Electron tomography of a novel non-cubic network phase in ABC copolymers

We report the discovery of a novel bicontinuous tetragonal phase in the linear ABC triblock terpolymer system polystyrene (PS), polyisoprene (PI) and polydimethylsilocane (PDMS). The data is consistent with spacegroup Fddd and is distinctly non-cubic. The channel topology is distinct from the better-known cubic bicontinuous mesophases (diamond and gyroid types, with channels). It consists in 2 identical intertwined labyrinths with 3- and 4-connected nodes. Our mesophase differs from an earlier report of a copolymer phase (also in a linear terpolymer system) with the same spacegroup by Epps {\em et al} (Macromolecules {\bf 37}, 8325-41, 2004), who deduced a single channel morphology, based on TEM and SAXS data. Our proposal is based on 3D $e^-$-tomography data. The channel geometry is identified via a medial surface (MS) algorithm. For a labyrinth, the MS is a generalised channel graph consisting in surface patches. In contrast to line graphs, the MS is a complete descriptor of both topology and geometry. It provides robust shape characteristics, and is a useful tool for visualisation of complicated hyperbolic mazes.