Quasicrystals and Their Approximants in a Crystalline–Amorphous Diblock Copolymer

Abstract

Discoveries of Frank–Kasper phases and closely related dodecagonal quasicrystals (DDQCs) in soft, mesoscopic systems have galvanized efforts to unveil the fundamental mechanisms that drive the formation of these remarkably complex micellar packings. Toward this end, we report temperature-dependent small-angle X-ray scattering analyses of a crystalline–amorphous poly­(ethylene oxide)-block-poly­(2-ethyl hexylacrylate) (OA) diblock copolymer with M n = 8300 g/mol, Đ = M w/M n = 1.10, and volume composition f O = 0.21. On heating at ambient temperature, this polymer assembles sequentially into five distinct morphologies prior to melt disordering at T ODT = 69 °C: semicrystalline lamellae (Lc), a liquid-like packing (LLP) of particles lacking translational order, an aperiodically ordered DDQC, a periodic FK σ phase, and a body-centered cubic (BCC) packing of particles. Detailed investigations of thermal processing conditions that foster DDQC formation reveal that this metastable morphology only forms in melts exhibiting LLP characteristics arising from either melting the Lc phase at low temperature or quenching a high-temperature disordered state, and that this DDQC eventually evolves into a σ approximant phase. Cooling a well-ordered BCC phase induces direct formation of a σ phase with no evidence of DDQC formation, suggesting the critical importance of particle size distribution of the disorganized yet segregated LLP state in triggering the emergence of a DDQC.

Expanding quasiperiodicity in soft matter: Supramolecular decagonal quasicrystals by binary giant molecule blends

“…in 1984 ( 2 ), various QC alloys have been successively identified ( 3 , 4 ), and among them are three-dimensional (3D) icosahedral QCs (IQC) ( 5 – 10 ), 10-fold two-dimensional (2D) decagonal QCs (DQC) ( 11 – 14 ), and 12-fold 2D dodecagonal QCs (DDQC) ( 15 , 16 ). Recently, various condensed soft matters [e.g., block copolymers ( 17 – 21 ), dendrimers ( 22 , 23 ), and giant molecules ( 24 – 26 )] were also reported to form supramolecular DDQCs by a hierarchical assembling procedure. In these cases, the submesoatomic (molecular) units first aggregate into mesoatoms (i.e., the supramolecular spherical motifs compared to “atoms” in the metal alloy crystals), and then, the mesoatoms further assemble into the quasicrystalline superlattices (QC-SLs).…”

Square-triangle tilings: an infinite playground for soft matter

“…If one takes into account the orientation of the tiles, each type of vertices may have different orientations. The 4 4 vertice can have three different orientations of the tiles, corresponding to the S 1 , S 2 and S 3 tiles. The 3 6 vertice has two orientations.…”

“…There is a renewal of interest in the geometrical properties of square-triangle tilings as they are observed in many experimental systems at the nanoscale such as liquid crystals, 1-3 copolymers, 4 mesoporous materials, [5][6][7] nanoparticles super-lattices, 8 photonic materials, [9][10][11] along with numerical simulations studies [12][13][14][15] . In all these soft matter systems, some phases can be described by an underlying square-triangle tiling as illustrated in Figure 1 by the example of a dodecagonal mesoporous material.…”

“…Such three dimensional stacks of 2D layers have been discussed elsewhere. 4,19 It is then sufficient to consider only bi-dimensional square-triangle phases.…”

Enhancing ion transport in charged block copolymers by stabilizing low symmetry morphology: Electrostatic control of interfaces

“…Recent discoveries of topologically close-packed phases from a few block copolymers with high conformational asymmetry opened a new forum for polymer science, as implicated by Shi et al ( 33 , 34 ), Bates et al ( 35 – 37 ), and Mahanthappa et al ( 37 ). To introduce interfacial curvature into low symmetry morphologies, a universally applied approach includes varying the chemical structures of the repeating units of the block copolymers to ensure they have largely dissimilar statistical segment lengths ( 38 , 39 ).…”