Stability of a dispersion of particles covered by a charge-regulated membrane: effect of the sizes of charged species

The influence of the sizes of charged species on the stability of a colloidal dispersion is investigated theoretically. We consider the case where a particle comprises a rigid core and an amphoteric, charge-regulated membrane layer, which simulates biocolloids and particles covered by artificial membranes. A modified Poisson-Boltzmann equation, which takes the sizes of all the charged species into account, is adopted to describe the electrical field. The effects of other key parameters such as electrolyte concentration, pH, and the valence of counterions on the behavior of a dispersion are also examined. We show that the larger the effective size of the counterions, the greater the stability ratio, which is consistent with experimental observations in the literature.