An Improved Bound on the Number of Unit Area Triangles

We show that the number of unit-area triangles determined by a set of n points in the plane is O(n ^9/4+ε ), for any ε>0, improving the recent bound O(n ^44/19) of Dumitrescu et al.     

Efficient preparation of an N-aryl β-amino acid via asymmetric hydrogenation and direct asymmetric reductive amination en route to Ezetimibe

Two routes for the preparation of an N-aryl β-amino acid, an important precursor for the cholesterol-lowering drug Ezetimibe, were investigated. The first pathway proceeds via an Rh- or Ir-catalyzed asymmetric hydrogenation of N-aryl enamine giving the desired product with up to 82% ee. The other pathway involves a direct asymmetric reductive amination (DARA) of the β-keto ester which yielded the β-amino ester in high yield and 97% ee. Subsequent copper-catalyzed N-arylation gave the target compound.     

Comparison of laser ablation-inductively coupled plasma-mass spectrometry and micro-X-ray fluorescence spectrometry for elemental imaging in Daphnia magna

Visualization of elemental distributions in thin sections of biological tissue is gaining importance in many disciplines of biological and medical research. Laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) and scanning micro-X-ray fluorescence spectrometry (micro-XRF) are two widely used microanalytical techniques for elemental mapping. This article compares the capabilities of the two techniques for imaging the distribution of selected elements in the model organism Daphnia magna in terms of detection power and spatial resolution. Sections with a thickness of 10 and 20 μm of the fresh water crustacean Daphnia magna were subjected to LA-ICP-MS and micro-XRF analysis. The elemental distributions obtained for Ca, P, S and Zn allow element-to-tissue correlation. LA-ICP-MS and micro-XRF offer similar limits of detection for the elements Ca and P and thus, allow a cross-validation of the imaging results. LA-ICP-MS was particularly sensitive for determining Zn (LOD 20 μg g⁻¹, 15 μm spot size) in Daphnia magna, while the detection power of micro-XRF was insufficient in this context. However, LA-ICP-MS was inadequate for the measurement of the S distributions, which could be better visualized with micro-XRF (LOD 160 μg g⁻¹, 5 s live time). Both techniques are thus complementary in providing an exhaustive chemical profiling of tissue samples.     

Study of the affinity of thermographic additives for silver by time-of-flight static secondary ion mass spectrometry and surface-enhanced Raman spectroscopy on silver nanoparticles

Detection of the interactions between low molecular weight organic compounds and metals in the form of sols on a nanoscale is analytically challenging. This study aims to provide experimental evidence using a combination of UV-Vis absorption spectrometry, surface-enhanced Raman spectrometry (SERS), and static secondary ion mass spectrometry (S-SIMS). The field of application is thermography where silver images are formed via heat-catalyzed reactions. Several organic compounds called tone modifiers and stabilizers are used in thermographic materials for the optimization of the image quality. With exploitation of the strengths of each of the above-mentioned methods, an affinity ranking of several tone modifiers and a stabilizer was established on the basis of competitive adsorption experiments using different model systems. Specifically, silver sols, SERS probes, and sputter-coated silver substrates were exposed to systems with one or two additives. The UV-Vis results provided insight on the aggregation of silver nanoparticles in a hydrosol, which was necessary for the interpretation of the SERS data. Both SERS and S-SIMS measurements led to a similar ranking of the relative affinity of the additives in two components, which was largely consistent with empirical knowledge derived from macroscopic behavior.     

Shape-induced frustration of hexagonal order in polyhedral colloids

The effect of a nonspherical particle shape and shape polydispersity on the structure of densely packed hard colloidal particles was studied in real space by confocal microscopy. We show that the first layer at the wall of concentrated size-monodisperse but shape-polydisperse polyhedral colloids exhibits significant deviations from a hexagonal lattice. These deviations are identified as bond-orientational fluctuations which lead to percolating "mismatch lines." While the shape-induced geometrical frustration of the hexagonal symmetry suppresses translational order, bond-orientational order is clearly retained, indicating a hexaticlike structure of the polyhedral colloids.     

Quantitative real-space analysis of self-assembled structures of magnetic dipolar colloids

We present the first real-space analysis on a single-particle level of the dipolar chains and branched clusters self-assembling in magnetic fluids in zero field. Spatial correlations and chain-length distributions directly obtained from tracked particle positions in vitrified films of synthetic magnetic (Fe3O4) dispersions provide a quantitative test for simulations and theory of dipolar fluids. A pertinent example is the cluster-size distribution that can be analyzed with a one-dimensional aggregation model to yield a dipolar attraction energy that agrees well with the dipole moment found from independent magnetization measurements.     

Analysis of in situ EXAFS data of supported metal catalysts using the third and fourth cumulant

X-Ray absorption spectra of supported Pt catalysts with various Pt cluster sizes were collected between 77 and 673 K, in inert and hydrogen atmospheres. When analyzing these spectra with the standard EXAFS equation, a Pt-Pt bond contraction and a large increase in the inner potential correction were observed with increasing temperature. These errors are up to 0.08 A and 10 eV for clusters of 1 nm diameter. They were corrected by including the third and fourth cumulants as fit parameters. Fit guidelines were developed to analyze EXAFS data of supported metal catalysts collected at elevated temperatures, allowing for asymmetry and broadening or sharpening of the pair distribution function. These comprise fixing fit parameters, using different k-weightings and identifying trends in a series of experiments. By fitting the EXAFS spectra using these guidelines, it was determined that in small Pt clusters the Pt-Pt bond is 0.10 A shorter than in bulk Pt. These contracted bonds relax to distances near that of bulk Pt upon hydrogen chemisorption.