The chromatic number of random Borsuk graphs

We study a model of random graph where vertices are n i.i.d. uniform random points on the unit sphere S^d in , and a pair of vertices is connected if the Euclidean distance between them is at least 2??. We are interested in the chromatic number of this graph as n tends to infinity. It is not too hard to see that if ?>0 is small and fixed, then the chromatic number is d+2 with high probability. We show that this holds even if ?→0 slowly enough. We quantify the rate at which ? can tend to zero and still have the same chromatic number. The proof depends on combining topological methods (namely the Lyusternik–Schnirelman–Borsuk theorem) with geometric probability arguments. The rate we obtain is best possible, up to a constant factor—if ?→0 faster than this, we show that the graph is (d+1)‐colorable with high probability.25     

Controlling the Length of Cooperative Supramolecular Polymers with Chain Cappers

The design and the characterization of supramolecular additives to control the chain length of benzene-1,3,5-tricarboxamide (BTA) cooperative supramolecular polymers under thermodynamic equilibrium is unraveled. These additives act as chain cappers of supramolecular polymers and feature one face as reactive as the BTA discotic to interact strongly with the polymer end, whereas the other face is nonreactive and therefore impedes further polymerization. Such a design requires fine tuning of the conformational preorganization of the amides and the steric hindrance of the motif. The chain cappers studied are monotopic derivatives of BTA, modified by partial N-methylation of the amides or by positioning of a bulky cyclotriveratrylene cage on one face of the BTA unit. This study not only clarifies the interplay between structural variations and supramolecular interactions, but it also highlights the necessity to combine orthogonal characterization methods, spectroscopy and light scattering, to elucidate the structures and compositions of supramolecular systems.     

Direct Synthesis of Peptide-Containing Silicones: A New Way to Bioactive Materials

A simple and efficient way to synthesize peptide-containing silicone materials is described. Silicone oils containing a chosen ratio of bioactive peptide sequences were prepared by acid-catalyzed copolymerization of dichlorodimethylsilane, hybrid dichloromethyl peptidosilane, and Si(vinyl)- or SiH-functionalized monomers. Functionalized silicone oils were first obtained and then, after hydrosilylation cross-linking, bioactive polydimethylsiloxane (PDMS)-based materials were straightforwardly obtained. The introduction of an antibacterial peptide yielded PDMS materials showing activity against Staphylococcus aureus. PDMS containing RGD ligands showed improved cell-adhesion properties. This generic method was fully compatible with the stability of peptides and thus opened the way to the synthesis of a wide range of biologically active silicones.     

Single‐Site Zeolite‐Anchored Organoiridium Carbonyl Complexes: Characterization of Structure and Reactivity by Spectroscopy and Computational Chemistry

A family of HY zeolite‐supported cationic organoiridium carbonyl complexes was formed by reaction of Ir(CO)₂(acac) (acac=acetylacetonate) to form supported Ir(CO)₂ complexes, which were treated at 298 K and 1 atm with flowing gas‐phase reactants, including C₂H₄, H₂, ¹²CO, ¹³CO, and D₂O. Mass spectrometry was used to identify effluent gases, and infrared and X‐ray absorption spectroscopies were used to characterize the supported species, with the results bolstered by DFT calculations. Because the support is crystalline and presents a nearly uniform array of bonding sites for the iridium species, these were characterized by a high degree of uniformity, which allowed a precise determination of the species involved in the replacement, for example, of one CO ligand of each Ir(CO)₂ complex with ethylene. The supported species include the following: Ir(CO)₂, Ir(CO)(C₂H₄)₂, Ir(CO)(C₂H₄), Ir(CO)(C₂H₅), and (tentatively) Ir(CO)(H). The data determine a reaction network involving all of these species.     

Click Chemistry Mediated Functionalization of Vertical Nanowires for Biological Applications

Semiconductor nanowires (NWs) are gaining significant importance in various biological applications, such as biosensing and drug delivery. Efficient and controlled immobilization of biomolecules on the NW surface is crucial for many of these applications. Here, we present for the first time the use of the Cu^I‐catalyzed alkyne–azide cycloaddition and its strain‐promoted variant for the covalent functionalization of vertical NWs with peptides and proteins. The potential of the approach was demonstrated in two complementary applications of measuring enzyme activity and protein binding, which is of general interest for biological studies. The attachment of a peptide substrate provided NW arrays for the detection of protease activity. In addition, green fluorescent protein was immobilized in a site‐specific manner and recognized by antibody binding to demonstrate the proof‐of‐concept for the use of covalently modified NWs for diagnostic purposes using minute amounts of material.     

Insights into the Complexity of Weak Intermolecular Interactions Interfering in Host–Guest Systems

The recognition properties of heteroditopic hemicryptophane hosts towards anions, cations, and neutral pairs, combining both cation–π and anion–π interaction sites, were investigated to probe the complexity of interfering weak intermolecular interactions. It is suggested from NMR experiments, and supported by CASSCF/CASPT2 calculations, that the binding constants of anions can be modulated by a factor of up to 100 by varying the fluorination sites on the electron‐poor aromatic rings. Interestingly, this subtle chemical modification can also reverse the sign of cooperativity in ion‐pair recognition. Wavefunction calculations highlight how short‐ and long‐range interactions interfere in this recognition process, suggesting that a disruption of anion–π interactions can occur in the presence of a co‐bound cation. Such molecules can be viewed as prototypes for examining complex processes controlled by the competition of weak interactions.     

Thermal transformations up to 1200 °C of Al-pillared montmorillonite precursors prepared by different OH–Al polymers

Aluminum-pillared montmorillonites are useful materials for their application as catalysts, adsorbents and ceramic composites. The precursor is a pillared montmorillonite that is not thermally stabilized. The precursor preparation methods, textural properties and catalytic activity have been extensively investigated, but comparatively, studies concerning their thermal transformations at high temperature are limited. In this work, precursors were prepared using two types of montmorillonites, Cheto (Ch) and Wyoming (W), and using two different OH–Al polymer sources: hydrolyzed (H) and commercial (C) solutions. Structural and thermal transformations of the precursors with heating up to 1200 °C were determined by X-ray diffraction and thermogravimetric analysis. Thermal analysis of these precursors below 600 °C revealed the influence of OH–Al polymers from the two solutions. The major phases developed at 1200 °C from the original montmorillonites were mullite for W and cordierite for Ch. The content of these phases depended on the aluminum in the octahedral sheet of the pristine montmorillonites. Amorphous phase, cristobalite, spinel, sapphirine and others phases were also found. The intercalation of OH–Al polymers in montmorillonites caused an increase in amorphous content after treatment at 1030 °C; however, it favored mullite development above 1100 °C. Although total aluminum content of both W and Ch precursors was similar, the transformation to mullite was directly related to the octahedral aluminum/magnesium ratio. The phase composition of the products at 1200 °C was not dependent on the type of intercalated OH–Al polymers. The increase in mullite content of the thermally treated precursors contributes to its possible application as advanced ceramic products.     

Reversibly self-assembled pH-responsive PEG-p(CL-g-TMC) polymersomes

Polymersomes have gained much interest within the biomedical field as drug delivery systems due to their ability to transport and protect cargo from the harsh environment inside the body. For an improved drug efficacy, control over cargo release is however also an important factor to take into account. An often employed method is to incorporate pH sensitive groups in the vesicle membrane, which induce disassembly and content release when the particles have reached a target site in the body with the appropriate pH, such as the acidic microenvironment of tumor tissue or the endosome. In this paper, biodegradable poly(ethylene glycol)-poly(caprolactone-gradient-trimethylene carbonate)-based polymeric vesicles have been developed with disassembly features at mild acidic conditions. Modifying the polymer backbone with imidazole moieties results in vesicle disassembly upon protonation due to the lowered pH. Furthermore, upon increasing the pH efficient re-assembly into vesicles is observed due to the switchable amphiphilic nature of the polymer. When this re-assembly process is conducted in presence of cargo, enhanced encapsulation is achieved. Furthermore, the potency of the polymeric system for future biomedical applications such as adjuvant delivery is demonstrated.