Wetting description of block copolymer thin films

Symmetric diblock copolymers undergo a weakly first-order microphase separation transition to a lamellar phase. In a thin film of thickness d this transition is altered for two reasons: the film geometry imposes commensurability restrictions on the concentration profiles, and the surface field favors one of the two blocks. The latter effect dominates for d>ξ, where ξ is the correlation length near [Formula Presented]. We construct a wetting Hamiltonian, in which the slowly varying amplitude ψ(z) of the composition c(z)=2ψ(z)cos([Formula Presented]z) is the order parameter, and explore the changes in the profile induced by changes in temperature, surface field, and d/ξ. The resulting phase diagram exhibits a line of first-order prewetting transitions ending in a critical point, and a capillary condensation transition to an ordered film. Turning to commensurability effects, we compute the ranges of thickness near half-integer numbers of layers for which the free surface of a copolymer film is unstable to capillary waves, analogous to spinodal decomposition in two dimensions.