N.M.R. solid echoes in systems of dipolar-coupled inequivalent spins-1 or dipolar-coupled inequivalent pairs of spins-1/2

Proton solid-echo transverse relaxation functions for many thermotropic and lyotropic mesophases, mapped by measurement of the echo amplitude S_yx (t′ = τ) as a function of τ using a P_y (90°)-τ-P_x (90°)-t′ sequence, yield gaussian behaviour of the form exp [-½M ^E ₂τ²] for decays up to 20–30 per cent of the value at τ = 0. M ^E ₂, the second moment for the dipolar interactions between the spin-½ pairs, is related to the van Vleck second moment M ^VV ₂ through a factor f. Whilst experiments suggested a value of 0·70–0·72 for f = M ^E ₂/M ^VV ₂, simple models that ignored the non-equivalence of the dipolar-coupled spin-pairs had predicted f = 0·65. In this paper we derive an exact analytic expression for the spin response of a model of two dipolar-coupled inequivalent spins-1 to the pulse sequence P_y (90°)-τ-P _α(β)-t′, and show that the present model, with the quenching of the spin-flip terms of the dipolar hamiltonian, resolves the afore-mentioned discrepancy. We also reconcile the differences between the experimental and the earlier predicted values of f for deuteron N.M.R. spin echoes in perdeuterated solids.     

N.M.R. dipolar echoes in solids containing spin-1/2 pairs

The proton echo responses to resonant 90°-τ-β_90° (XY) and 90-τ-β_0° (XX) pulse sequences in powdered crystalline hydrates are reported. The echo produced by the XY sequence consists of two components: one is proportional to sin² β and the other to sin² β cos² β; the former component decays much faster than the latter on increasing the pulse spacing τ. In contrast, the XX sequence produces a single component echo of the form - sin² β cosβ. The maximum echo amplitudes for the sequences 90°-τ-90°_90° and 90°-τ-54°44′_0° exhibit a gaussian dependence on τ² over at least 95 per cent of their decays. The decay constant for the 90-τ-90°_90° echo corresponds to M ₂(inter) = 5/6 M ₂ ^vv(inter), where M ₂ ^vv(inter) is the interpair second moment calculated by the van Vleck procedure. These observations can be explained in terms of a simple model consisting of a planar arrangement of two spin-1/2 pairs provided the interpair dipolar hamiltonian is truncated so that [?^o _a(intra) + ?^{o, t} _d(inter), ?_z] = 0 and [?^o _a(intra), ?^{o, t} _d(inter)] = 0.

The model predicts the echo behaviour only if the spin-1 character of the eigenfunctions of ?^o _d(intra) + ?_z is preserved in the presence of the interpair interactions. It is shown that the XX echo and the sin² β cos² β components of the XY sequence originate solely in the interpair interactions and contain no contributions from the intrapair interactions. The decay of the maximum echo amplitude with increasing τ is caused by the incomplete refocusing of the interpair interactions by the XX and XY sequences; the correct decay is only determined provided the interpair dipolar hamiltonian is correctly truncated. The model also accounts for the proton echo behaviour in solid hydrogen reported by Metzger and Gaines.

Interestingly, the N.M.R. behaviour observed for these spin-1/2 pair systems is largely determined by the eigenfunctions of the spin Hamiltonian with M_z = 0.     

N.M.R. study of self-diffusion in solid N2

From the measurement of the N.M.R. relaxation times T₂ in ¹⁵N₂ and in ¹⁴N₂ containing Ar impurities we extract the self diffusion coefficient D $\text{i}$n h.c.p. N₂. We find that self-diffusion is a thermally activated process with an activation enthalpy δH¹/k = 1030 ± 25 K. We discuss the diffusion process and conclude that it can be related to the motion of thermally activated vacancies.     

N.M.R. study of solid perfluorocyclobutane

spin-lattice relaxation times and linewidth measurements for fluorine nuclei in solid perfluorocyclobutane are presented. The results are discussed in terms of D _2d molecular species performing fast internal motion. The relaxation measurements corroborate the existance of four solid-solid phase transitions and give some insight into their nature. The activation energies for molecular reorientation and self-diffusion processes are found to be 28·0 and 32·2 kJ mol^-1, respectively.     

An N.M.R. study of molecular motion in solid trimethylaminegallane

Continuous wave and pulsed ¹H N.M.R. data have been obtained for solid H₃GaN(CH₃)₃ over the temperature range 63–300 K. A theoretical expression for the relaxation behaviour of a methyl group in a trimethylamine moeity undergoing various motions has been obtained to aid analysis of the data. We find the activation energy to rotation of the -GaH₃ group to be 3·6 ± 0·3 kJ/mole (0·86 ± 0·07 kcal/mole), and to a different motion in the molecule to be 21 ± 2 kJ/mole (5·0 ± 0·5 kcal/mole). In the continuous wave spectra effects due to motion of the -CH₃ groups and the whole -NMe₃ moeity may be distinguished.     

75As N.Q.R. and 19F N.M.R. study of solid AsF3

The temperature dependence of the ⁷⁵As pure quadrupole resonance frequency in AsF₃ has been studied from 77 K to a temperature very close to the melting point. It is found that the effective electric field gradient at the As site does not shift much from the gas-phase value and that the temperature dependence of the ⁷⁵As N.Q.R. frequency seems to follow the Bayer-Kushida model. The occurrence of a line-width transition in the ¹⁹F N.M.R. spectrum between 200 and 150 K demonstrates the presence of low-frequency, large-amplitude molecular motions which are too slow to average out the ⁷⁵As quadrupole coupling.     

19F N.M.R. and 127I N.M.R. and N.Q.R. study of the molecular motions and deformations of iodine heptafluoride in its solid phases

In solid IF₇, ¹⁹F and ¹²⁷I N.M.R. and ¹²⁷I N.Q.R. absorption line shapes, frequencies and relaxation times have been studied from the melting temperature down to 56 K. Two new solid-solid transitions have been found at 180 K and 96 K in addition to the one already known at 153 K. The two high temperature phases are shown to be plastic. The fast molecular rotations and the slow molecular diffusion are studied from ¹⁹F and ¹²⁷I relaxation times. In the ordered phases, an analysis of the ¹⁹F second moments and longitudinal relaxation times shows the existence of a fast intramolecular exchange between axial and equatorial fluorine atoms, together with a much faster reorientation about the D ₅ axis. The characteristic times of these two motions are obtained and a mechanism for the exchange process is proposed. The chemical shift values of ¹²⁷I, the temperature dependence of the N.Q.R. frequencies and of the N.Q.R. relaxation times of ¹²⁷I, as well as the dipolar energy relaxation times have been measured and are discussed.     

Proton N.M.R. studies of chemical and diffusive exchange in carbohydrate systems

A computer-simulated stochastic model is developed capable of predicting the combined effects of chemical and diffusive exchange on the transverse relaxation of spin-1/2 nuclei in a heterogeneous system. Comparison is first made with previous analytical theories for the special case of two site chemical exchange in a homogeneous system and the experimental data on several homogeneous aqueous carbohydrate systems are analysed. Results show that transverse water proton relaxation in these systems is dominated by proton exchange between water and carbohydrate hydroxyl groups. Analysis of model heterogeneous carbohydrate systems shows that in addition to chemical exchange, diffusion coefficients, particle morphology and local magnetic field gradients all have a role to play in determining the proton relaxation behaviour.     

Multiple field modulation in N.M.R.

The Bloch equations are solved in the case of multiple field modulation. The result is applied to the problem of homonuclear stabilization of the magnetic field. It is found that the stability of the field/frequency lock may be degraded by disturbance signals. A particular phase setting can be chosen to avoid disturbances.     

Molecular reorientations of 1-bromo- and 1-iodo-adamantanes 1H N.M.R. relaxation study

Second moments and spin-lattice relaxation times, T ₁ and T _1ρ, have been measured from 100 K to 400 K for the protons in powdered 1-bromo and 1-iodo-adamantanes. Analysis of these data have shown that the reorientations are uniaxial in the low temperature phases. In the high temperature disordered phase of bromo-adamantane, the reorientation is endospherical and a slow molecular translational motion also exists. In the high temperature disordered phase of iodo-adamantane the reorientation is 12-fold uniaxial, in agreement with the Incoherent Quasi-elastic Neutron Scattering (I.Q.N.S.) experiments. All the results correspond to the crystallographic structures deduced from X-ray scattering.     

N.M.R. spectra of oriented molecules

The phosphorescence spectra of anthracene-h₁₀ and -d₁₀ have been studied in a number of glasses and crystalline matrices. The line widths are very matrix dependent and they range from about 150 cm^-1 to 1 cm^-1 in n-heptane. There is a correlation between the line width and the wavenumber position of the origin. A study of the relative intensities of fluorescence and phosphorescence from various sites in Shpolskii matrices has shown that the intersystem crossing rate is site dependent. It is postulated that this involves the relative energies of the singlet state and a triplet state, nearly degenerate with it, which are site dependent.     

N.M.R. spectra of oriented molecules

By analysis of the high resolution N.M.R. spectrum of 1,2,2,3-tetrachloro-propane partially oriented in a liquid-crystal solvent, it has been shown that this molecule takes up predominantly the G′G′ type of conformation.     

Site factors in N.M.R. solvent effects

An algorithm was developed enabling implementation of a Nosé—Hoover thermostat within the framework of grand canonical molecular dynamics [Lynch, C. G. and Pettitt, B. M., 1997, J. chem. Phys., 107, 8594]. The proposed algorithm could readily be extended to mixtures of molecular species with different chemical potentials as shown in the paper. This algorithm was first applied to simulate a μVT ensemble of TIP4P water molecules at 298 K by means of a system comprising a number of full particles and a single scaled (fractional) particle, with the scaling factor considered as a dynamic variable in its own right and chemical potential a pre-set parameter. Our finding showed that the scheme with a single fractional particle tended to freeze in metastable states as well as failed to reproduce either the real-life (?24.05 kJmol^?1) or the model-specific chemical potential of water (?23.0kJ mol^?1). In order to overcome the inadequacy of a single fractional particle as a chemical potential ‘probe’ the treatment of Pettitt and co-workers was extended to introduce multiple fractional particles. The extended scheme (with 4 fractional particles) was able to reproduce the actual density of water for the driving chemical potential of -24.0k mo^?1. The actual behaviour of the density as a function of the chemical potential also agreed quite well with both the results of thermo-dynamic integration and the findings of Pettitt and co-workers.     

N.M.R. Spectral Studies of Some Quinolone Derivatives. Part VI.1 N-Methyl-2-Quinolone Derivatives

The chemical shifts of the N-CH₃ protons for a series of 1-methyl-2-quinolone derivatives has been studied. Compounds with an 8-methyl substituent exhibit a slight downfield shift.