Electric permittivity of concentrated suspensions of elongated goethite particles

This paper describes an investigation on the electric permittivity of concentrated suspensions of non-spherical particles, specifically prolate spheroids. It is first discussed how the determination of the frequency (omega) dependence of the electric permittivity (a phenomenon traditionally known as LFDD or low-frequency dielectric dispersion) can provide ample information on the properties of the dispersed material (shape, size, state of aggregation, conductivity) and of its interface with the (typically aqueous) medium. The basic quantities are the strength and frequency dependence of the dipole moment induced by the applied field, and its dimensionless counterpart, the dipole coefficient, C(*)(omega). It is explicitly shown how the (complex) relative permittivity of the suspension, epsilon(r)(*)(omega), can be calculated from it. Two theoretical models on the polarizability of spheroidal colloidal particles will be used as theoretical starting point; one of them (Model I) explicitly considers two relaxations of the permittivity, each associated to one of the particle axes. The other (Model II) is a semi-analytical theory that yields an LFDD practically independent of the axial ratio of the particles. Both models are aimed to be used if the suspensions are dilute (low volume fraction of solids, phi), and here they are generalized to concentrated systems by means of a previously published approximate evaluation of the permittivity of concentrated suspensions. Experiments are performed in the 1 kHz-1 MHz frequency range on suspensions of elongated goethite particles; the effects of ionic strength, pH, and volume fraction are investigated, and the two models are fitted to the data. In reality, taking into account that the particles are non-uniformly charged (a fact that contributes to their instability), two zeta potentials (roughly representing the lateral surface and the tip of the spheroid) are used as parameters. The results indicate that, when experimental conditions are optimal (high ionic strength and low zeta potential), the suspensions do indeed display two relaxations, that we ascribe to the long axis (and to flocs likely present in suspension) and to the short one. The permittivity increases with ionic strength, a result found with other systems, and compatible with a zeta potential that, on the average, decreases with ionic strength, an equally well known result, consequence of electric double layer compression. Another reasonable finding is the increase of estimated average dimensions and the decrease of electrokinetic potentials when the pH is close to the isoelectric point of goethite (around pH 9). The increase in volume fraction, finally, produces an overall increase in the permittivity, and the approximate model used for the evaluation of volume fraction variations can describe properly these effects, with basically constant zeta potentials and dimensions.