Electrostatic interactions for a particle-containing shell-and-core system

The electrostatic interactions for a particle-containing shell-and-core system are studied on the basis of the Poisson-Boltzmann equation under the Debye-Huckel approximation. Analytical expressions for the electrostatic potential distributions are obtained for arbitrary charge distributions on both the shell and the particle surfaces. On the basis of a charging process, the electrostatic free energy of the system is also obtained. The free energy consists of the self-energy and the interaction energy. The self-energy depends only on the surface charge density of the particle or the shell itself. The interaction energy arises from the interactions between the same modes on both surfaces when the particle is in concentric position with the outer shell. In general, the serf-energy dominates over the interaction energy. The effects of surface charge distributions of the inner particle on the electrostatic free energy of the systems are explored. The electrostatic free energy associated with the net charge effect in the aqueous core is also investigated. It is found that when the particle and the shell possess charges of the same sign, the free energy associated with net charge effect is lower than that of the opposite sign. The contribution due to net charge effect can he neglected when enough electrolytes are added into the aqueous core.