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

Abstract

A quasicrystalline tiling pattern with tile size of <i>ca</i>. 60 nm has been discovered in the bulk state of a four-component pentablock polymer molecule of the <i>AS</i>₁<i>IS</i>₂<i>P</i> 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, <i>AS</i>₁<i>IS</i>₂<i>P-4</i> (<i>M</i>_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>i</i>.<i>e</i>., 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/ <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≑</mo></math> 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 <i>ca</i>. 60 nm was created with a single block polymer molecule.