The Connes-Kreimer Hopf algebra of rooted trees is an operated Hopf algebra whose coproduct satisfies the classical Hochschild 1-cocycle condition. In this paper, we extend the setting from rooted trees to the space H_ RT(X,Ω) of (X,Ω)-rooted trees, in which internal vertices are decorated by a set Ω and leafs are decorated by X ∪ Ω. We introduce a new coalgebra structure on H_ RT(X,Ω) whose coproduct satisfies a weighted Hochschild 1-cocycle condition involving multiple operators, thereby generalizing the classical condition. A combinatorial interpretation of this coproduct is also provided. We then endow H_ RT(X,Ω) with a Hopf algebra structure. Finally, we define weighted Ω-cocycle Hopf algebras, characterized by a Hochschild 1-cocycle condition with weights, and show that H_ RT(X,Ω) is the free object in the category of Ω-cocycle Hopf algebras.

We report the facile and one-pot synthesis of a series of arene-bridged oligopyrrolic dialdehydes that enable new macrocycle construction.

Macrocycle-to-macrocycle interconversions are of interest because they can allow access to a variety of structures. However, reversible interconversion between different sized macrocycles remains challenging to control. Herein, we report a facile one-pot synthesis of a series of self-assembled macrocycles from readily prepared α,α'-linked oligopyrrolic dialdehydes and various alkyl diamines. The condensation of pyridine-bridged oligopyrrolic dialdehyde 3 and simple alkyl diamines proved independent of solvent, always yielding the [2 + 2] macrocyclic products. However, when 3 was condensed with 2,2'-oxybis(ethylamine) 14, either ([1 + 1] or [2 + 2]) products are obtained depending on the choice of solvent. Reaction of 3 and 14 in methanol, ethanol, or chloroform gave the [1 + 1] macrocycle as the sole product. In contrast, condensation of 3 and 14 in dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), or acetonitrile (MeCN) yielded the [2 + 2] macrocycle as the major product in the form of a precipitate. Reversible interconversion between the [1 + 1] and [2 + 2] macrocycles could be achieved by tuning the solvent, with the ratio driven by thermodynamic and solubility considerations.

Since the discovery of single‐layer graphene in 2004, the family of 2D inorganic nanosheets is considered as ideal membrane materials due to their ultrathin atomic thickness and fascinating physicochemical properties. However, the intrinsically nonporous feature of 2D inorganic nanosheets hinders their potential to achieve a higher flux to some extent. Recently, 2D polymer nanosheets, originated from the regular and periodic covalent connection of the building units in 2D plane, have emerged as promising candidates for preparing ultrafast and highly selective membranes owing to their inherently tunable and ordered pore structure, light weight, and high specific surface. In this review, the synthetic methodologies (including top–down and bottom–up methods) of 2D polymer nanosheets are first introduced, followed by the summary of 2D polymer nanosheets‐based membrane fabrication as well as membrane applications in the fields of gas separation, water purification, organic solvent separation, and ion exchange/transport in fuel cells and lithium‐sulfur batteries. Finally, based on their current achievements, the authors’ personal insights are put forward into the existing challenges and future research directions of 2D polymer nanosheets for membrane separation. The authors believe this comprehensive review on 2D polymer nanosheets‐based membrane separation will definitely inspire more studies in this field.

We report a fully organic pyridine-tetrapyrrolic U-shaped acyclic receptor 10, which prefers a supramolecular pseudo-macrocyclic dimeric structure (10)2 in a less polar, non-coordinating solvent (e.g., CHCl3). Conversely, when it is crystalized from a polar, coordinating solvent (e.g., N,N-dimethylformamide, DMF), it exhibited an infinite supramolecular one-dimensional (1D) “zig-zag” polymeric chain, as inferred from the single-crystal X-ray structures. This supramolecular system acts as a potential receptor for strong acids, e.g., p-toluenesulfonic acid (PTSA), methane sulfonic acid (MSA), H2SO4, HNO3, and HCl, with a prominent colorimetric response from pale yellow to deep red. The receptor can easily be recovered from the organic solution of the host–guest complex by simple aqueous washing. It was observed that relatively stronger acids with pKa < −1.92 in water were able to interact with the receptor, as inferred from 1H NMR titration in tetrahydrofuran-d8 (THF-d8) and ultraviolet–visible (UV–vis) spectroscopic titrations in anhydrous THF at 298 K. Therefore, this new dynamic supramolecular receptor system may have potentiality in materials science research.

We report here a fully organic, self-assembled dimeric receptor, constructed from acyclic naphthyridylpolypyrrolic building block. The cage-like dimer is stable in the solid state, in solution, and in gas phase, as inferred from X-ray diffraction, and spectroscopic analyses. This system acts as a receptor for oxalic acid, maleic acid, and malonic acid in the solid state and in THF solution. In contrast, acetic acid, propionic acid, adipic acid and succinic acid, with pKa values  ca. 2.8, were not bound effectively within the cage-like cavity. It is speculated that oxalic acid, maleic acid, and malonic acid serve to proto-nate the naphthyridine moieties of the host, which then favors binding of the corresponding carboxylate anions via hydrogen-bonding to the pyrrolic NH protons. The present naphthyridinepolypyrrole dimer is stable under acidic conditions, includ-ing in the presence of 100 equiv trifluoroacetic acid (TFA), para-toluenesulfonic acid (PTSA), H2SO4, and HCl. However, disassembly may be achieved by exposure to tetrabutylammonium fluoride (TBAF). Washing with water then regenerates the cage. This process of assembly and disassembly could be repeated ≥20 times with little evidence of degradation. The reversible nature of the present system, coupled with its dicarboxylic acid recognition features, leads us to suggest it could have a role to play in effecting the controlled 'capture' and 'release' of biologically relevant dicarboxylic acids.

Presented here is the synthesis of three new Schiff-base cryptands, 4–6. Dynamic covalent imine bond formation via the condensation of a dialdehyde (7 or 8) with two different tris-amines allowed for the preparation of 4–6 in 84%, 80% and 83% yield, respectively. These systems were characterized by NMR spectroscopy, mass spectra, and, in the case of 5, single crystal X-ray diffraction analysis. These cages act as selective CO[Formula: see text] gas adsorbing materials in the solid state.

Two cryptand-like, shape persistent [2+3] imine cages (1 and 2) derived from oligopyrrolic precursors (diformyl dipyrrylpyridine 3 and diformyl bipyrrole 4) were prepared. These cages contain open cavities as inferred from solid state structural analyses and act as selective CO2 gas adsorbing materials in the solid state.

An air-stable N, N'-dihydroporphycene, the two-electron reduced form of porphycene, possessing two quinoxaline moieties fused at meso positions, was prepared and characterized. Nuclear magnetic resonance (NMR) and ultraviolet-visible light (UV-vis) spectroscopic studies and single-crystal X-ray diffraction analyses support its formulation as a nonaromatic species. Upon treatment with tetrabutylammonium fluoride (TBAF) in chloroform, a color change is produced that is consistent with deprotonation. Selective detection of this anion is readily achieved.

Water dispersible polyisocyanate compounds consisting of polyisocyanate and poly(dimethylsiloxane) as hydrophobic chain and polyglycol as hydrophilic chain were designed and synthesized according to polymer self-assembly theory. Polyglycol with controlled hydroxyl number was prepared with octamethylcyclotetrasiloxane and polyglycol monomethyl ether beforehand and then amphipathic polyisocyanate was synthesized with certain NCO/OH proportion. Also examined was how colloidization was influenced by the proportion of hydrophilicity and hydrophobicity.