Topological and morphological signatures of disorder in a self-assembled, soft matter sponge network

Abstract

Many soft matter systems exhibit ordered, polycontinuous network morphologies, such as the cubic (double) gyroid or diamond, as well as disordered network morphologies known generically as ``random sponges". While presumed to share similar local packing geometry, the structural relationship between these ordered and disordered network morphologies has remained obscure. We use slice and view scanning electron microscopy to analyze and compare multi-scale morphological features of an ordered double-gyroid morphology to the amorphous sponge morphology formed in the same block copolymer sample. We find that node valence of the minority component network of the sponge is mostly gyroidal (trivalent), with a small fraction of diamond-like (tetravalent) connections. We analyze mesoatoms -- space-filling volumes occupied by chains around each network node -- finding significant differences in shape and size between ordered and amorphous regions. Local block thickness and inter-domain curvature within mesoatomic units of the disordered sponge exhibits a surprisingly similar degree of dispersity to the ordered double-gyroid. The mean differences in local packing geometry derive from topological distinction: loops of the minority networks of the ordered double-gyroid are intercatenated, while loops of the disordered sponge are not. In this way, the sponge may be viewed as disordered variant of a single-gyroidal morphology. We exploit these topological differences to demarcate the boundary region between ordered and disordered networks and highlight modulations of the mesoatom motifs at the boundary. These observations point to new questions about potential metastability of disordered networks and their possible role as kinetic precursors to long-range ordered network morphologies.