The renormalized Jellium model of colloidal suspensions with multivalent counterions

TL;DR

This paper extends the renormalized Jellium model to include trivalent counterions in colloidal suspensions, using a modified Poisson-Boltzmann equation with new boundary conditions to improve predictions of charges and osmotic pressures.

Contribution

The paper introduces a modified renormalized Jellium model that accounts for counterion correlations near colloidal surfaces with trivalent ions, enhancing the theoretical framework.

Findings

Good agreement of thermodynamic functions with Wigner-Seitz model

Significant differences in predicted effective charges

Simplified calculation of counterion profiles and pressures

Abstract

An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary condition. We find that while the thermodynamic functions obtained within the renormalized Jellium model are in a good agreement with their WS counterpart, the effective charges predicted by the two theories can be significantly different.