Electrokinetic transport of a spherical gel-layer model particle: Inclusion of charge regulation and application to polystyrene sulfonate

Abstract

An electrokinetic gel-layer model of a spherical, highly charged colloid particle developed previously [S. Allison, J. Colloid Interface Sci. 277 (2004) 248], is extended in several ways. The charge of the particle is assumed to arise from deprotonation of acidic groups that are present, in uniform concentration, over a portion (or all) of the gel layer. Free energy considerations coupled with Poisson–Boltzmann theory are used to estimate how the local electrostatic environment of a charged gel layer alters the local p K a of the acidic groups. This modulation of the charge of the colloidal particle, or “charge regulation,” can be significant even for colloidal particles with strongly acidic groups at moderate pH if the ambient salt concentration is low. The methodology is applied to the viscosity and electrophoretic mobility data of a particular polystyrene sulfonate latex over a broad range of monovalent salt (NaCl) concentration [M.J. Garcia-Salinas, F.J. de las Nieves, Langmuir 16 (2000) 715]. The experimental data can be accounted for by a gel layer model that decreases in thickness, but does not vanish, as the salt concentration is increased. Viscosity data provides valuable information about the degree of solvation of the colloidal particle and the thickness of the gel layer. The mobility data is best explained by a model in which only the outermost portion of the gel layer is charged. Charge regulation is significant at a monovalent salt concentration of 3 × 10 −3 mol / l and increases as the salt concentration decreases.