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A theoretical investigation was conducted upon the steric interaction between a spherical particle and a flat plate. The effects of curvature on both the segment density distribution of polymer and on the steric interaction energy between a particle and a plate were examined. It was found that the conventional approach using Derjaguin approximation may overestimate the interaction energy, especially for very small particles. Based on the results obtained from applying the Flory-Krigbaum theory with the accurate geometry change during the interaction, simple approximate expressions of exponential form were proposed for both the osmotic (mixing) and elastic contributions to the steric interaction energy for a sphere-plate interaction. The proposed model was validated against a set of experimental results from a reported study employing atomic force microscopy. Also investigated was the steric interaction between a spherical particle coated with polymer and an uncoated flat surface. It was found that the steric interaction energy from the osmotic contribution is significantly higher than that from the elastic contribution and that steric interaction is considerably weaker when the polymer exists on only one of the interacting surfaces.

The propensity of silver nanoparticles (AgNPs) having two different polymer coatings (poly(vinylpyrrolidone), PVP, or gum arabic, GA) to aggregate, or to deposit to a reference surface (silica), was explored as a basis for differentiating the effect of surface coating on the stability of nanoparticles in aggregation and in deposition. Surface polymeric coatings stabilize nanoparticles against aggregation as shown by either an increased critical coagulation concentration as for PVP-coated AgNPs (AgPVP) or the absence of observable aggregation even at a high ionic strength as for GA-coated AgNPs (AgGA). In experiments of AgNPs deposition in a silica porous medium, dissimilar surfaces favored deposition, such as the case where polymer coatings were present on the AgNPs but were absent on the porous medium. The increased affinity of the AgNPs for the porous medium in this case may be explained by a shifted contact frontier where electrical double layer interaction is weaker. When coating polymers were introduced to the porous medium and allowed to preadsorb to the silica surfaces, the attachment efficiencies for both the AgPVP and AgGA were reduced due to steric and electrosteric stabilization, respectively. The results suggest that polymeric coatings that are usually deemed as stabilizers (as they indeed are in the case of autoaggregation) might not necessarily stabilize nanoparticles against deposition unless the collector surfaces are also coated with polymer.

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.