Quadrupolar relaxation models

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. 

Both AP and Ga have a tightly bound hydrate shell in aqueous solution and both are prone to hydrolysis. In terms of the Hertz electrostatic model for quadrupolar relaxation of ionic nuclei in electrolyte solution (see Section III.C) one therefore expects effective quenching of the electric field gradient caused by the surrounding water dipoles, due to a nearly perfect coordination symmetry. Any contribution to the e.f.g. should therefore arise from outer-sphere solvent dipoles. In terms of the fully orientated solvation (FOS) model this would correspond to a distribution width parameter approaching zero (/. -> 0) with the first term in equation (4) vanishing. This is indeed what Hertz (24) found for both AF" and Ga ", and the experimental infinite dilution relaxation rates ( AP" 7-5 s Ga 350 s ) are remarkably well matched by the computed ones... 

There a been a number of interesting applications of the framework developed in the studies of the simple ions were MD simulations of the quadrupolar relaxation has been performed on counterions in heterogeneous systems. Studies of a droplet of aqueous Na embedded in a membrane of carboxyl groups [54], showed that the EFG was strongly effected by the local solvent structure and that continuum models are not sufficient to describe the quadrupolar relaxation. The Stemheimer approximation was employed, which had been shown to be a good approximation for the Na ion. Again, the division into molecular contributions could be employed to rationalize the complex behavior in the EFG tensor. Similar conclusions has been drawn from MD simulation studies of ions solvating DNA... 

The strong field of an ionic solute restricts the reorientational motion of the a polar solvent, which directly effects the EFG-TCF. This fact has been used to determine the structure in the solvation shell around the quadrupolar nucleus by comparing the performance of different theoretical models for the quadrupolar relaxation. In the models, the solvent electrical dipoles have been assumed either to be radially oriented to the solute or randomly oriented, which gives different expressions for the EFG-TCF [60,61]. The assumptions in these models has been examined in MD simulations [52,62], and different ways to describe the EFG-TCF in terms of different reorientational TCF was suggested. 

The theories for the quadrupolar relaxation, based on idealized solvation models, were not valid for noble gases in solution. In comparison, the model for radially oriented solvent molecule is applicable to ions [62,67]. However, the general ideas of the theoretical models have been employed to construct an ad hoc model, which has proven to be superior in many different systems [30,63,66,67]. 

Various models have been proposed relating quadrupolar relaxation times to the correlation times of molecular motions, (lc) The more sophisticated the model considered the greater the number of parameters involved and thus the necessity for more independent NMR measurements. These may be obtained from a consideration of both14N and 2H relaxation data on a series of closely related molecules. Ordinary and... 

The study of quadrupolar nuclei can provide unique and very valuable information on a variety of physico-chemical and biological systems. For one thing the relaxation of quadrupolar nuclei is in many ways easier to interpret than the relaxation of non-quadrupolar nuclei, since the former is in many cases caused by purely intramolecular interactions modulated by the molecular motion. Studies of quadrupolar relaxation have therefore furnished important information about molecular reorientation and association in liquids and have played - and will certainly play for many years - an important role in testing new theoretical models of molecular motion in liquids. 

Two theories have been developed to attempt to explain the different quadrupolar relaxation rates of these cations. The electrostatic model due to Valiev and Hertz is currently favored and considers the relaxation to be caused by the electric field gradients due to the dipole moments of the solvent molecules modulated by their rotational and translational motion. The fully random distribution (FRD) version of the model leads in the extreme narrowing limit to... 

In polymer networks, slow motions, which may occur at larger spatial scales, are frozen. This has been demonstrated in the PDMS model networks described in Section 15.3.1, by measuring the relaxation of the so-called quadrupolar magnetic order in the 2H spin system [29]. This relaxation (observed with an appropriate pulse sequence) is sensitive... 

Theoretical expressions for spin-lattice relaxation of 2H nuclei (determined by locally axially symmetric quadrupolar interactions modulated by molecular motions) can be derived for specific dynamic processes, allowing the correct dynamic model to be established by comparison of theoretical and experimental results [34,35]. In addition, T, anisotropy effects, which can be revealed using a modified inversion recovery experiment, can also be informative with regard to establishing the dynamic model [34,35]. 

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). 

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