Hexagonally Packed Cylindrical Structures with Multiple Satellites from Pentablock Quarterpolymers of the AB1CB2D Type and Their Blends with Homopolymers

Nearly Ideal Random Tiling with Dodecagonal Symmetry from Pentablock Quarterpolymers of the AB1CB2D Type

Two-dimensional tiling manners as cross-sectional views of cylindrical domain assembly formed by pentablock quarterpolymers of the AB1CB2D type in bulk were investigated. Several binary and ternary blends from three mother polymers having different ϕB1/ϕB2 ratios (ϕB1 and ϕB2 are the volume fractions of the B1 and B2 blocks, respectively) represent nonperiodic but ordered triangle/square tilings, where the N3/N4 ratios (N3 and N4 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 N3/N4 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.

The Largest Quasicrystalline Tiling with Dodecagonal Symmetry from a Single Pentablock Quarterpolymer of the AB1CB2D Type

A quasicrystalline tiling pattern with tile size of ca. 60 nm has been discovered in the bulk state of a four-component pentablock polymer molecule of the AS₁IS₂P type, where A, S, I, and P denote poly(4-vinylbenzyldimethylamine), polystyrene, polyisoprene, and poly(2-vinylpyridine), respectively. The polymer samples used were prepared by anionic polymerizations and have narrow molecular weight distribution. The sample films were obtained by an extremely slow solvent-cast process from dilute solutions of tetrahydrofuran for 14 days. It has been found by TEM observation that the quarterpolymer, AS₁IS₂P-4 (M_n = 149 kg/mol, ϕ_A/ϕ_S1/ϕ_I/ϕ_S2/ϕ_P = 0.12/0.27/0.20/0.29/0.13), reveals two final stable structures, i.e., a 3.3.4.3.4 periodic tiling pattern as a minor component and a quasicrystalline (QC) tiling with dodecagonal symmetry as a major component, where the former includes a triangle/square number ratio of 2 and the latter has one of approximately 2.28, which is close enough to the ideal ratio, 4/ 3 ≑ 2.31, for the triangle/square random tiling of the dodecagonal QC tiling (DDQC). Two structures were also clearly proved by SAXS diffraction patterns. Here, it should be noted this QC structure having a tile side length of ca. 60 nm was created with a single block polymer molecule.