Simulation of dielectric relaxation in periodic binary systems of complex geometry

Dielectric relaxation in binary mixtures containing particles or lamellae with complex geometry has been simulated within the quasielectrostatic approximation by a three-dimensional finite-difference method. The method was tested using simple models corresponding to water-in-oil (W/O) and oil-in-water (O/W) emulsions with volume fraction P up to 0.5. The dielectric spectra calculated by the finite difference method agreed with those expected from Wagner's equation at P < or =0.3 and approached those from Hanai's equation at P>0.4. This method was applied to more complicated binary mixtures of oil and water: a bicontinuous cubic structure, a suspension of particles with projections, and a planar bilayer with a rippled or interdigitated interface. The bicontinuous phase that is supposed to appear near the transition between W/O and O/W emulsions showed dielectric properties similar to those of the O/W emulsion. The undulation of the particle surface and the interface of the planar bilayer affected all parameters of dielectric relaxation, especially the relaxation intensity.