Assessing Pair Interaction Potentials of Nanoparticles on Liquid Interfaces.

The pair interaction potentials of polymer-grafted silica nanoparticles (NPs) at liquid surfaces were determined by scanning electron microscopy, exploiting the nonvolatility of ionic liquids to stabilize the specimens against microscope vacuum. Even at near contact, individual, two-dimensionally well-dispersed NPs were resolved. The potential of mean force, reduced to the pair interaction potential for dilute NPs, was extracted with good accuracy from the radial distribution function, as both NP diameter and grafted polymer chain length were varied. While NP polydispersity somewhat broadened the core repulsion, the pair potential well-approximated a hard sphere interaction, making these systems suitable for model studies of interfacially bound NPs. For short (5 kDa) poly(ethylene glycol) ligands, a weak (< k T) long-range attraction was discerned, and for ligands of identical length, pair potentials overlapped for NPs of different diameter; the attraction is suggested to arise from ligand-induced menisci. To understand better the interactions underlying the pair potential, NP surface-binding energies were measured by interfacial tensiometry, and NP contact angles were assessed by atomic force microscopy and transmission electron microscopy.