Adsorption of a charge-regulated particle to a charged surface

The adsorption of a spherical particle coated with an ion-penetrable membrane to a charged surface immersed in an electrolyte solution is analyzed, The former is capable of regulating the degree of dissociation of the functional groups in the membrane as a response to the variation in the electrical condition of the surrounding medium, The membrane contains both acidic and basic functional groups, and a general form for each is assumed which allows multiple-proton transfer among functional groups. Two classes of nonuniform distribution for the functional groups are considered. We show that the more concentrated the functional groups are distributed near the outer boundary of the membrane, the greater the electrostatic repulsion force between the particle and the surface, and the slower the rate of adsorption. Compared with a rigid particle carrying the same numbers of acidic and basic functional groups, the existence of the membrane has the effect of increasing the rate of adsorption. The electrostatic repulsion force between a particle with a membrane and a rigid surface is smaller than that between a rigid particle and a rigid surface if the separation distance is greater than a critical value. The reverse is true if the separation distance is smaller than the critical value.