A priori estimate for non-uniform elliptic equations

A priori estimate for non-uniform elliptic equations with periodic boundary conditions is concerned. The domain considered consists of two sub-regions, a connected high permeability region and a disconnected matrix block region with low permeability. Let ? denote the size ratio of one matrix block to the whole domain. It is shown that in the connected high permeability sub-region, the Hölder and the Lipschitz estimates of the non-uniform elliptic solutions are bounded uniformly in ?. But Hölder gradient estimate and Lp estimate of the second order derivatives of the solutions in general are not bounded uniformly in ?.     

Structural and mechanical properties of multi-element (TiVCrZrHf)N coatings by reactive magnetron sputtering

In this study, (TiVCrZrHf)N multi-component coatings with quinary metallic elements were deposited by reactive magnetron sputtering system. The composition, structure, and mechanical properties of the coatings deposited at different N₂ flow rates were investigated. The (TiVCrZrHf)N coatings deposited at N₂ flow rates of 0, 1, and 2 SCCM showed an amorphous structure, whereas those deposited at N₂ flow rates of 4 and 6 SCCM showed a simple face-centered cubic solid solution structure. A saturated nitride coating was obtained for N₂ flow of 4 SCCM and higher. By increasing N₂ flow to 4 SCCM, the hardness and modulus reached a maximum value of 23.8 ± 0.8 and 267.3 ± 4.0 GPa, respectively.     

Strain-induced pseudo-magnetic fields and charging effects on CVD-grown graphene

Atomically resolved imaging and spectroscopic characteristics of graphene grown by chemical vapor deposition (CVD) on copper are investigated by means of scanning tunneling microscopy and spectroscopy (STM/STS). For CVD-grown graphene remaining on the copper substrate, the monolayer carbon structures exhibit ripples and appear strongly strained, with different regions exhibiting different lattice structures and electronic density of states (DOS). In particular, ridges appear along the boundaries of different lattice structures, which exhibit excess charging effects. Additionally, the large and non-uniform strain induces pseudo-magnetic field up to ~ 50 T, as manifested by the DOS peaks at quantized energies that correspond to pseudo-magnetic field-induced integer and fractional Landau levels. In contrast, for graphene transferred from copper to SiO₂ substrates after the CVD growth, the average strain on the whole diminishes, so do the corresponding charging effects and pseudo-magnetic fields except for sample areas near topological defects. These findings suggest feasible nano-scale “strain engineering” of the electronic states of graphene by proper design of the substrates and growth conditions.     

Employing dual-saturable-absorber-based filter for stable and tunable erbium-doped fiber ring laser in single-frequency

In this demonstration, a stable and wavelength-tunable erbium-doped fiber (EDF) ring laser using dual-saturable-absorber-based (DSAB) filter inside loop cavity is proposed and experimentally investigated. The proposed DSAB filter not only can filter the side-mode in single-frequency output, but also can obtain the flattened output power spectrum within 1 dB variation in the effectively range of 1529 to 1563 nm. In addition, the output stabilities of wavelength and power are also measured experimentally and discussed.     

A theoretical investigation of low energy band gap polymers: polythiophene systems

Recently, the organic synthesis and electronic device applications of π-conjugated polymer-based materials with low energy band gap (below 2 eV) and high values of incident photon to current efficiency have been presented. In the present study, the physical properties of polythiophene (PTH) and its derivative systems (PTs) were investigated as π-conjugated low energy band gap polymers. Density functional theory with periodic boundary condition (PBC), the B3LYP functional, and the 6-31G(d) basis set was applied to determine their geometric and electronic structures and corresponding energies (E _HOMO, E _LUMO, and E _g = E _LUMO ? E _HOMO) from the monomer of thiophene and its derivatives for one-dimensional (1D) extension to polymer. The effects of 3-substitution in PTs including electron-donating (CH₃–, C₆H₁₃–, OH–, Cl–, OCH₃–, and CHO–) and electron-withdrawing groups (Cl–, CHO–, CN–, NO₂–, CF₃–, and COOH–) compared with PTH were investigated. According to the calculation results, PTs with electron-donating and electron-withdrawing substituents should exhibit red- and blue-shifts, respectively, compared with PTH. These calculation results show good agreement with experimental data and provide further information for molecular design considerations.     

Activation of Open‐Cage Fullerenes with Ruthenium Carbonyl Clusters

Reactions of the open‐cage fullerene C₆₃NO₂(Py)(Ph)₂ ( 1 ) with [Ru₃(CO)₁₂] produce [Ru₃(CO)₈(μ,η⁵‐C₆₃NO₂(Py)(Ph)₂)] ( 2 ), [Ru₂H(CO)₃(μ,η⁷‐C₆₃N(Py)(Ph)(C₆H₄))] ( 3 ), and [Ru(CO)(Py)₂₍η³‐C₆₃NO₂(Py)(Ph)₂)] ( 4 ), in which the orifice sizes are modified from 12 to 8, 11, and 15‐membered ring, through ruthenium‐mediated C?O and C?C bond activation and formation.     

Isocratic Separation of Dansylated Biogenic Amines on a C8‐Bonded Silica Column under the LC Elution of Methanol‐Based Mobile Phase

Under the elution of methanol‐based mobile phase, the isocratic resolution of 12 biogenic amines, including 1 aromatic, 2 heterocyclic and 9 aliphatic amines, as the dansylated derivatives has been accomplished in less than 25 minutes on a 15 cm C₈‐bonded column. The resolution can not be reproduced on other examined alkyl‐bonded phases (e.g., C₄ and C₁₈) under the same chromatographic conditions, or in the reversed‐phase mode. The retention, mainly as a result of hydrophobic interaction between analyte and stationary phase, can be adjusted by varying the percentage of methanol in the mobile phase. Also, incorporating acetic acid as additive to the mobile phase to protonate the analyte and silanol groups that are little shielding on the surface of silica gel reduces the dipole‐dipole interaction, and thus the retention scale, which in turn deteriorates the resolution. Furthermore, the elution reversal is plausible for some of analytes as a greater percent of acetic acid is used in the elution. Values of correlation coefficients (R²) range between 0.9995 and 0.9996, indicating good linearity.     

Compatible and tearing properties of poly(lactic acid)/poly(ethylene glutaric‐co‐terephthalate) copolyester blends

Fourier transform infrared and nuclear magnetic resonance results suggest that the carboxylic acid groups of poly(lactic acid) (PLA) molecules react with the hydroxyl groups of FePol (FP) molecules during the melt‐blending of PLA_xFP_y specimens. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) experiments of PLA and PLA/FP specimens suggest that only small amounts of poor PLA and/or FP crystals are present in their corresponding melt crystallized specimens. In fact, the percentage crystallinity, peak melting temperature, and onset re‐crystallization temperature values of PLA/FP specimens reduce gradually as their FP contents increase. However, the glass transition temperatures of PLA molecules found by DSC and DMA reduce to a minimum value as the FP contents of PLA_xFP_y specimens reach 6 wt %. Further DMA and morphological analysis of PLA/FP specimens reveal that FP molecules are compatible with PLA molecules at FP contents equal to or less than 6 wt %, as no distinguished phase‐separated FP droplets and tan δ transitions were found on fracture surfaces and tan δ curves of PLA/FP specimens, respectively. In contrast to PLA, the FP specimen exhibits highly deformable and tearing properties. After blending proper amounts of FP in PLA, the inherent brittle deformation and poor tearing behavior of PLA were successfully improved. Possible reasons accounting for these interesting crystallization, compatible and tearing properties of PLA/FP specimens are proposed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 913–920, 2010     

Characterizing fracture energy of proton exchange membranes using a knife slit test

Pinhole formation in proton exchange membranes (PEM) may be caused by a process of flaw formation and crack propagation within membranes exposed to cyclic hygrothermal loading. Fracture mechanics can be used to characterize the propagation process, which is thought to occur in a slow, time‐dependent manner under cyclic loading conditions, and believed to be associated with limited plasticity. The intrinsic fracture energy has been used to characterize the fracture resistance of polymeric material with limited viscoelastic and plastic dissipation, and has been found to be associated with long‐term durability of polymeric materials. Insight into this limiting value of fracture energy may be useful in characterizing the durability of proton exchange membranes, including the formation of pinhole defects. In an effort to collect fracture data with limited plasticity, a knife slit test was adapted to measure fracture energies of PEMs, resulting in fracture energies that were two orders of magnitude smaller than those obtained with other fracture test methods. The presence of a sharp knife blade reduces crack tip plasticity, providing fracture energies that may be more representative of the intrinsic fracture energies of the thin membranes. Three commercial PEMs were tested to evaluate their fracture energies (G_c) at temperatures ranging from 40 to 90 °C and humidity levels varying from dry to 90% relative humidity (RH). Experiments were also conducted with membrane specimens immersed in water at various temperatures. The time temperature moisture superposition principle was applied to generate fracture energy master curves plotted as a function of reduced cutting rate based on the humidity and temperature conditions of the tests. The shift with respect to temperature and humidity suggests that the slitting process is viscoelastic in nature. Also such shifts were found to be consistent with those obtained from constitutive tests such as stress relaxation. The fracture energy is more sensitive to temperature than on humidity. The master curves converge at the lowest reduced cutting rates, suggesting similar intrinsic fracture energies; but diverge at higher reduced cutting rates to significantly different fracture energies. Although the relationship between G_c and ultimate mechanical durability has not been established, the test method may hold promise for investigating and comparing membrane resistance to failure in fuel cell environments. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 333–343, 2010