Effective Forces Between Diamagnetic and Paramagnetic Ions in D 2 O at Low and Moderate Ionic Strengths: An NMR Relaxation Study

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Abstract
The dynamical behaviour of several pairs of dissociated, attractive and repulsive, ions is investigated in aqueous solutions for ionic strengths up to 1 mol l-1. The experimental information is provided by the NMR longitudinal relaxation rates of the protons on the diamagnetic ions. The ionic solutions were chosen so that the main relaxation mechanism of these protons is due to the time fluctuations of their dipolar magnetic coupling with the electronic spins on the paramagnetic ions. This coupling strongly depends on the ion-ion potential of mean force (PMF) and on the ion self-diffusion coefficients. The interionic spatial correlations and the associated PMF are derived from a new approximation of the integral equations of the statistical mechanics of liquids. This formalism, which treats all the ions as discrete particles, rests on the infinite dilution PMF of the various ion pairs. It mixes a Born-Oppenheimer theory at infinite dilution with a sort of McMillan-Mayer approximation to take the ionic concentration into account. It goes beyond the Debye-Hückel screening theory, in which a continuous screening charge distribution approximates the effects of the discrete surrounding ions. It is related to the concept of the local dielectric constants which replace the usual macroscopic dielectric constant and depend on the interionic distances. The self-diffusion coefficients of the diamagnetic ions were measured by the NMR pulsed magnetic field gradient (PMFG) techniques applied to the resonant protons. In paramagnetic solutions, where several protonated species coexist, special caution is required and this is discussed in detail. For all the investigated solutions the theory well accounts for the observed variation of the NMR relaxation as a function of the ion charges, of the ionic strength and of the NMR proton resonance frequency. The relaxation results predicted by the new approximation of the ion-ion PMF are compared with those derived from the simple Debye-Hückel screening formalism, which can be reasonably used up to moderate ionic strengths

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