Zeeman Spin-lattice Relaxation Times Research Articles

Rotational dynamics of a chiral mesogen by 2H NMR study: can it be anomalous?

Deuterium NMR spectroscopy is used to study a ring-deuteriated chiral liquid crystal 4-(2-methylbutyl)oxycarbonylphenyl 4-(10-undecenyloxy)benzoate. The quadrupolar and proton-deuteron dipolar splittings, and deuteron quadrupolar and Zeeman spin-lattice relaxation times were measured as a function of temperature in the smectic A phase at two different Larmor frequencies. The derived spectral densities of motion at different temperatures were analysed simultaneously using a rotational diffusion model which also includes internal ring rotations. Motional parameters (D ⊥, D ∥, D R) and order parameter tensors (Szz , Sxx -Syy ) were obtained. Although the present data seem insufficient to draw a definitive conclusion, we believe that it is possible for this particular chiral molecule to have D⊥ >D∥ , which is different from non-chiral rod-like liquid crystals.

Deuterium Spin-Lattice Relaxation in Thermotropic Liquid Crystals. Study of 4,4′-di-n-heptylazobenzene, 4,4′-di-n-heptylazoxybenzene and 4,4′-di-n-octylazoxybenzene

Abstract The deuterium Zeeman spin-lattice relaxation times TIZ in 4,4′-di-n-heptylazobenzene (HB), 4,4′-di-n-heptylazoxybenzene (HAB), and 4,4′-di n-octylazoxybenzene (OAB) deuterated on the aromatic rings and on the first methylene group of the chains were measured at 10 and 46.04 MHz by means of the inversion-recovery technique. Measurements were made throughout the mesomorphic range and also in the isotropic phase. The relaxation rates show a discontinuity at the isotropic-nematic transition for all deuterons not ascribable to the onset of orientational order. The trends of InR are linear within the different phases except near phase transitions, and allow to obtain apparent activation energies for the overall motions of the different C—D bonds.

Coupled (Zeeman-tunnel)-lattice relaxation of the methyl group in copper acetate.

A calculation is presented describing the coupled relaxation of the Zeeman and tunnel reservoirs of methyl groups, influenced by paramagnetic copper pairs. The transition rates are calculated following the approach introduced by Obata. Differential equations are derived which include the relaxation rates of both the intramethyl magnetic dipolar interaction and the interaction between the ${\mathrm{CH}}_{3}$-- protons and the paramagnetic copper pairs. The solution of the equations is compared with experimental data from polycrystalline copper acetate between 30 and 70 K. A time-dependent proton Zeeman spin-lattice relaxation time is observed. Its ``initial'' and ``final'' values are measured and explained. Moreover, resonant features in ${T}_{1}^{\mathrm{\ensuremath{-}}1}$(T) are observed near 40 K, which are related to the ${\mathrm{CH}}_{3}$-- tunnel splittings. The temperature dependence of the tunnel frequencies is studied. The correlation time of the ${\mathrm{CH}}_{3}$-- motion is determined from the dipolar spin-lattice relaxation. It is then used to evaluate theoretically the observed time constants of the Zeeman relaxation.

Nuclear-magnetic-resonance study of crystalline tellurium and selenium.

Nuclear-magnetic-resonance measurements of $^{125}\mathrm{Te}$ and $^{77}\mathrm{Se}$ have been carried out in single crystals of tellurium and selenium, respectively, between room temperature and the melting point ${T}_{m}$. In particular, both the time evolution of the nuclear magnetization in the laboratory frame as well as in the rotating frame, following both broadband and site-selective excitations, have been investigated in detail. In tellurium, the Zeeman spin-lattice relaxation is determined by three different mechanisms: (1) Below 300 K, spin-lattice relaxation is governed by a two-phonon (Raman) process; (2) in the temperature range between about 300 and 450 K, the influence of conduction electrons overcoming the gap energy of 0.30 eV becomes important; (3) above 450 K, the spin-lattice relaxation is due to mobile charged vacancies. From the high-temperature data, the formation energy of a charged vacancy was found to be 0.66 eV. In selenium, on the other hand, the Zeeman spin-lattice relaxation time is essentially caused by a two-phonon (Raman) process over the entire temperature range. In either system, the phonon-induced spin-lattice relaxation shows the same dependence on the crystal orientation relative to the direction of the external field. For T\ensuremath{\ge}0.74${T}_{m}$ in tellurium as well as in selenium, a diffusional contribution to the rotating-frame relaxation rate is observed, arising from fluctuations in the nuclear dipole and chemical shift interaction due to atomic self-diffusion. However, from these data alone the correlation time of atomic motion could be determined only with a relative large error. In contrast, from site-selective excitation experiments the correlation time was extracted directly with a high degree of accuracy without any assumption regarding the nature of the nuclear spin interactions. The observed correlation times are discussed in terms of Mehrer's model for monovacancy diffusion via nearest- and next-nearest-neighbor jumps. Diffusivities in tellurium deduced from this model are in good agreement with the tracer data obtained recently by Mehrer et al. In contrast, the observed diffusion coefficients in selenium are about a factor of 20 smaller than the tracer diffusion coefficients measured some years ago by Br\"atter and Gobrecht.

Nuclear magnetic resonance study of atomic motions in vanadium

Atomic motions in solid vanadium have been investigated by means of NMR. For that purpose, the Zeeman spin-lattice relaxation time T 1, the rotating-frame spin-lattice relaxation time T 1 ρ , and the Knight shift K of 51V in polycrystalline vanadium have been measured as a function of temperature in the range between 300 and 2000 K. At all temperatures, the relaxation time T 1 is mainly determined by electronic contributions leading to a temperature-dependent expression for the Korringa relation T 1, T · K 2. In contrast to the T 1,-data, two pronounced peaks in the relaxation rate T −1 1 ρ at about 750 and 1600 K, respectively, are observed. The peak at 750 K arises from fluctuations in the nuclear quadrupolar interaction between vanadium and interstitially migrating oxygen whereas the maximum at 1600 K is caused by fluctuations in the nuclear dipole interaction due to atomic self-diffusion. From the low-temperature data, the diffusivity of oxygen is determined to be D 1, = 3.2·10 −6exp(−0.73 eV/ kT)cm 2/s. By comparing the self-diffusion contribution to the relaxation rate with the tracer measurements of Pelleg, the correlation factor ∝ was found to be ∝= 0.77 ±0.11 consistent with a monovacancy diffusion mechanism. The uncorrelated self-diffusion coefficient was obtained as D SD = 0.14 exp(−3.09 eV/ kT)cm 2/s.

Proton Zeeman and dipolar relaxation study of the ferroelectric liquid crystal DOBAMBC

The proton Zeeman spin-lattice relaxation time T1 and the proton dipolar spin-lattice relaxation time T1D of a chiral compound p-decyloxybenzylidene p′-amino-2-methyl butyl cinnamate are studied as a function of temperature and sample rotation in a magnetic field at 30 MHz. In addition, proton T1 is measured in the smetic A, ferroelectric smectic C* and H* phase at 15.1 and 45.5 MHz. The spin relaxation mechanisms for the proton T1 and T1D in the smectic A and C* phase are ‘‘diffusion-induced’’ orientational order director fluctuations and molecular self-diffusion. In contrast with the achiral compound TBBA, the T1 angular dependence in the smectic C* and C phase are different, while the T1D angular dependence appears to be similar in these smectic phases.

NMR study of a smectic A-smectic B transition in a liquid crystal

Proton Zeeman spin-lattice relaxation time and dipolar spin-lattice relaxation time measurements are used to study the smectic A-smectic B transition in a pure liquid-crystal 4- n-butoxybenzylidene-4′-aminopropiophenone. Both the orientational order director fluctuations and the molecular self-diffusion are responsible for the Zeeman spin-lattice relaxation, while the latter is responsible for the dipolar spin-lattice relaxation.

Rotating frame spin-lattice relaxation in the presence of an off-resonance radio frequency field. Investigation of intermediate molecular motions

An NMR relaxation technique is described that should prove valuable in studies of intermediate molecular motions, i.e., these motions having correlation times greater than the inverse of the Larmor frequency. The technique is applicable to multiline spectra, the experiment being carried out on a commmercial Fourier transform NMR spectrometer. The experiment consists of measuring resonance peak intensities in the absence and presence of a radio frequency field applied far off-resonance as a function of the off-resonance frequency. Although it is not necessary to determine relaxation times in order to examine molecular motions, a value for the nuclear spin-lattice relaxation time in the rotating frame with off-resonance rf irradiation, T 1 Q off , may be determined if a value for T 1, the nuclear Zeeman spin-lattice relaxation time, is known. This technique is thus designed to supplement or supercede spin-spin relaxation time ( T 2) and normal on-resonance rotating frame spin-lattice relaxation time ( T 1 Q ) measurements. The utility of the off-resonance T 1 Q technique for investigating molecular motions is illustrated with a viscous liquid, glycerol, at low temperatures.

FREQUENCY DISPERSION OF THE PROTON ZEEMAN SPIN-LATTICE RELAXATION IN THE SMECTIC PHASES OF TBBA

Using a field cycling technique, the Larmor frequency (VL) dependence of the proton Zeeman spin-lattice relaxation time TI has been measured in the smectic A, smectic C, smectic B and smectic VII phases of terephtal-bis-butylaniline (TBBA) between VL = 90 MHz and VL = 0.14 MHz and a significant dispersion has been found. The observed coiJ2 dispersion law in the smectic A phase and the deviations from it at low frequencies can be explained by nematic director fluctuations in the smectic A phase and the coupling between nematic and smectic order.

Electron paramagnetic resonance in inhomogeneously broadened systems: A spin temperature approach

The EPR responses of inhomogeneously broadened electron spin systems are considered in detail under the assumption that a spin temperature situation in the rotating reference frame obtains in the constituent spin packets. Expressions are derived for the rapid passage and slow passage responses of such systems, including situations where magnetic field modulation and subsequent phase sensitive first harmonic detection is employed. It is shown that for rapid passage situations in which ω m T 1 ≫ 1 (where ω m is the angular frequency of the magnetic field modulation) a dispersive response n out of phase with the modulation is obtained, whereas when ω m T 1 ≪ 1 a response is obtained in quadrature with the modulation, both of which are in close agreement with experiment. Further, in very inhomogeneously broadened systems the first harmonic dispersive response has an absorption type shape given by G(Δ), where G(Δ) describes the inhomogeneous distribution of local fields, which is of the same form as the absorption response obtained under slow passage. In the slow passage regime it is shown that the saturation behavior of the system is strongly dependent on the relative values of the Zeeman spin-lattice relaxation time T 1 and the spin-spin reservoir relaxation time T ss. For situations in which T 1 = T ss, the saturation behavior of Bloembergen et al. is predicted, whereas when T ss ≪ T 1 the saturation behavior observed by Castner is obtained. Finally, techniques that allow measures of the spin packet width, T ss and T 1 are discussed.

Quantitative evaluation of cw methods for measurement of nuclear Zeeman spin-lattice relaxation times in solids

The Provotorov theory of partial saturation in solids is utilized to extract T 1 the Zeeman spin-lattice relaxation time, from on-resonance absorption mode second derivative, and dispersion mode first derivative cw signals, using conventional lock-in methods. Results are found to be in agreement with the usual 90°-τ-90° pulse method.

Effects of Electron-Electron Interactions on the Nuclear Spin-Lattice Relaxation Times in Aluminum

The "dipolar" spin-lattice relaxation time in aluminum has been measured for temperatures between $1.3\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<295\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. In contrast to the Zeeman spin-lattice relaxation time ${T}_{1z}$, the dipolar time does not vary linearly with $\frac{1}{T}$. This is interpreted in terms of cross relaxation between different groups of nuclear spins, some of which experience quadrupole interactions as a result of defects in the lattice, and others which are well removed from such defects. Both cross-relaxation and spin-lattice effects have been measured by our technique; a three-bath model of the nuclear-spin system permits a separation of these effects, with a true dipolar relaxation time ${T}_{1dd}$ related to ${T}_{1z}$ by $\ensuremath{\delta}=\frac{{T}_{1z}}{{T}_{1dd}}=2.15\ifmmode\pm\else\textpm\fi{}0.07$, $\ensuremath{\delta}$ being independent of temperature. This enhancement of $\ensuremath{\delta}$ over the value 2.00 and the enhancement of the Korringa relation between ${T}_{1z}$ and $K$, the Knight shift, are discussed and compared with the predictions of the theory of Wolff in which the effects of electron-electron interactions are considered. A similar analysis in sodium is included for comparison, sodium being the metal to which the theory is best applicable.