Universal Viscoelastic Response of Body-Centered-Cubic Block Copolymer Solutions: Time–Temperature–Concentration Superposition

Abstract

The microstructure and dynamic mechanical behavior of ordered block copolymer solutions are critical for tailoring the properties for various applications. While the microstructural evolution of block copolymers with polymer concentration is well understood, its correlation with rheological behavior remains insufficiently explored. In this study, we uncovered a universal relationship between the linear viscoelastic behavior and concentration of cubic ordered block copolymer solutions using a time–temperature–concentration superposition (tTcS) principle. Specifically, a polystyrene-block-poly(ethylene-alt-propylene) (SEP) copolymer (M_n = 75.2 kDa, Đ = 1.05, and f_PS = 0.18) dissolved in squalane was employed as a model system. The asymmetric SEP self-assembled into a body-centered cubic (BCC) structure across all concentrations, from 10% to the bulk. Increasing SEP content induced changes in both micelle and ordered lattice structures, resulting in higher aggregation numbers and reduced intermicelle distances. As the micelles became more closely packed, the enhanced entanglement of the corona chains influenced the rheological properties, establishing a direct correlation with the microstructural changes. The concentration-dependent horizontal shift factor (a_c) in the block copolymer solutions exhibited a stronger dependence on the degree of entanglement of corona chains compared to typical homopolymer solutions. This behavior arises from the terminally anchored PEP chains, which follows an exponential relationship with the degree of entanglement as in star polymers. In contrast, the vertical shift factor (b_c) reflected lattice elasticity dictated by the density of corona chains, which is directly determined by the intermicelle distance and aggregation number.