Block copolymer films with free interfaces: ordering by nanopatterned substrates.

We study block copolymers (BCPs) on patterned substrates, where the top polymer film surface is not constrained but is free and can adapt its shape self-consistently. In particular, we investigate the combined effect of free interface undulations with wetting of the BCP film as induced by nanopatterned substrates. Under wetting conditions and for a finite volume of BCP material, we find equilibrium droplets composed of coexisting perpendicular and parallel lamellar domains. The self-assembly of BCPs on topographic patterned substrates is also investigated and it is found that the free interface induces mixed morphologies of parallel and perpendicular domains coupled with a nonflat free interface. Our study has some interesting consequences for experimental setups of graphoepitaxy and nanoimprint lithography.