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.