The electrostatic interactions between two colloidal particles of zero net charge

The electrostatic interactions between two charged planes with zero net charge density are investigated on the basis of the Poisson-Boltzmann equation under the Debye-Hückel approximation. The electrostatic free energy and interaction energy are obtained by the charging process. Two cases have been investigated: (1) particles with periodic surface charge density, and (2) particles coated with ion-penetrable layers. For case (1), the interaction energy contains both repulsive and attractive contributions, the strength of which depends on the phase lag between the two particles. They experience repulsive forces in the proximity of the in-phase mode. However, in the proximity of the out-of-phase mode, the two particles experience attractive forces at sufficiently long distances and repulsive forces at closer distances. For case (2), the two particles repel each other and the repulsive forces decay monotonicaly with increasing interparticle distances. However, the compromise between the net charge effect and the screening effect leads to the existence of an ionic strength (or amount of salt addition) at which the at-contact repulsion is maximum for a specified thickness of the layer.