Self-assembly of cubic colloidal particles at fluid–fluid interfaces by hexapolar capillary interactions†
Colloidal particles adsorbed at fluid–fluid interfaces can self-assemble, thanks to capillary interactions, into 2D ordered structures. Recently, it has been predicted by theoretical and numerical calculations [G. Soligno et al., Phys. Rev. Lett., 2016, 116, 258001] that cubes with smooth edges adsorbed at a flat fluid–fluid interface generate hexapolar capillary deformations that cause the particles to self-assemble into honeycomb and hexagonal lattices, at equilibrium and for Young's contact angle π/2. Here we extend these results. Firstly, we show that capillary interactions induced by hexapolar deformations can drive the particles at the interface to form also thermodynamically-stable square lattices, in addition to honeycomb and hexagonal lattices. Then, we study the effects of tuning the particle shape on the particle self-assembly at the interface, considering, respectively, smooth-edge cubes, sharp-edge cubes, slightly truncated-edge cubes, and highly truncated-edge cubes. In our calculations, both capillary and hard-particle interactions are taken into account. We show that such variations in the particle shape significantly affect both qualitatively and quantitatively the self-assembly of the particles at the interface, and we sum up our results in the form of temperature–density phase diagrams. For example, using typical experimental parameters, our results show that only 4-to-5 nm sized sharp-edge and smooth-edge cubes can self-assemble into a honeycomb lattice, while slightly and highly truncated-edge cubes can form a honeycomb lattice only if they have a 8-to-12 and 10-to-16 nm size, respectively, for the same experimental parameters. Also, our results show that the capillarity-induced square lattice phase is stable only for the smooth-edge and truncated-edge cubes, but not for the sharp-edge cubes.