Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

Non-Hermitian Delocalization in a Two-Dimensional Photonic Quasicrystal

Theoretical and experimental studies suggest that both Hermitian and non-Hermitian quasicrystals show localization due to the fractal spectrum and to the transition to diffusive bands via exceptional points, respectively. Here, we present an experimental study of a dodecagonal photonic quasicrystal based on electromagnetically induced transparency in a Rb vapor cell. First, we observe the suppression of the wave packet expansion in the Hermitian case. We then discover a new regime, where increasing the non-Hermiticity leads to delocalization, demonstrating that the behavior in non-Hermitian quasicrystals is richer than previously thought.

Particle Dynamics in a Diblock-Copolymer-Based Dodecagonal Quasicrystal and Its Periodic Approximant by X-Ray Photon Correlation Spectroscopy

Temperature-dependent x-ray photon correlation spectroscopy (XPCS) measurements are reported for a binary diblock-copolymer blend that self-assembles into an aperiodic dodecagonal quasicrystal and a periodic Frank-Kasper σ phase approximant. The measured structural relaxation times are Bragg scattering wavevector independent and are 5 times faster in the dodecagonal quasicrystal than the σ phase, with minimal temperature dependence. The underlying dynamical relaxations are ascribed to differences in particle motion at the grain boundaries within each of these tetrahedrally close-packed assemblies. These results identify unprecedented particle dynamics measurements of tetrahedrally coordinated micellar block polymers, thus expanding the application of XPCS to ordered soft materials.

Self-assembled soft alloy with Frank-Kasper phases beyond metals

Soft building blocks, such as micelles, cells or soap bubbles, tend to adopt near-spherical geometry when densely packed together. As a result, their packing structures do not extend beyond those discovered in metallic glasses, quasicrystals and crystals. Here we report the emergence of two Frank-Kasper phases from the self-assembly of five-fold symmetric molecular pentagons. The μ phase, an important intermediate in superalloys, is indexed in soft matter, whereas the ϕ phase exhibits a structure distinct from known Frank-Kasper phases in metallic systems. We find a broad size and shape distribution of self-assembled mesoatoms formed by molecular pentagons while approaching equilibrium that contribute to the unique packing structures. This work provides insight into the manipulation of soft building blocks that deviate from the typical spherical geometry and opens avenues for the fabrication of 'soft alloy' structures that were previously unattainable in metal alloys.

Understanding the Role of Trapezoids in Honeycomb Self-Assembly-Pathways between a Columnar Liquid Quasicrystal and its Liquid-Crystalline Approximants

Quasiperiodic patterns and crystals-having long range order without translational symmetry-have fascinated researchers since their discovery. In this study, we report on new p-terphenyl-based T-shaped facial polyphiles with two alkyl end chains and a glycerol-based hydrogen-bonded side group that self-assemble into an aperiodic columnar liquid quasicrystal with 12-fold symmetry and its periodic liquid-crystalline approximants with complex superstructures. All represent honeycombs formed by the self-assembly of the p-terphenyls, dividing space into prismatic cells with polygonal cross-sections. In the perspective of tiling patterns, the presence of unique trapezoidal tiles, consisting of three rigid sides formed by the p-terphenyls and one shorter, incommensurate, and adjustable side by the alkyl end chains, plays a crucial role for these phases. A delicate temperature-dependent balance between conformational, entropic and space-filling effects determines the role of the alkyl chains, either as network nodes or trapezoid walls, thus resulting in the order-disorder transitions associated with emergence of quasiperiodicity. In-depth analysis suggests a change from a quasiperiodic tiling involving trapezoids to a modified one with a contribution of trapezoid pair fusion. This work paves the way for understanding quasiperiodicity emergence and develops fundamental concepts for its generation by chemical design of non-spherical molecules, aggregates, and frameworks based on dynamic reticular chemistry.

Design of Linear Block Copolymers and ABC Star Terpolymers That Produce Two Length Scales at Phase Separation

Quasicrystals (materials with long-range order but without the usual spatial periodicity of crystals) were discovered in several soft matter systems in the last 20 years. The stability of quasicrystals has been attributed to the presence of two prominent length scales in a specific ratio, which is 1.93 for the 12-fold quasicrystals most commonly found in soft matter. We propose design criteria for block copolymers such that quasicrystal-friendly length scales emerge at the point of phase separation from a melt, basing our calculations on the Random Phase Approximation. We consider two block copolymer families: linear chains containing two different monomer types in blocks of different lengths, and ABC star terpolymers. In all examples, we are able to identify parameter windows with the two length scales having a ratio of 1.93. The models that we consider that are simplest for polymer synthesis are, first, a monodisperse ALBASB melt and, second, a model based on random reactions from a mixture of AL, AS, and B chains: both feature the length scale ratio of 1.93 and should be relatively easy to synthesize.

Apex hydrogen bonds in dendron assemblies modulate close-packed mesocrystal structures

The close-packed mesocrystal structures from soft-matter assemblies have recently received attention due to their structural similarity to atomic crystals, displaying various sphere-packing Frank-Kasper (FK) and quasicrystal structures. Herein, diverse mesocrystal structures are explored in second-generation dendrons (G2-X) designed with identical wedges, in which the terminal functionalities X = CONH₂ and CH₂NH₂ represent two levels of the strong and weak hydrogen-bonding apexes, respectively. The cohesive interactions at the core apex, referred to as the core interactions, are effectively modulated by forming heterogeneous hydrogen bonds between these two functional units. For the dendron assemblies compositionally close to each pure component of G2-CONH₂ and G2-CH₂NH₂, their own FK A15 and C14 phases dominate other phases, respectively. We show the existence of the wide-range FK σ including the dodecagonal quasicrystal (DDQC) phases from the dendron mixtures between G2-CONH₂ and G2-CH₂NH₂, providing an experimental phase sequence of A15-σ-DDQC-C14 as the core interactions are alleviated. Intriguingly, the temperature dependence of particle sizes shows that the high plateau values of particle sizes are maintained equivalently until each threshold temperature (T_th), followed by a prompt decrease above the T_th. A decrease in T_th by alleviating the core interactions and its composition dependence suggest that the more size-dispersed particles, the more susceptibility to chain exchange with increasing temperature. Our results on the formation of supramolecular dendron assemblies provide a guide to understand the core-interaction-dependent mesocrystal structures toward the fundamental principle underlying the temperature dependence of their particle sizes.

Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal type. Here we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length scales that form aperiodic stable states with two different examples of rectangle-triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.

Inverse ISAsomes in Bio-Compatible Oils—Exploring Formulations in Squalane, Triolein and Olive Oil

In contrast to their more common counterparts in aqueous solutions, inverse ISAsomes (internally self-assembled somes/particles) are formulated as kinetically stabilised dispersions of hydrophilic, lyotropic liquid-crystalline (LC) phases in non-polar oils. This contribution reports on their formation in bio-compatible oils. We found that it is possible to create inverse hexosomes, inverse micellar cubosomes (Fd3m) and an inverse emulsified microemulsion (EME) in excess squalane with a polyethylene glycol alkyl ether as the primary surfactant forming the LC phase and to stabilise them with hydrophobised silica nanoparticles. Furthermore, an emulsified -phase and inverse hexosomes were formed in excess triolein with the triblock-copolymer Pluronic® P94 as the primary surfactant. Stabilisation was achieved with a molecular stabiliser of type polyethylene glycol (PEG)-dipolyhydroxystearate. For the inverse hexosomes in triolein, the possibility of a formulation without any additional stabiliser was explored. It was found that a sufficiently strong stabilisation effect was created by the primary surfactant alone. Finally, triolein was replaced with olive oil which also led to the successful formation of inverse hexosomes. As far as we know, there exists no previous contribution about inverse ISAsomes in complex oils such as triolein or plant oils, and the existence of stabiliser-free (i.e., self-stabilising) inverse hexosomes has also not been reported until now.

An Accelerated Modular-Orthogonal Ni-Catalyzed Methodology to Symmetric and Nonsymmetric Constitutional Isomeric AB2 to AB9 Dendrons Exhibiting Unprecedented Self-Organizing Principles

Five libraries of natural and synthetic phenolic acids containing five AB₃, ten constitutional isomeric AB₂, one AB₄, and one AB₅ were previously synthesized and reported by our laboratory in 5 to 11 steps. They were employed to construct seven libraries of self-assembling dendrons, by divergent generational, deconstruction, and combined approaches, enabling the discovery of a diversity of supramolecular assemblies including Frank-Kasper phases, soft quasicrystals, and complex helical organizations, some undergoing deracemization in the crystal state. However, higher substitution patterns within a single dendron were not accessible. Here we report three libraries consisting of 30 symmetric and nonsymmetric constitutional isomeric phenolic acids with unprecedented sequenced patterns, including two AB₂, three AB₃, eight AB₄, five AB₅, six AB₆, three AB₇, two AB₈, and one AB₉ synthesized by accelerated modular-orthogonal Ni-catalyzed borylation and cross-coupling. A single etherification step with 4-(n-dodecyloxy)benzyl chloride transformed all these phenolic acids, of interest also for other applications, into self-assembling dendrons. Despite this synthetic simplicity, they led to a diversity of unprecedented self-organizing principles: lamellar structures of interest for biological membrane mimics, helical columnar assemblies from rigid-solid angle dendrons forming Tobacco Mosaic Virus-like assemblies, columnar organizations from adaptable-solid angle dendrons forming disordered micellar-like nonhelical columns, columns from supramolecular spheres, five body-centered cubic phases displaying supramolecular orientational memory, rarely encountered in previous libraries forming predominantly Frank-Kasper phases, and two Frank-Kasper phases. Lessons from these self-organizing principles, discovered within a single generation of self-assembling dendrons, may help elaborate design principles for complex helical and nonhelical organizations of synthetic and biological matter.

Mesoscale Frank-Kasper Crystal Structures from Dendron Assembly by Controlling Core Apex Interactions

Single-component polymeric materials open up a great potential for self-assembly into mesoscale complex crystal structures that are known as Frank-Kasper (FK) phases. Predicting the packing structures of the soft-matter spheres, however, remains a challenge even when the molecular design is precisely known. Here, we investigate the role of the molecules' enthalpic interaction in determining the low-symmetry crystal structures. To this end, we synthesize architecturally asymmetric dendrons by varying their apex functionalities and examine the packing structures of the second-generation (G2) dendritic wedges. Our work shows that weakening the hydrogen bonding of the dendron apex makes the particles softer and smaller, and leads to the formation of various FK structures at lower temperatures, including the new observation of a FK C14 phase in the cone-shaped dendron systems. As a consequence of the free energy balance between the particle's interfacial tension and the chain's stretching, various packing structures are mainly tuned by designing the hydrogen bonding interaction.