The polydisperse cell model: Non-linear screening and charge renormalization in colloidal mixtures

TL;DR

This paper introduces a generalized cell model for calculating charge renormalization and osmotic properties in colloidal mixtures, extending previous models to account for non-linear screening effects in multi-component systems.

Contribution

It develops a polydisperse cell model that self-consistently determines cell sizes for mixtures, incorporating non-linear Poisson-Boltzmann equations, advancing the understanding of charged colloidal mixtures.

Findings

Model accurately predicts charge renormalization in mixtures.

Enables calculation of thermodynamic properties with non-linear screening.

Generalizes single-component models to polydisperse systems.

Abstract

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.