On electrophoresis of a pH-regulated nanogel with ion partitioning effects

The electrophoresis of a polyelectrolyte nanoparticle, whose charge condition depends on the salt concentration and pH of the suspended medium as well as the dielectric permittivity difference, is analyzed. The present nonlinear model for the electrophoresis of this pH-regulated polyelectrolyte (PE) particle is based on the consideration of full set of governing equations of fluid and ion transport coupled with the equation for electric field. The Born energy of the ions are incorporated to account for the difference in the dielectric permittivity of the PE and the electrolyte. The governing equations are computed numerically through a control volume approach. The nonlinear effects are highlighted by comparing with the existing linear model as well as results based on the first-order perturbation analysis valid for a weak applied field. The ion partitioning effect arising due to the difference in self energy of ions between the two media, have a strong impact on the mobility of the PE. The ion partitioning effect attenuates the penetration of counterions in the PE, which enhances the electric force and hence, results in a larger mobility of the PE. The nonlinear effects due to the double layer polarization and relaxation are intensified due to the ion partitioning effect. The ion partitioning effect influences the association/dissociation of PE functional group by tuning the hydrogen/hydroxide ions. Present study shows that the ion partitioning effect is profound for higher salt concentration and/or higher volume density of PE functional groups.