Dielectric anisotropy, volume potential anomalies and the persistent Maxwellian equivalent body

Potentially, lipid membranes possess a high tangential conductivity and permittivity due to their surface charges and the in-plane orientation of the headgroup dipoles. Electrically, membranes exhibit a sandwich structure with a largely isotropic centre formed by the fatty acid chains and confined by two anisotropic headgroup layers. Accordingly, we described spherical vesicles by an aqueous core covered by three shells. For a theoretical comparison, models with an anisotropic single shell and anisotropic homogeneous spheres were also considered. Two effects can be clearly demonstrated. (1) High tangential conductivities or permittivities may lead to cyclic variations in the phase of the electric potential in the radial direction, resulting in a hemi-shell structure of the electric potential inside the objects with oppositely charged facets. The thickness of the anisotropic shell restricts the number of phase oscillations. (2) Despite the strong local field inhomogeneities, an isotropic homogeneous Maxwellian equivalent body with an identical external field distribution exists for any of the anisotropic models. Its properties can be found from a comparison of the numerically calculated surface potential and the classical expression of the Clausius-Mossotti factor at any given frequency. The permittivity conductivity pairs obtained exhibit a sigmoidal-like frequency dependence