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Stability and interactions of nanocolloids at fluid interfaces: effects of capillary waves and line tensions

We analyze the effective potential for nanoparticles trapped at a fluid interface within a simple model which incorporates surface and line tensions as well as a thermal average over interface fluctuations (capillary waves). For a single colloid, a reduced steepness of the potential well hindering movements out of the interface plane compared to rigid interface models is observed, and an instability of the capillary wave partition sum in case of negative line tensions is pointed out. For two colloids, averaging over the capillary waves leads to an effective Casimir--type interaction which is long--ranged, power-like in the inverse distance but whose power sensitively depends on possible restrictions of the colloid degress of freedom. A nonzero line tension leads to changes in the magnitude but not in the functional form of the effective potential asymptotics.