Effective interactions between a pair of nanoparticles

We investigate the effective interactions between two nanoparticles (or colloids) immersed in a solvent exhibiting two-phase separation. Using a non-local density functional theory, we determine the dependence of the effective potential on the separation of the nanoparticles when the solvent is near bulk two-phase coexistence. If identical nanoparticles preferentially adsorbing phase $\alpha$ are inserted into phase $\beta$, thick wetting layers of the preferable phase $\alpha$ develop at their surfaces. At some particular separation $h_b$ of the nanoparticles, the wetting layers connect to form a single bridge, and the induced effective potential becomes strongly attractive for all distances $h<h_b$. The bridging is a first order capillary condensation like transition for all radii of the nanoparticles greater than the critical radius $R_c$, the value of which was estimated to be approximately $R_c\approx20\sigma$ for a temperature $T/T_c\approx0.9$, where $\sigma$ is the size of the solvent (square-well) particles. For radii $R<R_c$ the process of bridging is continuous. If the same particles are inserted into the preferable phase $\alpha$, the only effective interaction between them is induced by the short-ranged depletion potential. If the nanoparticles have opposite adsorption preferences, only a single wetting layer forms around one of the nanoparticles and the effective interaction is strongly repulsive in both phases. The repulsion, induced by a disruption of the wetting film by the presence of the second particle, is larger and slightly longer-ranged in a low density state.