Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators     

Nitroxide‐mediated radical polymerization in miniemulsion: Bimolecular termination in monomer‐free model systems

Bimolecular termination in nitroxide‐mediated radical polymerization in miniemulsion has been investigated through the heating of a polystyrene–2,2,6,6‐tetramethylpiperidinyl‐1‐oxy macroinitiator and its 4‐hydroxy‐2,2,6,6‐tetramethylpiperidinyl‐1‐oxy analogue in an aqueous toluene dispersion with sodium dodecyl benzenesulfonate as a surfactant at 125 °C. The level of bimolecular termination by combination, evaluated from the high‐molecular‐weight shoulder, was higher in miniemulsion than in solution and increased with decreasing particle size. Quantitative analysis revealed that these results cannot be rationalized solely by nitroxide partitioning to the aqueous phase. The results are explained by an interface effect, by which nitroxide is adsorbed or located at the aqueous–organic interface. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4995–5004, 2007     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

A neutron polarization analysis study of Ce2Fe17 in its paramagnetic phase

Spin-flip (paramagnetic) scattering and neutron depolarization studies were performed on Ce₂Fe₁₇ in its paramagnetic phase on the Dhruva neutron polarization analysis spectrometer. The absence of normalQ dependence of the scattered spin flip intensity shows that Ce₂Fe₁₇ is not a normal paramagnetic and there exist superparamagnetic clusters of sufficiently large dimensions (～100Å). The observed neutron depolarization gives an indication of the dynamics of these Ce₂Fe₁₇ superparamagnetic clusters.     

Synthesis and studies of antibacterial activity of pongaglabol

Pongaglabol [8-hydroxy-5-phenyl-furo[2,3-h]benzo(b)pyran-7-one] was synthesized and tested for antibacterial effects againstShigella dysenteriae, Salmonella typhi, Streptococcus β-haemolyticus andStaphylococcus aureus. The synthesized compounds were characterized using UV, IR and¹H NMR spectral data     

Synthesis and comparative solution properties of single‐, twin‐, and triple‐tailed associating ionic polymers based on diallylammonium salts

The cycloterpolymerizations of single‐, twin‐, and triple‐tailed hydrophobes with hydrophilic monomer N,N‐diallyl‐N‐carboethoxymethylammonium chloride and sulfur dioxide afforded a series of cationic polyelectrolytes (CPEs) in excellent yields. These CPEs, upon the acidic hydrolysis of the pendent ester groups, gave the corresponding pH‐responsive cationic acid salts, which, upon a treatment with sodium hydroxide, were converted to polybetaines (PBs), anionic polyelectrolytes (APEs), and PB/APE polymers containing various proportions of zwitterionic (PB) and anionic fractions (APE) in the polymer chain. At a shear rate of 0.36 s⁻¹ at 30 °C, salt‐free water solutions of the CPEs (2 g/dL) containing 8, 4, and 2.67 mol % of the single‐, twin‐, and triple‐tailed hydrophobes (all having 8 mol % octyloxy tails) had apparent viscosity values of 70, 2800, and 396,000 cps, respectively. The PB/APE polymer with a ratio of 33:67 for the zwitterionic and anionic fractions in the polymer chain gave the highest viscosity value. The superior viscosity behavior of the polymers containing the triple‐tailed hydrophobe was attributed to the blocky nature of the comonomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5480–5494, 2006     

Thermal behaviour of ethynyl and ethenyl terminated imide resins

A series of ethynyl and ethenyl end-capped imide resins were synthesised by the reaction of 9,9-bis(4-aminophenyl) fluorene (BAF) with pyromellitic dianhydride (PMDA)3/3′, 4,4′-benzophenone tetracarboxylic acid dianhydride (BTDA)/2,2-bis(3,4-dicarboxy phenyl) hexafluoropropane dianhydride (6F) and 3-ethynyl aniline/maleic anhydride. Structural characterisation was done by infra red and elemental analysis. Thermal characterisation was done by differential scanning calorimetry and thermogravimetric analysis. The decomposition temperatures of cured resins were above 200°C in nitrogen atmosphere. Char yield at 800°C ranged from 59–65.5%.     

Crystal structure of dicyclohexano-18-crown-6 potassium 2-nitrophenoxide

The first crystal structure of a potassium cation complex with dicyclohexano-18-crown-6 is reported. The potassium 2-nitrophenoxide complex ofsyn-cis-syn dicyclohexano-18-crown-6 crystallizes in the triclinic space group P with cell constantsa=8.604(2),b=10.772(4),C=16.123(5)Å, =73.86(3)°,=77.61(3)°, =82.68(3)° andZ=2 forD _c =1.31 g cm^–3. Least-squares refinement based on 2742 observed reflections led to a final conventionalR value of 0.040. Dicyclohexano-18-crown-6 has the shape of a saddle with the potassium cation sitting at the saddlepoint. The structure of the 2-nitrophenoxide anion is dominanted by the quinoid resonance contributor. Because the complex is devoid of significant intercomplex interactions, it is a prototypical 1:1:1 complex. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82043 (26 pages).Now Mrs. K. M. Balo.