Jellium and Cell Model for Titratable Colloids with Continuous Size Distribution

TL;DR

This paper develops and implements generalized cell and jellium models to accurately predict the thermodynamic and structural properties of polydisperse, charge-regulating colloidal suspensions, addressing the complexity introduced by size distribution and many-body interactions.

Contribution

It introduces two novel algorithms based on generalized cell and jellium models for polydisperse colloids with charge regulation, validated against experimental data.

Findings

Models accurately predict colloidal interactions in polydisperse suspensions.

Size and charge polydispersity significantly influence effective interactions.

The models are validated with experimental silica dispersion data.

Abstract

A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided.The methods, inspired by the seminal work of Torres et al., are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models are discussed in light of the results.