Formation of two-dimensional colloid crystals in liquid films under the action of capillary forces

When two similar small particles are attached to a liquid interface they attract each other due to a lateral capillary force. This force appears because the gravitational potential energy of the floating particles decreases when they are approaching each other. This force is proportional to R6 (R is the particle radius), so it decreases very fast with particle size and becomes negligible for R<10 mu m. We found that the situation is quite different when the particles (instead of being freely floating) are partially immersed in a liquid layer on a substrate. In this case the energy of capillary attraction is proportional to R2 and turns out to be much larger than kT even with particles of diameter about 10 nm. The effect is related to the particle three-phase contact angle, i.e. to the intermolecular forces, rather than to gravity. The experiments show that the lateral capillary forces can bring about the formation of a two-dimensional array (2D-crystal) from both micrometre-size and submicrometre particles: latex spheres, protein globules, etc.