Complex dielectric response of ellipsoidal particles with surface conduction

Abstract

Both particle shape and surface phenomena significantly affect the effective complex dielectric properties of colloidal systems. The treatment of particle shape has generally relied on the extrapolation from the solution of the spherical case proposed by O'Konski [J. Chem. Phys. 64, 605 (1960)] that treats ellipsoidal particles possessing surface conductivity as equivalent homogeneous anisotropic ellipsoids with bulk conduction. To test this approach, we have performed a rigorous analysis of the complex dielectric response of an ellipsoidal particle with surface conductivity using the generalization of the O'Konski boundary conditions to an ellipsoidal shape. The resulting closed-form solution obtained shows that surface conduction effects are represented by an equivalent inhomogeneous anisotropic ellipsoid. For the case of a spheroidal particle, the principle axes of the effective dielectric permittivity tensor of the equivalent particle are aligned with its geometrical principal axes; the effective permittivity varies in the direction of the unique spheroidal axis. In addition, numerical results indicate that the product of the surface area to volume ratio and the specific surface conductivity completely characterizes the effect of the surface phenomena on the response of spheroidal particles with a given shape. Numerical simulations show that spherical and prolate spheroidal particles exhibit a progressive dielectric enhancement while more disklike oblate spheroidal particles undergo an initial dielectric suppression followed by a subsequent enhancement with increasing surface conduction. A comparison of our model predictions with those obtained using the O'Konski approximation revealed significant differences in the magnitude of the low-frequency dielectric enhancement and relaxation frequency for ellipsoidal particle suspensions.