High-frequency dielectric response of a spheroidal particle with a thin double layer

This paper addresses the dielectric response of a charged, oblate spheroidal particle immersed in an electrolyte. Analytic solutions are obtained for the polarization coefficient in the thin double layer limit for frequencies in the megahertz to gigahertz range. Two different distributions of the equilibrium surface charge density in the double layer are considered. The first is when the surface charge density is uniform. The second is a particular nonuniform distribution with more charges along the flat surface of the spheroid than along the edges. For this latter case, an exact solution for the polarization coefficients is obtained. In these solutions for the polarization coefficients, to a good approximation, the particles act as if they have conductivity in addition to permittivity, with different values for the conductivity depending on whether the applied electric field is parallel or perpendicular to the flat surface of the particle. When it is parallel to the flat surface, the apparent conductivity of the particle is roughly proportional to total charge on the particle and, hence, does not appear to depend on the details of the surface charge density. When the electric field is perpendicular to the flat surface, the apparent conductivity decreases as the particle becomes more platy and as the charge along the edges decreases. The effect on the dielectric dispersion of a dilute mixture of these charged spheroids in an electrolyte is also calculated. When their symmetry axes are aligned parallel to the applied electric field, the charges on the spheroids reduce the dielectric dispersion, while for spheroids aligned in the other direction, the charges increase both the conductivity and the dielectric dispersion.