Confinement-induced morphologies of cylinder-forming asymmetric diblock copolymers

Self-assembly of cylinder-forming diblock copolymers confined in cylindrical nanopores is studied systematically using a simulated annealing method. The diblock copolymers form hexagonally packed cylinders in the bulk with a period L-0, whereas novel structures spontaneously form when the copolymers are confined inside cylindrical pores. It is discovered that the sequence of structures is controlled by the ratio between the pore diameter (D) and L-0, as well as the selectivity of the pores. For selective small pores (D/L-0 < 2.7), the following structural sequence occurs as the pore size is increased: a string of spheres, a single cylinder, a straight band, a twisted band or stacked disks,a single helix, a set of degenerate structures (includes single helix, stacked toroids and double helices), and double helices. For larger pores (D/L-0 > 2.7), the outer ring of the minority block-domain forms helices or stacked toroids, while the inner structure repeat the sequence of structures observed in smaller pores. For neutral pores, cylinders oriented parallel and nearly perpendicular to the cylindrical pore are observed besides helical or toroidal structures. These morphologies are consistent with available experiments and theoretical studies. Mechanisms of the morphological transitions can be understood based on the degree of commensurability between the pore diameter and bulk period of the copolymer L-0, parametrized by the ratio D/L-0. The effect of the cylindrical pore length on final morphologies is investigated. The chain conformations as a function of morphologies are calculated and analyzed. A mechanism for the formation of helices is proposed based on a packing model, which gives a reasonable description of the radius and pitch of the observed helices.