Universality and Specificity in the Self-Assembly of Cylinder-Forming Block Copolymers under Cylindrical Confinement

Both experimental and theoretical studies have shown that a cylinder-forming block copolymer melt under the confinement of a nanopore can self-assemble into an interesting sequence of ordered nanostructures in terms of the pore size, including single cylinder, stacked disks, single helix, double-helix, and so on. However, most of these studies focused on the normal cylinder phase formed by a simple AB diblock copolymer at a low volume fraction (e.g., f(A) of A-block). Whether this phase sequence is universal or specifically depends on the copolymer architecture is a question to be answered. In particular, when an "inverted" A-cylinder phase is formed by a special type of AB block copolymer at a high volume fraction of f(A) > 0.5, for example, the A(AB)(n) miktoarm star copolymer, whether the phase sequence still exists is an interesting question. In this work, we investigate the self-assembly of cylinder-forming A(AB)(n) copolymer confined in nanopores using the pseudospectral method of self-consistent field theory coupled with the masking technique. By varying the arm number n and the ratio r of the linear A-block to the total A-blocks, the volume fraction of the bulk A-cylinder phase region of A(AB), changes in a large range even for a fixed chi N = 60, allowing us to study the cases of a normal cylinder and an inverted cylinder. Our results reveal that the common phase sequence can only be maintained when the cylinder phase is not close to the boundaries of its phase region, as in the case of the pore wall attracting the B-blocks; otherwise, some structures will disappear. For example, the double-helix structure disappears when the cylinder phase is close to the cylinder/gyroid boundary. In contrast, the phase sequence becomes more robust in the case of the pore wall attracting the A-blocks. In both cases of surface preference, stable helical structures are predicted for an inverted cylinder with the volume fraction as large as f(A) = 0.64. For f(A) >= 0.5, the packing frustration of short B-blocks is severe, leading to a lot of astonishing distortions to many structures. Our work not only deepens the understanding on the self-assembly of block copolymers under cylindrical confinement but also provides guidance for the experimental preparation of helical structures with large volume fractions.