Reexamine the emergence and stability of the square cylinder phase in block copolymers.

Recently, a few AB-type multiblock copolymers have been successfully designed to form stable square cylinder phase based on self-consistent field theory (SCFT) calculations. The previous works only identify the stability region of the square phase but not analyzing its stability, which is closely related to the free-energy landscape. In this work, we have reexamined the stability of the square phase in $\mathrm{B_1 A_1 B_2 A_2 B_3}$ linear pentablock and $\mathrm{(B_1AB_2)_5}$ star triblock copolymers by drawing the free-energy landscape with respect to the two dimensions of a rectangular unit cell. Our results demonstrate that the square phase continuously transfers to the rectangular phase as the degree of packing frustration is gradually released. Moreover, the prolate contour lines of the free-energy landscape indicate the weak stability of the square phase in the $\mathrm{B_1 A_1 B_2 A_2 B_3}$ copolymer. In contrast, the stability of the square phase is notably improved in the $\mathrm{(B_1AB_2)_5}$ copolymer due to its enhanced concentration of bridging configurations. Our work sheds light on the understanding of the stability of the square cylinder phase in block copolymers. Accordingly, we propose some possible strategies for further designing new AB-type block copolymer systems to obtain more stable square phase.