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 agreement 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

The extended law of corresponding states when attractions meet repulsions

“…This is a rather surprising finding, as the SANS data of MA3 colloids with c s = 1.5 mM were previously modelled with a combination of a highly accurate density functional theory description of the polymer-mediated attractions, and fully non-linear Poisson-Boltzmann repulsions with a fixed value of Z = 275. 39 It should be noted, though, that the agreement between modelled and experimental data in Fig. 3A and C is consistently closer than in ref.…”

“…1 shows a comparison of the various potentials for colloids MA3 in 50 and 1.5 mM salt and polymer concentrations close to the gel transition, using the same parameters as in ref. 39. Although there is still a quantitative discrepancy between the more accurate DF-nlPB potentials and the empirical GS-PB potentials, the GS-PB captures the qualitative properties This journal is © The Royal Society of Chemistry 2018 Soft Matter, 2018, 14, 3704--3715 | 3707 of the DF-nlPB reasonably well.…”

“…The good-solvent potential U dep,GS is obtained by inserting g GS 0 = (g GS + 1) and P GS in eqn (6). The pre-factor 0.83 is empirically estimated to match the DF results, 39 and in line with a B20% overestimation of the part in brackets in eqn (9). 40 Fig.…”

“…The second approach uses empirically adjusted analytical expressions that mimic accurate interaction potentials that were deduced from a full theoretical description of the system, combining classical polymer density functional (DF) theory for the polymer-mediated attractions and fully non-linear Poisson-Boltzmann (nlPB) theory for the electrostatic repulsions. 39 The strong short-range repulsions predicted by Poisson-Boltzmann (PB) theory are mimicked by a double Coulomb potential:…”

Non-monotonic temperature response of polymer mediated interactions

“…Inspired by recent DFT modelling of PEG in water at low temperatures (good solvent conditions) 9 , where an optimized bond length (chosen to reproduce experimentally observed radii of gyrations) typically is 2-3 times the monomer bead diameter, we have set b = 2σ . We will consider two different choices for the ratio between monomer state degeneracies.…”