Supersymmetry and the ladder operator technique in quantum mechanics: The radial Schrödinger equation

Using the ladder operator technique, a construction of the supersymmetric Hamiltonian is proposed. We show that the accidental degeneracies associated with the Coulomb and isotropic oscillator problems may be attributed to the existence of a supersymmetry of the Hamiltonians.     

A new perspective on single and multi-variate differential equations

We elaborate upon a new method of solving linear differential equations, of arbitrary order, which is applicable to a wide class of single and multi-variate equations. Our procedure separates the operator part of the equation under study in to a part containing a function of the Euler operator and constants, and another one retaining the rest. The solution of the equation is then obtained from the monomials (or the monomial symmetric functions, for the multi-variate case), which are the eigenfunctions of the Euler operator. Novel exponential forms of the solutions of the differential equations enable one to analyze the underlying symmetries of the equations and explore the algebraic structures of the solution spaces in a straightforward manner. The procedure allows one to derive various properties of the orthogonal polynomials and functions in a unified manner. After showing how the generating functions and Rodriguez formulae emerge naturally in this method, we briefly outline the generalization of the present approach to the multi-variate case.     

pH-Dependent self-assembly of water-soluble sulfonate-tetraphenylethylene with aggregation-induced emission

The fabrication of well-defined nanostructures with luminescent properties in the solid or aggregated state is of intense interest due to their applications in nano- and biotechnology. We report the synthesis of water-soluble tetraphenylethylene bearing four sulfonate groups as a sodium salt (Su-TPE), and investigations concerning its AIE characteristics by the addition of organic solvent into the aqueous solution, which is the reverse procedure to conventional AIE-active TPE derivatives. The resultant compound is weakly emissive in pure water, however, emits strongly upon addition of THF solvent (with THF fraction > 60%). The emission properties and the morphologies of the aggregates were greatly dependent upon the solution pH. Su-TPE self-assembled into variety of structures in water/THF mixture with pH control, for the first time. Well-defined uniform nanorods with a width of about 200 nm and a length of up to 10 μm were obtained at solution pH of 1. The Su-TPE showed very good mechanochromic properties were observed during the process of grounding and fuming.     

Photo-induced decolorization of dimethylmethylene blue with selenious acid: a novel method to examine selective monomer-dimer distribution of the dye in micelle

In this report, selenious acid (H2SeO3) has been exploited to study the decolorization of a cationic dye, dimethylmethylene blue (DMMB) with UV-light. Micelles have effectively been employed as organized media to promote the rate of decolorization of the dye molecules. Micellar catalysis has been explained as a consequence of electrostatic, hydrophobic and charge transfer interactions. It has also been shown that strong charge transfer and electrostatic interaction lead to an appreciable enhancement of the reaction rate in micelle, whereas, weak hydrophobic interaction is of marginal importance. Existence of monomer-dimer equilibrium for the dye molecules under certain selective environments has been identified spectrophotometrically. Then the shift of dimer-monomer equilibrium of the dye has been successfully studied in aqueous and micellar environments exploiting photodecolorization process for the dye in solution. 'Salting-in' and 'salting-out' agents were introduced into the reaction mixture to examine the viability of the dye decolorization process for dye contaminated water samples.     

Cofluorescence of Eu in complexes of aromatic carboxylic acids

The fluorescence of Eu³⁺ in certain Eu³⁺–aromatic acid complexes were enhanced by over two orders of magnitude, by the addition of La³⁺; a process referred to as cofluorescence. Cofluorescence was observed only with certain aromatic acid ligands; trismesic acid, pyromellitic acid and mellitic acid; thereby clearly establishing a correlation between the structure of the ligand and the process of cofluorescence. While cofluorescence has been extensively studied using β-diketones as ligands, our studies demonstrate cofluorescence for the first time in ligands other than β-diketones. Furthermore, the mechanism of cofluorescence in the aromatic acid complexes studied by us appears to be different from that operating in the β-diketones. While intermolecular energy transfer is believed to occur in the β-diketones, formation of polynuclear complexes appears to be responsible for cofluorescence in the aromatic acid ligands.     

Fluorimetric estimation of DNA content using sensitized lanthanide fluorescence

Lanthanide fluorescence enhancement on complexation with calf thymus DNA was studied in aqueous solution. The DNA sensitized and enhanced fluorescence of terbium and europium by nearly two orders of magnitude. By applying this ligand sensitized lanthanide fluorescence enhancement, DNA could be estimated at 10 ppb level. Further, effect of addition of TOPO in Triton X-100 micellar medium to Tb-DNA complex in solution was also studied. On addition of TOPO, no synergistic terbium fluorescence enhancement was observed.     

Formation constants ofN-o-tolylbenzohydroxamic acids with manganese(II), nickel(II), copper(II) and zinc(II)

Summary The thermodynamic metal ligand stability constants with some divalent metal ions ofN-o-tolylbenzohydroxamic acids at 25° and 35° were determined in 11 dioxan:water. The order of stability constants is discussed.     

Ferroelectric phase transition of Ba1− x Sr x Ti0.6Zr0.4O3 ceramics

Perovskite type Ba_{1? x} Sr _x Ti_0.6Zr_0.4O₃ (with x = 0.0, 0.1, 0.2, 0.4 and 0.5) ceramics have been synthesized through solid oxide reaction route. The room temperature XRD study suggests the compositions have single phase cubic symmetry. Microstructural studies have shown a step decrease in grain size. The dielectric study reveals that the materials are of relaxor type and undergo a diffuse type ferroelectric phase transition. The diffusivity increases with increase in Sr contents in the studied composition range. The transition temperature decreases with increase in Sr contents due to the decrease in grain size.     

Ferroelectric studies for soft Gd-modified PZT ceramics

The polycrystalline samples of gadolinium-modified lead–zirconate–titanate (Pb_1?xGd_x (Zr_0.52Ti_0.48)_1?x/4O₃) (x?=?0, 0.07, 0.10 and 0.12) (PGZT x/52/48) ceramics near morphotropic-phase boundary were prepared using conventional solid-state reaction route. XRD patterns show the formation of single-phase compounds in rhombohedral crystal system. SEM textures of the samples reveal uniform grain distribution. Frequency and temperature dependence of dielectric constant of the materials indicates non-relaxor behavior and indication of the diffuse phase transition at higher values of Gd concentration. The temperature dependence of P–E loops confirms ferroelectricity in the materials. The piezoelectric studies of the samples show enhancement in piezoelectric coefficients on substitution of Gd at the Pb site.