Electrical polarizability of differently shaped dielectric objects in the presence of localized interfacial charge distribution: a unifying scenario

We present the dielectric relaxation spectra of non-spherical shelled particles (namely cylindrical and toroidal particles) with a layer of localized electrical charges at the interfaces, uniformly dispersed in a continuous aqueous phase. Our numerical simulations extend over a wide frequency range, covering both the relaxation region due to the presence of localized layers of charges at the interface (alpha-relaxation) and the one due to the mismatch of the permittivity and conductivity of the adjoining phases (beta-relaxation or the Maxwell-Wagner effect). Although there is a general formulation for determining the electrical polarizability alpha(omega) of arbitrarily shaped particles, based on the knowledge of the internal electric field distribution, the presence of the localized charge distribution makes its use formally rather elaborate. Contrarily, in this paper we show that, in the dipolar approximation, the polarizability alpha(omega), assuming the same functional dependence for spherical, cylindrical and toroidal particles, can be calculated in a very simple way and that the dielectric (and conductometric) properties of particle suspensions, adopting a simple inductive procedure, can be treated under a unifying scenario. Moreover, the method holds both for homogeneous and heterogeneous layered particles. A detailed prediction of the dielectric relaxations for both alpha- and beta-processes in heterogeneous systems composed of spherical, cylindrical and toroidal particles is made for a wide range of electrical phase parameter values.