A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

Proton-ionizable crown compounds : 5. Macrocycle-mediated proton-coupled transport of alkali metal cations in H2OCH2Cl2H2O liquid membrane systems

Alkali cation transport is studied using proton-ionizable macrocycle carriers of the 4-hydroxypyridine and pyridone types in a bulk H₂OCH₂Cl₂H₂O liquid membrane system as a function of source and receiving phase pH. A pyridone crown-6 type macrocycle containing an octyl substituent (3) transports Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ from MOH solutions by a proton-coupled mechanism in which no co-anion is transported. In these cases, alkali cation transport increases exponentially with increasing source phase pH above pH 12. Generally, alkali cation transport at source phase pH 14 is higher when nitric acid is present (receiving pH = 1.5) than when it is absent. In competitive transport experiments with macrocycle 3 involving K⁺) and one other alkali cation M⁺, K⁺ is transported selectively over M⁺ by 4.6 (Na⁺), 2.7 (Rb⁺) and 6.3 (Cs⁺) fold when the source and receiving phase pH values are 14 and 7, respectively.     

Organic synthesis with sulfones XXXVIII: On the mechanism of the stereospecific hydrogenolysis of vinylic sulfones by sodium dithionite

The stereospecific hydrogenolysis of vinylic sulfones by sodium dithionite in a protic medium proceeds by addition of HSO₂ to give an intermediate which could be isolated after alkylation in situ to a 1,2-bissulfone. The mechanism is therefore of the β-addition-elimination type. In the case of E-2-benzenesulfonyl-2-butene and ethyl iodide a single crystalline diastereoisomer was obtained and shown to have the threo configuration by X-ray crystallography. The addition step follows the syn and the elimination step the anti stereochemistry, thus accounting for the overall retention of configuration observed.     

Total synthesis of 1-thio-α-tocopherol: A sulfur-containing analogue of vitamin E.

The title compound, has been synthesized in ten steps in an overall yield of 2%.     

A Mild and Efficient Route to 3-Vinylchromones in Aqueous Micellar Media

A simple, mild, and ecofriendly method has been developed for the synthesis of 3-vinylchromones from 4-oxo-4H-1-benzopyran-3-carboxaldehyde (3-formylchromone) by simple Knoevenagel condensation with various active methylene compounds (AMC) in aqueous micellar media in the presence of catalytic amounts of cetyl trimethylammonium bromide (CTAB) and 1,4-diazabicyclo[2.2.2]octane (DABCO). In the case of malonic acid as AMC, the reaction resulted in formation of only Doebner decarboxylated products under the standard reaction condition. It has been also observed that 3-formylchromone derivatives primarily undergo tandem Knoevenagel and Michael reactions in the presence of > 2 equiv. of ethyl acetoacetate to produce benzophenone derivatives, by opening of pyran ring, as the sole product in good yields.     

Theoretical insights into the mechanism of photocatalytic reduction of CO2 over semiconductor catalysts

Photocatalytic reduction of CO₂ is one important approach to alleviate greenhouse gas emission and energy crisis, which has gained huge attention in the past decades. However, the lack of understanding complex reaction mechanism impedes new catalysts design. It is also very difficult to understand the mechanism by using only experimental approaches. For this concern, theoretical calculations can effectively supplement the experimental deficiency and thus play an important role. Recently theoretical calculations have been performed on adsorption, migration and reduction of CO₂ molecule on the photocatalyst surface, leading to useful information that have contributed greatly to this field. This review summarizes recent advances in first-principles calculations about CO₂ photoreduction over various semiconductor photocatalysts like metal oxides, sulfides and g-C₃N₄. The methods, models, adsorption and reaction pathways have been discussed in detail. The perspective about future investigation on the photocatalytic reduction of CO₂ using first principles calculations is also presented.     

Electrical conductivity,optical properties and mechanical stability of 3, 4, 9, 10-perylenetetracarboxylic dianhidride based organic semiconductor

The 3, 4, 9, 10-perylenetetracarboxylic dianhydride (PTCDA) doped polymer films were prepared with Polypyrrole (PPy) and Polyvinyl alcohol (PVA) polymers by solution-casting. The change in structure and chemical composition of samples was identified by XRD and FTIR respectively. The UV–visible spectroscopy demonstrates the optical characteristics and band gap properties of sample. The homogeneous morphology of sample for higher wt% of PTCDA was examined by atomic force microscopy (AFM). The differential scanning calorimetry (DSC) results demonstrate the decrease in melting temperature (T_m) and degree of crystallinity (χ_c%) of polymeric organic semiconductor. The mechanical property demonstrates the high tensile strength and improved plasticity nature. Impedance spectroscopy was evaluated to determine the conductivity response of polymeric organic semiconductor. The highest DC conductivity (2.08×10⁻³ S/m) was obtained for 10 wt% of PTCDA at 140 °C. The decrease in activation energy (E_a) represents the non-Debye process and was evaluated from the slope of ln σ_dc vs. 10³/T plot.     

Ultrathin films of functionalised single-walled carbon nanotubes: a potential bio-sensing platform

ABSTRACT

The Langmuir monolayer is a special class of lyotropic liquid crystalline system wherein phase transition essentially depends on surface density, temperature and ion-content in the aqueous medium. The variety of surface phases can be transferred onto devices by the Langmuir–Blodgett (LB) technique. The Langmuir monolayer of pristine single-walled carbon nanotubes (SWCNTs) exhibited gas and liquid-like phases. The LB film of SWCNTs shows target surface pressure dependent interesting morphologies. The methane gas sensing using parallel alignment of SWCNTs was found to be better than that of randomly oriented SWCNTs. The SWCNTs can be functionalised chemically to enhance the ease of film processability and affinity towards analytes. These are essential parameters for the development of a sensor. In this article, we present our work on Langmuir monolayer and LB films of octadecylamine functionalised SWCNTs (ODACNTs) and its sensing application towards bio-analytes, e.g. L-aspartic acid and bovine serum albumin. The sensing performance of LB film of ODACNTs was compared with that of spin-coated films of ODACNTs. The sensing performance of LB films of ODACNTs indicated a potential platform for bio-sensing application.