The polydisperse cell model: Non-linear 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 and his collaborators (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 non-linear Poisson-Boltzmann equation with appropriate boundary conditions. This generalizes Alexanders's model where the (unique) Wigner-Seitz cell radius is fixed solely by the colloids packing fraction. We illustrate the technique by considering a binary mixture of 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 non-linear screening into account.