We compare theory to experiment to study the suitability of different classical density functional theory (DFT) strategies to predict interactions and stability in different-size colloid mixtures in an electrolyte solution. Atomic force microscopy (AFM) measures the interaction force between a spherical silica microcolloid and a flat silica substrate across a suspension of silica nanoparticles in a solution of sodium chloride. The calculated and measured oscillatory structural and repulsive electrostatic forces give insight on the stability of microcolloids in suspensions of nanoparticles relevant to biological liquids, e.g., blood, plasma, and milk, as well as to particulate suspensions of broad size distributions. We examine a simple uniform-weight hard-sphere functional and the more advanced fundamental measure theory (FMT) functional to capture the contribution of the nanoparticle finite (excluded) volume to the free energy of the system. The two functionals reproduce the experimental force oscillation amplitudes over the nanoparticle and salt concentration range examined to a reasonable extent. FMT additionally captures the experimental scaling of the force oscillation wavelength. We further introduce internanoparticle electrostatic repulsion as a "soft" potential superimposed on the hard-sphere potential and compare this classical approach to defining an effective nanoparticle hard-sphere diameter based on the "hard" and "soft" interactions using the nonideal gas theory. The latter approach significantly simplifies the numerical implementation of the problem and compares well with experiment. Additionally, we capture the electrostatic interactions across the suspension between the microcolloid and the flat substrate by using the jellium approximation and discuss the fundamental assumptions made in this approach.
Riva et al. (Tue,) studied this question.