S. Alexander

Pure Nuclear Quadrupole Resonance in Triethylene Diamine

A detailed study of the pure nuclear quadrupole resonance of 14N in solid triethylene diamine is described. The resonance frequency, spin–lattice relaxation time (T1), and the free‐induction decay time (T2) were measured as a function of temperature from 80°K to the plastic transition at 351°K. From 200°–300°K T1 is dominated by hindered molecular rotations about the trigonal axis of the molecule modulating the dipolar interaction with the protons. The activation for this reorientation was found to be 8.17 kcal/mole, in reasonable agreement with NMR results of Smith. The linewidth is discussed in detail and indicates an acentric structure of the molecule. Effects of the approach to the plastic transition are evident in all the three quantities measured but could not be interpreted in detail.

Displacive Phase Transitions in Malononitrile

The crystallographic phases and phase transitions of molecular crystals of malononitrile were investigated using 14N pure nuclear quadrupole resonance. The resonance frequencies, linewidths, and spin–lattice relaxation times were measured using pulse techniques. The relation between quadrupole resonance results and the order parameter of a phase transition are analyzed. Detailed measurements were carried out near one of the transitions (at 294.7°K) and the results are interpreted in terms of critical exponents. The resonance frequencies give β = 0.5 ± 0.02 and the linewidths γ = 0.3 ± 0.07 and γ′ < 0.1 ± 0.1. Our quadrupole resonance results are compared with specific‐heat measurement of Girdhar, Westrum, and Wulff. As two of the phase transitions show very small transition entropies, it is suggested that these are displacive phase transitions associated with instabilities in the collective modes of the crystal. The meaning of such transitions is discussed both from a thermodynamic and a microscopic point...

Relative Signs of Spin‐Spin Interactions in Nuclear Magnetic Resonance. II

The spectrum of the allyl group in allyl amine is discussed in detail. The interpretation of the spectra of 1‐butene and 3,3‐dimethyl‐1‐butene are also discussed. It is shown how the chemical shifts, spin‐spin interactions, and in particular the relative signs of the latter can be determined by numerical methods.In all three molecules all spin‐spin interactions among the vinyl protons have the same sign. One of the three vinyl‐methylene interactions is found to have a different sign than the other two. This interaction has the same sign (and approximately the same magnitude) as the methyl‐methylene interaction in 1‐butene.

Spin‐Spin Interactions in Nuclear Magnetic Resonance. Contact Contribution

A method for calculating the contact contribution to spin‐spin interactions between nuclei in nonaromatic molecules is described. The method is based on the valence bond model. The equivalent Hamiltonian of the Dirac vector model is used for a perturbation calculation in a representation where the total spin of the two electrons in each bond in the molecule is a good quantum number. The Ramsey‐Purcell contact term in the interaction is calculated by a double perturbation method where only terms linear in the electron‐nuclear interactions are considered but the perturbation is carried to higher order in the exchange integrals. In this way the interaction constants can be obtained explicitly in terms of the exchange integrals, and the calculation of the valence bond wave functions is avoided. It is then possible to see how the signs and magnitudes of the interaction constants depend on these integrals and what the dominant interaction mechanisms are. The perturbation series is evaluated explicitly with the ...

Theory of dynamic magic angle spinning nuclear magnetic resonance and its application to carbon‐13 in solid bullvalene

Carbon‐13 magic angle spinning (MAS) spectra of bullvalene, at a spinning frequency of about 4 kHz, are presented for the temperature range −30 °C to +85 °C. At low temperatures (<−10 °C), separate center peaks are observed for the aliphatic and olefinic carbons, as well as spinning sidebands for the latter. Upon heating to room temperature and above, the peaks broaden and eventually coalesce to a single line at the weighted average chemical shift frequency. These results are interpreted in terms of two independent processes—a concerted Cope rearrangement reorientation and symmetric threefold jumps about the molecular C3 axes. In both processes, the high order of the bullvalene crystals is preserved. A quantitative analysis of the spectra yields the following kinetic equations for, respectively, the Cope rearrangement reorientation and the threefold jump processes: kC(s−1)=1.38×1014 exp(−14.5/RT); kJ(s−1)=2.53×1019 exp(−21.0/RT), where R is in kcal/mol degree. The analysis of the spectra was performed by ...

Dynamic magnetic resonance line shapes in a symmetric threefold potential

A method for calculation of dynamic nuclear magnetic resonance (NMR) line shapes of molecules undergoing reorientation diffusion about a single rotation axis in a symmetric threefold potential is developed using the general theory of Freed. The method is used to calculate deuterium NMR spectra of molecules undergoing reorientational diffusion in a model potential of the form V(φ)=−V0 cos 3φ, as a function of the diffusion constant DR, and the potential strength V0. It is found that for V0 smaller than kT the resulting line shapes are very similar to those obtained in a potential‐free diffusion. When V0>kT the uneven distribution of the molecules and the hindering effect of the potential barrier have significant effects on the line shape. In this region two distinct motional effects of the diffusion process are observed: (i) At low DR values molecular diffusion within the potential wells results in averaging of the local distribution and consequently to line narrowing. (ii) At sufficiently high DR values d...

Planar diffusion and discrete jumps in pyramidic liquid crystals

Deuterium nuclear magnetic resonance (NMR) spectra are presented for homologues of two series of pyramidic liquid crystals, viz., hexaalkyloxytribenzocyclononatriene, I‐n, and hexaalkanoyloxytribenzocyclononatriene, II‐n, (where n represents the number of carbon atoms per side chain). The homologues of series I‐n exhibit a single hexagonal columnar mesophase PA, while those of series II‐n exhibit one or two columnar mesophases (depending on n); a low‐temperature biaxial phase PD, and a high‐temperature hexagonal phase PC. NMR measurements were performed in the mesophase region on compounds specifically deuterated at the crown methylene groups of the tribenzocyclononatriene core. The spectra in both systems exhibit dynamic features typical of molecules reorienting about their C3 axes within the columnar structures. The experimental spectra were compared with simulated line shapes calculated on the basis of two reorientation mechanisms, (i) symmetric threefold jumps and (ii) planar diffusion about the molec...

Nuclear Quadrupole Spectra in Very Asymmetric Field Gradients

Pure nuclear quadrupole resonance spectra in asymmetric field gradients are discussed. Contrary to the usual approach, the fully asymmetric case (η=1) is taken as a starting point. It is shown that in this case the Hamiltonian has an important symmetry property, which gives information on the energy‐level spectrum and relations between the eigenfunctions. Closed solutions in terms of quadratic equations can be obtained for spins up to 92. A perturbation expansion around η=1, which seems to converge very well, is also described.

Vacancy‐controlled interdiffusion: Nonlinear effects

We derive the nonlinear equations governing vacancy‐controlled interdiffusion in a two‐component noninteracting lattice gas. We observe that when the diffusion constants of the two species are not equal, the problem cannot be reduced to a simple linear diffusion. In order to treat the strongly nonlinear limit of large kinetic asymmetry and small concentration of vacancies, we introduce an adiabatic approximation in which the ‘‘fast’’ species is in an equilibrium state defined by the instantaneous distribution of the ‘‘slow’’ species, which obeys a linear diffusion equation with a renormalized diffusion coefficient. Comparison with numerical solutions of the nonlinear equations shows that the adiabatic approximation captures the essential physics of the diffusion process.