Symmetry-breaking in double gyroid block copolymer films by non-affine distortion

Soft-matter bicontinuous networks find a double gyroid structure from block copolymer (BCP) self-assembly. A gyroid structure composed of dissimilar blocks has proven its potential as a soft crystal capable of tuning structural periodicity and symmetry, of which the lattice dimension is variable with molecular weight of the polymer. Using an asymmetric polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA), here we show that the self-assembled gyroid films formed via a solvent vapor annealing (SVA) process undergo unique structural distortion due to directional deformation immediately upon deswelling. During the SVA process with PS-b-PMMA films, transient cylinders developed from the as-cast morphology transform into a cubic gyroid structure in a swollen state. Rapid and spontaneous deswelling processes ̶ the manners in which the films contract along the z-direction while retaining an enlarged lateral dimension of the cubic form ̶ lead to triclinic gyroid structures with z-directional contraction ratios (C_z) of 2.5 and 2.0, respectively. Our X-ray analysis reveals that the deswelling process of the swollen gyroid films produces a notable symmetry-breaking in non-affine gyroid structure that elicits several forbidden reflections such as {110} and {200} reflections. For further characterization of the symmetry-breaking, we delineate the structural features of noncubic gyroid films by computing electron-density difference maps assisted with X-ray measurements. Level-set approach is accordingly developed to quantitate the structural characteristics of the maps in terms of inversion symmetry-breaking, suggesting its possible application to optical Weyl photonic crystals.