Particle charges in nonaqueous colloidal dispersions

Numerical solutions of the Poisson-Boltzmann equation for potentials in the electrical double layer surrounding a particle are used to derive a new relationship between the particle charge q and the surface potential zeta. Unlike the linear zeta-q relation for a particle in charge-free media, the new relation shows that as the particle charge increases, the initial linear increase of the potential slows down and asymptotes to a finite value. The asymptotic values of the potential at high particle charges are dependent on the Debye length (or the ionic charge density) of the media and are of the order of a few hundred millivolts for particles in typical nonaqueous dispersions, e.g., those used as liquid developers for electrographic images. Thus, with this relationship, the reported values of charge and the electrophoretic mobility determined experimentally for these dispersions correspond to physically reasonable values of zeta potentials, which are smaller than that expected from the linear relation by more than an order of magnitude. In addition, the variations of particle charges with ionic charge densities and particle concentrations are examined.