Nearly Ideal Random Tiling with Dodecagonal Symmetry from Pentablock Quarterpolymers of the ABCBD Type.

Two-dimensional tiling manners as cross-sectional views of cylindrical domain assembly formed by pentablock quarterpolymers of the ABCBD type in bulk were investigated. Several binary and ternary blends from three mother polymers having different ϕ/ϕ ratios (ϕ and ϕ are the volume fractions of the B and B blocks, respectively) represent nonperiodic but ordered triangle/square tilings, where the / ratios ( and are the numbers of triangles and squares in the observed area, respectively) are all close enough to the theoretical value of 4/√3 ≑ 2.31 for the dodecagonal quasicrystalline (DDQC) state, irrespective of the total number of polygons. The TEM images, having almost the same / ratios, were proved to show 4- and 6-fold symmetries in terms of the angular appearance of equilateral polygon sides via image analyses. Among them, a ternary blend showed a nearly ideal random tiling pattern that is almost equivalent to the theoretically predicted tiling by SCFT. Moreover, the magnitude of phason strain estimated for a TEM image from the ternary blend was proved to be quite small when the observing area is narrow, while it deviates from the ideal quasicrystalline tiling with an increasing number of vertices in the observing area.