Systematic transitions of tiling patterns formed by ABC star-shaped terpolymers

New tiling patterns with complex arrangements have been identified for ABC star-shaped terpolymers and ABC/A/B copolymer/homopolymer blends characterized by transmission electron microscopy and microbeam small-angle X-ray scattering. The samples are composed of polyisoprene (I), polystyrene (S), and poly(2-vinylpyridine) (P), whose volume ratios of I:S:P are 1.0:1.8:X, where X covers the range 0.8 ≤ X ≤ 3.2. The other series of the type I _1.0S_yP_2.0 with Y in the range of 1.1 ≤ Y ≤ 2.7 was also prepared by adding I or S homopolymers to the terpolymers of the type I_1.0S_1.8P_X. The systematic phase transition takes place in both series when the X or K variables are increased and four new tiling patterns have been observed: [5.3, 5.3, 8], [4.5, 6, 9], [5, 5, 10], and [4, 6.7, 10], where the three numbers in the brackets denote the average coordination number (ACN) for the I, S, and P components, respectively. A very simple transition rule has been established: the ACN of the ascendant component increases monotonically with an increase of the variable X or Y, accompanied by the monotonic decrease in the ACN for the descendant component, which is polyisoprene in these cases.