Deuteron NMR study of ammonium ion mobility near the order–disorder phase transition in (ND4)2PbCl6

Deuteron NMR spectroscopy was applied to study ammonium ion mobility below 50 K in fully deuterated ammonium hexachloroplumbate. Tunnelling frequencies from the spectra and correlation times from spin-lattice relaxation were measured. The spectra down to about 41 K show also a motionally narrowed component. The order–disorder phase transition takes place at 38.4 K. Below the phase transition two components are found and attributed to ions in ordered domains and transition regions between them, characterised below 25 K by tunnelling frequencies equal 0.35 and 1 MHz, respectively. A gradual change of the potential experienced by ammonium ions was observed.     

Fingerprints of damped quantum rotation observed in solid-state proton NMR spectra.

(1)H NMR spectra of the methyl group in an oriented crystal sample of methylmalonic acid with all three non-methyl protons replaced by deuterons are interpreted in terms of the damped quantum rotation (DQR) theory of NMR line shapes. The DQR approach offers a perfect theoretical reproduction of the observed spectra while the conventional Alexander-Binsch line-shape model shows evident defects in the present case. The temperature trends of the quantities characterizing the coherent and incoherent dynamics of the methyl group in the DQR approach (the effective tunnelling frequency and two coherence-damping rates) derived from the spectra are fairly reproduced using a model reported previously. The present findings provide further evidence of limitations to the validity of the common belief that molecular rate processes in condensed phases are necessarily classical.     

Singlet state relaxation via intermolecular dipolar coupling

The intermolecular contribution to the relaxation of singlet states has been derived on the basis of a translational-rotational diffusion model that describes molecules as impenetrable spheres which translate and rotate in an isotropic low-viscosity medium. The equations for the relaxation rate constants obtained are discussed and the dependence on physical parameters is exploited. Theoretical predictions are compared with experiments when the intermolecular relaxation is due to both protons and deuterons present in the sample. An agreement between experiments and theory of ±4% was obtained when the physical parameters are estimated from first-principles calculation.     

Anisotropy of spin-lattice relaxation

The anisotropy is determined for the spin-lattice relaxation time in the presence of a strong magnetic field in crystals of the NaCl type due to the components of a generalized hyperfine-interaction spin-Hamiltonian. It is shown that taking into account components other than the contact, dipole, and quadrupole interactions leads to an additional angular dependence for the relaxation time and also to additional relaxation transitions.     

13C NMR spectroscopy of 13C1-labeled octanethiol-protected Au nanoparticles: shifts,relaxations, and particle-size effect

We report here an investigation of metal-ligand interactions in nanoparticles with 13C NMR, using a labeled 13C1-octanethiol, a protecting ligand for self-assembled monolayer (SAM) systems, in which close proximity of the 13C1 to the metal surface serves as an effective probe for the changing electronic environment. Several remarkable results have been obtained: as the metal core size increases from 1.6 to 4.0 nm, the 13C1 spectrum is downshifted from 40.5 to 53 ppm, and the spin-spin relaxation rate, T2-1, increases while the spin-lattice relaxation ratio decreases. Although the spin-lattice relaxation may be due to particle tumbling and ligand motion in the liquid state, the main source of the spin-spin relaxation, and NMR shift, is most possibly due to the changing electronic properties of the metal core.     

Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation

We report (1)H spin-lattice relaxation measurements in polycrystalline 4,4'-dimethoxybiphenyl at temperatures between 80 and 300 K at NMR frequencies of ω(0)/2π = 8.50, 22.5, and 53.0 MHz. The data are interpreted in terms of the simplest possible Bloch-Wangsness-Redfield methyl group hopping model. Different solid states are observed at low temperatures. The (1)H spin-lattice relaxation is nonexponential at higher temperatures where a stretched-exponential function fits the data very well, but this approach is phenomenological and not amenable to theoretical interpretation. (We provide a brief literature review of the stretched-exponential function.) The Bloch-Wangsness-Redfield model applies only to the relaxation rate that characterizes the initial (1)H magnetization decay in a high-temperature nonexponential (1)H spin-lattice relaxation measurement. A detailed procedure for determining this initial relaxation rate is described since large systematic errors can result if this is not done carefully.     

Structural interpretation of non-exponential hydrogen transfer in glassy methanol

The non-exponential time dependence of hydrogen abstraction by methyl radicals in a methanol glass is reinvestigated and explained as due to a narrow random distribution of hydrogen tunnelling distances. Possible implications for other non-exponential relaxation processes in non-crystalline materials are briefly discussed.     

Theory for spin-lattice relaxation of spin probes on weakly deformable DNA

The weakly bending rod (WBR) model of double-stranded DNA (dsDNA) is adapted to analyze the internal dynamics of dsDNA as observed in electron paramagnetic resonance (EPR) measurements of the spin-lattice relaxation rate, R(1e), for spin probes rigidly attached to nucleic acid-bases. The WBR theory developed in this work models dsDNA base-pairs as diffusing rigid cylindrical discs connected by bending and twisting springs whose elastic force constants are kappa and alpha, respectively. Angular correlation functions for both rotational displacement and velocity are developed in detail so as to compute values for R(1e) due to four relaxation mechanisms: the chemical shift anisotropy (CSA), the electron-nuclear dipolar (END), the spin rotation (SR), and the generalized spin diffusion (GSD) relaxation processes. Measured spin-lattice relaxation rates in dsDNA under 50 bp in length are much faster than those calculated for the same DNAs modeled as rigid rods. The simplest way to account for this difference is by allowing for internal flexibility in models of DNA. Because of this discrepancy, we derive expressions for the spectral densities due to CSA, END, and SR mechanisms directly from a weakly bending rod model for DNA. Special emphasis in this development is given to the SR mechanism because of the lack of such detail in previous treatments. The theory developed in this paper provides a framework for computing relaxation rates from the WBR model to compare with magnetic resonance relaxation data and to ascertain the twisting and bending force constants that characterize DNA.     

Pressure and temperature dependence of the chlorine NQR in caesium and sodium chlorates

The (35)Cl nuclear quadrupole resonance (NQR) frequencies (nu(Q)) in caesium and sodium chlorates were measured as a function of temperature, from 77 to 300 K at different pressures up to 5.1 kbar, and the data were analysed to estimate the volume dependence of the electric field gradient (EFG), torsional frequency and also the contributions to the NQR frequency from static and dynamic effects. The variation of spin-lattice relaxation time with pressure at different temperatures was studied in the case of sodium chlorate and at room temperature in case of caesium chlorate. The pressure dependence of the spin-lattice relaxation time (T(1)) suggests that the relaxation is mainly due to the torsional motions.     

A new mechanism for spin--lattice relaxation of heavy nuclei in the solid state: 207Pb relaxation in lead nitrate.

A detailed investigation of the spin-lattice relaxation time, T1, for 207Pb in solid lead nitrate has been undertaken in an effort to understand the mechanism of relaxation. The results show that the 207Pb T1 is independent of magnetic field strength and inversely proportional to the square of the temperature. These are signatures of relaxation by a spin-phonon Raman scattering mechanism. Nuclear spin-lattice relaxation in solid lead salts is more efficient for sites with smaller magnetic shielding anisotropy. A coupling mechanism is proposed whereby phonons create a local magnetic field by modulating the valence electron shell motion relative to the nuclear/electron core. Literature data suggest that spin-phonon scattering is a common relaxation pathway for other spin-1/2 heavy nuclei in solids.     

Identification of halogen substituents in natural products by measurement of 13c spin-lattice relaxation times and integrated intensities

A method is proposed for differentiating brominated carbons from chlorinated carbons by means of natural-abundance ¹³C NMR spectroscopy. The basis of the method is that the spin-lattice relaxation behaviour of brominated carbons is influenced by carbon-bromine scalar interactions, which can lead to shortened ¹³C spin-lattice relaxation times and reduced values of the nuclear Overhauser enhancement. C-Cl scalar interactions make a negligible contribution to the spin-lattice relaxation of chlorinated carbons. These effects are illustrated by measurement of the ¹³C spin-lattice relaxation times and integrated intensities of chloro-, bromo and iodobenzene and chloro-, bromo- and iodocyclohexane. The method is then tested on four polyhalogenated marine natural products. The results indicate that ¹³C relaxation measurements can be used to distinguish brominated carbons from chlorinated carbons in the case of halogenated quaternary carbons, sp² hydridized methine carbons and some sp³ hydridized methine carbons, but not in the case of halogenated methylene carbons or gem-dihalo substituted methine carbons.     

NMR study of hindered rotation in solid (ND4)2GeF6

Nuclear spin-lattice relaxation times T₁ for deuterons and ¹⁹F nuclei in polycrystalline (ND₄)₂GeF₆ were measured by the pulse method at 8 MHz between 40 K and 300 K and between 4 K and 400 K, respectively. Correlation times and activation energies for the reorientational motions of ND₄⁺ and GeF₆^2? ions were calculated from the measured T₁ values.     

Explanation of spin-lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR

Electron paramagnetic resonance (EPR) pulsed saturation recovery (pSR) measurements of spin-lattice relaxation rates have been made on nitroxide-containing fatty acids embedded in lipid bilayers by Hyde and co-workers. The data have been collected for a number of spin-labeled fatty acids at several microwave spectrometer frequencies (from 2 to 35 GHz). We compare these spin-lattice relaxation rates to those predicted by the Redfield theory incorporating several mechanisms. The dominant relaxation mechanism at low spectrometer frequencies is the electron-nuclear dipolar (END) process, with spin rotation (SR), chemical shift anisotropy (CSA), and a generalized spin diffusion (GSD) mechanism all contributing. The use of a wide range of spectrometer frequencies makes clear that the dynamics cannot be modeled adequately by rigid-body isotropic rotational motion. The dynamics of rigid-body anisotropic rotational motion is sufficient to explain the experimental relaxation rates within the experimental error. More refined models of the motion could have been considered, and our analysis does not rule them out. However, the results demonstrate that measurements at only two suitably chosen spectrometer frequencies are sufficient to distinguish anisotropic from isotropic motion. The results presented demonstrate that the principal mechanisms responsible for anisotropically driven spin-lattice relaxation are well understood in the liquids regime.     

Muonium diffusion in ice

Muonium (Mu, μ⁺e⁻) is generally regarded as a light isotope of hydrogen. The procession signals of muonium in single crystals of H₂O and D₂O ice have been studied from 8 to 263 K using the muon spin rotation (μSR) technique. Transverse spin relaxation rates have been extracted and interpreted in terms of modulation of the dipolar interaction between muonium and the protons/deuterons in the lattice by translational diffusion of muonium. In contrast to the situation for H and a previous claim for Mu, muonium is found to be diffusing at temperatures as low as 8 K. An activation energy of 40 meV is obtained by fitting the highest temperature data to an Arrhenius expression. At low temperature muonium is thought to diffuse by quantum tunnelling.     

Application of Schrödinger equation to study the tunnelling dynamics of proton transfer in the hydrogen bond of 2,5-dinitrobenzoic acid: proton T1 T1rho, and deuteron T1 relaxation methods

Temperature measurements of proton T1 (24.7 MHz), deuteron (deuterated hydroxyl group) T1 (55.2 MHz), and proton T1(rho) (B1 = 9 G) spin-lattice relaxation times of 2,5-dinitrobenzoic acid have been performed. An analysis of present experimental data together with previously published proton T1 (55.2 MHz) data has revealed the following molecular motions: proton/deuteron transfer in the hydrogen bond and two-site hopping of the whole dimer. It is shown that the proton-transfer dynamics are characterized by two correlation times tau(ov) and tau(tu), describing two fundamentally different motional processes, namely, thermally activated jumps over the barrier and tunneling through the barrier. The temperature dependence of 1/tau(tu) is the solution of Schr?dinger's equation, which also yields the temperature T(tun), where begins the tunnel pathway for proton transfer. A new equation for the spectral density function of complex motion consisting of the three motions is derived. The third motion (two-site hopping of the whole dimer characterized by tau(lib) correlation time) is responsible for a proton T1(rho) minimum in high temperatures, just below the melting point. Such a minimum is not reached by T1 temperature dependencies. The minimum of T1(rho) assigned to the classical hopping of a hydrogen-bonded proton occurs in the same low-temperature regime in which the flattening of the temperature dependencies of T1 points to the dominance of incoherent tunneling. This experimental fact denies the known theories predicting the intermediate temperature regime where a smooth transition between classical and quantum tunneling dynamics is expected. The fit of the derived theoretical equations to the experimental data T1(rho) and T1 is satisfactory. The correlation times obtained for deuterons indicate deuteron-transfer dynamics much slower than proton-transfer dynamics. It is concluded that the classical proton transfer takes place over the whole temperature regime, while the incoherent tunneling occurs below 46.5 (hydrogen) or 87.2 K (deuterium) only.     

An investigation of contributions to carbon-13 spin-lattice relaxtion in amino acids and peptide hormones

Carbon-13 spin-lattice relaxation times have been measured in glycine and the tripeptide pro-leu-gly-NH₂. These times are compared with those measured in the same compounds where the glycine α-carbon has been deuterated. In this manner evidence is obtained which indicates that mechanisms other than dipolar interactions with covalently bonded protons may contribute to carbon-13 spin-lattice relaxation. The effect of these additional mechanisms is found to be non-negligible for the carbonyl carbon of glycine and the glycine α-carbon of the tripeptide. The implication of these findings for deducing motional information from carbon-13 relaxation measurements is briefly discussed.     

Spin-lattice relaxation of radicals in the solid state. Part 3

Some causes of spin-lattice relaxation in the solid state are considered. It is found that anisotropic hyperfine interaction can make an appreciable contribution to the spin-lattice relaxation time, which becomes dependent on the orientation of the radical relative to the external field and on the number of HS components. There is no appreciable contribution from frequency modulation of the vibrations (of the radical as a whole or purely intramolecular) caused by the lattice vibrations.     

Miscibility of nifedipine and hydrophilic polymers as measured by (1)H-NMR spin-lattice relaxation

The miscibility of a drug with excipients in solid dispersions is considered to be one of the most important factors for preparation of stable amorphous solid dispersions. The purpose of the present study was to elucidate the feasibility of (1)H-NMR spin-lattice relaxation measurements to assess the miscibility of a drug with excipients. Solid dispersions of nifedipine with the hydrophilic polymers poly(vinylpyrrolidone) (PVP), hydroxypropylmethylcellulose (HPMC) and alpha,beta-poly(N-5-hydroxypentyl)-L-aspartamide (PHPA) with various weight ratios were prepared by spray drying, and the spin-lattice relaxation decay of the solid dispersions in a laboratory frame (T(1) decay) and in a rotating frame (T(1rho) decay) were measured. T(1rho) decay of nifedipine-PVP solid dispersions (3 : 7, 5 : 5 and 7 : 3) was describable with a mono-exponential equation, whereas T(1rho) decay of nifedipine-PHPA solid dispersions (3 : 7, 4 : 6 and 5 : 5) was describable with a bi-exponential equation. Because a mono-exponential T(1rho) decay indicates that the domain sizes of nifedipine and polymer in solid dispersion are less than several nm, it is speculated that nifedipine is miscible with PVP but not miscible with PHPA. All the nifedipine-PVP solid dispersions studied showed a single glass transition temperature (T(g)), whereas two glass transitions were observed for the nifedipine-PHPA solid dispersion (3 : 7), thus supporting the above speculation. For nifedipine-HPMC solid dispersions (3 : 7 and 5 : 5), the miscibility of nifedipine and HPMC could not be determined by DSC measurements due to the lack of obviously evident T(g). In contrast, (1)H-NMR spin-lattice relaxation measurements showed that nifedipine and HPMC are miscible, since T(1rho) decay of the solid dispersions (3 : 7, 5 : 5 and 7 : 3) was describable with a mono-exponential equation. These results indicate that (1)H-NMR spin-lattice relaxation measurements are useful for assessing the miscibility of a drug and an excipient in solid dispersions.     

Molecular reorientation of CD(4) in gas-phase mixtures

Spin-lattice relaxation times were measured for the deuterons in CD(4) in pure gas and in mixtures with the following buffer gases: Ar, Kr, Xe, HCl, N(2), CO, CO(2), CF(4), and SF(6). Effective collision cross sections sigma(theta, 2) for the molecular reorientation of CD(4) in collisions with these ten molecules are obtained as a function of temperature. These cross sections are compared with the corresponding cross sections sigma(J) obtained from (1)H spin-rotation relaxation in mixtures of CH(4) with the same set of buffer gases. Various classical reorientation models typically applied in liquids predict different ratios of the reduced correlation times for the reorientation of spherical tops. The Langevin model comes closest to predicting the magnitude of the sigma(theta, 2)/sigma(J) ratio that we obtain for CD(4).