Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers

Abstract

We develop a theoretical model to describe structural effects on a specific system of charged colloidal polystyrene particles, upon the addition of non-adsorbing PEG polymers. This system has previously been investigated experimentally, by scattering methods, so we are able to quantitatively compare predicted structure factors with corresponding experimental data. Our aim is to construct a model that is coarse-grained enough to be computationally manageable, yet detailed enough to capture the important physics. To this end, we utilize classical polymer density functional theory, wherein all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. We make efforts to counteract drawbacks with this mean-field approach, resulting in structural predictions that agree very well with computationally more demanding simulations. Electrostatic interactions are handled at the fully non-linear Poisson–Boltzmann level, and we demonstrate that a linearization leads to less accurate predictions. The particle charge is an experimentally unknown parameter. We define the surface charge such that the experimental and theoretical gel point at equal polymer concentration coincide. Assuming a fixed surface charge for a certain salt concentration, we find very good agreements between measured and predicted structure factors across a wide range of polymer concentrations. We also present predictions for other structural quantities, such as radial distribution functions, and cluster size distributions. Finally, we demonstrate that our model predicts the occurrence of equilibrium clusters at high polymer concentrations, but low particle volume fractions and salt levels.