Approximants of dodecagonal quasicrystals in aqueous diblock polymer dispersions

Abstract

Aqueous lyotropic liquid crystals (LLCs) are structured soft materials with long range crystallographic order, which derive from minimal hydration of amphiphilic molecules in water. In certain composition windows, amphiphiles self-assemble into quasispherical micelles that pack on body-centered cubic (BCC), face-centered cubic (FCC) and hexagonally close packed (HCP) lattices [1]. Herein, we describe investigations of the aqueous LLC phase behavior of polyethylene-poly(ethylene oxide) (PE-PEO) diblock polymers using temperature-dependent small-angle X-ray scattering (SAXS). With increasing polymer concentration, we show that these aqueous LLCs self-assemble into FCC, BCC, and Frank-Kasper (FK) A15 phases (Cr3Si structure type). Upon heating the A15 phase, we find that it undergoes a transition to a BCC phase that gives way to a hexagonally-packed cylindrical micelle phase (H) at high temperatures. Quenching the H phase to room temperature drives formation of a FK σ phase, which transforms into the original A15 structure after several months. These findings suggest that various, complex intermediate phases may form in LLCs depending on their thermal histories. We discuss the formation of these phases in the context of a delicate balance between minimization of free energy at the local micelle length scale against the global LLC unit cell scale. The specific observations of FK A15 and  phases, both periodic approximants of dodecagonal quasicrystals, suggest the possibility that suitable processing of these aqueous LLCs may lead to soft liquid quasicrystals. In view of recent discoveries of dodecagonal quasicrystals and their approximants in other soft systems[2-5], our discovery provides a new context for understanding the factors driving periodic and quasiperiodic order in soft materials.

Reevaluation of Poly(ethylene-alt-propylene)-block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth

“…34,35 In 2019, reevaluation of hydrated poly(ethylene oxide)-block-polyethylene (PEO-PE) diblock co-oligomers studied extensively between 1996 and 2005 36−38 revealed a transient, yet longlived, FK σ phase. 40 As recently as 2020, a return to the bidisperse diblock copolymer blends widely explored in the 1990s by the Hashimoto group 28,29,39 and others 30,31 after substantial annealing periods prior to synchrotron smallangle X-ray scattering (SAXS). 19 Motivated by these discoveries, we revisit here a 1999 report of an unusual progression of phases observed on cooling a low molecular weight, compositionally asymmetric poly(ethylene-alt-propylene)-block-polydimethylsiloxane (PEP-PDMS) diblock copolymer with volume fraction f PEP = 0.22 and molecular weight M n = 12.5 kg/mol.…”

Shear-Modulated Rates of Phase Transitions in Sphere-Forming Diblock Oligomer Lyotropic Liquid Crystals

“…21,22 For example, the FK A15 phase consists of two populations of quasi-spherical micelles where the aggregation number varies by ±3% around a mean value. 23 Phase transitions among these complex structures have been induced by controlling thermal processing history under quiescent conditions, some of which mimic metallurgical processing procedures. 19,20,23 Unlike metallic crystals, LLC phases of packed micelles can be easily manipulated at the micelle, lattice, and grain size length scales by using relatively weak external forces.…”

“…23 Phase transitions among these complex structures have been induced by controlling thermal processing history under quiescent conditions, some of which mimic metallurgical processing procedures. 19,20,23 Unlike metallic crystals, LLC phases of packed micelles can be easily manipulated at the micelle, lattice, and grain size length scales by using relatively weak external forces. In these soft systems, shear is effective in enabling long-range structure and grain orientation refinement resulting in pseudomonodomain crystals of soft materials.…”

“…The rapid and direct, shear-induced transition from BCC → A15 significantly differs from the slower, indirect BCC → σ → A15 transition sequence observed during quiescent isothermal annealing. 23 In the latter report, signatures of the A15 phase emerge only after several days with the complete phase transformation after 150 days at 25 °C. We note that those quiescent phase behavior studies employed small samples enclosed in metal pans that were cooled by immersion into a thermostated water bath.…”

“…An increase in the BCC unit cell size with decreasing C 16 E 20 concentration has been previously reported in this system. 23 Peaks that are not labeled with markers for the calculated A15 or BCC peak positions correspond to the σ phase, which is the expected intermediate structure. 23 Increasing γ 0 at this frequency increases the rate of A15 formation, decreases the intensity of residual σ and BCC reflections, and leads to larger grain sizes after 20 min of shear as shown by qualitatively sharper SAXS peaks in Figure 2b.…”