Quadrupolar nuclei frequency

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

Another source of microdynamic information comes from the deuterium relaxation rates. The quadrupolar coupling constant (e2qQ/h) expresses the magnitude of the coupling between the electric quadrupole moment Q of the nucleus and the efg q at the nucleus (e is the electronic charge, and h is Planck s constant). It provides a relaxation mechanism for the quadrupolar nucleus of its Fourier component at the Larmor (resonance) frequency for this nucleus is non-negligible. It has such a Fourier component because tumbling of the molecule the quadrupolar nucleus is part of, in a... 

We saw in Chapter 7 that the resonance frequency of a quadrupolar nucleus is dependent on the orientation of the molecule in which it resides. Molecular tumbling now causes fluctuating electric fields, which induce transitions among the nuclear quadrupole energy levels. The resulting nuclear relaxation is observed in the NMR just as though the relaxation had occurred by a magnetic mechanism. 

It is this absorption of electromagnetic energy that is measured in NQR spectroscopy. Radiation in the radio-frequency region is actually employed to effect transitions among the various orientations of a quadru-polar nucleus in a nonspherical field. In the experiment, which is generally carried out on a powder sample, one set of resonances is exposed for each chemically or crystallographically inequivalent quadrupolar nucleus... 

In Section 2.2.6, the nutation frequency of a quadrupolar nucleus was seen to vary from (I + /2)v] when vi << vq to V when V >> vq. The nutation spectra display distinct features in the region where vi vq. Simulation of nutation behaviour has shown that the useful range of rf field-strengths lies with vq/vi in the range 0.05-1. The distinct features of nutation spectra allow the quadrupole parameters to be obtained. This means that only quadrupole frequencies up to a certain limit are accessible with currently available rf-fields of 500 kHz in specially dedicated probeheads, and in fields of around 100 kHz in most commercially available systems. This constraint especially limits the investigation of spin I = 3/2 nuclei such as Na. 

The application of relaxation time measurements to study segmental motion (in polymers) as well as diffusional chain motion is very well documented but is still a subject of study, particularly using the frequency dependence of relaxation times to test the detailed predictions of models (McBriety and Packer 1993). The anisotropy of reorientation can also be studied conveniently, and recent interest in motion of molecules on surfaces (e.g. water on porous silica) has been investigated with great sueeess (Gladden 1993). Since the dipolar interaction is usually both intermolecular and intramolecular, the relaxation of spin- /2 nuclei (e.g. H) in the same molecule as a quadrupolar nucleus (e.g. H) can permit a complete study of reorientation and translation at a microscopic level (Schmidt-Rohr and Spiess 1994). 

Equation (16) is very important because it imcovers two central ideas. First, the second-order frequency splitting depends inversely on the Larmor frequency, thus the importance of this term diminishes with increasing external magnetic field strength. Second, the k=0 term has no orientation dependence (Do 0 = 1) or, in other words, it is an isotropic term. This means that the isotropic shift observed in the NMR spectriun of a quadrupolar nucleus has, in addition to the usual isotropic chemical shift, a contribution from the quadrupole cou-phng, which is given by... 

Trebosc et al. introduced a frequency-selective (FS) REDOR approach to a multi-spin system Sl y where S is a quadrupolar nucleus. FS-REDOR may be used for accurate trough-space distance measurements in spin pairs that involve quadrupolar nuclei [106]. The experiment reveals heteronuclear dipolar and scalar couplings, which can be reintroduced selectively, site after site. Importantly, FS-REDOR may also be used under high-resolution provided by MQMAS, STMAS or I-STMAS. 

Another very important experiment for spectral editing is a heterocorrelation experiment combining MQMAS (in the indirect dimension) with CP. Introducing CP at the MQMAS echo position following a split-fj MQMAS scheme creates a spin-j detected spectra (in the dimension), which is modulated by the isotropic frequency of the quadrupolar nucleus in F. HETCOR has been demonstrated on Na- P pairs, on 2 A1- P pairs and lately on a- H pairs,where proton resolution during F was obtained with the wPMLGS multiple pulse decoupling technique. ... 

The principle of sample spinning has been described in Section 3.3.3. As a result of sample spinning, the interaction Hamiltonian and thus the resonance frequency (cf. eqn (3.3.6)) becomes time dependent. For the simple case of a pair ij of dipolar coupled spins i, equivalent to a quadrupolar nucleus spin 1 like with, the time-dependent spin Hamiltonian is given by [Mehl, Schl]... 

To a good approximation, powder NMR line shapes for the STs of quadrupolar nuclei may be understood by first-order perturbation theory thus, we first consider these transitions. To first order, the transition frequencies, —1), expected for a quadrupolar nucleus, are given by... 

In the simplest case when the frequency of modulation of the quadrupolar interaction is very rapid compared to the Larmor frequency of the halogen nucleus, u),., the relaxation of the quadrupolar nucleus... 

---