Modified colloidal primitive model as a homogeneous surface charge distribution: ζ-potential

An integral equations theory is derived and applied to a modified colloidal primitive model (MCPM), for finite concentration colloidal dispersions. In MCPM, the charge on the colloidal particle is assumed to be smeared on its surface. We find important quantitative and qualitative differences of the ζ-potential, induced charge, and the colloid-colloid electric effective force, calculated in the MCPM, with those obtained from the colloidal primitive model (CPM), where the colloidal charge is assumed to be in the center of the particle, in spite of the fact that, due to Gauss's law, both models have the same particle distribution function. In particular, for the same parameters, while the ζ-potential is positive in MCPM, is negative in the CPM, implying opposite electrophoretic mobilities, μ. An inverse μ has been theoretically predicted in the past, for infinite dilution colloidal dispersions. The MCPM could be a better model for some colloidal particles. In both models, the CPM and the MCPM, it is found a very long-range colloid-colloid correlation, in accordance with previous Monte Carlo simulations. The electrostatic, as well as entropic, like-charged colloid-colloid forces are oscillatory, implying a long-range attraction.