Structure and stability of molybdenum sulfide fullerenes

MoS2 nanooctahedra are believed to be the smallest stable closed-cage structures of MoS2, i.e., the genuine inorganic fullerenes. Here a combination of experiments and density functional tight binding calculations with molecular dynamics annealing are used to elucidate the structures and electronic properties of octahedral MoS2 fullerenes. Through the use of these calculations MoS2 octahedra were found to be stable beyond nMo > 100 but with the loss of 12 sulfur atoms in the six corners. In contrast to bulk and nanotubular MoS2, which are semiconductors, the Fermi level of the nanooctahedra is situated within the band, thus making them metallic-like. A model is used for extending the calculations to much larger sizes. These model calculations show that, in agreement with experiment, the multiwall nanooctahedra are stable over a limited size range of 104-105 atoms, whereupon they are converted into multiwall MoS2 nanoparticles with a quasi-spherical shape. On the experimental side, targets of MoS2 and MoSe2 were laser-ablated and analyzed mostly through transmission electron microscopy. This analysis shows that, in qualitative agreement with the theoretical analysis, multilayer nanooctahedra of MoS2 with 1000-25 000 atoms (Mo + S) are stable. Furthermore, this and previous work show that beyond approximately 105 atoms fullerene-like structures with quasi-spherical forms and 30-100 layers become stable. Laser-ablated WS2 samples yielded much less faceted and sometimes spherically symmetric nanocages.     

Fast Algorithms for Nonparametric Curve Estimation

Abstract

Naive implementations of local polynomial fits and kernel estimators require almost O(n ²) operations. In this article two fast O(n) algorithms for nonparametric local polynomial fitting are presented. They are based on updating normal equations. Numerical stability is guaranteed by controlling ill-conditioned situations for small bandwidths and data-tuned restarting of the updating procedure. Restarting at every output point results in a moderately fast but highly stable O(n ^7/5) algorithm. Applicability of algorithms is evaluated for estimation of regression curves and their derivatives. The idea is also applied to kernel estimators of regression curves and densities.     

Periodic solutions of certain hybrid delay-differential equations and their corresponding difference equations

In this paper we use a method due to Carvalho (A method to investigate bifurcation of periodic solution in retarded differential equations, J. Differ. Equ. Appl. 4 (1998), pp. 17–27) to obtain conditions for the existence of nonconstant periodic solutions of certain systems of hybrid delay-differential equations. We first deal with a scalar equation of Lotka–Valterra type; then a system of two equations in two unknowns that could model the interactions of two identical neurons. It will be seen that such solutions are determined by solutions of corresponding difference equations. Another paper in which this method is used is by Cooke and Ladeira (Applying Carvalho's method to find periodic solutions of difference equations, J. Differ. Equ. Appl. 2 (1996), pp. 105–115).

We first state Carvalho's result.     

The Chiral Trimer and a Metastable Chiral Dimer of Achiral Hexafluoroisopropanol: A Multi‐Messenger Study

1,1,1,3,3,3‐hexafluoro‐propan‐2‐ol aggregates preferentially into an achiral dimer of achiral monomers, but the trimer is found to prefer three metastable chiral monomer units arranged into a strained OH???O hydrogen‐bonded ring, which is reinforced by secondary CH???FC interactions. This is shown by a combination of infrared, microwave, and Raman spectroscopy in supersonic jet expansions and supported by high‐level quantum chemical calculations. It involves an activation of the monomers by >15 kJ mol^?1, clearly driven by the much stronger hydrogen‐bond interaction available to the gauche and even more to the cis monomer units.     

Optimization of anionic conductivity through the coexistence of ionomer cluster and backbone-backbone morphologies in anion exchange membranes

Random copolymers of poly(4-vinylpyridine) and polyisoprene were synthesized, and subsequently quaternized with 1-alkylbromides. The number of carbons on the pendant side-chain of the resultant comb-shaped polymer, n, ranged from 2–8. The comb-shaped polymers were crosslinked employing thiol-ene chemistry to give mechanically robust ion conducting membranes. Analysis by wide and medium-angle X-ray scattering show three morphology regimes that are dependent on the number of carbons on the pendant side-chains. When n = 2, ionomer cluster morphology was dominant, when n = 8 backbone-backbone morphology was dominant, and when n = 3–6, the membrane showed a coexistence of both ionomer cluster and backbone-backbone morphologies. Evaluation of the water uptake of the membranes showed a maximum water uptake per cation of 9.5 when n = 5 at 95% relative humidity (RH) and 60°C. Conductivity of the samples characterized by electrochemical impedance spectroscopy showed bromide conductivity as high as 110 mS/cm when n = 3 at 95% RH and 90°C.     

Optimality of the quantified Ingham–Karamata theorem for operator semigroups with general resolvent growth

We prove that a general version of the quantified Ingham–Karamata theorem for $$C_0$$-semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results contained in a recent paper by the same authors. It follows in particular that the well-known Batty–Duyckaerts theorem is optimal even for bounded $$C_0$$-semigroups whose generator has subpolynomial resolvent growth. Our proof is based on an elegant application of the open mapping theorem, which we complement by a crucial technical lemma allowing us to strengthen our earlier results.     

Multivariate Analysis of MALDI Imaging Mass Spectrometry Data of Mixtures of Single Pollen Grains

Mixtures of pollen grains of three different species (Corylus avellana, Alnus cordata, and Pinus sylvestris) were investigated by matrix-assisted laser desorption/ionization time-of-flight imaging mass spectrometry (MALDI-TOF imaging MS). The amount of pollen grains was reduced stepwise from >?10 to single pollen grains. For sample pretreatment, we modified a previously applied approach, where any additional extraction steps were omitted. Our results show that characteristic pollen MALDI mass spectra can be obtained from a single pollen grain, which is the prerequisite for a reliable pollen classification in practical applications. MALDI imaging of laterally resolved pollen grains provides additional information by reducing the complexity of the MS spectra of mixtures, where frequently peak discrimination is observed. Combined with multivariate statistical analyses, such as principal component analysis (PCA), our approach offers the chance for a fast and reliable identification of individual pollen grains by mass spectrometry.

Open image in new window

Graphical Abstract ?

     

In situ growth of nano-structures by metal-organic vapour phase epitaxy

Using spontaneous self-organization effects is an efficient way to produce nano-structures, as for instance quantum wires and quantum dots. This article is focused on the strain-induced self-organization, or “self-assembling” effect, producing quantum dots. Particularly the following aspects will be addressed: (i) the phenomenology of the 2D–3d morphology transition, (ii) the effects of materials choices and growth conditions on density, size and homogeneity of dots, and (iii) manipulations to get laterally aligned and vertically stacked dot structures.