Acetone mobility in zeolite cages with new features in the deuteron NMR spectra and relaxation.

We studied deuteron NMR spectra and spin-lattice relaxation of deuterated acetone-d6, adsorbed into zeolites NaX (1.3) and NaY(2.4) at 100% coverage of sodium cations. At temperatures roughly below 160 K the deuterons are localized and their NMR characteristics are determined by CD3 rotation and rotational oscillations of acetone molecules. In NaX the CD3 rotation and rotational oscillations about the twofold axis of acetone dominate the spectra below 100 K, while above it oscillations also about other axes become important. In NaY dominant features are related to methyl tunnelling and to a smaller extent to rigid acetones, before the rotational oscillations about twofold axis start to prevail above 40 K. The analysis of the strongly non-exponential magnetization recovery was done by applying the recently introduced method (Ylinen et al., 2015 [12]), improved here to take into account the limited fast recovery at the level crossings, 10% at ωt=ω0 and 28% at ωt=2ω0. At first the experimental recovery is fitted by three exponentials with adjustable weights and decay rates. Then these quantities are calculated from activation energy distributions and known expressions for the deuteron relaxation rate. In NaY two distinctly separate activation energy distributions were needed, the dominant one being very broad. The use of three distributions, two of them covering practically the same energies as the broad one, lead to a somewhat better agreement with experiment. In general the theoretical results agree with experiment within experimental scatter. As the final result the mean activation energies and widths are obtained for activation energy distributions.

The effect of a broad activation energy distribution on deuteron spin-lattice relaxation.

Deuteron NMR spectra and spin-lattice relaxation were studied experimentally in zeolite NaY(2.4) samples containing 100% or 200% of CD3OH or CD3OD molecules of the total coverage of Na atoms in the temperature range 20-150K. The activation energies describing the methyl and hydroxyl motions show broad distributions. The relaxation data were interpreted by improving a recent model (Stoch et al., 2013 [16]) in which the nonexponential relaxation curves are at first described by a sum of three exponentials with adjustable relaxation rates and weights. Then a broad distribution of activation energies (the mean activation energy A0 and the width σ) was assumed for each essentially different methyl and hydroxyl position. The correlation times were calculated from the Arrhenius equation (containing the pre-exponential factor τ0), individual relaxation rates computed and classified into three classes, and finally initial relaxation rates and weights for each class formed. These were compared with experimental data, motional parameters changed slightly and new improved rates and weights for each class calculated, etc. This method was improved by deriving for the deuterons of the A and E species methyl groups relaxation rates, which depend explicitly on the tunnel frequency ωt. The temperature dependence of ωt and of the low-temperature correlation time were obtained by using the solutions of the Mathieu equation for a threefold potential. These dependencies were included in the simulations and as the result sets of A0, σ and τ0 obtained, which describe the methyl and hydroxyl motions in different positions in zeolite.

Deuteron spin-lattice relaxation in the presence of an activation energy distribution: application to methanols in zeolite NaX.

A new method is introduced for analyzing deuteron spin-lattice relaxation in molecular systems with a broad distribution of activation energies and correlation times. In such samples the magnetization recovery is strongly non-exponential but can be fitted quite accurately by three exponentials. The considered system may consist of molecular groups with different mobility. For each group a Gaussian distribution of the activation energy is introduced. By assuming for every subsystem three parameters: the mean activation energy E(0), the distribution width σ and the pre-exponential factor τ(0) for the Arrhenius equation defining the correlation time, the relaxation rate is calculated for every part of the distribution. Experiment-based limiting values allow the grouping of the rates into three classes. For each class the relaxation rate and weight is calculated and compared with experiment. The parameters E(0), σ and τ(0) are determined iteratively by repeating the whole cycle many times. The temperature dependence of the deuteron relaxation was observed in three samples containing CD(3)OH (200% and 100% loading) and CD(3)OD (200%) in NaX zeolite and analyzed by the described method between 20K and 170K. The obtained parameters, equal for all the three samples, characterize the methyl and hydroxyl mobilities of the methanol molecules at two different locations.

Translational and rotational mobility of methanol-d4 molecules in NaX and NaY zeolite cages: a deuteron NMR investigation.

Nuclear magnetic resonance (NMR) provides means to investigate molecular dynamics at every state of matter. Features characteristic for the gas phase, liquid-like layers and immobilized methanol-d(4) molecules in NaX and NaY zeolites were observed in the temperature range from 300 K down to 20K. The NMR spectra at low temperature are consistent with the model in which molecules are bonded at two positions: horizontal (methanol oxygen bonded to sodium cation) and vertical (hydrogen bonding of hydroxyl deuteron to zeolite framework oxygen). Narrow lines were observed at high temperature indicating an isotropic reorientation of a fraction of molecules. Deuteron spin-lattice relaxation gives evidence for the formation of trimers, based on observation of different relaxation rates for methyl and hydroxyl deuterons undergoing isotropic reorientation. Internal rotation of methyl groups and fixed positions of hydrogen bonded hydroxyl deuterons in methyl trimers provide relaxation rates observed experimentally. A change in the slope of the temperature dependence of both relaxation rates indicates a transition from the relaxation dominated by translational motion to prevailing contribution of reorientation. Trimers undergoing isotropic reorientation disintegrate and separate molecules become localized on adsorption centers at 166.7 K and 153.8K for NaX and NaY, respectively, as indicated by extreme broadening of deuteron NMR spectra. Molecules at vertical position remain localized up to high temperatures. That indicates the dominating role of the hydrogen bonding. Mobility of single molecules was observed for lower loading (86 molecules/uc) in NaX. A direct transition from translation to localization was observed at 190 K.

Deuteron NMR spectra and relaxation in fully and partly deuterated (NH4)2ZnCl4.

Deuteron NMR spectra and relaxation were studied at the resonance frequency of 46MHz in polycrystalline fully and partly deuterated (NH(4))(2)ZnCl(4) between 300 and 5K. Spectral components confirm existence of ammonium positions with different potential symmetry, resulting in two- and threefold reorientation of ammonium ions. The temperature dependence of the spin-lattice relaxation rate discloses two time constants in the whole range. The fitting procedure allows the separation into contributions from subsystems of ions in respective potentials. Two relaxation rate maxima are attributed to ions performing threefold uniaxial reorientation at low temperatures. The lower-temperature maximum is observed at T36K. With increasing temperature reorientations about remaining axes start to contribute leading to the other maximum near 100K. The other category of ammonium ions gives rise to the maximum at about 50K. Below this temperature the dominant motion seems to be 180( composite function) reorientations about one twofold axis according to observed spectra. Consistent picture of ion mobility is accomplished for 5%, 30%, 70% and 100% deuterated compounds.

Deuteron spin-lattice relaxation in ammonium hexachlorometallates.

Deuteron spin-lattice relaxation via the motion-dependent part of the electric quadrupole interaction is discussed in partly and fully deuterated ammonium ions of ammonium hexachlorometallates. The dominant motion at temperatures T>50K is normally 120 degrees reorientations of the ammonium ions. In some hexachlorometallates the instantaneous equilibrium directions of the nitrogen-hydrogen vectors make a certain angle Delta with the metal-nitrogen vectors and they appear in groups of six near each metal-hydrogen vector. Each N-D vector jumps between the six directions of one group and this motion (called limited jumps) dominates the deuteron relaxation at lower temperatures. In some samples one direction of each group seems to become more populated than the others when the deuteration degree exceeds a certain value and the ammonium ions become ordered. A model is derived for the relaxation rate in the absence of tunnelling splittings, which includes the effects of reorientations and limited jumps also in the ordered structure, where the limited-jump rate of a N-D vector to the preferred direction, r(p), differs from that to the nonpreferred direction, r(n). The obtained relaxation rate depends, in addition to the angle Delta, also on the ratio d=r(n)/r(p). The effect of d is discussed and estimates for it are presented on the basis of earlier experiments. The recent model for the deuteron relaxation in NH(3)D(+) ions, including the effect of proton tunnelling, is shortly reviewed. At lowest temperatures the motional rates can be dominated by corresponding incoherent tunnelling and the rate of the incoherent tunnelling contributing to limited jumps is argued to be clearly larger than that of the incoherent tunnelling contributing to approximately 120 degrees rotations.

Deuteron spin-lattice relaxation in partly and fully deuterated (NH(4))(2)PdCl(6).

Deuteron spin-lattice relaxation and spectra were studied in partially and fully deuterated (NH(4))(2)PdCl(6) in the temperature range 5-300K. The relaxation rate maximum was observed at 45K in (ND(4))(2)PdCl(6). Its value is reduced due to limited jumps by about 33% relative to the theoretical value expected for threefold reorientations. Limited jumps correspond to an N-D vector jumping between six directions on a cone around a Pd-N vector, the angle between the N-D and Pd-N vectors being denoted Delta. This motion makes a part of the quadrupole interaction ineffective in relaxation thus reducing the maximum rate at 45K. The observed reduction leads to the value Delta=21( composite function). Limited jumps are quenched to a large extent at the order-disorder phase transition and consequently a decrease is observed in the rate. Below the transition ND(4)(+) ions reorient between the tetrahedral orientations of the ordered phase, therefore the quadrupole interaction has the full relaxing efficiency. In the 10% deuterated sample the temperature of the rate maximum is shifted to 35K and below 20K the rate itself is one order of magnitude larger than in (ND(4))(2)PdCl(6). The increase is related to (1) the absence of the order-disorder phase transition and (2) to the enhanced mobility of NH(3)D(+) because of its electric dipole moment. Limited jumps are claimed to be the dominant relaxation mechanism below 20K. The relaxation in the disordered 30% deuterated sample is quite similar to that in 10% sample. The 50% and 70% deuterated samples undergo a transition to the ordered phase. The relaxation is biexponential with the characteristic rates somewhat smaller than those in (ND(4))(2)PdCl(6), but approaching them with increasing deuteration. This variation can be explained with different mobilities and varying relative numbers of the various isotopomers NH(4-n)D(n)(+), n=1-4.

Deuteron NMR relaxation, spectra, and evidence for the order-disorder phase transition in (ND4)2PtCl6.

Deuteron NMR relaxation and spectra were studied at the resonance frequency of 46 MHz in polycrystalline (ND(4))(2)PtCl(6) between 300-5 K. The relaxation rate maximum near 50 K is about 53% smaller than the calculated maximum related to 120 degrees rotations about the threefold symmetry axes of the ammonium ion. The difference is explained by assuming for a N-D vector a total of 24 equilibrium directions, which in groups of six deviate from the nearest Pt-N vector by a certain angle Theta. So-called limited jumps between the directions of each group take place much more frequently than the large-angle rotations, thus rendering a fraction of the deuteron quadrupole coupling ineffective in relaxation. A motional model is presented, which takes into account both these motions simultaneously. A comparison with experimental data leads to Theta=26.0 degrees , in reasonable agreement with earlier neutron diffraction data. A sharp decrease found in the relaxation rate at the order-disorder phase transition temperature of 27.2 K is related to the fact that one of the six equilibrium directions becomes preferred. This leads to a formation of ordered domains, in which the active motion driving the relaxation is 120 degrees rotations. Two components in the spectra found below 55 K are related to domains (broad) and transition regions between domains (narrow). Reasons for the nonexponentiality observed below 20 K are discussed, the most likely explanation being that limited jumps dominate within transition regions and make the corresponding deuterons relax faster than those in domains.

Spectral spin diffusion and magnetic dipolar energy in the NMR of 13CH3 compounds.

Spin diffusion between 13CH3 groups in solids is studied both theoretically and experimentally. It is shown to be dominated by mutual spin flip-flops of protons belonging to neighbouring methyl groups. Also nonmethyl protons may contribute significantly if present in the sample. The spin-rotational ground state of 13CH3 consists of 16 sublevels. When their populations are used to describe spin diffusion, eight population combinations are shown to be important, two of them corresponding to the 13C-proton and proton-proton intra-methyl magnetic dipolar energies, Dc and Dp, respectively. Spin-diffusion transitions modulate these combinations so that a further reduction to two sets of four combinations is possible, with no coupling between the sets. Coupled differential equations are derived to describe the time dependence of the combinations in each set. They are solved numerically and compared with experimental results on a single crystal of aspirin with 13C-labelled methyl groups at the carbon resonance. The 13C NMR induction signal was observed as a function of time after the preparation either at the carbon resonance (a two-pulse sequence) or at the proton resonance (proton saturation). Usually carbon spectra were computed first and then three of the mentioned population combinations were obtained from the individual spectral components. Some results on the time dependence of Dc were also obtained directly from the amplitude of the out-of-phase induction signal. Theoretical predictions are found to describe semiquantitatively the overall time dependence of these three combinations and especially their variation with different initial conditions, which are discussed in detail. Also the partial transfer of the magnetic dipolar energy between Dc and Dp is nicely explained. Reasons for discrepancies are discussed.

Van Vleck second moments and hydrogen diffusion in YH2.1--measurements and simulations.

Proton magnetic resonance absorption spectra of yttrium dihydride (YH(2+x)), with x = 0.10, were recorded in the temperature ranges 4.2-310 K at 36.01 MHz and 150-400 K at 299.8 MHz. The evidence of proton self-diffusion follows from the changes of linewidth with temperature. The second moment of the resonance lines was determined from the experimental spectra and was compared with values calculated from the crystallographic data. The averaging effect of diffusion on the second moment was taken into account through Monte Carlo simulations of the diffusion process. The simulation was performed in a block of unit cells 5 x 5 x 5 with periodic boundary conditions. They compensated the effect of finite dimensions of the block. The calculated temperature dependence of the proton second moment values was fitted to the experimental ones. The fitting parameters were: the attempt frequency v0 and the activation energy Ea for hydrogen diffusion, assuming Arrhenius behavior of the jump frequencies vc = v0 exp(-Ea/k(B)T). In these preliminary studies, the Monte Carlo simulations were performed for tetrahedral-octahedral exchanges while direct tetrahedral-tetrahedral jumps were neglected for simplicity. Three models of hydrogen diffusion, differing in the maximum jump lengths allowed for a given model, were considered. These lengths were taken as the distances from the hydrogen attempting to jump to the first (1NN), second (2NN), and third (3NN) nearest neighbor position able to accept the jumping atom. Assuming the same attempt frequency v0 = 6.0 x 10(12)s(-1) for all three models, the activation energies giving the best fit to experimental data were 0.5, 0.54, and 0.55 eV for 1NN, 2NN, and 3NN models, respectively.

Spin-lattice relaxation of 13CH3 groups in 13C-enriched aspirin after proton saturation.

We studied the spin-lattice relaxation of the 13C magnetisation, M(C), in 13C-enriched single crystal of aspirin (only methyl carbons enriched to 99%) at the carbon resonance frequency of 54.5 MHz. After the carbon saturation the recovery appears exponential except below 30K, where it is biexponential due to the presence of the level crossing omega(t)=omega(C)+omega(H) (the symbols refer, respectively, to the tunnel frequency and the carbon and proton resonance frequencies in angular units). After the saturation of the proton magnetisation, M(H), the description of the M(C) recovery needs three exponentials. The evaluation of the time constants is easiest from the data in this case, since M(C) varies with time in an initial growth-subsequent decrease (or an initial decrease-subsequent growth depending on temperature) manner, instead of the monotonous growth after the carbon saturation. Experimental data agree semiquantitatively with the predictions of our recent model. According to the model the relaxation of M(C) is coupled to M(H) and the tunnel energy TE at temperatures below the minimum of the 13C relaxation time. Sufficiently above this minimum M(C) is coupled to M(H) and the rotational polarization (but not to TE) in agreement with experiment. Also the effect of torsional oscillations of a methyl group on the magnitude of various 13C-related transition rates was considered in detail. In aspirin the rates are reduced roughly by 10% and the reduction should become larger in samples with a larger tunnel splitting. The reduction also changes somewhat the angular dependence of these rates.

Ammonium tunnel levels and spin-rotational wavefunctions in (NH4)2S2O8.

Proton spin-lattice relaxation in a single crystal of (NH4)2S2O8 was studied as a function of resonance frequency at various constant temperatures between 4.2 and 30 K. Two T1 minima were found, one at 8.6 MHz and the other at 4.3 MHz. They are related to the splitting between the lowest T level and the A level, equal to 8.6 MHz nearly independently of temperature below 25 K. Together with the large tunnel splitting of 269 MHz, determined earlier by Clough et al. (Chem. Phys. 152, 343 (1991)) our results define the spin-rotational wavefunction of the lowest T level very accurately, although those of the two higher T levels remain largely undetermined.

14N NMR echo in NH4ClO4 after the pulse sequence (theta1)x-tau-(theta2)y-t.

We have derived a closed-form expression for the solid echo signal of quadrupolar I = 1 nuclei after the pulse sequence (theta1)x-tau-(theta2)y-t for arbitrary values of the RF nutation frequency omega1 = gammaB1 and the quadrupolar frequency omegaQ. In the case of single crystals both the true echo term of this expression and its induction-signal-like terms are important as shown by experiments on 14N nuclei in NH4ClO4 crystal. Conditions for obtaining the maximal echo in powder samples are presented. A very low B1 field together with long RF pulses may distort even the central part of the spectrum, resulting in strange looking apparent spectra.

Five quantum coherence of I=5/2 nuclei: 27Al in polycrystalline AlCl3.

Optimal conditions were calculated for the excitation and detection of the five quantum coherence of quadrupolar nuclei with I = 5/2 in powder samples, observed by the two-pulse sequence (theta1)x - tau1 - (theta2)alpha - tau2, where alpha is the phase cycling angle. We varied the pulse lengths and the relative values of the nutation frequency omega1 = gammaB1 and the quadrupolar frequency omegaQ. Also, the effect of the resonance offset was studied under optimal conditions. Besides, the conditions for obtaining the maximal echo amplitude after the two-pulse sequence with alpha = y were found. Theoretical results were compared with experiments on 27Al nuclei in polycrystalline AlCl3.

Proton double quantum coherence and cross-relaxation in (NH4)2SnBr6.

A proton double quantum coherence signal can be observed exclusively from the T species NH4 groups (with the total spin I = 1) in ammonium compounds at low temperatures by the three-pulse sequence 90x degrees - tpr - 90x degrees - tev - 90x degrees - ta, where tpr and ta are of the magnitude of the inverse line width and tev very short. The usefulness of this pulse sequence, preceded by the additional pulse sequence 90x degrees - t1 -90(-x) degrees - t2 for creating an unbalance between the A and T species magnetizations, was demonstrated by applying it to cross-relaxation studies in (NH4)2SnBr6.

Spin-lattice relaxation in ammonium compounds with a complex molecular dynamics.

Expressions are derived for the initial relaxation rate 1/T1 of protons and deuterons of nontunnelling NH4 and ND4 groups reorienting about various symmetry axes in solids. The reorientation rates are modified by a trigonal, tetragonal or monoclinic distortion of the predominantly cubic hindering potential. When the rates differ sufficiently from each other, two T1 minima are observed with a characteristic ratio. Experiments were performed in NH4VO3, (NH4)2S2O8, (NH4)2PtCl4, and their deuterated modifications, which all exhibit two T1 minima. In NH4VO3 and ND4VO3 the relaxation and spectral data agree rather well with the model of trigonal distortion. Also (NH4)2S2O8 has a preferred threefold axis but there, the large tunnel splitting of protons has to be taken into account before an agreement is reached. All the purely reorientational models fail with (NH4)2PtCl4, where, instead, the ammonium groups are proposed to be ordered into domains at low temperatures. The groups inside the domains and boundary regions give rise to the high- and low-temperature T1 minima, respectively. The boundaries are also believed to give rise to the narrow component in the deuteron spectrum at low temperatures. Evidence for a proton tunnelling frequency of 32 MHz is found in (NH4)2PtCl4.

Double quantum coherence of quadrupolar I = 1 nuclei: 14N in NH4ClO4.

We have calculated optimal conditions for observing the double quantum coherence of quadrupolar nuclei I = 1 in single crystals and powders after the two and three pulse sequences (theta1)x-tau1-(theta2)alpha-tau2 [-(theta3)beta-tau3] Here alpha and beta are the phase-cycling angles, which were incremented properly to select the desired coherence transfer pathways. Experiments for double quantum excitation and detection were performed on the single crystal and powder samples of NH4ClO4. Because of a fast decay of the signal from the powder after the two-pulse sequence, we employed the third pulse to produce an echo related to the double quantum coherence.

Deuteron NMR spectra of ND4ClO4 single crystal at low temperatures.

2H NMR spectra of ND4ClO4 single crystal were obtained at v0 = 44 MHz. Orientation and temperature (1.9-75 K) dependences were measured. Fitting the spectra gives the effective quadrupole coupling constants for all deuterons and the ground torsional level structure. The isotope reduction of the (A-T) and (A-E) tunnelling splittings, i.e., the ratios of the respective splittings for NH4+ and ND4+, were found to be different. The splittings at T = 24 K are about 60% of the helium temperature values. The spectrum undergoes intermediate narrowing by reorientations between 26 and 34 K and tunnelling related features in the spectra are eradicated. After reaching the extreme narrowing limit, a doublet with gradually decreasing separation was observed, what was attributed to averaging by torsional oscillations of increasing amplitude. At high temperatures (T > 75 K), the narrow spectrum reflects fast multiaxial reorientation of the ammonium ion.