Tuning the photocatalytic activity of CdS nanocrystals through intermolecular interactions in ionic-liquid solvent systems

Synthetic solvent systems for the fine-tuned preparation of CdS nanocrystallites, active in visible-light photocatalytic hydrogen production, were studied. To control crystallite size and spectral properties, the CdS crystals were synthesised by using different solvent systems, containing a series of tetrabutylammonium amino carboxylate ionic liquids as the crystal-growth control agents. Six samples of CdS, all with similar physical and spectral properties, exhibited greatly varying photocatalytic activity, with the most active sample outperforming the least active one by almost 60%. To rationalise this effect, the intermolecular interactions of the synthesis solvent system with the growing CdS nanocrystallites were characterised by using the Reichart betaine dye and the E(T)(N) polarity scale. A correlation was observed between the E(T)(N) values of the solvent system and the photocatalytic activity of the CdS nanocrystallite, suggesting that the hydrogen-bond-donating ability and/or dipolarity/polarisability interactions of the solvent system led to the preferential formation of active surfaces/surface sites on the CdS crystals.     

Generation of (nonafluoro-tert-butoxy)methyl ponytails for enhanced fluorous partition of aromatics and heterocycles

The reaction of sodium perfluoro-tert-butoxide with benzylic carbon-bromide bond(s) leads to the formation of (nonafluoro-tert-butoxy)methyl ponytail(s), which can enhance the fluorous solubility and partition of aromatics and heterocycles.     

The near edge structure of cubic boron nitride

We compare the near edge structure (NES) of cubic boron nitride (cBN) measured using both electron energy loss spectroscopy (EELS) and X-ray absorption spectroscopy (XAS) with that calculated using three commonly used theoretical approaches. The boron and nitrogen K-edges collected using EELS and XAS from cBN powder were found to be nearly identical. These experimental edges were compared to calculations obtained using an all-electron density functional theory code (WIEN2k), a pseudopotential density functional theory code (CASTEP) and a multiple scattering code (FEFF). All three codes were found to reproduce the major features in the NES for both ionisation edges when a core-hole was included in the calculations. A partial core hole (1/2 of a 1s electron) was found to be essential for correctly reproducing features near the edge threshold in the nitrogen K-edge and to correctly obtain the positions of all main peaks. CASTEP and WIEN2k were found to give almost identical results. These codes were also found to produce NES which most closely matched experiment based on χ² calculations used to qualitatively compare theory and experiment. This work demonstrated that a combined experimental and theoretical approach to the study of NES is a powerful way of investigating bonding and electronic structure in boron nitride and related materials.     

Degree bounded matroids and submodular flows

We consider two related problems, the Minimum Bounded Degree Matroid Basis problem and the Minimum Bounded Degree Submodular Flow problem. The first problem is a generalization of the Minimum Bounded Degree Spanning Tree problem: We are given a matroid and a hypergraph on its ground set with lower and upper bounds f(e)≤g(e) for each hyperedge e. The task is to find a minimum cost basis which contains at least f(e) and at most g(e) elements from each hyperedge e. In the second problem we have a submodular flow problem, a lower bound f(v) and an upper bound g(v) for each node v, and the task is to find a minimum cost 0–1 submodular flow with the additional constraint that the sum of the incoming and outgoing flow at each node v is between f(v) and g(v). Both of these problems are NP-hard (even the feasibility problems are NP-complete), but we show that they can be approximated in the following sense. Let opt be the value of the optimal solution. For the first problem we give an algorithm that finds a basis B of cost no more than opt such that f(e)?2Δ+1≤|B∩e|≤g(e)+2Δ?1 for every hyperedge e, where Δ is the maximum degree of the hypergraph. If there are only upper bounds (or only lower bounds), then the violation can be decreased to Δ?1. For the second problem we can find a 0–1 submodular flow of cost at most opt where the sum of the incoming and outgoing flow at each node v is between f(v)?1 and g(v)+1. These results can be applied to obtain approximation algorithms for several combinatorial optimization problems with degree constraints, including the Minimum Crossing Spanning Tree problem, the Minimum Bounded Degree Spanning Tree Union problem, the Minimum Bounded Degree Directed Cut Cover problem, and the Minimum Bounded Degree Graph Orientation problem.     

An experimental-theoretical analysis of protein adsorption on peptidomimetic polymer brushes

Surface-grafted water-soluble polymer brushes are being intensely investigated for preventing protein adsorption to improve biomedical device function, prevent marine fouling, and enable applications in biosensing and tissue engineering. In this contribution, we present an experimental-theoretical analysis of a peptidomimetic polymer brush system with regard to the critical brush density required for preventing protein adsorption at varying chain lengths. A mussel adhesive-inspired DOPA-Lys (DOPA = 3,4-dihydroxy-phenylalanine; Lys = lysine) pentapeptide surface grafting motif enabled aqueous deposition of our peptidomimetic polypeptoid brushes over a wide range of chain densities. Critical densities of 0.88 nm(-2) for a relatively short polypeptoid 10-mer to 0.42 nm(-2) for a 50-mer were identified from measurements of protein adsorption. The experiments were also compared with the protein adsorption isotherms predicted by a molecular theory. Excellent agreements in terms of both the polymer brush structure and the critical chain density were obtained. Furthermore, atomic force microscopy (AFM) imaging is shown to be useful in verifying the critical brush density for preventing protein adsorption. The present coanalysis of experimental and theoretical results demonstrates the significance of characterizing the critical brush density in evaluating the performance of an antifouling polymer brush system. The high fidelity of the agreement between the experiments and molecular theory also indicate that the theoretical approach presented can aid in the practical design of antifouling polymer brush systems.     

Spin coupling and orbital angular momentum quenching in free iron clusters

Magnetic spin and orbital moments of size-selected free iron cluster ions Fe{n}{+} (n=3-20) have been determined via x-ray magnetic circular dichroism spectroscopy. Iron atoms within the clusters exhibit ferromagnetic coupling except for Fe{13}{+}, where the central atom is coupled antiferromagnetically to the atoms in the surrounding shell. Even in very small clusters, the orbital magnetic moment is strongly quenched and reduced to 5%-25% of its atomic value while the spin magnetic moment remains at 60%-90%. This demonstrates that the formation of bonds quenches orbital angular momenta in homonuclear iron clusters already for coordination numbers much smaller than those of the bulk.     

An efficient palladium-benzimidazolyl phosphine complex for the Suzuki-Miyaura coupling of aryl mesylates: facile ligand synthesis and metal complex characterization

A new class of easily accessible hemilabile benzimidazolyl phosphine ligands has been developed. The ligand skeleton is prepared from commercially available and inexpensive o-phenylenediamine and 2-bromobenzoic acid. With catalyst loading down to 0.5 mol% palladium, excellent catalytic activity towards the Suzuki-Miyaura coupling of aryl mesylates is still observed. This represents the lowest catalyst loading achieved so far for this reaction in general. X-Ray crystallography shows that new ligand L2 is coordinated with Pd in a κ(2)-P,N fashion.     

Tuning the Photocatalytic Activity of CdS Nanocrystals through Intermolecular Interactions in Ionic‐Liquid Solvent Systems

Synthetic solvent systems for the fine‐tuned preparation of CdS nanocrystallites, active in visible‐light photocatalytic hydrogen production, were studied. To control crystallite size and spectral properties, the CdS crystals were synthesised by using different solvent systems, containing a series of tetrabutylammonium amino carboxylate ionic liquids as the crystal‐growth control agents. Six samples of CdS, all with similar physical and spectral properties, exhibited greatly varying photocatalytic activity, with the most active sample outperforming the least active one by almost 60 %. To rationalise this effect, the intermolecular interactions of the synthesis solvent system with the growing CdS nanocrystallites were characterised by using the Reichart betaine dye and the ${E{{{\rm N}\hfill \atop {\rm T}\hfill}}}$ polarity scale. A correlation was observed between the ${E{{{\rm N}\hfill \atop {\rm T}\hfill}}}$ values of the solvent system and the photocatalytic activity of the CdS nanocrystallite, suggesting that the hydrogen‐bond‐donating ability and/or dipolarity/polarisability interactions of the solvent system led to the preferential formation of active surfaces/surface sites on the CdS crystals.     

On linear and semidefinite programming relaxations for hypergraph matching

The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a well-studied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method. Our main results are the following:

We consider the standard linear programming relaxation of the problem. We provide an algorithmic proof of a result of Füredi, Kahn and Seymour, showing that the integrality gap is exactly ${k-1+\frac{1}{k}}$ for k-uniform hypergraphs, and is exactly k ? 1 for k-partite hypergraphs. This yields an improved approximation algorithm for the weighted 3-dimensional matching problem. Our algorithm combines the use of the iterative rounding method and the fractional local ratio method, showing a new way to round linear programming solutions for packing problems.

We study the strengthening of the standard LP relaxation by local constraints. We show that, even after linear number of rounds of the Sherali-Adams lift-and-project procedure on the standard LP relaxation, there are k-uniform hypergraphs with integrality gap at least k ? 2. On the other hand, we prove that for every constant k, there is a strengthening of the standard LP relaxation by only a polynomial number of constraints, with integrality gap at most ${\frac{k+1}{2}}$ for k-uniform hypergraphs. The construction uses a result in extremal combinatorics.

We consider the standard semidefinite programming relaxation of the problem. We prove that the Lovász ${\vartheta}$ -function provides an SDP relaxation with integrality gap at most ${\frac{k+1}{2}}$ . The proof gives an indirect way (not by a rounding algorithm) to bound the ratio between any local optimal solution and any optimal SDP solution. This shows a new connection between local search and linear and semidefinite programming relaxations.