Theory of lithographically-induced self-assembly

Recent experiments show that, when a two-phase fluid confined between parallel substrates is subject to an electric field, one phase can self-assemble into a triangular lattice of islands in another phase. We describe a theory of the stability of the island lattice. It is well known that the total interface energy reduces when the island diameter increases. We show that, under certain conditions, the electrostatic free energy reduces when the island diameter decreases. The islands select the equilibrium diameter to minimize the combined interface energy and electrostatic energy. We describe the conditions for electrostatic field to stabilize the island lattice, and analyze an idealized model. The theory suggests considerable experimental control over stable island size.