Fabrication of Microporous Metal–Organic Frameworks in Uninterrupted Mesoporous Tunnels: Hierarchical Structure for Efficient Trypsin Immobilization and Stabilization

Hierarchically porous metal–organic frameworks (HP-MOFs) are promising in various applications. Most reported HP-MOFs are prepared based on the generation of mesopores in microporous frameworks, and the formed mesopores are connected by microporous channels, limiting the accessibility of mesopores for bulky molecules. A hierarchical structure is formed by constructing microporous MOFs in uninterrupted mesoporous tunnels. Using the confined space in as-prepared mesoporous silica, highly dispersed metal precursors for MOFs are coated on the internal surface of mesoporous tunnels. Ligand vapor-induced crystallization is employed to enable quantitative formation of MOFs in situ, in which sublimated ligands diffuse into mesoporous tunnels and react with metal precursors. The obtained hierarchically porous composites exhibit record-high adsorption capacity for the bulky molecule trypsin. The thermal and storage stability of trypsin is improved upon immobilization on the composites.     

Synthesis of Small‐Sized,Porous, and Low‐Toxic Magnetite Nanoparticles by Thin POSS Silica Coating

In this communication, we report the synthesis of small‐sized (<10 nm), water‐soluble, magnetic nanoparticles (MNPs) coated with polyhedral oligomeric silsesquioxanes (POSS), which contain either polyethylene glycol (PEG) or octa(tetramethylammonium) (OctaTMA) as functional groups. The POSS‐coated MNPs exhibit superparamagnetic behavior with saturation magnetic moments (51–53 emu g^?1) comparable to silica‐coated MNPs. They also provide good colloidal stability at different pH and salt concentrations, and low cytotoxicity to MCF‐7 human breast epithelial cells. The relaxivity data and magnetic resonance (MR) phantom images demonstrate the potential application of these MNPs in bioimaging.     

Close‐Packed Two‐Dimensional Silver Nanoparticle Arrays: Quadrupolar and Dipolar Surface Plasmon Resonance Coupling

Silver nanoparticles (NPs) ranging in size from 40 to 100 nm were prepared in high yield by using an improved seed‐mediated method. The homogeneous Ag NPs were used as building blocks for 2D assembled Ag NP arrays by using an oil/water interface. A close‐packed 2D array of Ag NPs was fabricated by using packing molecules (3‐mercaptopropyltrimethoxysilane) to control the interparticle spacing. The homogeneous 2D Ag NP array exhibited a strong quadrupolar cooperative plasmon mode resonance and a dipolar red‐shift relative to individual Ag NPs suspended in solution. A well‐arranged 2D Ag NP array was embedded in polydimethylsiloxane film and, with biaxial stretching to control the interparticle distance, concomitant variations of the quadrupolar and dipolar couplings were observed. As the interparticle distance increased, the intensity of the quadrupolar cooperative plasmon mode resonance decreased and dipolar coupling completely disappeared. The local electric field of the 2D Ag NP array was calculated by using finite difference time domain simulation and qualitatively showed agreement with the experimental measurements.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.