Understand the Relative Stability of Single-Gyroid to Double-Gyroid in AB-Type Block Copolymer: Chain Packing and Geometric Analysis

Abstract

It has been commonly accepted that the bicontinuous double-gyroid (DG) network structure is the usual stable phase formed in pure AB-type block copolymer melts. Thus, the emergence of the single-network counterpart, i.e., single-gyroid (SG), is mysterious. In previous work, it was proposed that the SG phase was stabilized by the synergistic effect of the local segregation between two unequal end B-blocks and the stretched bridging middle B 2 -block of the linear B 1 AB 2 AB 3 pentablock; however, this was not sufficiently verified. Here, we reexamine the stabilization mechanism of the single-gyroid phase and reveal that the bridging middle B-blocks do not play a key role in stabilizing the SG phase over DG due to their negligibly low bridging fraction. Instead, the middle B 2 -blocks mainly concentrate near the interface in the form of loops, helping the short end B 1 -block to push the long B 3block to fill the further space and thus relieving the packing frustration of B-blocks in the matrix of SG on the one hand. On the other hand, the middle B-block is distributed more uniformly on the interface in the SG structure than in the DG structure due to the more uniform interfacial curvature of the former. These two factors lower the relative interaction energy of SG compared to DG, consequently stabilizing SG. Clearly elucidating the stabilization mechanism of SG may provide guidance for further improving its stability or obtaining other single-network phases (e.g., single-diamond).