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. Here we use the self-consistent field calculations with high accuracy to study the thin-film morphology of symmetric diblock copolymers. Results under different boundary conditions (zero-density vs. non-flux) are compared to examine the hard-surface effects. We also determine the conditions under which the mixed lamellae are a stable phase.
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 are systematically varied to examine their effects on chain conformations, structures of various morphologies and their phase transitions. Various ensemble-averaged profiles and quantities are used to provide detailed information about the system. The simulation results are also compared with the predictions of a strong-stretching theory commonly used in the study of block copolymer self-assembly. Such comparisons reveal the deficiencies of this theory in describing the morphologies under cylindrical confinement, and call for further theoretical studies using more accurate formalisms.