Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory

On the basis of the modified strain gradient elasticity theory, the free vibration characteristics of curved microbeams made of functionally graded materials (FGMs) whose material properties vary in the thickness direction are investigated. A size-dependent first-order shear deformation beam model is developed containing three internal material length scale parameters to incorporate small-scale effect. Through Hamilton’s principle, the higher-order governing equations of motion and boundary conditions are derived. Natural frequencies of FGM curved microbeams corresponding to different mode numbers are evaluated for over a wide range of material property gradient index, dimensionless length scale parameter and aspect ratio. Moreover, the results obtained via the present non-classical first-order shear deformation beam model are compared with those of degenerated beam models based on the modified couple stress and the classical theories. It is found that the difference between the natural frequencies predicted by the various beam models is more significant for lower values of dimensionless length scale parameter and higher values of mode number.     

New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method

In this paper, the nonlinear Boussinesq equations with the conformable time-fractional derivative are solved analytically using the well-established modified Kudryashov method. As a consequence, a number of new exact solutions for this type of equations are formally derived. It is believed that the method is one of the most effective techniques for extracting new exact solutions of nonlinear fractional differential equations.     

Porphyrin N-Pincer Pd(II)-Complexes in Water: A Base-Free and Nature-Inspired Protocol for the Oxidative Self-Coupling of Potassium Aryltrifluoroborates in Open-Air

Metalloporphyrins (and porphyrins) are well known as pigments of life in nature, since representatives of this group include chlorophylls (Mg-porphyrins) and heme (Fe-porphyrins). Hence, the construction of chemistry based on these substances can be based on the imitation of biological systems. Inspired by nature, in this article we present the preparation of five different porphyrin, meso-tetraphenylporphyrin (TPP), meso-tetra(p-anisyl)porphyrin (TpAP), tetrasodium meso-tetra(p-sulfonatophenyl)porphyrin (TSTpSPP), meso-tetra(m-hydroxyphenyl)porphyrin (TmHPP), and meso-tetra(m-carboxyphenyl)porphyrin (TmCPP) as well as their N-pincer Pd(II)-complexes such as Pd(II)-meso-tetraphenylporphyrin (PdTPP), Pd(II)-meso-tetra(p-anisyl)porphyrin (PdTpAP), Pd(II)-tetrasodium meso-tetra(p-sulfonatophenyl)porphyrin (PdTSTpSPP), Pd(II)-meso-tetra(m-hydroxyphenyl)porphyrin (PdTmHPP), and Pd(II)-meso-tetra(m-carboxyphenyl)porphyrin (PdTmCPP). These porphyrin N-pincer Pd(II)-complexes were studied and found to be effective in the base-free self-coupling reactions of potassium aryltrifluoroborates (PATFBs) in water at ambient conditions. The catalysts and the products (symmetrical biaryls) were characterized using their spectral data. The high yields of the biaryls, the bio-mimicking conditions, good substrate feasibility, evading the use of base, easy preparation and handling of catalysts, and the application of aqueous media, all make this protocol very attractive from a sustainability and cost-effective standpoint.     

Refractive index and dispersion measurements in prismatic thin film of phasmidic columnar liquid crystals

In this work, we explore the refractive index of the phasmidic columnar liquid crystal for homeotropic oriented samples (column perpendicular to the plates). To measure the ordinary index n_o of the columnar liquid crystal C₁₀, a simple and accurate method is presented using the deflection by reflection of a laser beam (λ = 633nm) through a prismatic phasmidic thin film placed between two glass plates in the homeotropic orientation. For the C₁₀ samples, we found n_o = 1.5512 ± 0.0002 at T = 100°C. We used the same method to determine the isotropic index n_l of the isotropic phase and found n_l = 1.5301 ± 0.0002 at T = 120°C. Using the precision of the same method in polychromatic laser beam, we measured the variation of the ordinary index with the wavelength λ and characterize the dispersion by the known Cauchy's dispersion relationship n_o = A + B/λ². We deduce an estimation of the birefringence for several samples.     

Synthesis,characterization, dielectric and rectification properties of PANI/Nd2O3:Al2O3 nanocomposites

Polyaniline–Nd₂O₃:Al₂O₃ nanocomposites were prepared by in situ oxidative polymerization method using different weight percentages of oxide powders. The prepared nanocomposites were characterized by Fourier transform infrared spectroscopy and X‐ray diffraction for molecular and crystal structures. Scanning electron microscopy and transmission electron microscopy images show the tubular structure of polyaniline nanocomposite with embedded metal oxides. The electrical conductivity of the nanocomposites increases with increase in temperature as well as with concentration of Nd₂O₃:Al₂O₃ particles in polyaniline. This is because of the hopping of charge polarons and extended chain length of the nanocomposites as evidenced by the negative thermal coefficient (NTC) characteristic. A high NTC value of 2.67 was found in nanocomposites with 15 wt% of oxide particles. These nanocomposites show low dielectric constant and dielectric loss; the electrical conductivity is higher than 0.3 S/cm as confirmed by Cole–Cole plot that indicates a decrease in both grain resistance and bulk resistance of the nanocomposites. The current–voltage and capacitance–voltage measurements were also carried out. The carrier mobility μ values of pure polyaniline and nanocomposites were found to be 4.27 × 10^?3 and 1.45 × 10^–2 H.M^?1, respectively. A significant enhancement in carrier mobility was observed in comparison with the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Novel copolymers of styrene. 5. Alkyl and alkoxy ring-disubstituted propyl 2-cyano-3-phenyl-2-propenoates

Novel trisubstituted ethylenes, alkyl and alkoxy ring-disubstituted propyl 2-cyano-3-phenyl-2-propenoates, RPhCH?C(CN)CO₂C₃H₇ (where R is 2,3-dimethyl, 2,5-dimethyl, 2,6-dimethyl, 3,4-dimethyl, 2,3-dimethoxy, 2,4-dimethoxy, 2,5-dimethoxy, 2,6-dimethoxy 3,4-dimethoxy, 3,5-dimethoxy) were prepared and copolymerized with styrene. The monomers were synthesized by the piperidine catalyzed Knoevenagel condensation of ring-substituted benzaldehydes and propyl cyanoacetate and characterized by CHN elemental analysis, IR, ¹H- and ¹³C-NMR. All the ethylenes were copolymerized with styrene (M₁) in solution with radical initiation (ABCN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C-NMR, GPC, DSC, and TGA. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 200–500°C range with residue (0.6–5.0% wt.), which then decomposed in the 500–800°C range.     

Estimation of optical abnormalities in breast phantom by diffuse equation

Optical imaging is an emerging method for bio-imaging. The advantages of this imaging provide non-ionizing and safe radiation, non-invasive and functional medical imaging. Due to diffusion of photons inside biological tissues, its image processing is complicated. So in spite of these advantages, this imaging method has not been progressed like ultrasound imaging and magnetic resonance imaging (MRI). Also, the penetration depth of photons inside biological phantom is low. To overcome this problem, the complicated diffusion of photons through tissue must be modeled. The diffuse equation can be applied to simulate photons through turbid media like biological tissues. In this paper, the diffuse equation is used to study propagation of diffuse photons. The green function method is applied to solve this equation, and then the optical properties of abnormalities in breast phantom are estimated. This fast method can be applied for image processing.     

Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory

In this paper, a size-dependent first-order shear deformable shell model is developed based upon the modified strain gradient theory (MSGT) for the axial buckling analysis of functionally graded (FG) circular cylindrical microshells. It is assumed that the material properties of FG materials, which obey a simple power-law distribution, vary through the thickness direction. The principle of virtual work is utilized to formulate the governing equations and corresponding boundary conditions. Numerical results are presented for the axial buckling of FG circular cylindrical microshells subject to simply-supported end conditions and the effects of material length scale parameter, material property gradient index, length-to-radius ratio and circumferential mode number on the size-dependent critical buckling load are extensively studied. For comparison purpose, the critical buckling loads predicted by modified couple stress theory (MCST) and classical theory (CT) are also presented. Results show that the size effect plays an important role for lower values of dimensionless length scale parameter. Moreover, it is observed that the critical buckling loads obtained based on MSGT are greater than those obtained based on MCST and CT.     

Luminescence properties of Tb(3+)-doped CaMoO(4) nanoparticles: annealing effect, polar medium dispersible, polymer film and core-shell formation

Tb(3+)-doped CaMoO(4) (Tb(3+) = 1, 3, 5, 7, 10, 15 and 20 atom%) core and core-shell nanoparticles have been prepared by urea hydrolysis in ethylene glycol (EG) as capping agent as well as reaction medium at low temperature ～150 °C. As-prepared samples were annealed at 500 and 900 °C for 4 h to eliminate unwanted hydrocarbons and/or H(2)O present in the sample and to improve crystallinity. The synthesised nanophosphors show tetragonal phase structure. The crystallite size of as-prepared sample is found to be ～18 nm. The luminescence intensity of the (5)D(4) → (7)F(5) transition at 547 nm of Tb(3+) is much higher than that of the (5)D(4) → (7)F(6) transition at 492 nm. 900 °C annealed samples show the highest luminescence intensity. The intensity ratio R (I[(5)D(4) → (7)F(6)]/I[(5)D(4) → (7)F(5)]) lies between 0.3-0.6 for as-prepared, 500 and 900 °C annealed samples. The luminescence decay of (5)D(4) level under 355 nm excitation shows biexponential behaviour indicating availability of Tb(3+) ions on surface and core regions of particle; whereas, contribution of Mo-O charge transfer to lifetime is obtained under 250 nm excitation. The CIE coordinates of as-prepared, 500 and 900 °C annealed 5 atom% Tb(3+)-doped CaMoO(4) samples under 250 nm excitation are (0.28, 0.32), (0.22, 0.28) and (0.25, 0.52), respectively. The dispersed particles in polar medium and its polymer film show green light emission. The luminescence intensity is improved significantly after core-shell formation due to extent of decrease of non-radiative rates arising from surface dangling bonds and capping agent. Quantum yields of as-prepared samples of 1, 5 and 7 atom% Tb(3+)-doped CaMoO(4) samples are found to be 10, 3 and 2, respectively.