Transition mechanisms of three-dimensional nanostructures formed from geometrically constraining (AB) star block copolymers

Influence of Branches on the Phase Behavior of (AB)f Starlike Block Copolymer under Cylindrical Confinement

“…To investigate the influence of the number of arms on the stability of these nanostructures, we calculated and depicted the corresponding phase diagram of 9-, 15-, and 21-arm starlike block copolymers in Figure . As a comparison, the phase diagram of the 3-arm block copolymer is reproduced from ref . Notably, in our previous work, as pore size increases, the phase transition sequences at ϕ A = 0.3 for a different number of arms are the same; however, the phase transition points shift slightly to large pore diameter.…”

“…Within the established structural knowledge of our previous work, ,,, the formed three-dimensional nanostructures under cylindrical confinement are a single cylindrical microdomain ( C 1 A ; subscript 1 and superscript A refer to a single cylinder which is composed by A block), stacked disk ( Dk A ), single helix ( H 1 A ; subscript 1 refers to single helix), double helix ( H 2 A ; subscript 2 refers to double helix), perforated-cylinder ( P A ), perforated-cylinder around a central cylinder ( P 2 C A ; subscript 2 refers to two perforated areas in the cross section), alternating toroids and spheres ( TS A ), a double helix winding around a central cylinder ( H 2 C A ; subscript 2 refers to double helix), and a triple helix winding around a central cylinder ( H 3 C A ; subscript 3 refers to triple helix). Notably, for the chirality of helical nanostructures, we obtained both right-handed and left-handed helical nanostructures (Figure S5) and found that there is no free energy difference between these two nanostructures .…”

“…We first calculated the phase diagram of different pore size at small A volume fraction, where the minority A block forms the discrete phases, such as helix, cylinder, perforated cylinder, and so on. At a suitable range of χ, the phase transition sequence is almost unaffected; therefore, we fixed χ N/f at 20 in our calculations . The density profiles of these three-dimensional nanostructures are listed in Figure .…”

“…However, the minima free energies are almost the same at different box sizes, resulting in the fact that it is reasonable to use the periodic boundary condition in the z -direction (Figures S1–S3). Many published papers adopted this method to investigate the self-assembly of block copolymer under cylindrical confinement, and we followed this method here, too. − , Therefore, the periodic boundary conditions on all edges of the square cell are applicable.…”

“…Importantly, a universal phase transition sequence, which is H 1 A (single helix) → P 2 A (perforated cylinder) → L 2 A (double-layer concentric lamellae) → P 3 C B (perforated cylinder around a central cylinder) → H 3 C B (a triple helix winding around a central cylinder), was identified when we studied the self-assembly of block copolymer under cylindrical confinement. Notably, this phase transition sequence is corresponding to the phase transition of C (cylinder)→ G (gryoid) → L (lamellae) → G → C in bulk, where helical morphologies are regarded as one type of cylindrical phase in bulk, and perforated layers nanostructure can be treated as the derivation of gyroid morphologies in bulk. , Interestingly, this transition sequence is universal for block copolymer with different architectures, including linear (AB diblock, BAB triblock) and starlike block copolymers by exploring the corresponding phase diagrams.…”