Electrostatic interaction of colloidal surfaces with variable charge

When two surfaces with ionizable groups interact across an electrolyte solution, both their equilibrium charge density and the corresponding electrostatic surface potential will depend on the surface separation (charge regulation). The corresponding nonlinear boundary conditions are often replaced, for simplicity, by the limiting conditions of constant charge or constant surface potential. A strategy to linearize the boundary conditions, initially devised for the case of low potentials only, has recently been adapted to situations of arbitrary potential. Within a 1-pK Basic Stem Model suitable for a large class of surface materials, we now address the implications of charge regulation on the level of Poisson-Boltzmann theory. The regulation behavior can be characterized in terms of a single parameter taking values between 0 for constant potential and 1 for constant charge conditions. This parameter depends on the capacities associated with the diffuse part and the compact part of the electrical double layer and can be inferred from acid-base titrations. We discuss the effect of regulation on a variety of measurable quantities for exemplary surfaces of carboxyl latex, silica, and iron hydroxide.