Block copolymers have great potential for applications in nanotechnology due to their self-assembly. Nano-confinement of block copolymers can be used to control the self-assembled morphology and to produce novel morphologies that cannot be obtained otherwise. The influence of confinement on block copolymer self-assembly is also of fundamental interest in polymer science.

Here we consider the simplest system of symmetric diblock copolymers under two forms of nano-confinement. In the first case of thin-film (1D) confinement between two flat and homogeneous surfaces, three morphologies (parallel, perpendicular, and mixed lamellae) have been observed in experiments. While the effects of surface preference and film thickness on the thin-film morphology are well understood, less studied is the influence of a hard (impenetrable) surface on the copolymer chain conformations, referred to as the "hard-surface effects". Whether or not the mixed lamellae are a stable phase has also been controversial. We have used the self-consistent field calculations with high accuracy to study the thin-film morphology of symmetric diblock copolymers. The hard-surface effects were examined in detail and the conditions under which the mixed lamellae are stable were also determined.

In the second case of cylindrical (2D) confinement, we have performed lattice Monte Carlo simulations to study the morphology in nanopores. The pore diameter and surface preference were systematically varied to examine their effects on chain conformations, structures of various morphologies and their phase transitions. Various ensemble-averaged profiles and quantities were used to provide detailed information about the system. The simulation results were also compared with the predictions of a strong-stretching theory commonly used in the study of block copolymer self-assembly. Such comparisons revealed the deficiencies of this theory in describing the morphologies under cylindrical confinement.