Capillary assembly of colloidal particles on patterned surfaces

Capillary attraction at the meniscus between tiny objects plays a crucial role in self-assembly processes. The shape of the meniscus governed by the Laplace equation devotes to a long-range attraction distinct to the DLVO defined forces. Rather than considering trapped particles on ideal smooth surfaces, we use patterned substrates with ordered nano-arrays for theoretical modeling toward the capillary assembly. The vertical elevation of particles is found to change the shape of the meniscus between particles, therefore the interaction energy and capillary force. A minimal model is developed to determine the capillary force between particles and thus the motility of particles, therefore the criterion of the crystallization of colloidal particles. It turns out that the formation of a colloidal crystal or amorphous medium depends on the optimization between the scaled particle separation by its size and the geometrical design of the supporting nano-arrays. Finally, we experimentally confirmed the capillary assembly from colloidal suspensions, by playing the control parameters defined in our theoretical model, with a nice agreement. This model system can mimic the practical applications of nano-structure fabrication on versatile real surfaces for functionality purposes.