Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts

The hexagonally close-packed (HCP) sphere phase is predicted to be stable across a narrow region of linear block copolymer phase space, but the small free energy difference separating it from face-centered cubic spheres usually results in phase coexistence. Here, we report the discovery of pure HCP spheres in linear block copolymer melts with A = poly(2,2,2-trifluoroethyl acrylate) ("F") and B = poly(2-dodecyl acrylate) ("2D") or poly(4-dodecyl acrylate) ("4D"). In 4DF diblocks and F4DF triblocks, the HCP phase emerges across a substantial range of A-block volume fractions (circa f_A = 0.25-0.30), and in F4DF, it forms reversibly when subjected to various processing conditions which suggests an equilibrium state. The time scale associated with forming pure HCP upon quenching from a disordered liquid is intermediate to the ordering kinetics of the Frank-Kasper σ and A15 phases. However, unlike σ and A15, HCP nucleates directly from a supercooled liquid or soft solid without proceeding through an intermediate quasicrystal. Self-consistent field theory calculations indicate the stability of HCP is intimately tied to small amounts of molar mass dispersity (Đ); for example, an HCP-forming F4DF sample with f_A = 0.27 has an experimentally measured Đ = 1.04. These insights challenge the conventional wisdom that pure HCP is difficult to access in linear block copolymer melts without the use of blending or other complex processing techniques.