Self-assembled ordered polymer nanocomposites directed by attractive particles

We theoretically investigate general conditions under which an inorganic phase can direct the self-assembly of an ordered polymer nanocomposite. For this purpose, we consider a solution of triblock copolymers forming a hexagonal phase of micelles and investigate the effect of adding attractive particles. We show that if the triblock is functionalized at its ends by attaching groups with specific affinity for the particles, thus effectively becoming a pentablock, the particles direct the self-assembly of the system into phases where both the polymers and the particles exhibit mesoscopic order. Different lamellar and gyroid phases (both with Ia3d and I4(1)32 space symmetries) are presented in detail. Our results show that functionalization is a very powerful route for directing self-assembly of polymer nanocomposites. We briefly discuss the connections with recent theoretical and experimental results in diblock melts with nanoparticles as well as for problems where polymers are used to template the growth of an inorganic phase in solution.