  A twin boundary (TB) is a common low energy planar defect in crystals
including those with the atomic diamond structure (C, Si, Ge, etc.). We study
twins in a self-assembled soft matter block copolymer (BCP) supramolecular
crystal having the double diamond (DD) structure, consisting of 2
translationally shifted, interpenetrating diamond networks of the minority
polydimethyl siloxane block embedded in a polystyrene block matrix. The
coherent, low energy, mirror-symmetric double tubular network twin has one
minority block network with its nodes offset from the (222) TB plane while
nodes of the second network lie in the plane of the boundary. The offset
network, although at a scale about a factor of 103 larger, has precisely the
same geometry and symmetry as a (111) twin in atomic single diamond where the
tetrahedral units spanning the TB retain nearly the same strut (bond) lengths
and strut (bond) angles as in the normal unit cell. In the DD, the second
minority block network undergoes a dramatic restructuring - the tetrahedral
nodes transform into 2 new types of mirror-symmetric nodes (pentahedral and
trihedral) which alternate and link to form a hexagonal mesh in the plane of
the TB. The collective re-organization of the supramolecular packing highlights
the hierarchical structure of ordered BCP phases and emphasizes the remarkable
malleability of soft matter.
