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.     

A view about the short histories of the mole and Avogadro’s number

The mole and Avogadro’s number are two important concepts of science that provide a link between the properties of individual atoms or molecules and the properties of bulk matter. It is clear that an early theorist of the idea of these two concepts was Avogadro. However, the research literature shows that there is a controversy about the subjects of when and by whom the mole concept was first introduced into science and when and by whom Avogadro’s number was first calculated. Based on this point, the following five matters are taken into consideration in this paper. First, in order to base the subject matter on a strong ground, the historical development of understanding the particulate nature of matter is presented. Second, in 1811, Amedeo Avogadro built the theoretical foundations of the mole concept and the number 6.022 × 10²³ mol^?1. Third, in 1865, Johann Josef Loschmidt first estimated the number of molecules in a cubic centimetre of a gas under normal conditions as 1.83 × 10¹⁸. Fourth, in 1881, August Horstmann first introduced the concept of gram-molecular weight in the sense of today’s mole concept into chemistry and, in 1900, Wilhelm Ostwald first used the term mole instead of the term ‘gram-molecular weight’. Lastly, in 1889, Károly Than first determined the gram-molecular volume of gases under normal conditions as 22,330 cm³. Accordingly, the first value for Avogadro’s number in science history should be 4.09 × 10²² molecules/gram-molecular weight, which is calculated by multiplying Loschmidt’s 1.83 × 10¹⁸ molecules/cm³ by Than’s 22,330 cm³/gram-molecular weight. Hence, Avogadro is the originator of the ideas of the mole and the number 6.022 × 10²³ mol^?1, Horstmann first introduced the mole concept into science/chemistry, and Loschmidt and Than are the scientists who first calculated Avogadro’s number. However, in the science research literature, it is widely expressed that the mole concept was first introduced into chemistry by Ostwald in 1900 and that Avogadro’s number was first calculated by Jean Baptiste Perrin in 1908. As a result, in this study, it is particularly emphasised that Horstmann first introduced the mole concept into science/chemistry and the first value of Avogadro’s number in the history of science was 4.09 × 10²² molecules/gram-molecular weight and Loschmidt and Than together first calculated this number.     

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.