Electrophoretic Mobility and Electric Conductivity in Dilute Suspensions of Charge-Regulating Composite Spheres

The electrophoresis and electric conduction in a dilute suspension of charged composite particles, each composed of a solid core and a surrounding porous shell, with an arbitrary thickness of the electric double layers are analytically studied. The porous shell of a particle is treated as a solvent-permeable, ion-penetrable, and charge-regulating surface polymer layer of finite thickness with uniformly distributed ionogenic functional groups and frictional segments. The electrokinetic equations that govern the electrostatic potential profile, the electrochemical potential distributions of ionic species, and the fluid flow field inside and outside the surface polymer layer of the particle migrating in an unbounded electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved for a composite sphere in a uniform applied electric field with the dimensionless fixed charge densities on the surface of the rigid core and of the surface polymer layer as the small perturbation parameters. Analytical expressions for the electrophoretic mobility of the charge-regulating composite sphere and for the effective electric conductivity of the suspension are derived as linear functions of these charge densities. The results demonstrate that the charge regulation phenomenon tends to thin down the electric double layer and to reduce the magnitudes of the electrophoretic mobility and the electric conductivity compared to the case that the fixed charge density in the surface polymer layer is a constant. The intensity of this effect depends on the regulation characteristics such as the association/dissociation equilibrium constants of the ionogenic functional groups in the surface polymer layer and the concentration of the potential-determining ions in the bulk solution.