  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.
