Dodecagonal quasicrystalline order in a diblock copolymer melt

Abstract

We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (T ODT = 66°C) using small-angle X-ray scattering (SAXS) measurements. Between T ODT and the order-order transition temperature T OOT = 42°C, an equilibrium body-centered cubic (BCC) structure forms, whereas below T OOT the Frank-Kasper σ phase is the stable morphology. At T < 40°C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35°C and more than 10 and 200 d at 25°C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the σ phase grows directly when the BCC phase is cooled below T OOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40°C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.quasicrystals | Frank-Kasper phases | block polymers T he discovery of aperiodic order, today referred to as quasicrystalline order, in rapidly cooled Al-Mn alloys by Shechtman and coworkers in 1984 heralded a paradigm shift in the understanding of what constitutes long-range order in matter (1, 2). More recently, quasicrystalline order has been found in an expanding variety of soft materials including self-assembling wedge-shaped dendrimers, mixtures of ligand coated nanoparticles, concentrated solutions of surfactant and block polymer micelles, multicomponent polymer blends containing ABC-type miktoarm star polymers, and an ABA′C-type linear multiblock polymer (3-8). The underlying principles that govern the formation of quasicrystals in soft materials remain largely unresolved.Block polymers are uniquely tunable self-assembling soft materials in which the nanoscale morphology, characteristic length scale, chemical and physical properties, and dynamics can be precisely controlled through the judicious choice of block repeat unit chemistries, block molecular weights, and molecular architecture (9, 10). Such exquisite control over structure, and the associated dynamics, makes block polymers ideal model materials for fundamental inquiries into the formation and stability of soft quasicrystals. In this article, we report the discovery of a long-lived metastable dodecagonal quasicrystalline phase (DDQC) in a (nominally) single-component poly(1,4-is...

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity

“…Thus, this discovery bridges previous reports of FK phases neutral soft materials (2, 18, 19, 21-23, 31, 35) and metal alloys. However, the ubiquity of icosahedral QCs in multicomponent metal alloys (36) starkly contrasts the observation of only dodecagonal QCs in soft materials to date (23)(24)(25)(26). Icosahedral QCs, which are quasiperiodic in 3D, typically form in ternary alloys wherein the metal sites exhibit decoupled variations in both particle mass (atomic number) and charge distribution.…”

“…More recently, FK A15 and σ phases were documented in thermotropic LCs of wedge-shaped dendrons (18)(19)(20), linear diblock and multiblock polymers (21,22), and giant shape amphiphiles (2,23). These studies culminated in the discovery of soft, dodecagonal QCs (23)(24)(25)(26), for which the A15 and σ phases are 3D periodic approximants.…”

Photoswitchable Nanomaterials Based on Hierarchically Organized Siloxane Oligomers

“…More interestingly, SAXS shows that 4-HOMAZOSi16 does not form a lamellar structure with crystalline layers but instead phase separates into a complex ordered morphology ( Figure 6C). Complex morphologies, such as the dodecagonal quasicrystal [41] or the Frank-Kasper σ phase, [42] have been shown to occur in highly asymmetric block copolymers. A similar scenario likely exists in our supramolecular material, as the azobenzene end groups have lower volume fraction and are significantly more rigid than the siloxane midblock.…”

Geometry induced sequence of nanoscale Frank–Kasper and quasicrystal mesophases in giant surfactants

“…Dodecagonal quasicrystals (DQCs) with 12-fold rotational symmetry have also been reported; representative examples include mesoporous silica constructed from small-molecule surfactant micelles (20), micelles of linear diblock copolymers (21), specifically designed single-component dendrimers (22), and tetrablock copolymers (23). Very recently, a DQC phase was identified as a metastable state in supercooled diblock copolymer melts (24).…”