Ionic determinant relaxation

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. 

The fluctuations are often caused by atomic motion e.g. Brownian motion in liquids, ionic hopping, molecular rotations, librations and atomic vibrations. These motions are often complex and it is the range of frequencies that are present in the motions that determine relaxation. The spectral density function describes the relative intensities of different frequencies in the motions and can be used to calculate relaxation rates. 

When an external electric field is imposed on an electrolyte solution by electrodes dipped into the solution, the electric current produced is proportional to the potential difference between the electrodes. The proportionality coefficient is the resistance of the solution, and its reciprocal, the conductivity, is readily measured accurately with an alternating potential at a rate of 1 kHz in a virtually open circuit (zero current), in order to avoid electrolysis at the electrodes. The conductivity depends on the concentration of the ions, the carriers of the current, and can be determined per unit concentration as the molar conductivity Ae. At finite concentrations ion-ion interactions cause the conductivities of electrolytes to decrease, not only if ion pairs are formed (see Sect. 2.6.2) but also due to indirect causes. The molar conductivity Ae can be extrapolated to infinite dilution to yield Ae" by an appropriate theoretical expression. The modern theory, e.g., that of Fernandez-Prini (1969), takes into account the electrophoretic and ionic atmosphere relaxation effects. The molar conductivity of a completely dissociated electrolyte is ... 

The total effect of the single excitations is a large step in the right direction, both spin polarization and the relaxation of the ionic determinants cause antiferromagnetic contributions, but still the value of the coupling is only 50 % of the final value and other mechanisms have to be included. 

As discussed in Sect. 6.2, the electronic states of a paramagnetic ion are determined by the spin Hamiltonian, (6.1). At finite temperamres, the crystal field is modulated because of thermal oscillations of the ligands. This results in spin-lattice relaxation, i.e. transitions between the electronic eigenstates induced by interactions between the ionic spin and the phonons [10, 11, 31, 32]. The spin-lattice relaxation frequency increases with increasing temperature because of the temperature dependence of the population of the phonon states. For high-spin Fe ", the coupling between the spin and the lattice is weak because of the spherical symmetry of the ground state. This... 

The equivalent conductivity of an electrolyte solution decreases with increasing concentration due to interionic attractions described mainly by the electrophoretic and relaxation field effects 2-35>. This decrease is more pronounced if in addition the electrolyte is associated. Association of ionic salts by ion-pairing is commonly observed in solvents of low or moderate dielectric constant. The immediate goals in the analysis of conductance data are the. determination of the limiting equivalent conductance at infinite dilution, A0, and the evaluation of the association constant, KA, if ion-pairing occurs. 

A number of methods have been used for determining Kg values cation selective electrodes, pH-metric methods, conductimetry, calorimetry, temperature-jump relaxation measurements, membrane conductance measurements, nuclear magnetic resonance, optical rotatory dispersion. The results listed in Tables 7—10 have been obtained by various methods and at different ionic strengths so they may not always be strictly comparable. However, the corrections are probably small and the experimental accuracy is generally the same or very similar within a certain ligand type. 

Hachiya et al. (1979) determined the relationship between slow and fast reciprocal relaxation times (t T1 and rf1, respectively) at various ionic strength and pH values and found that the value of r 1 depended on the concentration of Pb2+ and pH but was independent of ionic strength, whereas rf1 decreased with increasing Pb2+ concentration. 

---