Sinc-Galerkin method for solving nonlinear weakly singular two point boundary value problems

A study of Sinc-Galerkin method based on double exponential transformation for solving a class of nonlinear weakly singular two point boundary value problems with non-homogeneous boundary conditions is given. The properties of the Sinc-Galerkin approach are utilized to reduce the computation of nonlinear problem to nonlinear system of equations with unknown coefficients. This method tested on several test examples. We compare our numerical results with several numerical results of existing methods. The demonstrated results confirm that proposed method is considerably efficient, accurate nature and rapidly converge.     

Rheological characterization of polypropylene/poly(ethylene-<Emphasis Type="Italic">co</Emphasis>-propylene) in-reactor blends synthesized under different polymerization conditions

In-reactor blends of polypropylene/poly(ethylene-co-propylene) with complex microstructure, synthesized through different polymerization procedures; two-step (one homopolymerization and one copolymerization under high ethylene concentration) and three-step (with an additional copolymerization step under low ethylene concentration), were characterized by rheological measurements. The effects of a change in the polymerization process on the types and amounts of block copolymers in the blends were evaluated using small amplitude oscillation rheometry in the linear viscoelastic region. The Palierne model in its complete form was employed to model the rheological behavior of the blends. For this analysis the reactor products were separated into xylene cold insoluble (XCI) and xylene cold soluble fractions. Besides, another two copolymer fractions at 80 and 100 °C, which are crystallizable copolymer fractions and contain block copolymers rich in polyethylene and polypropylene, respectively, were separated from XCI fraction by xylene using temperature gradient elution fractionation method. Considering all copolymer fractions as dispersed and the remained fraction (mostly polypropylene) as matrix phase, it was shown that the rheological properties of the blends could not be predicted by Palierne model. It was found that only by considering part of block copolymer fractions having long polypropylene sequences along with polypropylene homopolymer as one phase, the rheological properties of the blends could be predicted by Palierne model. By rheological modeling, it was confirmed that the amounts of copolymers with long polypropylene sequences which are miscible with the matrix are higher in the case of three-step blends and also the elasticity of three-step polymerized blends is higher than two-step polymerized blends.     

Reconciliation between experimental and Monte Carlo-based simulation of the pore size distribution in mesoporous silicon

It is demonstrated for the first time that mesoporous PS structures obtained by the electrochemical etching of p(+)(100) oriented silicon wafers might assume the peculiarity of invariance of the first peak positions in their pore size distribution curves, albeit for current densities far from the electropolishing region and at constant electrolyte composition. A new Monte Carlo-based simulation model is presented that predicts reasonably the pore size distribution of the PS layers and the observed invariance of peak position with respect to changes in current density. The main highlight of the new model is the introduction of a 'light avalanche breakdown' process in a mathematical fashion. The model is also able to predict an absolute value of 4.23?? for the smallest pore created experimentally. It is discussed that the latter value has an exact physical meaning: it corresponds with great accuracy to the width of a void created on the surface due to the exclusion of one Si atom.     

Confinement-Induced Phonon Softening and Hardening in Sb2Te3 Thin Films

Scaling effects in Sesqui-chalcogenides are of major interest to understand and optimize their performance in heavily scaled applications, including topological insulators and phase-change devices. A combined experimental and theoretical study is presented for molecular beam epitaxy-grown films of antimony-telluride  (Sb₂Te₃). Structural,vibrational, optical, and bonding properties upon varying confinement are studied for thicknesses ranging from 1.3 to 56 nm. In ultrathin films, the low-frequency coherent phonons of A_1g¹ symmetry are softened compared to the bulk (64.5 cm⁻¹ at 1.3 nm compared to 68 cm⁻¹ at 55.8 nm). A concomitant increase of the high-frequency A_1g² Raman mode is seen. X-ray diffraction analyses unravel an accompanying out of plane stretch by 5%, mainly stemming from an increase in the Te-Te gap. This conclusion is supported by density functional theory slab models, which reveal a significant dependency of chemical bonding on film thickness. Changes in atomic arrangement, vibrational frequencies, and bonding extend over a thickness range much larger than observed for other material classes. The finding of these unexpectedly pronounced thickness-dependent effects in quasi-2D material Sb₂Te₃ allows tuning of the film properties with thickness. The results are discussed in the context of a novel bond-type, characterized by a competition between electron localization and delocalization.     

Comparing thermal and mechanochemical decomposition of ammonium paratungstate (APT)

In this research, the possibility of mechanochemical decomposition of ammonium paratungstate (APT) has been studied, and compared with thermal decomposition method. For this purpose, APT powders were milled using a planetary ball mill up to 36 h and under air atmosphere. For thermal decomposition, APT powders were heated for 30 minutes at 300 and 450 °C in air atmosphere. X-ray diffraction (XRD), differential scanning calorimeter (DSC), and thermo gravimetric analyzer (TGA) were used to study the decomposition progress, and products. The XRD results showed that APT completely decomposed to WO₃ by thermal decomposition, while the final product of mechanochemical decomposition was WO₃ (H₂O)_0.5. According to DSC and TGA results, during thermal decomposition, ammonia and water released in four steps, and leaved WO₃. By mechanochemical decomposition crystal water and ammonia liberated from APT structure, but structural water of APT remained. In both methods, an X-ray amorphous phase was the intermediate product of APT decomposition.     

Electron tunneling through ultrathin boron nitride crystalline barriers

We investigate the electronic properties of ultrathin hexagonal boron nitride (h-BN) crystalline layers with different conducting materials (graphite, graphene, and gold) on either side of the barrier layer. The tunnel current depends exponentially on the number of h-BN atomic layers, down to a monolayer thickness. Conductive atomic force microscopy scans across h-BN terraces of different thickness reveal a high level of uniformity in the tunnel current. Our results demonstrate that atomically thin h-BN acts as a defect-free dielectric with a high breakdown field. It offers great potential for applications in tunnel devices and in field-effect transistors with a high carrier density in the conducting channel.     

Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices

By stacking various two-dimensional (2D) atomic crystals on top of each other, it is possible to create multilayer heterostructures and devices with designed electronic properties. However, various adsorbates become trapped between layers during their assembly, and this not only affects the resulting quality but also prevents the formation of a true artificial layered crystal upheld by van der Waals interaction, creating instead a laminate glued together by contamination. Transmission electron microscopy (TEM) has shown that graphene and boron nitride monolayers, the two best characterized 2D crystals, are densely covered with hydrocarbons (even after thermal annealing in high vacuum) and exhibit only small clean patches suitable for atomic resolution imaging. This observation seems detrimental for any realistic prospect of creating van der Waals materials and heterostructures with atomically sharp interfaces. Here we employ cross sectional TEM to take a side view of several graphene-boron nitride heterostructures. We find that the trapped hydrocarbons segregate into isolated pockets, leaving the interfaces atomically clean. Moreover, we observe a clear correlation between interface roughness and the electronic quality of encapsulated graphene. This work proves the concept of heterostructures assembled with atomic layer precision and provides their first TEM images.     

Novel tunable dynamic tweezers using dark-bright soliton collision control in an optical add/drop filter

We propose a novel system of the dynamic optical tweezers generated by a dark soliton in the fiber optic loop. A dark soliton known as an optical tweezer is amplified and tuned within the microring resonator system. The required tunable tweezers with different widths and powers can be controlled. The analysis of dark-bright soliton conversion using a dark soliton pulse propagating within a microring resonator system is analyzed. The dynamic behaviors of soliton conversion in add/drop filter is also analyzed. The control dark soliton is input into the system via the add port of the add/drop filter. The dynamic behavior of the dark-bright soliton conversion is observed. The required stable signal is obtained via a drop and throughput ports of the add/drop filter with some suitable parameters. In application, the trapped light/atom and transportation can be realized by using the proposed system.     

Fluorographene: a two-dimensional counterpart of Teflon

A stoichiometric derivative of graphene with a fluorine atom attached to each carbon is reported. Raman, optical, structural, micromechanical, and transport studies show that the material is qualitatively different from the known graphene-based nonstoichiometric derivatives. Fluorographene is a high-quality insulator (resistivity >10(12) Ω) with an optical gap of 3 eV. It inherits the mechanical strength of graphene, exhibiting a Young's modulus of 100 N m(-1) and sustaining strains of 15%. Fluorographene is inert and stable up to 400 °C even in air, similar to Teflon.     

Fluorinated graphene: Fluorographene: A Two‐Dimensional Counterpart of Teflon (Small 24/2010)

A stoichiometric derivative of graphene with a fluorine atom attached to each carbon is reported. Raman, optical, structural, micromechanical, and transport studies show that the material is qualitatively different from the known graphene‐based nonstoichiometric derivatives. Fluorographene is a high‐quality insulator (resistivity >10¹² Ω) with an optical gap of 3 eV. It inherits the mechanical strength of graphene, exhibiting a Young’s modulus of 100 N m^?1 and sustaining strains of 15%. Fluorographene is inert and stable up to 400 °C even in air, similar to Teflon.