High frequency elastic modulus of hairy particle dispersions in relation to their microstructure

The high-frequency elasticity G′∞ of polymerically stabilized colloidal dispersions is the result of a complex interplay between the particle configuration, pair potential and hydrodynamics. In the analysis of this relation, frequent use is made of simplifications in describing the structure and/or hydrodynamics. Especially in the case of polymerically stabilized particles such approximations may give erroneous results. We demonstrate this for particles where the polymer layer thickness is comparable to the radius of the core. For our particles the repulsive potential is rather steep, whereas the permeability length is small. Hydrodynamics was found to be unimportant at very high particle concentrations, but at lower concentrations it is not negligible. Most crucial in the modeling of G′∞ is the particle configuration. Existing approaches in which inconsistencies are introduced between the pair potential and the locations where it is probed, fail to give even semi-quantitative predictions. This problem can be avoided by performing Monte Carlo simulations to obtain the particle configuration (with the pair potential as input). Even so, predictions for G′∞ may be obscured at high concentrations. Our simulations showed that above a certain concentration, crystallization occurred but also disordered states were found, depending on the initial configuration. A resemblance was found with the freezing transition for hard spheres. For our particle systems it turned out that the calculated elastic moduli for disordered structures and for crystals differ only modestly.