Frank-Kasper and related quasicrystal spherical phases in macromolecules

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.

Fine-tuning of colloidal polymer crystals by molecular simulation

Through extensive molecular simulations we determine a phase diagram of attractive, fully flexible polymer chains in two and three dimensions. A rich collection of distinct crystal morphologies appear, which can be finely tuned through the range of attraction. In three dimensions these include the face-centered cubic, hexagonal close packed, simple hexagonal, and body-centered cubic crystals and the Frank-Kasper phase. In two dimensions the dominant structures are the triangular and square crystals. A simple geometric model is proposed, based on the concept of cumulative neighbors of ideal crystals, which can accurately predict most of the observed structures and the corresponding transitions. The attraction range can thus be considered as an adjustable parameter for the design of colloidal polymer crystals with tailored morphologies.

Topological dual and extended relations between networks of clathrate hydrates and Frank-Kasper phases

Clathrate hydrates are a class of ordered structures that are stabilized via the delicate balance of hydrophobic interactions between water and guest molecules, of which the space-filling network of hydrogen-bonded (H-bonded) water molecules are closely related to tetrahedrally close-packed structures, known as Frank-Kasper (FK) phases. Here we report an alternative way to understand the intricate structures of clathrate hydrates, which unveils the diverse crystalline H-bonded networks that can be generated via assembly of one common building block. In addition to the intrinsic relations and pathways linking these crystals, we further illustrate the rich structural possibilities of clathrate hydrates. Given that the topological dual relations between networks of clathrate hydrates and tetrahedral close-packed structures, the descriptors presented for clathrate hydrates can be directly extended to other ordered materials for a more thorough understanding of their nucleation, phases transition, and co-existence mechanisms.

ABC-Type, Bola-Form Giant Surfactants: Synthesis and Self-Assembly

Due to the fast phase separation kinetics and small feature size, the self-assembly of giant molecules has attracted lots of attention. However, there is not much study on multicomponent giant surfactants. In this work, through a modular synthetic strategy, different polyhedral oligomeric silsesquioxane (POSS)-based molecular nanoparticles are installed with diverse functionalities (hydrophobic octavinyl POSS (VPOSS), hydrophilic dihydroxyl-functionalized POSS (DPOSS), and omniphobic perfluoroalkyl-chain-functionalized POSS (FPOSS)) on the ends of one polystyrene (PS) chain to build up a series of triblock bola-form giant surfactants denoted as XPOSS-PS_n -FPOSS (X represents V or D). The target molecules are prepared by a combination of atom transfer radical polymerization (ATRP), esterification, as well as Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) and thiol-ene "click" reactions. These macromolecules are thoroughly characterized by combined technologies including nuclear magnetic resonance (NMR), size exclusion chromatography (SEC), and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) analyses. It is revealed by small angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) that VPOSS-PS_n -FPOSS adopts a two-phase separation scenario where VPOSS and POSS are segregated in one phase. DPOSS-PS_n -FPOSS with a third hydrophilic DPOSS shows a three-phase separation scenario, where highly ordered phase structures are difficult to develop owing to the competition of mutual phase separation processes and may be trapped in kinetically metastable states.

Progress in the self-assembly of organic/inorganic polyhedral oligomeric silsesquioxane (POSS) hybrids

This Review describes recent progress in the self-assembly of organic/inorganic POSS hybrids derived from mono-, di-, and multi-functionalized POSS cages. We highlight the self-assembled structures and physical properties of giant surfactants and chain-end- and side-chain-type hybrids derived from mono-functionalized POSS cages; main-chain-type hybrids derived from di-functionalized POSS cages; and star-shaped hybrids derived from multi-functionalized POSS cages; with various polymeric attachments, including polystyrene, poly(methyl methacrylate), phenolic, PVPh, and polypeptides.

Multiple 2D crystal structures in bilayered lamellae from direct self-assembly of 3D systems of soft Janus particles

Numerous crystals and Frank-Kasper phases in two-dimensional (2D) systems of soft particles have been presented by theoretical investigations. How to realize 2D crystals or Frank-kasper phases by direct self-assembly of...

Transition pathways connecting crystals and quasicrystals

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz-Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

The C36 Laves phase in diblock polymer melts

The C14 and C15 Laves phases form as micelle packing structures in many types of soft matter, but the related C36 phase, which consists of alternating C14-type and C15-type layers, has not been observed in any such system. To understand this absence in the context of diblock polymers, we used self-consistent field theory to relate the morphology and energetics of C36 to other known mesophases. Two case studies were conducted: blends of AB diblock polymers with A homopolymers (where A forms the micelle core), in which C14 and C15 have stability windows, and neat AB diblock melts, in which Laves phases are metastable. Laves phases exhibit nearly identical micelle morphologies and nearly degenerate free energies, with the free energy of C36 being a near-perfect bisector of the C14 and C15 free energies in all cases, revealing an intrinsic symmetry in free energy that is attributed solely to the structural relationship between the phases in which the packing of C36 is intermediate between C14 and C15. Based on this connection between structure and free energy, C36 is thus not expected to form in flexible diblock polymers, since C14 and C15 can always form instead via facile mass transfer.

Intercluster Exchange-Stabilized Novel Complex Colloidal χc Phase

Designing complex cluster crystals with a specific function using simple colloidal building blocks remains a challenge in materials science. Herein, we propose a conceptually new design strategy for constructing complex cluster crystals via hierarchical self-assembly of simple soft Janus colloids. A novel and previously unreported colloidal cluster-χ (χ_c) phase, which resembles the essential structural features of α-manganese but at a larger length scale, is obtained through molecular dynamics simulations. The formation of the χ_c phase undergoes a remarkable two-step self-assembly process, that is, the self-assembly of clusters with specific size dispersity from Janus colloids, followed by the highly ordered organization of these clusters. More importantly, the dynamic exchange of particles between these clusters plays a critical role in stabilizing the χ_c phase. Such a conceptual design framework based on intercluster exchange has the potential to effectively construct novel complex cluster crystals by hierarchical self-assembly of colloidal building blocks.

Crowding-Induced Unconventional Phase Behaviors in Dendritic Rodlike Molecules via Side-Chain Engineering

Dendritic molecules with a fanlike or conelike conformation are common molecular building blocks to construct supramolecular columnar or spherical phases. Although it is well-accepted that the preferred molecular conformation of dendritic molecules dictates their packing schemes, manipulation of this crucial parameter usually requires significant changes in molecular structures and tedious synthetic efforts. Herein, we report a simple yet highly efficient strategy to tune the molecular conformation of dendritic rodlike molecules by adjusting the length of alkyl side chains tethered to the rods. Strikingly, tiny chemical structure differences can largely change the "crowding" near the branching point to induce the "fanlike to conelike" conformational transitions and thus result in the formation of diverse supramolecular structures, including the columnar phase, double gyroid phase, and the unconventional Frank-Kasper σ and A15 phases. Our study provides a practical platform for further investigation of unconventional structure formation and phase transitions in soft matter.

Liquid Organic Frameworks: A Liquid Crystalline 8-Connected Network with Body-Centered Cubic Symmetry

Liquid state self-assembly is important for the understanding of the complex structures developed in abiogenesis and biogenesis as well as for numerous potential technological applications. Herein we report the first body-centered cubic liquid crystalline phase with 8-connected network topology and open octahedral network structure. It is formed by dynamic soft self-assembly of X-shaped polyphiles with oligo(para-phenylene-ethynylene) cores. The π-conjugated rods with perfluorinated inner benzene rings form networks conjoined by eight-way junctions, which are formed by nano-segregated spheres involving hydrogen-bonded polar end groups, while the branched aliphatic chains at opposite sides of the cores fill the continuum. This novel cubic phase is based on the I-WP minimal surface separating the frameworks of polyaromatic cores from the most disordered chain segments. It can also be considered as a dense sphere packing. Such liquid organic frameworks, representing hybrids of sphere packings and networks could be of interest for organic photonics and other technologies.

Discrete Block Copolymers with Diverse Architectures: Resolving Complex Spherical Phases with One Monomer Resolution

This work describes the first rigorous example of a single-component block copolymer system forming unconventional spherical phases. A library of discrete block polymers with uniform chain length and diverse architectures were modularly prepared through a combination of a step-growth approach and highly efficient coupling reactions. The precise chemical structure eliminates all the molecular defects associated with molar weight, dispersity, and compositional ratio. Complex spherical phases, including the Frank-Kasper phase (A15 and σ) and quasicrystalline phase, were experimentally captured by meticulously tuning the composition and architectures. A phase portrait with unprecedented accuracy was mapped out (up to one monomer resolution), unraveling intriguing details of phase behaviors that have long been compromised by inherent molecular weight distribution. This study serves as a delicate model system to bridge the existing gaps between experimental observations and theoretical assessments and to provide insights into the formation and evolution of the unconventional spherical phases in soft matter systems.

Which Wave Numbers Determine the Thermodynamic Stability of Soft Matter Quasicrystals?

For soft matter to form quasicrystals an important ingredient is to have two characteristic length scales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wave numbers should be favored, and the ratio of these wave numbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wave numbers can be involved, other wave numbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials that can suppress or encourage density modes with wave numbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.

Crystal Structures of α- and β-Nitrogen Trifluoride

The crystal structures of α-NF₃ and β-NF₃ are reported for the first time. As shown by powder neutron diffraction, the low-temperature α-NF₃ crystallizes in the orthorhombic space group Pnma ( oP16) with lattice parameters a = 6.71457(13) Å, b = 7.30913(14) Å, c = 4.55189(8) Å, V = 223.396(7) ų, and Z = 4 at T = 6 K. The intramolecular atom distances in α-NF₃ are 1.3639(16) and 1.3677(11) Å for N-F, and 2.1216(16) and 2.120(2) Å for F···F. The F-N-F bond angles are 101.92(7)° and 101.63(10)°. All data are in excellent agreement with quantum-chemical predictions and previously reported experimentally obtained gas-phase data. The high-temperature β-NF₃ is a plastic crystal, space group P4₂/ mnm ( tP120), with the lattice parameters a = 15.334(6) Å, c = 7.820(3) Å, V = 1838.6(12) ų, and Z = 30 at T = 60 K. Its crystal structure is closely related to that of the Frank-Kasper sigma phase.

Losing supramolecular orientational memory via self-organization of a misfolded secondary structure

Comparing the self-organization of two dendronized perylene bisimides reveals how structurally defective primary structure eliminates memory function via hierarchical self-organization.