The polydisperse cell model: nonlinear screening and charge renormalization in colloidal mixtures

We propose a model for the calculation of renormalized charges and osmotic properties of mixtures of highly charged colloidal particles. The model is a generalization of the cell model and the notion of charge renormalization as introduced by Alexander et al. J. Chem. Phys. 80, 5776 (1984)]. The total solution is partitioned into as many different cells as components in the mixture. The radii of these cells are determined self-consistently for a given set of parameters from the solution of the nonlinear Poisson-Boltzmann equation with appropriate boundary conditions. This generalizes Alexanders's model where the (unique) Wigner-Seitz cell radius is solely fixed by the colloid packing fraction. We illustrate the technique by considering a binary mixture of the colloids with the same sign of charge. The present model can be used to calculate thermodynamic properties of highly charged colloidal mixtures at the level of linear theories, while taking the effect of nonlinear screening into account.