Charging mechanism in colloidal particles leading to a linear relation between charge and size

Colloidal particles that are dissolved in a liquid can become charged by preferential adsorption or dissociation of surface molecules. The assumption of a constant surface charge density leads to a particle charge that is proportional to the square of the radius. Recent experiments however have shown that in a number of cases the charge is linearly proportional to its size. We present a simple model for the charging of colloidal particles leading to a linear relation between charge and size in the framework of the mean-field Poisson-Boltzmann theory. The model is based on preferential adsorption or dissociation of surface molecules, in combination with a large concentration of chargeable surface sites. The model also predicts a surface potential that is independent of the particle size. Numerical simulations show that this model is in good agreement with analytical approximations.