Some generating functions of Jacobi polynomials

In this paper, Weisner’s group-theoretic method of obtaining generating functions is utilized in the study of Jacobi polynomialsP> _n ^(a,ß)(x) by giving suitable interpretations to the index (n) and the parameter (β) to find out the elements for constructing a six-dimensional Lie algebra.     

Indium-mediated allylation/propargylation of α-diazoketones: a facile synthesis of 1-bromo-2-alkyl- or 2-arylpent-4-en-2-ols

α-Diazoketones undergo smooth allylation with successive bromide insertion with allylindium bromide generated in situ from allyl bromide and indium metal to produce 1-bromo-2-alkyl- or 2-arylpent-4-en-2-ols in high yields. Addition of propargylindium bromide produces 1-bromo-2-alkyl-or 2-arylpent-4-yn-2-ols under similar conditions.     

Studies on antimony oxides: Part I

Thermogravimetry (TG), differential thermal analysis (DTA) and X-ray diffraction studies of antimony(III) oxide, (Sb₂O₃), in air, nitrogen and argon atmospheres have been made. In air Sb₂O₃ becomes oxidized to Sb₂O₄ above 510°. The oxidation reaction proceeds in two stages as revealed by the TG and DTA curves. The behaviour of Sb₂O₃ is similar in both N₂ and Ar. Sb₂O₃ remains unaffected up to 430°, above which there is a slow, and continuous mass loss up to 550°. Above 550° Sb₂O₃ volatilizes resulting in an enormous weight loss. X-ray studies of the sublimate and the residue indicate the former to be the cubic form of Sb₂O₃ (Senarmontite) while the residue is the orthorhombic (Valentinite) structure. From the DTA curves in air, N₂ and Ar, the transition temperature for the cubic to the orthorhombic modification has been estimated to be around 610°.     

A carbazole-based polymeric azodye

A new polymeric azodye has been synthesized from carbazole by diazotization of its derivative N-methylcarbazole-3,6-diamine and subsequent coupling reaction with 2,2-bis(4-hydroxyphenyl-3-sulfonate-Na)-propane prepared from bisphenol-A. Its physico-chemical, electrical, and thermal properties have been characterized; finally, its application to the preparation of colored semiconductive films from polyvinyl alcohol has been studied.     

Polymerization of vinylcarbazole on copper(II)-13X molecular sieves: Role of copper(II) salts

Copper(II)-exchanged-13X molecular sieves, prepared from four copper(II) salts, namely, sulfate, nitrate, chloride, and acetate, and their activities in the polymerization of N-vinylcarbazole at a fixed copper ion exchange level were studied. From the kinetic characteristics of polymerization it was established that the variation in activities of the Cu-exchanged sieves is due primarily to the difference in the pH of the original salt solution, which is responsible for the varying degree of proton exchange with the zeolite during copper ion exchange. A first-order dependence of the rate of polymerization was observed with respect to H⁺ ion concentration of the original copper-salt solution. It was further established that the rate of polymerization of exchanged copper ion, at a hypothetical zero proton concentration, is low. A mechanism of polymerization of NVC on copper-exchanged-13X zeolite was suggested on the basis of the results obtained.     

Potentiometric titration of hydrogen peroxide with an electropolished stainless steel electrode

The preparation and use of a stainless steel indicator electrode in the accurate potentiometric titration of aqueous hydrogen peroxide are described. The results agree excellently with those obtained by a standard colorimetric weight-titration procedure. The nature of the titration curves, potential changes and the factors affecting them are discussed. Rapid potentiometric titrations directly to the equivalence-point potential are possible, owing to the nature of the titration curve.     

Effects of chain length and heat treatment on the nanotribology of alkylsilane monolayers self-assembled on a rough aluminum surface

The conformational order of alkylsilane monolayers self-assembled on a rough aluminum surface is affected by the molecular chain length and the thermal history of the sample. These monolayers have been characterized by grazing angle FTIR spectroscopy. Tribological mechanisms were explored using initial molecular conformation order, sliding distance, normal load, and substrate compliance as experimental variables. Results indicate that the initial conformational disorder of the molecules determines the level of friction at the commencement of sliding. Adverse changes in dynamic friction and monolayer life during sliding are not thermally induced but are related to substrate roughness and local plasticity. Plastic deformation reduces the spatial density of the alkylsilane monolayer and is accentuated by an increase in the normal load.     

Thermodynamics of 2,2′-dipyridinium ion and its iron(II) complex in methanol—water mixture at 25°C

The enthalpies of formation of the 2,2′-dipyridinium ion and the 2,2′-dipyridyl-iron(II) complex in methanol—water media at 25°C have been determined by caloriumetry. The entropy-changes have been calculated combining the enthalpy values with the corresponding free-energy changes previously reported. The role of solvents on the thermodynamic parameters has been discussed.     

Studies on adsorption of 5-amino tetrazole on silver nanoparticles by SERS and DFT calculations

The surface-enhanced Raman scattering (SERS) studies of 5-amino tetrazole (5AT), a tetrazole derivative, in aqueous silver sol at pH approximately 9 and on deposited colloidal silver films were carried out and compared with the normal Raman spectrum of the molecule. The experimentally observed Raman bands along with their corresponding infrared bands were assigned based on the results of density functional theory (DFT) calculations. The significant changes evidenced between the SERS and the normal Raman spectra combined with the theoretical data obtained for Ag-5AT system demonstrated that the molecule is adsorbed on colloidal Ag particles through the lone pair of electrons of the nitrogen atom. The contribution of the chemical mechanism for the SERS enhancement was proved by the behavior of the electronic absorption spectrum of the Ag colloid upon addition of 5AT. This is further supported by the theoretical calculations that show that the favorable interaction of the frontier orbitals localized on Ag(+) and the negatively charged nitrogen from the tetrazole ring leads to the formation of the stable (up to 130 kJ mol(-1)) charge-transfer complex. The orientation of the adsorbed species with respect to the metal surface was also predicted by applying the "surface selection rule". In addition, the feasibility of the formation of the polymeric species has also been discussed.     

Studies of carbazole-based polyarylates

A low temperature solution condensation method with pyridine as acceptor-catalytic reagent was applied to the synthesis of polyarylates from carbazole and bisphenol A/phenolphthalein. The polyarylates were classified with respect to their structure, thermal stability, and dielectric behavior.