Quasicrystals and Their Approximants in a Crystalline–Amorphous Diblock Copolymer

Abstract

Discoveries of Frank–Kasper phases and closely related dodecagonal quasicrystals (DDQCs) in soft, mesoscopic systems have galvanized efforts to unveil the fundamental mechanisms that drive the formation of these remarkably complex micellar packings. Toward this end, we report temperature-dependent small-angle X-ray scattering analyses of a crystalline–amorphous poly(ethylene oxide)-block-poly(2-ethyl hexylacrylate) (OA) diblock copolymer with Mₙ = 8300 g/mol, Đ = Mw/Mₙ = 1.10, and volume composition fO = 0.21. On heating at ambient temperature, this polymer assembles sequentially into five distinct morphologies prior to melt disordering at TODT = 69 °C: semicrystalline lamellae (Lc), a liquid-like packing (LLP) of particles lacking translational order, an aperiodically ordered DDQC, a periodic FK σ phase, and a body-centered cubic (BCC) packing of particles. Detailed investigations of thermal processing conditions that foster DDQC formation reveal that this metastable morphology only forms in melts exhibiting LLP characteristics arising from either melting the Lc phase at low temperature or quenching a high-temperature disordered state, and that this DDQC eventually evolves into a σ approximant phase. Cooling a well-ordered BCC phase induces direct formation of a σ phase with no evidence of DDQC formation, suggesting the critical importance of particle size distribution of the disorganized yet segregated LLP state in triggering the emergence of a DDQC.