Mesophase formation of block copolymer in cylindrical nanopore

We investigate the influence of the confinement on the mesophase formation of diblock copolymer caged in a cylindrical pore in which the surface of the pore preferentially attracts one of the blocks. Using cell dynamics simulation, we construct phase maps as a function of the composition of diblock copolymer ($f)$ and the pore diameter ($D)$ relative to the period at bulk ($L_{o})$. Depending on $f$ and $D$/$L_{o}$, we observe a variety of confinement-induced mesophases ranging from a simple dartboard-like structure to more complicated structures involving various forms of helices or doughnuts. We also find that the creation of a new central domain of the layered structure in the cylindrical pore occurs at a critical value of $D$/$L_{o}$ larger than the critical value for the layered structure under the flat confinement, indicating that the block copolymers under curved confinement afford to be more stretched than that under flat confinement. These results are compared with experimental observations.