Nonexponential Spin-lattice Relaxation Research Articles

Spatial heterogeneity in glassy polystyrene detected by deuteron NMR relaxation

Using deuteron NMR, the dynamics of supercooled polystyrene-d3 was investigated near the calorimetric glass transition. At these temperatures non-exponential spin lattice relaxation is found, indicating the presence of spatial heterogeneity. With increasing temperature, structural relaxation becomes fast enough to average efficiently over different spatial environments, leading to exponential magnetization decays. A qualitative comparison with toluene as a representative of a low molecular weight glass former is carried out. Indications are found that in polystyrene the observed averaging process is more effective at Tg than it is in toluene.

Effects of paramagnetic cations on the nonexponential spin-lattice relaxation of rare spin nuclei in solids

Nonexponential spin-lattice relaxation is often observed for rare spin nuclei in the solid state. Deviation from single-component decay may be amplified by the coupling of rare spin nuclei to paramagnetic centers. Nonexponential spin-lattice relaxation was observed in derivatized silica gels resins. This phenomenon was localized and enhanced when paramagnetic transition metal cations were bound to surface functional groups. A stretched exponential analysis method was determined to be robust in fitting nonexponential relaxation curves for silica gels both with and without bound paramagnetic ions. Spin-lattice relaxation rates ( T 1 −1) for functional group nuclei increased as a function of percent surface coverage with metal ion. The magnitude of the relaxation rate increase was dependent upon internuclear distances from the paramagnetic center. At low surface coverages, a semi-random distribution of paramagnetic centers increased the degree of stretching of spin-lattice relaxation decays, as measured by decreases in the calculated stretching parameter β. At higher surface coverages, calculated β values reached a limiting value, indicating that while the spin-diffusion mechanism in metal-ex-changed silica gels is restricted, it is not completely diminished.

Characterizing Nonexponential Spin-Lattice Relaxation in Solid-State NMR by Fitting to the Stretched Exponential

Spin-lattice relaxation in solids often deviates from the usual exponential law, for example, in dilute spin-12 solids like silicon carbide, when relaxation arises from fixed paramagnetic impurities. We examine nonexponential spin-lattice relaxation from the point of view of nonlinear regression to the stretched-exponential function M(τ) = a − bexp[−(τ/T′)n], where n is typically 1 or 0.5 but can have intermediate values. Criteria for error estimation as well as an optimal choice of delay times τ are examined in detail and tested on typical data from our studies on silicon carbide. Two methods are outlined for the estimation of confidence intervals which are typically found to be somewhat larger than the standard errors in the parameters. The typical experiment for determination of spin-lattice relaxation time is found to be robust even when relaxation is nonexponential. The determinant of the curvature matrix is a good experimental design criterion and correlates well with the estimated errors. While any reasonable choice of points yields good results, an optimal choice of delay times τ can be made by following the guidelines presented here.

1H and19F nuclear magnetic relaxation study of the dynamics of the hydrogen difluoride ion, FHF–, in the α- and β-phases of caesium hydrogen difluoride

A 1H and 19F nuclear magnetic resonance spin–lattice relaxation investigation of polycrystalline caesium hydrogen difluoride, CsHF2, in the temperature range 175–390 K is reported. There is a discontinuous change in the relaxation behaviour in the region 330 ± 2 K which corresponds to the structural phase transition. In the low temperature, or α–phase, the relaxation measurements are interpreted in terms of a model in which the FHF– ions undergo a 180 °-flip motion for which the activation energy is found to be 24.8 ± 2.5 kJ mol–1. General relaxation expressions for a polycrystalline sample are developed for this motional model. A particular feature of the measurements is the cross-relaxation, or spin exchange, between the hydrogen and fluorine nuclei which results in non-exponential spin–lattice relaxation behaviour at temperatures below 200 K. In the cubic, or β-phase, the relaxation measurements are shown to be consistent with a restricted rotational model in which reorientations of the FHF– ion occur at random among the three cubic unit cell directions. The activation energy for this type of motional process is found to be 19.6 ± 1.5 kJ mol–1.

Using saturation-recovery EPR to measure exchange couplings in proteins: application to ribonucleotide reductase

The stable tyrosine radical of ribonucleotide reductase (RNR) from Escherichia coli, Tyr 122 of the B2 subunit, exhibits single-exponential spin-lattice relaxation lunetics for T≤16 K and nonexponential spin-lattice relaxation kinetics at higher temperatures. Saturation-recovery transients of the tyrosine radical are analyzed using a model developed to treat the interaction of two paramagnets in a rigid lattice at a fixed distance apart but with a randon orientation in the static magnetic field

The molecular dynamics around the glass transition and in the glassy state of molecular organic systems: A 2H−nuclear magnetic resonance study

2H-nuclear magnetic resonance(NMR)-spin–lattice relaxation experiments have been performed for studying the crossover from viscous (α process) to secondary (β processes) dynamics in the van der Waals liquid orthoterphenyl and the H-bridged network glycerol. The essential and general features, observed in both systems, are the following: (a) a dominating α process in the liquid and viscous regime; (b) a change from exponential to nonexponential spin–lattice relaxation as the temperature is lowered below a characteristic temperature above Tg; (c) the existence of a slow (>10−9 s) secondary reorientational process in the highly viscous regime; and (d) the existence of a fast (∼10−12 s) local process in the glassy state. Whereas the slower process is shown to be the one known from dielectric studies, we attribute the fast mode to a β process found in quasielastic neutron scattering.

Silicon-29 MAS NMR of the aluminosilicate mineral kyanite: residual dipolar coupling to aluminum-27 and nonexponential spin-lattice relaxation

Silicon-29 MAS NMR of the aluminosilicate mineral kyanite: residual dipolar coupling to aluminum-27 and nonexponential spin-lattice relaxation

Hexamethylbenzene as a sensitive nuclear magnetic resonance probe for studying organic crystals and glasses

Deuterated hexamethylbenzene (HMB) is used as a probe molecule for 2H NMR studies of the crystalline state of hexachlorobenzene and of several organic glasses. By measuring the spin–lattice relaxation and the line shape in the temperature range of 4–300 K the dynamical parameters of the molecular reorientation are investigated. For the system HMB/hexachlorobenzene, we find exponential relaxation and for the corresponding T1 an increase of its activation energy by a factor of 2 in comparison to the neat HMB. A homogeneous mixing of the guest and host molecules is found at least for guest concentrations up to 7%. In contrast, nonexponential spin–lattice relaxation is characteristic for all glass matrices, indicating motional heterogeneities. A log–Gauss distribution for the corresponding motional correlation times gives a good fit of the data. Its width parameter decreases linearly with temperature, while the mean correlation times are described by an Arrhenius law. The mean activation energy is reduced by a factor of about 3.5 as compared to neat HMB, demonstrating a loose packing of the molecules in the glass matrices.

Nonexponential spin-lattice relaxation from hindered rotations in dipolar solids

A general formalism is presented for the computation of the longitudinal magnetization in a broad class of molecular crystals allowing for the effects of cross correlations between the motions of different spin–spin vectors. These effects will manifest themselves, in general, in a departure from exponentiality of the relaxing magnetization as a function of time. The molecular motion concerned is that of random, thermally-activated. hindered reorientations about the available symmetry axes. Any combination of available reorientations is covered by the theory, provided only that the motion preserves the complete equivalence of all the rij. The present work is essentially concerned with outlining the principles of the calculation, but to demonstrate the formalism, one simple example, amenable to analytic solution, is examined in detail.

Multiexponential spin-lattice relaxation ofTe125in tellurium due to ultraslow atomic motion

Nonexponential spin-lattice relaxation is shown to result under selective excitation due to ultraslow site exchange. The hopping rate kappa of the nuclei can be obtained directly without any further assumption on the nuclear spin interactions and spin thermodynamics. In tellurium single crystals, hopping rates of /sup 125/Te less than kappa = 1 sec/sup -1/ have been observed.

A nuclear magnetic resonance study of some solid alkylamines and their clathrate deuterates

A proton second-moment and spin-lattice relaxation data are reported on solid N,N-d 2 -isopropylamine, N,N-d 2 -isopropylamine clathrate deuterate, solid trimethylamine, and trimethylamine clathrate deuterate. The second-moment data on isopropylamine indicate that a nearly rigid structure exists at 77 K, and that a hindered rotation of both the methyl groups takes place around 165 K. The barrier hindering the methyl group rotation, as estimated from nonexponential spin-lattice relaxation data, is found to be 3.50 kcal mole −1 with τ c = (1.78 ± 0.22) × 10 −13, exp (3.50 ± 0.07)/ RT. In N-N-d 2 -isopropylamine deuterate there is, in addition to the methyl group rotation, a rotation of the molecule arond its pseudo threefold axis near 212 K. Measurements of T 1 on this deuterate exhibited a single broad minimum of 45 ± 1 msec in the temperature range of 170 to 178 K which we assign as a rotation of the isopropylamine molecule around its pseudo threefold axis. The activation energy associated with the pseudo-threefold-axis rotation was found to be > 1.63 ± 0.03 kcal mole −1. In solid trimethylamine there was found, in addition to methyl group reorientation, a reorientation of the molecule around its molecular threefold axis from ∼145 to 157 K. The barrier associated with methyl group reorientation in its upper limit was found from T 1 measurements to be 5.75 ± 0.14 kcal mole −1. The second-moment data on the trimethylamine clathrate deuterate gave a second moment of 8.46 ± 0.76 G 2 at 77 K (all three methyl groups rotating), 1.42 ± 0.02 G 2 (methyl plus rotation around the molecular threefold axis), and a plateau value of 0.6 G 2. Only a single broad minimum was noticed in the T 1 measurements, and this was assigned to rotation of methyl groups around the threefold axis of the whole trimethylamine molecule. The activation energy for this rotation was found to be ⩾2.90 ± 0.13 kcal mole −1.

Limited spin diffusion and non-exponential spin—lattice relaxation of CH3 groups in solids

Limited spin diffusion and non-exponential spin—lattice relaxation of CH3 groups in solids

Limited spin diffusion and non-exponential spin-lattice relaxation of CH 3 groups in solids

It is shown that in a solid which consists of CH 3 groups, even if thesegroups are non-isolated, spin diffusion is strongly limited due to the symmetry of a CH 3 group with respect to its neighbours. It is furthermore restricted under the condition ω 0⪢∥ d∥⪢ b, where ω 0 is the Zeeman splitting, d the intramolecular dipolar shift and b the intermolecular dipolar broadening. According to this “limited spin diffusion” model the relaxation of the longitudinal magnetization is in general determined by the sum of three exponentials. The result is in closer agreement with the experiments than the theory of Hilt and Hubbard where isolated CH 3 groups are considered.

Limited spin diffusion and non-exponential spin—lattice relaxation of CH3 groups in solids

Limited spin diffusion and non-exponential spin—lattice relaxation of CH3 groups in solids

Non-Exponential Nuclear Spin-Lattice Relaxation in the Solid Phases of EMC

Abstract Measurements of the proton spin-lattice relaxation time in the solid phases of ethyl-[p-(p-methoxybenzilidene)-amino]-cinnamate (EMC) are reported. A model for the non-exponential relaxation observed is discussed as well as mathematical technique for treating the experimental data. This model, based on the assumption of the coexistence of two non-interacting groups of indentical spins, was tested using a model liquid-solid system. Results of the measurements on EMC indicate that the two possible solid phases coexist at low temperatures and that a slow annealing takes place near room temperature. The dominant spin-lattice relaxation mechanism at low temperatures is determined to be a rotational motion with an activation energy of ∼ 2.3 kcal/mole.

Nonexponential spin lattice relaxation and its orientation dependence in a three-spin system

Nonexponential spin lattice relaxation due to cross correlation of the intramolecular dipole interaction has been observed in a trifluoromethyl group. The orientation dependence of the spin lattice relaxation as described by the theory of Hilt and Hubbard has been confirmed experimentally. A value of τc=4.0× 10−11 sec for the correlation time at room temperature was obtained.

Cross-correlations and nonexponential spin-lattice relaxation behavior in solid and liquid ketones

The nonexponential magnetization recovery curve of solid CD 3COCD 2CH 3 is in good agreement with the theory of Hilt and Hubbard, which describes the spin—lattice relaxation of an isolated methyl group reorienting around its symmetry axis. The deviation from exponential spin—lattice relaxation behavior of ketones decreases with increasing chain length. Spin-diffusion breaks down the cross-correlations. Liquid CD 3COCD 2CH 3 also shows a nonexponential magnetization recovery curve. This is a consequence of the anisotropic motion of the methyl groups. This result is, to our knowledge, the first experimental evidence for the occurrence of nonexponential relaxation in liquids produced by anisotropic motion of methyl groups.