Good correlation between the calculated gas-phase first proton macroaffinities of some triazacycloalkanes ([X]aneN3, X = 9–12) with their protonation constants in solution

A theoretical study on first protonation step of a series of triazacycloalkanes with general formula {([X]aneN₃, X = 9–12)} (X = 9, L222; X = 10, L223; X = 11, L233; X = 12, L333) is reported. The geometry of all ligands and their monoprotonated forms were fully optimized at both the Hartree–Fock and DFT (B3LYP) levels of theory using 6-31+G* basis set. Then the first proton macroaffinities were calculated from the proton microaffinities according to defined equations. It is shown that there are good correlations between the calculated gas-phase first proton macroaffinities of these ligands with their protonation constants in solution.     

Yb3+sensitized Er3+-doped waveguide amplifiers: a theoretical approach

Silicate and phosphate glass waveguide amplifiers doped with Er³⁺, and co-doped with Er³⁺/Yb³⁺ are theoretically studied. Configurations for core and core–cladding doped waveguide amplifiers are considered. It is shown that gain in the core–cladding doped amplifiers is considerably higher than core doped amplifiers. It is also shown that with input signal power up to 1 and 200mW pump power, a 12.5dB gain can be achieved in a 3cm long waveguide amplifier, with a noise figure of 3dB.     

Nanoparticulate Hollow TiO2 Fibers as Light Scatterers in Dye‐Sensitized Solar Cells: Layer‐by‐Layer Self‐Assembly Parameters and Mechanism

Hollow structures show both light scattering and light trapping, which makes them promising for dye‐sensitized solar cell (DSSC) applications. In this work, nanoparticulate hollow TiO₂ fibers are prepared by layer‐by‐layer (LbL) self‐assembly deposition of TiO₂ nanoparticles on natural cellulose fibers as template, followed by thermal removal of the template. The effect of LbL parameters such as the type and molecular weight of polyelectrolyte, number of dip cycles, and the TiO₂ dispersion (amorphous or crystalline sol) are investigated. LbL deposition with weak polyelectrolytes (polyethylenimine, PEI) gives greater nanoparticle deposition yield compared to strong polyelectrolytes (poly(diallyldimethylammonium chloride), PDDA). Decreasing the molecular weight of the polyelectrolyte results in more deposition of nanoparticles in each dip cycle with narrower pore size distribution. Fibers prepared by the deposition of crystalline TiO₂ nanoparticles show higher surface area and higher pore volume than amorphous nanoparticles. Scattering coefficients and backscattering properties of fibers are investigated and compared with those of commercial P25 nanoparticles. Composite P25–fiber films are electrophoretically deposited and employed as the photoanode in DSSC. Photoelectrochemical measurements showed an increase of around 50 % in conversion efficiency. By employing the intensity‐modulated photovoltage and photocurrent spectroscopy methods, it is shown that the performance improvement due to addition of fibers is mostly due to the increase in light‐harvesting efficiency. The high surface area due to the nanoparticulate structure and strong light harvesting due to the hollow structure make these fibers promising scatterers in DSSCs.     

A multiple times scale solution for non-linear vibration of mass grounded system

In this paper, the vibration of a mass grounded system which includes two linear and non-linear springs in series has been considered. Since this system, depending on its parameters can oscillate symmetrically and asymmetrically, both cases have been solved using multiple times scales (MTS) method and some analytical relations have been obtained for natural frequency of oscillations. The results have been compared with previous work and good agreement has been obtained. Also forced vibrations of system in primary and secondary resonances have been studied for the first time and the effects of different parameters on the frequency-response have been investigated.     

Nonlinear-forced vibrations of piezoelectrically actuated viscoelastic cantilevers

This paper aims to study the nonlinear-forced vibrations of a viscoelastic cantilever with a piecewise piezoelectric actuator layer on its top surface using the method of Multiple Scales. The governing equation of motion is a second-order nonlinear ordinary differential equation with quadratic and cubic nonlinearities which appear in stiffness, inertia, and damping terms. The nonlinear terms are due to the piezoelectricity, viscoelasticity, and geometry of the system. Forced vibrations of the system are investigated in the cases of primary resonance and non-resonance hard excitation including subharmonic and superharmonic resonances. Analytical expressions for frequency responses are derived, and the effects of different parameters including damping coefficient, thickness to width ratio of the beam, length and position of the piezoelectric layer, density of the beam, and the piezoelectric coefficient on the frequency-response curves are discussed for each case. It is shown that in all these cases, the response of the system follows a softening behavior due to the existence of the piezoelectric layer. The piezoelectric layer provides an effective tool for active control of vibration. In addition, the effect of the viscoelasticity of the beam on passive control of amplitude of vibration is illustrated.     

An efficient procedure to find shape functions and stiffness matrices of nonprismatic Euler–Bernoulli and Timoshenko beam elements

Nonprismatic beam modeling is an important issue in structural engineering, not only for versatile applicability the tapered beams do have in engineering structures, but also for their unique potential to simulate different kinds of material or geometrical variations such as crack appearing or spreading of plasticity along the beam. In this paper, a new procedure is proposed to find the exact shape functions and stiffness matrices of nonprismatic beam elements for the Euler–Bernoulli and Timoshenko formulations. The variations dealt with here include both tapering and abrupt jumps in section parameters along the beam element. The proposed procedure has found a simple structure, due to two special approaches: The separation of rigid body motions, which do not store strain energy, from other strain states, which store strain energy, and finding strain interpolating functions rather than the shape functions which suffer complex representation. Strain interpolating functions involve low-order polynomials and can suitably track the variations along the beam element. The proposed procedure is implemented to model nonprismatic Euler–Bernoulli and Timoshenko beam elements, and is verified by different numerical examples.