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

Abstract

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(2,2,2trifluoroethyl 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.

Self‐assembly of block copolymers for biological applications

“…), where N is the overall degree of polymerization of the BCP and χ is the Flory–Huggins interaction parameter between the blocks, then d can be readily tailored by controlling N and χ . For instance, a hexagonally close‐packed sphere phase can be achieved from linear block copolymer with high χ across a wide range of compositions, which is supported by the experimental and simulation results 6 . Beyond χ , complex inaccessible morphologies from linear BCPs can be obtained by manipulating the combination parameters (e.g.…”

Frank–Kasper Phases in Block Polymers

“…The selection of the ordered state can be posed as identifying the least expensive distortion of the otherwise spherical particle to fill space . For decades, there was a general consensus that the optimal particle packing for diblock copolymers is the body-centered cubic (bcc) lattice in Figure , , with self-consistent field theory (SCFT) predicting a very narrow region of close-packed spheres (face-centered cubic, fcc, or hexagonally close-packed, hcp) near the order–disorder transition. , Theory predicts that the close-packed structure predicted in the mean field limit is destroyed by fluctuations at finite molecular weights, although close packing has been observed experimentally. − The consensus surrounding the formation of a bcc lattice, achieved in the 1980s, , was upended by the theoretical prediction of a Frank–Kasper A15 phase in a multiply branched block polymer by Grason and co-workers in 2003 and the subsequent discovery of a Frank–Kasper σ phase in both a diblock copolymer and a tetrablock terpolymer by Bates and co-workers in 2010 …”

Precisely Encoding Geometric Features into Discrete Linear Polymer Chains for Robust Structural Engineering

“…A synthetic polymer is virtually a mixture of chains with the same repeating unit but varied chain lengths (known as dispersity , Đ ). It has been recently recognized that the formation and transition of ordered structures are surprisingly susceptible to molecular weight distribution, and even batch-to-batch variation would be sufficient to result in disparate assemblies. ,− Quantitatively unraveling the role of molecular geometry/architecture demands independent and precise control of molecular parameters to decouple undesired interferences (such as compositional variation). Recent progress in polymer syntheses (e.g., solid-phase synthesis and iterative growth) has allowed the preparation of discrete oligomers/polymers with uniform chain lengths (i.e., Đ = 1). − The precision feature offers unparalleled control over chain arrangements, revealing intriguing phase behaviors that have long been compromised by inherent molecular weight distribution and bridging the existing gaps between experiments and theories. ,,− In this study, we (i) elaborately designed a library of monomers based on glutamic acid derivatives with similar constitution but varied alkyl side chains and (ii) modularly prepared discrete linear polymers with programmable molecular geometries (Scheme ).…”