High-frequency dielectric relaxation of spherical colloidal particles

Abstract

The high-frequency limit of the conductivity and dielectric constant increment spectra for dilute suspensions of spherical colloidal particles is obtained from numerical solutions of the standard electrokinetic model. Our numerical method allows frequencies beyond 1 GHz to be reached, allowing Maxwell–Wagner relaxation to be observed. Contrary to previous thinking, the conductivity increment passes through a maximum as the momentum diffusion length becomes comparable to and then smaller than the double-layer thickness. Therefore, at sufficiently high frequencies, fluid inertia within the double layer causes the phase of the double-layer relaxation to further lag the applied electric field. As expected from elementary scaling, these ‘exact’ calculations show that a maximum in the conductivity increment can be observed with an aqueous electrolyte at a frequency of 10 MHz when the double-layer thickness is ca. 300 nm. With thinner double layers, inertial effects become important inside the double layer at even higher frequencies.