, unexpected observations are described which appear in the latter experiment when considering very broad distributions G(lgtau). Because of these effects, time scale and geometry of a considered motion cannot be extracted from a straightforward analysis of experimental results. Copyright 2000 Academic Press.

Multiple-time correlation functions in spin-3/2 solid-state NMR spectroscopy

Stimulated echo spectroscopy of nonselectively excitable I = 3/2 nuclei offers new perspectives for the investigation of ultraslow motions predominantly in inorganic solids and solid-like materials. Conditions for the generation of pure, quadrupole modulated multipolar spin orders and for the detection of two- and four-time correlation functions are discussed. The case of spins I > 3/2 is also briefly considered. Copyright 2000 Academic Press.

Direct determination of motional correlation times by 1D MAS and 2D exchange NMR techniques

One- and two-dimensional static and magic-angle spinning (MAS) exchange NMR experiments for quantifying slow (tauc > 1 ms) molecular reorientation dynamics are analyzed, emphasizing the extent to which motional correlation times can be extracted directly from the experimental data. The static two-dimensional (2D) exchange NMR experiment provides geometric information, as well as exchange time scales via straightforward and model-free application of Legendre-type orientational autocorrelation functions, particularly for axially symmetric interaction tensors, as often encountered in solid-state 2H and 13C NMR. Under conditions of MAS, increased sensitivity yields higher signal-to-noise spectra, with concomitant improvement in the precision and speed of correlation time measurements, although at the expense of reduced angular (geometric) resolution. For random jump motions, one-dimensional (1D) exchange-induced sidebands (EIS) 13C NMR and the recently developed ODESSA and time-reverse ODESSA experiments complement the static and MAS two-dimensional exchange NMR experiments by providing faster means of obtaining motional correlation times. For each of these experiments, the correlation time of a dynamic process may be obtained from a simple exponential fit to the integrated peak intensities measured as a function of mixing time. This is demonstrated on polycrystalline dimethylsulfone, where the reorientation rates from EIS, ODESSA, time-reverse ODESSA, and 2D exchange are shown to be equivalent and consistent with literature values. In the analysis, the advantages and limitations of the different methods are compared and discussed. Copyright 1998 Academic Press.