Electrostatic, depletion, and structural interactions of ions and nanoparticles across confined dispersions

HYPOTHESIS: Oscillatory structural forces in dispersions of different-size particles and across particulate films are abundant in experiments due to their capacity to introduce both depletion attraction and structural repulsion between colloids. They are commonly described using semi-empirical analyses, which capture part of the complex mechanism and suggest the need for a self-consistent theory that may better capture the full implications of structural interactions while describing the additional colloidal forces across a confined particulate film. THEORY: We use a free-energy variational approach to model an atomic force microscopy (AFM) measurement of structural forces and electrical double layer (EDL) interactions across a nanoparticle suspension in electrolyte, which is confined between a flat solid and a colloidal probe. The theory, devoid of fitting parameters, reproduces the measurement. We demonstrate the contributions of the electrolyte and charged nanoparticles to the repulsive EDL interaction across the suspension and the contributions of the nanoparticle hard cores, entangled with inter-particle EDL repulsion, to the measured oscillatory force. FINDINGS: The nanoparticle bulk concentration, size, and the inter-nanoparticle EDL repulsion intensity contribute to the force oscillation amplitude on the probe. The nanoparticle bulk concentration determines the force spatial period. This is in agreement with the conclusions of previous experiments and simulations. We further identify possible nanoparticle lattice structures in the confined suspension and mediate the discrepancy highlighted previously between inter-layer spacing of solid nanoparticles and micelles suspensions. The theory captures the different coexisting colloidal interactions traversing nanometer to micrometer length scales that translate to the measured interaction force.