Archimedean tiling

Figure 4.2 An Archimedean tile morphology for blends of poly(2-vinylpyridine-/)-isoprene-/)-vinylpyridine) with poly(styrene-/)-4-hydroxystyrene) in a 2 1 vinylpyridine/hydroxystyrene blend. The vinylpyridine/hydroxystyrene domains are the cylinders at the vertices of polystyrene hexagons within a polyisoprene continuous phase. Reprinted from Asari et al. (2006). Copyright 2006 American Chemical Society.

Asari T, Aral S, Takano A, Matsushita Y. Archimedean tiling structures from ABA/CD block copolymer blends having intermolecular association with hydrogen bonding. Macro-molecules 2006 39 2232-2237. 

Takano A, Kawashima W et al (2005) A mesoscopic Archimedean tiling having a new complexity in an ABC star polymer. J Polym Sci B 43 2427-2432... 

Hayashida, K., Kawashima, W., Takano, A. etal. (2006a) Archimedean tiling patterns of ABC star-shaped terpolymers studied by microbeam small-angle X-ray scattering. Macromolecules, 39,4869 872. 

Figure 18.15 (a) The known 11 Archimedean tilings having the tessellation of regular polygons with every vertex under the same environment and the quasicrystalline tiling (3. 4.3.4). Each tiling pattern is denoted by... 

Ueda, K., Dotera, T, and Gemma, T. (2(X)7) Photonic band structure calculatioiis of two-dimensional Archimedean tiling patterns. Physical Review B, IS, 195122. 

This could be confirmed by theory as the PS block is nonselective toward the other two components, while PB and P2VP have a much higher repulsion between one another. In these stractures the junction point between the different arms is located within the polystyrene microdomain. Thrrs in these stractmes there is no line of junction points cormecting all three microdomains. Matsushita s group carried out very detailed systematic studies on 3-miktoatm star terpolymers of PS, PI, and P2VP. They analyzed their data in terms of Archimedean tiling patterns and also found a quasiciystalline stractme in one case. They used a lot of blends in their studies, which will be discussed in Section 7.02.2.3.3. 

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