The synthesis and physical evaluation of 5-alkoxy-1,3-thiazoles prepared via Lawesson's reagent-mediated cyclisation of α-benzamido esters

The synthesis of the first series of 5-alkoxy-1,3-thiazole-based liquid crystals is reported. The aforementioned liquid crystals were synthesised through a Lawesson's reagent-mediated cyclisation of appropriate α-benzamido esters. This methodology was found to be highly efficient, even on a large scale, and the resulting 5-alkoxy-1,3-thiazoles could be purified without the use of column chromatography. The synthesis and mesomorphic properties of a family of 5-alkoxy-2-(4-cyanophenyl)-1,3-thiazole liquid crystals prepared via this approach are discussed and compared with their thiophene and phenyl analogues.     

Temperature dependent electrical conductivity of polyaniline/Y2O3 composites

Composites of polyaniline with yttrium oxide (Y₂O₃) nanoparticles have been prepared by chemical polymerizations method by increasing the weight percentage of yttrium oxide. X-Ray diffraction (XRD) and Fourier Transform Infrared Spectra (FTIR) were used to characterize the composites. XRD and FTIR pattern indicate that Polyaniline (PANI) is intercalated into the layers of Y₂O₃ nanoparticles successfully by in situ polymerization and therefore the degree of crystallinity increases due to crystalline of yttrium oxide nanoparticles. The scanning electron micrographs (SEM) also confirm the formation of dual phase of platelet as well as of flaky structure in PANI-Y₂O₃. Temperature dependant DC conductivity showed three dimensional variable ranges hopping (3D VRH) model. Activation energy, density of states and hopping length are calculated and found to be influenced by intercalating PANI into the layers of Y₂O₃ clay.     

Infrared evidence for the folded-chain model of trans-1,4-polybutadiene

The influence of the first-order crystalline transformation at about 60°C on the infrared bands of trans-1,4-polybutadiene yields microscopic information that supports the two-component microcrystalline model of a folded chain having loose and tight end loops at the lamellar surfaces. The temperature dependence of the band parameters of the 908-cm^?1 vinyl band indicates that 1,2-(side vinyl) units are not easily taken into the crystalline component, thus forming long loops at the crystal surface that account for the micro-Brownian motion detected in the low-temperature phase. The results argue that infrared band parameters are excellent probes for details of the thermodynamics and morphology of polymers.     

Effects of built-in electric field on donor binding energy in InGaN/ZnSnN2 quantum well structures

In_xGa${}_{1?x}$N/ZnSnN₂ quantum well structures are studied in terms of a binding energy of a donor atom. 1s and $2p_{\pm }$ impurity states are considered. The Schrödinger's and Poisson's equations are solved self-consistently. A hydrogenic type wave function to represent each impurity state is assumed. The calculations include band-bending in the potential energy profile introduced by the built-in electric field existing along the structures. The binding energy and the energy of the transition between the impurity states are represented as a function of the quantum well width, the donor position, and the indium concentration. An external magnetic field up to 10 T is included into the calculations to compute the Zeeman splitting. The maximum value of the transition energy is around 30 meV (nearly 7.3 THz) which occurs in a 15-Å In_0.3Ga_0.7N/ZnSnN₂ quantum well. Being strong, the built-in electric field makes the transition energy drop quickly with the decreasing well width. For the same reason, the energy curves are found to be highly asymmetric function of the donor position around the well center. Compared to the bulk value, the transition energy in the quantum well structures enhances nearly two-fold.     

Electrical Impedance Spectroscopic Study of CNT/Ethylene-alt-CO/Propylene-alt-CO Polyketones Nanocomposite

Impedance spectroscopy was utilized to investigate the dielectric properties, ac conductivity and charge transport mechanisms in propylene-alt-CO/ethylene-alt-CO (EPEC) random terpolymer filled with multi-walled carbon nanotubes (MWCNT) as a function of nanofiller content, frequency, and temperature. Equivalent resistor-capacitor (RC) circuit models were proposed to describe the impedance characteristics of the unfilled terpolymer and the nanocomposite at different temperatures. For the nanocomposites, the ac conductivity tended to be frequency independent at low frequencies. At high frequencies, the ac conductivity increased with frequency. The dc conductivity (i.e., plateau of the ac conductivity at low frequencies) at room temperature increased from 10^?9 (Ω·m)^?1 for the unfilled polymer to l0^?3 (Ω·m)^?1 for the 6 wt% MWCNT/EPEC nanocomposite. At low temperatures, the equivalent RC model for EPEC-0 and EPEC-2 was found to consist of a parallel RC circuit. However, for 6 wt% MWCNT/EPEC nanocomposite, an RC model consisting of an R/constant phase element (CPE) circuit and a resistor in series was required to describe the impedance behavior of the nanocomposite.     

Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.