Hotspot decorations map plasmonic patterns with the resolution of scanning probe techniques

In high definition mapping of the plasmonic patterns on the surfaces of nanostructures, the diffraction limit of light remains an important obstacle. Here we demonstrate that this diffraction limit can be completely circumvented. We show that upon illuminating nanostructures made of nickel and palladium, the resulting surface-plasmon pattern is imprinted on the structures themselves; the hotspots (regions of local field enhancement) are decorated with overgrowths, allowing for their subsequent imaging with scanning-probe techniques. The resulting resolution of plasmon pattern imaging is correspondingly improved.     

Near IR Bandgap Semiconducting 2D Conjugated Metal-Organic Framework with Rhombic Lattice and High Mobility

Two-dimensional conjugated metal–organic frameworks (2D c-MOFs) are emerging as a unique class of electronic materials. However, 2D c-MOFs with band gaps in the Vis-NIR and high charge carrier mobility are rare. Most of the reported conducting 2D c-MOFs are metallic (i.e. gapless), which largely limits their use in logic devices. Herein, we design a phenanthrotriphenylene-based, D_2h-symmetric π-extended ligand ( OHPTP ), and synthesize the first rhombic 2D c-MOF single crystals ( Cu₂(OHPTP) ). The continuous rotation electron diffraction (cRED) analysis unveils the orthorhombic crystal structure at the atomic level with a unique slipped AA stacking. The Cu₂(OHPTP) is a p-type semiconductor with an indirect band gap of ≈0.50 eV and exhibits high electrical conductivity of 0.10 S cm⁻¹ and high charge carrier mobility of ≈10.0 cm² V⁻¹ s⁻¹. Theoretical calculations underline the predominant role of the out-of-plane charge transport in this semiquinone-based 2D c-MOF.     

Ethylene polymerization with a catalytic system containing an organomagnesium compound

Ethylene polymerization with the catalytic system TiCl₄-aluminium alkyl-diphenylmagnesium was studied. The system is highly active even at a low AlTi molar ratio and is notable in that it is formed by simple mixing of the catalytic components. The catalytic activity depends on the molar ratio of the components; in the studied range, activity increases as the AlTi ratio increases and as the MgTi ratio decreases. The resulting polyethylene is of ultra-high molecular weight.     

On the Dirichlet problemfor the Beltrami equation

We show that homeomorphic W _loc ^1,1 solutions of the Beltrami equations $\overline \partial f = \mu \partial f$ satisfy certain modular inequalities. On this basis, we develop the theory of the boundary behavior of such solutions and prove a series of criteria for the existence of regular, pseudoregular and multi-valued solutions for the Dirichlet problem to the Beltrami equation in Jordan domains and finitely connected domains, respectively. These results have important applications to various problems of mathematical physics.     

On some families of multi-point iterative methods for solving nonlinear equations

Some semi-discrete analogous of well known one-point family of iterative methods for solving nonlinear scalar equations dependent on an arbitrary constant are proposed. The new families give multi-point iterative processes with the same or higher order of convergence. The convergence analysis and numerical examples are presented.     

Note on the distribution of poles of the scattering matrix

Trapping obstacles, having at least one isolated multiple reflecting trapping ray, are considered. It is proved that for every ε > 0 there are poles λ_j of the scattering matrix such that $\text{0 <}\text{Im}\text{λ}{}_{\mathrm{j}}\text{< ε}\text{Log}\text{|λ}{}_{\mathrm{j}}\text{¦}$.     

Investigation of the sorption properties of thin Ge–S–AgI films deposited on cantilever-based gas sensor

Thin amorphous Ge–S–AgI films were thermally evaporated on cantilever sensors and their sorption properties were investigated upon exposure to volatile analytes, such as water, ethanol, acetone, and ammonia vapours. The films were smooth and uniform in thickness as revealed by atomic force and scanning electron microscopies. The exposure to the analytes resulted in a change of the resonance frequency of the cantilever. Initially, the largest dynamic responses (frequency shifts) were observed towards acetone, i.e. the cantilever acted as a resonant microbalance. When the sensor was exposed to ammonia, its molecules were chemisorbed on the surface of the sensitive layer. This surface modification increased the sensor sensitivity towards water molecules by the creation of new interaction sites. PACS 81.05.-t; 85.85.+j; 07.07.Df     

A study of short-range correlation effects on nuclear spatial and momentum distribution

The relation between the nuclear spatial and momentum densities is studied by means of their integral representations in terms of uniform distributions. Examples of this approach are given for the harmonic oscillator model of⁴He and¹⁶O, with and without Jastrow correlations, and for the single-particle potential model of⁴⁰Ca.