Gradient Transformation of the Double Gyroid to the Double Diamond in Soft Matter.

Transitions between gyroid and diamond intercatenated double network phases occur in many types of soft matter, but to date, the structural pathway and the crystallographic relationships remain unclear. Slice and view scanning electron microscopy tomography of a diblock copolymer affords monitoring of the evolving shape of the intermaterial dividing surface, allowing structural characterization of both the majority and minority domains. Two trihedral malleable mesoatoms combine to form a single tetrahedral mesoatom in a volume additive manner while preserving network topology, as the types of loops, the number of mesoatoms in a loop, minority domain strut lengths, and directions that connect a given mesoatom to its neighbors evolve across a 150 nm wide transition zone (TZ). The [111] DD direction is coincident with the [110] DG direction so that the (111) DD and (110) DG planes define the boundaries of the TZ. Selection of the particular crystal orientations and direction and width of the transition zone is to minimize the cost of morphing the mesoatoms from one structure to the other, by maximizing like-block continuity and minimizing the variation of the surface curvature and thickness of the domains across the TZ. Such coherent continuity of the independent, intercatenated networks across the transition zone is critical for applications such as graded mechanical trusses where the pair of different networks are joined to provide different mechanical properties for adjacent grains or could serve as a nanoscale anode/cathode allowing super charging and discharging provided the networks are continuous and rigorously separate.