Small-angle x-ray scattering experiments conducted with compositionally asymmetric low molar mass poly(isoprene)--poly(lactide) diblock copolymers reveal an extraordinary thermal history dependence. The development of distinct periodic crystalline or aperiodic quasicrystalline states depends on how specimens are cooled from the disordered state to temperatures below the order-disorder transition temperature. Whereas direct cooling leads to the formation of documented morphologies, rapidly quenched samples that are then heated from low temperature form the hexagonal C14 and cubic C15 Laves phases commonly found in metal alloys. Self-consistent mean-field theory calculations show that these, and other associated Frank-Kasper phases, have nearly degenerate free energies, suggesting that processing history drives the material into long-lived metastable states defined by self-assembled particles with discrete populations of volumes and polyhedral shapes.
The self-assembly of block polymers into well-ordered nanostructures underpins their utility across fundamental and applied polymer science, yet only a handful of equilibrium morphologies are known with the simplest AB-type materials. Here, we report the discovery of the A15 sphere phase in single-component diblock copolymer melts comprising poly(dodecyl acrylate)−block−poly(lactide). A systematic exploration of phase space revealed that A15 forms across a substantial range of minority lactide block volume fractions (fL = 0.25 − 0.33) situated between the σ-sphere phase and hexagonally close-packed cylinders. Self-consistent field theory rationalizes the thermodynamic stability of A15 as a consequence of extreme conformational asymmetry. The experimentally observed A15−disorder phase transition is not captured using mean-field approximations but instead arises due to composition fluctuations as evidenced by fully fluctuating field-theoretic simulations. This combination of experiments and field-theoretic simulations provides rational design rules that can be used to generate unique, polymer-based mesophases through self-assembly.
Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order-disorder transition temperature (). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank-Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)--poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEX) upon heating and cooling. The process-path-dependent formation of crystalline order shapes the number of particles per unit volume, /, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed / is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank-Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.
Small angle x-ray scattering experiments on three model low molar mass diblock copolymer systems containing minority polylactide and majority hydrocarbon blocks demonstrate that conformational asymmetry stabilizes the Frank-Kasper σ phase. Differences in block flexibility compete with space filling at constant density inducing the formation of polyhedral shaped particles that assemble into this low symmetry ordered state with local tetrahedral coordination. These results confirm predictions from self-consistent field theory that establish the origins of symmetry breaking in the ordering of block polymer melts subjected to compositional and conformational asymmetry.
A renewed focus on the phase behavior of nominally single-component, compositionally asymmetric diblock copolymers has revealed a host of previously unanticipated Frank–Kasper (FK) and quasicrystalline phases. However, these periodic and aperiodic particle packings have thus far only been reported in low molecular weight, highly conformationally asymmetric diblock copolymers, leaving researchers with a relatively small library of polymers in which these phases can be studied. In this work, we report on a simple approach to access these morphologies: blending two diblock copolymers with the same corona block length and varied core block lengths. Compositionally symmetric and asymmetric polystyrene-b-1,4-polybutadiene (SB) diblock copolymers with constant corona block lengths were blended together and shown via small-angle X-ray scattering and transmission electron microscopy to order into the FK A15 and σ phases, as well as a dodecagonal quasicrystal, providing a route to various particle packings in high molecular weight diblock copolymer melts.
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