Single crystals of purely organic free-standing two-dimensional woven polymer networks

The aesthetic and practicality of macroscopic fabrics continue to encourage chemists to weave molecules into interlaced patterns with the aim of providing emergent physical and chemical properties when compared with their starting materials. Weaving purely organic molecular threads into flawless two-dimensional patterns remains a formidable challenge, even though its feasibility has been proposed on several occasions. Herein we describe the synthesis of a flawless, purely organic, free-standing two-dimensional woven polymer network driven by dative B-N bonds. Single crystals of this woven polymer network were obtained and its well-defined woven topology was revealed by X-ray diffraction analysis. Free-standing two-dimensional monolayer nanosheets of the woven polymer network were exfoliated from the layered crystals using Scotch Magic Tape. The surface features of the nanosheets were investigated by integrated low-dose and cryogenic electron microscopy imaging techniques. These findings demonstrate the precise construction of purely organic woven polymer networks and highlight the unique opportunities for the application of woven topologies in two-dimensional organic materials.

Reticular Chemistry and In Situ "One-Pot" Strategy: A Dream Combination to Construct Metal-Organic Frameworks

The establishment of reticular chemistry has significantly facilitated the development of porous materials, especially for metal-organic frameworks (MOFs). On the other hand, as an alternative approach, in situ "one-pot" strategy has been explored as a promising approach to constructing MOFs, in which the synthesis of organic linkers and the sequential construction of MOFs are integrated into one solvothermal condition. This strategy can efficiently avoid the limitations faced in the traditional construction method, such as time-consuming organic synthesis and multiple separation and purification. Herein, inspired by the reaction of aldehydes and o-phenylenediamine and deep structural analysis of UiO-68, a series of tetra-, hexa-, and octa-topic carboxylic acids are synthesized using 2',3'-diamino-[1,1':4',1'"-terphenyl]-4,4'"-dicarboxylic acid and di-, tri-, and tetra-topic aldehydes as precursor. Then nine multicarboxylate-based zirconium MOFs (Zr-MOFs) are successfully constructed via the combination of reticular chemistry and in situ "one-pot" strategy. The resultant Zr-MOFs can be regarded as the partial face decoration of UiO-68. More importantly, the emission properties of resultant Zr-MOFs can be well controlled using aldehydes with tunable electronic structures. This work provides a new path to rational design and construction of porous materials with specific structures guided by reticular chemistry and conducted using in situ "one-pot" strategy.

From individuals to families: design and application of self-similar chiral nanomaterials

Establishing an intimate relationship between similar individuals is the beginning of self-extension. Various self-similar chiral nanomaterials can be designed using an individual-to-family approach, accomplishing self-extension. This self-similarity facilitates chiral communication, transmission, and amplification of synthons. We focus on describing the marriage of discrete cages to develop self-similar extended frameworks. The advantages of utilizing cage-based frameworks for chiral recognition, enantioseparation, chiral catalysis and sensing are highlighted. To further promote self-extension, fractal chiral nanomaterials with self-similar and iterated architectures have attracted tremendous attention. The beauty of a fractal family tree lies in its ability to capture the complexity and interconnectedness of a family's lineage. As a type of fractal material, nanoflowers possess an overarching importance in chiral amplification due to their large surface-to-volume ratio. This review summarizes the design and application of state-of-the-art self-similar chiral nanomaterials including cage-based extended frameworks, fractal nanomaterials, and nanoflowers. We hope this formation process from individuals to families will inherit and broaden this great chirality.

Reticular chemistry guided precise construction of zirconium-pentacarboxylate frameworks with 5-connected Zr6 clusters

Zirconium-based metal-organic frameworks (Zr-MOFs) have been extensively studied due to their very rich structural chemistry. The combination of nearly unlimited carboxylic acid-based linkers and Zr6 clusters with multiple connectivities has led to diverse structures and specific properties of resultant Zr-MOFs. Herein, we demonstrate the successful use of reticular chemistry to construct two novel Zr-MOFs, HIAM-4040 and HIAM-4040-OH, with zfu topology. Based on a thorough structural analysis of (4,4)-connected lvt-type Zr-tetracarboxylate frameworks and a judicious linker design, we have obtained the first example of a Zr-pentacarboxylate framework featuring unprecedented 5-connected organic linkers and 5-connected Zr6 clusters. Compared with HIAM-4040, a larger Stokes shift is achieved in HIAM-4040-OH via hydroxyl group induced excited-state intramolecular proton transfer (ESIPT). HIAM-4040-OH exhibits high chemical and thermal stability and is used for HClO detection in aqueous solution with excellent sensitivity and selectivity.

Assembly and Utility of a Drawstring-Mimetic Supramolecular Complex

Inspired by the drawstring structure in daily life, here we report the development of a drawstring-mimetic supramolecular complex at the molecular scale. This complex consists of a rigid figure-of-eight macrocyclic host molecule and a flexible linear guest molecule which could interact through three-point non-covalent binding to form a highly selective and efficient host-guest assembly. The complex not only resembles the drawstring structure, but also mimics the properties of a drawstring with regard to deformations under external forces. The supramolecular drawstring can be utilized as an interlocked crosslinker for poly(methyl acrylate), and the corresponding polymer samples exhibit comprehensive enhancement of macroscopic mechanical performance including stiffness, strength, and toughness.

Periodic Borromean rings, rods and chains

This article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2-periodic vertex-, edge- and ring-transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1- and 3-periodic ring-transitive (isonemal) families. A second isonemal 2-periodic family is identified, as is a unique 3-periodic Borromean assembly of equilateral triangles. Also reported is a notable 2-periodic structure comprising chains of linked rings in which the chains are locked in place but no two chains are directly interlinked, being held in place as a novel `quasi-Borromean' set of four repeating components.

Isogonal 2-periodic polycatenanes: chain mail

For 2-periodic polycatenanes with isogonal (vertex-transitive) embeddings, the basic units linked are torus knots and links including the unknots (untangled polygons). Twenty-four infinite families have been identified, with hexagonal, tetragonal or rectangular symmetry. The simplest members of each family are described and illustrated. A method for determining the catenation number of a ring based on electromagnetic theory is described.

Symmetry groups of two-way twofold and three-way threefold fabrics

This work discusses the symmetry groups of two classes of woven fabrics, two-way twofold fabrics and three-way threefold fabrics. A method to arrive at a design of a fabric is presented, employing methods in color symmetry theory. Geometric representations of all possible layer group or diperiodic symmetry structures of the fabrics are derived. There are 50 layer symmetry groups corresponding to two-way twofold fabrics and 27 layer symmetry groups corresponding to three-way threefold fabrics.

Recent Progress on Phase Engineering of Nanomaterials

As a key structural parameter, phase depicts the arrangement of atoms in materials. Normally, a nanomaterial exists in its thermodynamically stable crystal phase. With the development of nanotechnology, nanomaterials with unconventional crystal phases, which rarely exist in their bulk counterparts, or amorphous phase have been prepared using carefully controlled reaction conditions. Together these methods are beginning to enable phase engineering of nanomaterials (PEN), i.e., the synthesis of nanomaterials with unconventional phases and the transformation between different phases, to obtain desired properties and functions. This Review summarizes the research progress in the field of PEN. First, we present representative strategies for the direct synthesis of unconventional phases and modulation of phase transformation in diverse kinds of nanomaterials. We cover the synthesis of nanomaterials ranging from metal nanostructures such as Au, Ag, Cu, Pd, and Ru, and their alloys; metal oxides, borides, and carbides; to transition metal dichalcogenides (TMDs) and 2D layered materials. We review synthesis and growth methods ranging from wet-chemical reduction and seed-mediated epitaxial growth to chemical vapor deposition (CVD), high pressure phase transformation, and electron and ion-beam irradiation. After that, we summarize the significant influence of phase on the various properties of unconventional-phase nanomaterials. We also discuss the potential applications of the developed unconventional-phase nanomaterials in different areas including catalysis, electrochemical energy storage (batteries and supercapacitors), solar cells, optoelectronics, and sensing. Finally, we discuss existing challenges and future research directions in PEN.

Infinite Twisted Polycatenanes

Poly[n]catenanes have exceptional mechanical bonding properties that give them tremendous potential for use in the development of molecular machines and soft materials. Synthesizing these compounds has, however, proven to be a formidable challenge. Herein, we describe a concise method for the construction of twisted polycatenanes. Our approach involves using preorganized double helicates as templates, linked crosswise in a linear fashion by either silver ions or triple bonds. By using this approach, we successfully synthesized twisted polycatenanes with both coordination and covalent bonding employing Ag(I) ions and ethynylene units, respectively, as the linkages and leveraging the same Ag(I)-templated double helicate in both cases. Synthesis with Ag(I) ions formed a single-crystalline one-dimensional (1D) coordination poly[n]catenane, and synthesis using ethynylene units generated 1D fibers which self-assembled with solvents to form a gel. Our results confirm the potential of multi-stranded metallohelicates for creating sophisticated mechanically interlocked molecules and polymers, which could pave the way for exploration in the realms of molecular nanotopology and materials design.

Isogonal embeddings of interwoven and self-entangled honeycomb (hcb) nets and related interpenetrating primitive cubic (pcu) nets

Two- and three-periodic vertex-transitive (isogonal) piecewise-linear embeddings of self-entangled and interwoven honeycomb nets are described. The infinite families with trigonal symmetry and edge transitivity (isotoxal) are particularly interesting as they have the Borromean property that no two nets are directly linked. These also lead directly to infinite families of interpenetrating primitive cubic nets (pcu) that are also vertex- and edge-transitive and have embeddings with 90° angles between edges.

Woven, Polycatenated, or Cage Structures: Effect of Modulation of Ligand Curvature in Heteroleptic Uranyl Ion Complexes

Combining the flexible zwitterionic dicarboxylate 4,4'-bis(2-carboxylatoethyl)-4,4'-bipyridinium (L) and the anionic dicarboxylate ligands isophthalate (ipht^2-) and 1,2-, 1,3-, or 1,4-phenylenediacetate (1,2-, 1,3-, and 1,4-pda^2-), of varying shape and curvature, has allowed isolation of five uranyl ion complexes by synthesis under solvo-hydrothermal conditions. [(UO₂)₂(L)(ipht)₂] (1) and [(UO₂)₂(L)(1,2-pda)₂]·2H₂O (2) have the same stoichiometry, and both crystallize as monoperiodic coordination polymers containing two uranyl-(anionic carboxylate) strands united by L linkers into a wide ribbon, all ligands being in the divergent conformation. Complex 3, [(UO₂)₂(L)(1,3-pda)₂]·0.5CH₃CN, with the same stoichiometry but ligands in a convergent conformation, is a discrete, binuclear species which is the first example of a heteroleptic uranyl carboxylate coordination cage. With all ligands in a divergent conformation, [(UO₂)₂(L)(1,4-pda)(1,4-pdaH)₂] (4) crystallizes as a sinuous and thread-like monoperiodic polymer; two families of chains run along different directions and are woven into diperiodic layers. Modification of the synthetic conditions leads to [(UO₂)₄(LH)₂(1,4-pda)₅]·H₂O·2CH₃CN (5), a monoperiodic polymer based on tetranuclear (UO₂)₄(1,4-pda)₄ rings; intrachain hydrogen bonding of the terminal LH⁺ ligands results in diperiodic network formation through parallel polycatenation involving the tetranuclear rings and the LH⁺ rods. Complexes 1-3 and 5 are emissive, with complex 2 having the highest photoluminescence quantum yield (19%), and their spectra show the maxima positions usual for tris-κ²O,O'-chelated uranyl cations.

Suppressing Nonradiative Recombination by Electron-Donating Substituents in 2D Conjugated Triphenylamine Polymers toward Efficient Perovskite Optoelectronics

Highly efficient perovskite optoelectronics (POEs) have been limited by nonradiative recombination. We report a strategy to inhibit the nonradiative recombination of 2D triphenylamine polymers in the hole transport layer (HTL) via introducing electron-donating groups to enhance the conjugation effect and electron cloud density. The conjugated systems with electron-donating groups present smaller energy level oscillation compared to the ones with electron-absorbing groups, as confirmed by nonadiabatic molecular dynamics (NAMD) calculation. Further study reveals that the introduction of low-frequency phonons in the electron-donating group systems shortens the nonadiabatic coupling and inhibits the nonradiative recombination. Such electron-donating groups can decrease the valence band maximum of 2D polymers and promote hole transport. Our report provides a new design strategy to suppress nonradiative recombination in HTL for application in efficient POEs.

Woven Polymer Networks: From Crystalline to Elastomeric Materials

Weaving technology has been extensively used for manufacturing macroscopic fabrics and satisfying the artistic demands of humans through the ages. Integrating woven geometries into molecular structures is a persistent pursuit, and yet a significant challenge to chemists, owing to the lack of effective methodologies to guide the regular mutual interlacing of molecular strands. In this Concept article, recent progress and related strategies in constructing woven polymer networks (WPNs) are summarized and discussed. An outlook is then given to highlight the future opportunities and challenges in the development of both molecularly woven structures and molecularly woven functional materials.

Reticular Chemistry with Art: A Case Study of Olympic Rings-Inspired Metal-Organic Frameworks

Herein, we demonstrate the successful utilization of reticular chemistry as an excellent designing strategy for the deliberate construction of a zirconium-tetracarboxylate metal-organic framework (MOF) inspired by the Olympic rings. HIAM-4017, with an unprecedented (4,8)-c underlying net topology termed jcs, was developed via insightful reconstruction of the rings and judicious design of a nonsymmetric organic linker. HIAM-4017 exhibits high porosity and excellent chemical and thermal stability. Furthermore, excited-state intramolecular proton transfer (ESIPT) was achieved in an isoreticular MOF, HIAM-4018, with a large Stokes shift of 155 nm as a result of introducing the hydroxyl group to the linker skeleton to induce OH···N interactions. Such interactions were analyzed thoroughly by employing the time-dependent density functional theory (TD-DFT). Because of their good thermal and chemical stability, and strong luminescence, nanosized HIAM-4017 and HIAM-4018 were fabricated and used for Cr₂O₇^2- detection. Both MOFs demonstrate excellent sensitivity and selectivity. This work represents a neat example of building structure- and property-specific MOFs guided by reticular chemistry.

The Jones polynomial of collections of open curves in 3-space

Measuring the entanglement complexity of collections of open curves in 3-space has been an intractable, yet pressing mathematical problem, relevant to a plethora of physical systems, such as in polymers and biopolymers. In this manuscript, we give a novel definition of the Jones polynomial that generalizes the classic Jones polynomial to collections of open curves in 3-space. More precisely, first we provide a novel definition of the Jones polynomial of linkoids (open link diagrams) and show that this is a well-defined single variable polynomial that is a topological invariant, which, for link-type linkoids, coincides with that of the corresponding link. Using the framework introduced in (Panagiotou E, Kauffman L. 2020 Proc. R. Soc. A 476 , 20200124. (( doi:10.1098/rspa.2020.0124 )), this enables us to define the Jones polynomial of collections of open and closed curves in 3-space. For collections of open curves in 3-space, the Jones polynomial has real coefficients and it is a continuous function of the curves’ coordinates. As the endpoints of the curves tend to coincide, the Jones polynomial tends to that of the resultant link. We demonstrate with numerical examples that the novel Jones polynomial enables us to characterize the topological/geometrical complexity of collections of open curves in 3-space for the first time.

Piecewise-linear embeddings of decussate extended θ graphs and tetrahedra

An nθ graph is an n-valent graph with two vertices. From symmetry considerations, it has vertex–edge transitivity 1 1. Here, they are considered extended with divalent vertices added to the edges to explore the simplest piecewise-linear tangled embeddings with straight, non-intersecting edges (sticks). The simplest tangles found are those with 3n sticks, transitivity 2 2, and with 2⌊(n − 1)/2⌋ ambient-anisotopic tangles. The simplest finite and 1-, 2- and 3-periodic decussate structures (links and tangles) are described. These include finite cubic and icosahedral and 1- and 3-periodic links, all with minimal transitivity. The paper also presents the simplest tangles of extended tetrahedra and their linkages to form periodic polycatenanes. A vertex- and edge-transitive embedding of a tangled srs net with tangled and polycatenated θ graphs and vertex-transitive tangled diamond (dia) nets are described.

Soft 2D Covalent Organic Framework with Compacted Honeycomb Topology

In this contribution, we report the synthesis of an imine-based soft 2D covalent organic framework (S-COF) with compacted honeycomb topology via inveterately selecting a helically folded ditopic flexible linker and a trigonal building block. In contrast to various topological structures of rigid monomer-based COFs (R-COFs) reported so far, owing to the presence of flexible skeleton S-COF can spontaneously form a compacted and nonporous topological structure via intramolecular π stacking of presupposed honeycomb-like topology. Such S-COFs with a compacted honeycomb topology have neither been proposed theoretically nor been achieved experimentally. The compacted topological structure of 2D S-COF was clearly characterized by transmission electron microscopy (TEM), atomic force microscopy (AFM), powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), Fourier-transform infrared spectroscopy (FT-IR), and circular dichroism (CD) measurements. This study opens a new window to the development of S-COFs and will significantly expand the scope of COF materials.

Knotting matters: orderly molecular entanglements

Entangling strands in a well-ordered manner can produce useful effects, from shoelaces and fishing nets to brown paper packages tied up with strings. At the nanoscale, non-crystalline polymer chains of sufficient length and flexibility randomly form tangled mixtures containing open knots of different sizes, shapes and complexity. However, discrete molecular knots of precise topology can also be obtained by controlling the number, sequence and stereochemistry of strand crossings: orderly molecular entanglements. During the last decade, substantial progress in the nascent field of molecular nanotopology has been made, with general synthetic strategies and new knotting motifs introduced, along with insights into the properties and functions of ordered tangle sequences. Conformational restrictions imparted by knotting can induce allostery, strong and selective anion binding, catalytic activity, lead to effective chiral expression across length scales, binding modes in conformations efficacious for drug delivery, and facilitate mechanical function at the molecular level. As complex molecular topologies become increasingly synthetically accessible they have the potential to play a significant role in molecular and materials design strategies. We highlight particular examples of molecular knots to illustrate why these are a few of our favourite things.

Symmetric Tangling of Honeycomb Networks

Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.

The topology of crystalline matter

In this chapter an overview is given in which way framework-like crystalline compounds can be regarded as nets, how a net is derived out of a particular crystal structure, what nets actually are, how they can be appropriately described, what the characteristics of nets are, and how this topological approach helps to categorize framework compounds. Finally the term reticular chemistry is explained and a number of examples are given how the topology-guided approach opens up new possibilities to intentionally develop new framework structures on a rational basis.

Crystal structures

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Portable metal-organic framework alginate beads for high-sensitivity fluorescence detection and effective removal of residual pesticides in fruits and vegetables

Pesticides have been emerged as major organic pollutants in environment, owing to widely spread and intrinsic high toxicity in agricultural productivity. Herein, we designed and synthesized a practicability and portable metal-organic framework (MOF) based composite beads MOF-alginate-Ca²⁺-polyacrylic acid (kgd-M1@ACPs) consist of biocompatible host material (sodium alginate) and fluorescent center with blue emission (where kgd-M1 stands for {[Cd(tbia)·H₂O]·2H₂O}_n), which was further developed for high-efficiency and naked-eye 2,6-dichloro-4-nitroaniline (DCN) monitoring in fruits and vegetables. Significantly, the kgd-M1@ACPs shows obvious fluorescent quench towards toxic pesticide DCN with a low limit of detection (LOD) of 0.09 μM and high recovery from 98.08 to 104.37%. Moreover, the kgd-M1@ACPs also presents an excellent DCN adsorption ability. This work demonstrates that smart material kgd-M1@ACPs is expected to be a good candidate for detection and removal of DCN in real fruits and vegetables, which will present a broad prospect for monitoring and treating pesticides.

Self-Assembly of Molecular Trefoil Knots Featuring Pentadecanuclear Homoleptic AuI -, AuI /AgI -, or AuI /CuI -Alkynyl Coordination

Metal-free and metal-containing molecular trefoil knots are fascinating ensembles that are usually covalently assembled, the latter requiring the rational design of di- or multidentate/multipodal ligands as connectors. In this work, we describe the self-assembly of pentadecanuclear Au^I trefoil knots [Au₁₅ (C≡CR)₁₅ ] from monoalkynes HC≡CR (R=9,9-X₂ -fluorenyl with X=nBu, n-hexyl) and [Au^I (THT)Cl]. Hetero-bimetallic counterparts [Au₉ M₆ (C≡CR)₁₅ ] (M=Cu/Ag) were self-assembled by reactions of [Au₁₅ (C≡CR)₁₅ ] with [Cu(MeCN)₄ ]⁺ /AgNO₃ and HC≡CR. The type of pentadecanuclear trefoil knots described herein is characterized by X-ray crystallography, 2D NMR and HR-ESI-MS. [Au₉ Cu₆ (C≡CR)₁₅ ] is relatively stable in hexane; its excited state properties were investigated. DFT calculations revealed that non-covalent metal-metal and metal-ligand interactions, together with longer alkyl chain-strengthened inter-ligand dispersion interactions, govern the stability of the trefoil knot structures.

The Symmetry and Topology of Finite and Periodic Graphs and Their Embeddings in Three-Dimensional Euclidean Space

We make the case for the universal use of the Hermann-Mauguin (international) notation for the description of rigid-body symmetries in Euclidean space. We emphasize the importance of distinguishing between graphs and their embeddings and provide examples of 0-, 1-, 2-, and 3-periodic structures. Embeddings of graphs are given as piecewise linear with finite, non-intersecting edges. We call attention to problems of conflicting terminology when disciplines such as materials chemistry and mathematics collide.

Isogonal piecewise-linear embeddings of 1-periodic knots and links, and related 2-periodic chain-link and knitting patterns

Families of 1- and 2-periodic knots and weavings that have isogonal (vertex-transitive) piecewise-linear embeddings are described. In these structures there is just one thread, or multiple threads with parallel or collinear axes. The principal structures are a large family of 1-periodic knots and related multi-thread infinite links, knitting patterns and chain-link weaving. The relevance to synthetic chemistry is described in terms of targets for designed synthesis such as mechanically interlocked polymers.

Porous covalent organic nanotubes and their assembly in loops and toroids

Carbon nanotubes, and synthetic organic nanotubes more generally, have in recent decades been widely explored for application in electronic devices, energy storage, catalysis and biosensors. Despite noteworthy progress made in the synthesis of nanotubular architectures with well-defined lengths and diameters, purely covalently bonded organic nanotubes have remained somewhat challenging to prepare. Here we report the synthesis of covalently bonded porous organic nanotubes (CONTs) by Schiff base reaction between a tetratopic amine-functionalized triptycene and a linear dialdehyde. The spatial orientation of the functional groups promotes the growth of the framework in one dimension, and the strong covalent bonds between carbon, nitrogen and oxygen impart the resulting CONTs with high thermal and chemical stability. Upon ultrasonication, the CONTs form intertwined structures that go on to coil and form toroidal superstructures. Computational studies give some insight into the effect of the solvent in this assembly process.

Molecular weaving

Historically, the interlacing of strands at the molecular level has mainly been limited to coordination polymers and DNA. Despite being proposed on a number of occasions, the direct, bottom-up assembly of molecular building blocks into woven organic polymers remained an aspirational, but elusive, target for several decades. However, recent successes in two-dimensional and three-dimensional molecular-level weaving now offer new opportunities and research directions at the interface of polymer science and molecular nanotopology. This Perspective provides an overview of the features and potential of the periodic nanoscale weaving of polymer chains, distinguishing it from randomly entangled polymer networks and rigid crystalline frameworks. We review the background and experimental progress so far, and conclude by considering the potential of molecular weaving and outline some of the current and future challenges in this emerging field.

Tangled piecewise-linear embeddings of trivalent graphs

A method is described for generating and exploring tangled piecewise-linear embeddings of trivalent graphs under the constraints of point-group symmetry. It is shown that the possible vertex-transitive tangles are either graphs of vertex-transitive polyhedra or bipartite vertex-transitive nonplanar graphs. One tangle is found for 6 vertices, three for 8 vertices (tangled cubes), seven for 10 vertices, and 21 for 12 vertices. Also described are four isogonal embeddings of pairs of cubes and 12 triplets of tangled cubes (16 and 24 vertices, respectively). Vertex 2-transitive embeddings are obtained for tangled trivalent graphs with 6 vertices (two found) and 8 vertices (45 found). Symmetrical tangles of the 10-vertex Petersen graph and the 20-vertex Desargues graph are also described. Extensions to periodic tangles are indicated. These are all interesting and viable targets for molecular synthesis.

Symmetric tangled Platonic polyhedra

Tangled tetrahedra, octahedra, cubes, icosahedra, and dodecahedra are generalizations of classical—untangled—Platonic polyhedra. Like the Platonic polyhedra, all vertices, edges, and faces are symmetrically equivalent. However, the edges of tangled polyhedra are curvilinear, or kinked, to allow entanglement, much like warps and wefts in woven fabrics. We construct the most symmetric entanglements of these polyhedra via assemblies of multistrand helices wound around edges of the conventional polyhedra; they are all necessarily chiral. The construction gives self-entangled chiral polyhedra and compound polyhedra containing catenated multiple tetrahedra or “generalized θ-polyhedra.” An unlimited variety of tangling is possible for any given topology. Related structures have been observed in synthetic materials and clathrin assemblies within cells.

Conventional embeddings of the edge-graphs of Platonic polyhedra, {f, z}, where f, z denote the number of edges in each face and the edge-valence at each vertex, respectively, are untangled in that they can be placed on a sphere (S2) such that distinct edges do not intersect, analogous to unknotted loops, which allow crossing-free drawings of S1 on the sphere. The most symmetric (flag-transitive) realizations of those polyhedral graphs are those of the classical Platonic polyhedra, whose symmetries are *2fz, according to Conway’s two-dimensional (2D) orbifold notation (equivalent to Schönflies symbols I_h, O_h, and T_d). Tangled Platonic {f, z} polyhedra—which cannot lie on the sphere without edge-crossings—are constructed as windings of helices with three, five, seven,… strands on multigenus surfaces formed by tubifying the edges of conventional Platonic polyhedra, have (chiral) symmetries 2fz (I, O, and T), whose vertices, edges, and faces are symmetrically identical, realized with two flags. The analysis extends to the “θ_z” polyhedra, {2,z}. The vertices of these symmetric tangled polyhedra overlap with those of the Platonic polyhedra; however, their helicity requires curvilinear (or kinked) edges in all but one case. We show that these 2fz polyhedral tangles are maximally symmetric; more symmetric embeddings are necessarily untangled. On one hand, their topologies are very constrained: They are either self-entangled graphs (analogous to knots) or mutually catenated entangled compound polyhedra (analogous to links). On the other hand, an endless variety of entanglements can be realized for each topology. Simpler examples resemble patterns observed in synthetic organometallic materials and clathrin coats in vivo.

Two-Dimensional Polymers and Polymerizations

Synthetic chemists have developed robust methods to synthesize discrete molecules, linear and branched polymers, and disordered cross-linked networks. However, two-dimensional polymers (2DPs) prepared from designed monomers have been long missing from these capabilities, both as objects of chemical synthesis and in nature. Recently, new polymerization strategies and characterization methods have enabled the unambiguous realization of covalently linked macromolecular sheets. Here we review 2DPs and 2D polymerization methods. Three predominant 2D polymerization strategies have emerged to date, which produce 2DPs either as monolayers or multilayer assemblies. We discuss the fundamental understanding and scope of each of these approaches, including: the bond-forming reactions used, the synthetic diversity of 2DPs prepared, their multilayer stacking behaviors, nanoscale and mesoscale structures, and macroscale morphologies. Additionally, we describe the analytical tools currently available to characterize 2DPs in their various isolated forms. Finally, we review emergent 2DP properties and the potential applications of planar macromolecules. Throughout, we highlight achievements in 2D polymerization and identify opportunities for continued study.

Robust recognition and exploratory analysis of crystal structures via Bayesian deep learning

Due to their ability to recognize complex patterns, neural networks can drive a paradigm shift in the analysis of materials science data. Here, we introduce ARISE, a crystal-structure identification method based on Bayesian deep learning. As a major step forward, ARISE is robust to structural noise and can treat more than 100 crystal structures, a number that can be extended on demand. While being trained on ideal structures only, ARISE correctly characterizes strongly perturbed single- and polycrystalline systems, from both synthetic and experimental resources. The probabilistic nature of the Bayesian-deep-learning model allows to obtain principled uncertainty estimates, which are found to be correlated with crystalline order of metallic nanoparticles in electron tomography experiments. Applying unsupervised learning to the internal neural-network representations reveals grain boundaries and (unapparent) structural regions sharing easily interpretable geometrical properties. This work enables the hitherto hindered analysis of noisy atomic structural data from computations or experiments.

Smooth Triaxial Weaving with Naturally Curved Ribbons

Triaxial weaving is a handicraft technique that has long been used to create curved structures using initially straight and flat ribbons. Weavers typically introduce discrete topological defects to produce nonzero Gaussian curvature, albeit with faceted surfaces. We demonstrate that, by tuning the in-plane curvature of the ribbons, the integrated Gaussian curvature of the weave can be varied continuously, which is not feasible using traditional techniques. Further, we reveal that the shape of the physical unit cells is dictated solely by the in-plane geometry of the ribbons, not elasticity. Finally, we leverage the geometry-driven nature of triaxial weaving to design a set of ribbon profiles to weave smooth spherical, ellipsoidal, and toroidal structures.

Piecewise-linear embeddings of knots and links with rotoinversion symmetry

This article describes the simplest members of an infinite family of knots and links that have achiral piecewise-linear embeddings in which linear segments (sticks) meet at corners. The structures described are all corner- and stick-2-transitive - the smallest possible for achiral knots.

On Borromean links and related structures

The creation of knotted, woven and linked molecular structures is an exciting and growing field in synthetic chemistry. Presented here is a description of an extended family of structures related to the classical `Borromean rings', in which no two rings are directly linked. These structures may serve as templates for the designed synthesis of Borromean polycatenanes. Links of n components in which no two are directly linked are termed `n-Borromean' [Liang & Mislow (1994). J. Math. Chem. 16, 27-35]. In the classic Borromean rings the components are three rings (closed loops). More generally, they may be a finite number of periodic objects such as graphs (nets), or sets of strings related by translations as in periodic chain mail. It has been shown [Chamberland & Herman (2015). Math. Intelligencer, 37, 20-25] that the linking patterns can be described by complete directed graphs (known as tournaments) and those up to 13 vertices that are vertex-transitive are enumerated. In turn, these lead to ring-transitive (isonemal) n-Borromean rings. Optimal piecewise-linear embeddings of such structures are given in their highest-symmetry point groups. In particular, isonemal embeddings with rotoinversion symmetry are described for three, five, six, seven, nine, ten, 11, 13 and 14 rings. Piecewise-linear embeddings are also given of isonemal 1- and 2-periodic polycatenanes (chains and chain mail) in their highest-symmetry setting. Also the linking of n-Borromean sets of interleaved honeycomb nets is described.

Different Phenomena in Magnetic/Electrical Properties of Co(II) and Ni(II) Isomorphous MOFs

Two unprecedented and stable metal-organic frameworks, {[Co₂(H₂O)₂(L)(OH)]·2.5H₂O·0.5DMF} _n (1) and {[Ni₂(H₂O)₂(L)(OH)]·1.75H₂O} _n (2), have been synthesized (H₃L = 5-(5-carboxy-pyridin-3-yloxy)-isophthalic acid, DMF = N,N-dimethylformamide). Structural analysis shows that 1 and 2 are heteronuclear isomorphous, possessing a three-dimensional (3D) (4,8)-connected flu/fluorite topological framework formed through the interconnection of tetranuclear butterfly {M₄(COO)₆(OH)₂} clusters and the ligands. Although the frameworks of these two compounds are similar, their magnetic properties are different. Compound 1 exhibits an antiferromagnetic interaction in the high-temperature region, while 2 shows a weak ferromagnetic interaction in the whole-temperature region. Furthermore, considering the presence of hydroxyl groups and water molecules in the frameworks, we tested their proton conductivity. The efficient proton transfer pathway in the framework endowed 1 and 2 with excellent proton conductivities of 9.07 × 10^-5 and 1.29 × 10^-4 S·cm^-1 at 363 K and 98% relative humidity (RH), respectively.

Isogonal piecewise linear embeddings of 1-periodic weaves and some related structures

Crystallographic descriptions of isogonal piecewise linear embeddings of 1-periodic weaves and links (chains) are presented. These are composed of straight segments (sticks) that meet at corners (2-valent vertices). Descriptions are also given of some plaits - woven periodic bands, three simple periodic knots and isogonal interwoven rods.

Synthetic multi-layer nanoparticles for CRISPR-Cas9 genome editing

The clustered regularly interspaced short palindromic repeat (CRISPR) has great potential to revolutionize biomedical research and disease therapy. The specific and efficient genome editing strongly depends on high efficiency of delivery of the CRISPR payloads. However, optimization of CRISPR delivery vehicles still remains a major obstacle. Recently, various non-viral vectors have been utilized to deliver CRISPR tools. Many of these vectors have multi-layer structures assembled. In this review, we will introduce the development of CRISPR-Cas9 systems and their general therapeutic applications by summarizing current CRISPR-Cas9 based clinical trials. We will highlight the multi-layer nanoparticles (NPs) that have been developed to deliver CRISPR cargos in vitro and in vivo for various purposes, as well the potential building blocks of multi-layer NPs. We will also discuss the challenges in making the CRISPR tools into viable pharmaceutical products and provide potential solutions on efficiency and biosafety issues.

Recent progress in the design and synthesis of zeolite-like metal–organic frameworks (ZMOFs)

ZMOFs are a subset of MOFs that exhibit zeolite-like topologies. Using molecular building block strategy, many ZMOFs with high stability and excellent performance can be rationally designed and synthesized using different secondary building units.

Reticular Chemistry in the Construction of Porous Organic Cages

Reticular chemistry offers the possibility of systematic design of porous materials with different pores by varying the building blocks, while the emerging porous organic cage (POC) system remains generally unexplored. A series of new POCs with dimeric cages with odd-even behaviors, unprecedented trimeric triangular prisms, and the largest recorded hexameric octahedra have been prepared. These POCs are all constructed from the same tetratopic tetraformylresorcin[4]arene cavitand by simply varying the diamine ligands through Schiff-base reactions and are fully characterized by X-ray crystallography, gas sorption measurements, NMR spectroscopy, and mass spectrometry. The odd-even effects in the POC conformation changes of the [2 + 4] dimeric cages have been confirmed by density functional theory calculations, which are the first examples of odd-even effects reported in the cavitand-based cage system. Moreover, the "V" shape phenylenediamine linkers are responsible for the novel [3 + 6] triangular prisms. The window size and environment can be easily functionalized by different groups, providing a promising platform for the construction of multivariate POCs. Use of linear phenylenediamines led to record-breakingly large [6 + 12] truncated octahedral cages, the maximum inner cavity diameters and volumes of which could be readily modulated by increasing the spacer length of the phenylenediamine linkers. This work can lead to an understanding of the self-assembly behaviors of POCs and also sheds light on the rational design of POC materials for practical applications.