Microstructures of lamella-forming diblock copolymer melts under nanorod-array confinements

The microstructures of lamellae-forming diblock copolymer melts confined in nanorod arrays are investigated using the real-space self-consistent field theory. The nanorod array leads to the incomplete confinement at each direction so that the confinement-dimension is fractional between zero and two. This incomplete confinement can yield a rich variety of mixture microstructures by varying its fractional confinement-dimension, such as the mixture of concentric lamellae and parallel lamellae and the mixture of the concentric lamellae and cylinders, as well as a series of continuous network mixtures. By comparing with the available simulations and experiments, these novel microstructures can be understood based on the symmetry competition and structural frustration that originated from the incomplete confinement. Our theoretical predictions may be helpful to the design of nanomaterials.