Tailoring the donor moieties in TPA-based organic dyes for efficient photovoltaic,optical and nonlinear optical response properties

The current study reports tailoring the electronic donor structures of organic dyes to modify their optical and nonlinear optical (NLO) response properties. Five (5) tri-phenyl amine (TPA) based Donor-π-Acceptor (D-π-A) organic dyes with the codes ICAA1 , ICAA2 , ICAA3 , ICAA4 , and ICAA5 were designed and investigated for their optical and NLO properties using quantum chemical methods. Optical and NLO properties of these dyes were studied by CAM-B3LYP method and 6-311G* basis set. The focus has been on the impact of adding secondary donors and shifting their substitutions at ortho (o), meta (m) and para (p) positions. Among all designed compounds, ICAA4 showed the highest amplitude of average third-order NLO polarizability <γ>, which is calculated to be 1316 × 10⁻³⁶ esu. Time-dependent Density Functional Theory (TD-DFT) method was used to determine how a change in the position of the donor affected the excitation energy (E_g) and NLO response properties. The findings showed that changing the position of the secondary donor results in a red shift among absorption spectra as well as the increase in their NLO responses. Complete process of intramolecular charge transfer (ICT) has been investigated in terms of different optical parameters such as frontier molecular orbitals (FMOs), molecular electrostatic potentials (MEPs), transition density matrix (TDMs), density of states (DOS), electron density difference (EDD), and natural bond orbital (NBO) analysis. Our calculations for study of ICT process indicate that p-position of methoxy group performs better among all other positions and even it has better NLO response properties than the compound with three collective methoxy groups. The calculated V_oc values of all designed molecules range from 1.09 to 1.30, all of them are positive while their ΔG_inject is found to be in the range of −0.87 to −1.79 eV indicating their decent potential for photovoltaic applications. The studied optical, NLO and photovoltaic parameters illustrated that ICAA1 to ICAA5 are appropriate molecules not only for NLO applications but also for efficient photovoltaic purposes.     

Mathematical proof of closed form expressions for finite difference approximations based on Taylor series

Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.     

Tin sulfide nanoparticles supported on activated carbon as an efficient and reusable Lewis acid catalyst for three-component one-pot synthesis of 4H-pyrano[2,3-c]pyrazole derivatives

Tin sulfide nanoparticles (SnS‐NPs) were prepared in aqueous solution at room temperature on the surface of activated carbon (AC) and were investigated using field‐emission scanning electron mi‐croscop...     

On the Hydrodynamics and Heat Convection of an Impinging External Flow Upon a Cylinder with Transpiration and Embedded in a Porous Medium

This paper extends the existing studies of heat convection by an external flow impinging upon a flat porous insert to that on a circular cylinder inside a porous medium. The surface of the cylinder is subject to constant temperature and can include uniform or non-uniform transpiration. These cylindrical configurations are introduced in the analyses of stagnation-point flows in porous media for the first time. The equations governing steady transport of momentum and thermal energy in porous media are reduced to simpler nonlinear differential equations and subsequently solved numerically. This reveals the dimensionless velocity and temperature fields of the stagnation-point flow, as well as the Nusselt number and shear stress on the surface of the cylinder. The results show that transpiration on the surface of the cylinder and Reynolds number of the external flow dominate the fluid dynamics and heat transfer problems. In particular, non-uniform transpiration is shown to significantly affect the thermal and hydrodynamic responses of the system in the circumferential direction. However, the permeability and porosity of the porous medium are found to have relatively smaller influences.     

A wide potential window aqueous supercapacitor based on LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript>–rGO nanocomposite

Aqueous supercapacitors based on neutral solutions have the advantages of high-ionic conductivity, being environmentally friendly, safe, and low cost. However, the operating potential window for most aqueous electrolytes is far lower than that of organic electrolytes that are commonly used in commercial supercapacitors. In this work, we report on the fabrication of a wide potential window, high-energy aqueous asymmetric supercapacitor, without sacrificing power, by using a nanostructured LiMn₂O₄/reduced graphene oxide (LMO–rGO) nanocomposite. We synthesized the uniformly distributed LMO in the LMO–rGO nanocomposite using a co-precipitation route followed by a low-temperature hydrothermal treatment. In a three-electrode cell setup, the specific capacitance of the LMO–rGO nanocomposite electrode at 1 A/g (1.2 mA/cm²) is 268.75 F/g (258 mF/cm²), which shows a dramatic improvement over the sum of the specific capacitances of pristine LMO (162.5 F/g) and pure rGO (29.94 F/g) electrodes in their relative ratios, when used alone. This finding suggests a synergistic coupling of LMO and rGO in the nanocomposite. We also assembled the LMO–rGO nanocomposite, as the positive electrode, with activated carbon, as the negative electrode, into an asymmetric cell configuration. The device shows an ultra-wide potential window of 2.0 V in a neutral aqueous Li₂SO₄ electrolyte, with a maximum energy density of 29.6 Wh/kg (which approaches the commercial lead-acid batteries), power density of up to 7408 W/kg, and an excellent cycle life (5% loss after 6000 cycles). These findings confirm that an LMO–rGO nanocomposite is a promising material to meet the demands of real world energy storage.     

Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system

This paper deals with the analytical property of the first Melnikov function for general Hamiltonian systems possessing a cuspidal loop of order 2 and its expansion at the Hamiltonian value corresponding to the loop. The explicit formulas for the first coefficients of the expansion have been given. We prove that at least 13 limit cycles can bifurcate from the cuspidal loop of order 2 under certain conditions. Then we consider the cyclicity of a cuspidal loop in some Liénard and Hamiltonian systems, and determine the number of limit cycles that can bifurcate from the perturbed system.     

Computational Modeling of Liquid Droplets Moving on Rough Surfaces

We present a de-coupled approach for computational modeling of liquid droplets moving on rough substrate surfaces. The computational model comprises solving the membrane deformation problem and the fluid flow problem in a segregated manner. The droplet shape is first computed by solving the Young-Laplace equation where contact constraints, due to the droplet-substrate contact, are applied through the penalty method [1]. The resulting configuration constitutes the domain for the fluid flow problem, where the bulk fluid behavior is modeled by the unsteady Stokes' flow model expressed in Arbitrary Lagrangian-Eulerian (ALE) framework. The entire analysis is performed in the framework of Finite Element Method (FEM). Application of the approach to the case of a droplet moving on a rough surface is presented as an example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Recollements of Functor Categories

This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category \(\mathcal {S}\) and a maximal object s of \(\mathcal {S}\) and construct a recollement of \(\text {Mod-}\mathcal {S}\) in terms of \(\text {Mod-End}_{\mathcal {S}}(s)\) and \(\text {Mod-}(\mathcal {S}\setminus \{s\})\) in four different levels. In case \(\mathcal {S}\) is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N-complexes.