Exact Linearization and Invariant Solutions of the Generalized Burgers Equation with Linear Damping and Variable Viscosity

The generalized Burgers equation with linear damping and variable viscosity is subjected to Lie's classical method. Five distinct expressions for the variable viscosity are identified. Both the reduced ordinary differential equations and their corresponding Euler-Painlevé transcendents admit first integrals in the form of Bernoulli's equation and are linearized to obtain solutions in closed form.     

Processing and properties of sintered submicron IR transparent alumina derived through sol–gel method

For the first time, sintered alumina with high transparency in mid infrared region, composed of submicron grains, has been fabricated using sol–gel processing. Commercially available boehmite powder was used to prepare the stable sol. The sol was mixed with appropriate amount of sintering aids and alumina seeds. The sol was further gelled, dried, and heat treated at 1000?°C for producing alumina powder. The powder was further shaped into pellets by compaction and sintered at temperatures between 1200 and 1400?°C in air. Sintered samples were further pressed hot isostatically to produce sintered submicron transparent alumina. The synthesized powder was characterized for its morphology and phase. The sintered and hot isostatically pressed samples were characterized for their physical, mechanical, and optical properties. The present method produced transparent alumina with transparency upto 87% in mid-wave infrared region. These transparency values were at par with the transparency of single crystal sapphire in the mid-wave infrared region and the hardness values were even superior than sapphire.

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Selective and low potential electrocatalytic oxidation of NADH using a 2,2-diphenyl-1-picrylhydrazyl immobilized graphene oxide-modified glassy carbon electrode

DPPH (2,2-diphenyl-1-picrylhydrazil), a free radical-containing organic compound, is used widely to evaluate the antioxidant properties of plant constituents. Here, we report an efficient electroactive DPPH molecular system with excellent electrocatalytic sensor properties, which is clearly distinct from the traditional free radical-based quenching mechanism. This unusual molecular status was achieved by the electrochemical immobilization of graphene oxide (GO)-stabilized DPPH on a glassy carbon electrode (GCE). Potential cycling of the DPPH adsorbed-GCE/GO between ??1 and 1 V (Ag/AgCl) in a pH 7 solution revealed a stable and well-defined pair of redox peaks with a standard electrode potential, E⁰′?=?0?±?0.01 V (Ag/AgCl). Several electrochemical characterization studies as well as surface analysis of the GCE/GO@DPPH-modified electrode by transmission electron microscopy, Raman, and infrared spectroscopy collectively identified the imine/amine groups as the redox centers of the electroactive DPPH on GO. The use of different carbon-supports showed that only oxygen-functionalized GO and MWCNTs could provide major electroactivity for DPPH. This highlights the importance of a strong hydrogen-bonded network structure assisted by the concomitant π-π interactions between the organic moiety and oxygen function groups of carbon for the high electroactivity and stability of the GCE/GO@DPPH-NH/NH₂-modified electrode. The developed electrode exhibited remarkable performance towards the electrocatalytic oxidation of NADH at 0 V (Ag/AgCl). The amperometric i-t sensing of NADH showed high sensitivity (488 nA μM^?1 cm^?2) and an extended linear range (50 to 450 μM) with complete freedom from several common biochemical/chemical interferents, such as ascorbic acid, hydrazine, glucose, cysteine, citric acid, nitrate, and uric acid.     

On the reaction of 1-oxa-4-thiaspiro[4.5]decan-7-one with PhLi. A reinvestigation

Two diastereomeric alcohols are formed from the reaction of 1-oxa-4-thiaspiro[4.5]decan-7-one with PhLi as against the single diastereomer reported earlier. The diastereoselectivity achieved from PhMgBr is significantly higher than with PhLi. The use of Et(2)O/hexane = 2:1 as the solvent for the reaction with PhMgBr offered the highest (14:1) diastereocontrol.     

Voronoi cell volume distribution and configurational entropy of hard-spheres

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume vf, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2gamma) or a three-parameter (3gamma) gamma distribution. The free parameter m in both the 2gamma and 3gamma models is identified as the "regularity factor." The regularity factor is the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of vf. Simulations carried out using a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural inhomogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)] for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system, D, is found necessary for the hard-disk and hard-sphere systems. Thus, for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.     

A phosphorus supported multisite coordinating tris hydrazone P(S)[N(Me)N=CH-C6H4-o-OH]3 as an efficient ligand for the assembly of trinuclear metal complexes: synthesis, structure, and magnetism

A phosphorus supported multisite coordinating ligand P(S)[N(Me)N=CH-C(6)H(4)-o-OH](3) (2) was prepared by the condensation of the phosphorus tris hydrazide P(S)[N(Me)NH(2)](3) (1) with o-hydroxybenzaldehyde. The reaction of 2 with M(OAc)(2).xH(2)O (M = Mn, Co, Ni, x = 4; M = Zn, x = 2) afforded neutral trinuclear complexes [P(S)[N(Me)N=CH-C(6)H(4)-o-O](3)](2)M(3) [M = Mn (3), Co (4), Ni (5), and Zn (6)]. The X-ray crystal structures of compounds 2-6 have been determined. The structures of 3-6 reveal that the trinculear metal assemblies are nearly linear. The two terminal metal ions in a given assembly have an N(3)O(3) ligand environment in a distorted octahedral geometry while the central metal ion has an O(6) ligand environment also in a slightly distorted octahedral geometry. In all the complexes, ligand 2 coordinates to the metal ions through three imino nitrogens and three phenolate oxygens; the latter act as bridging ligands to connect the terminal and central metal ions. The compounds 2-6 also show intermolecular C-H...S=P contacts in the solid-state which lead to the formation of polymeric supramolecular architectures. The observed magnetic data for the (s = 5/2)3 L(2)(Mn(II))(3) derivative, 3, show an antiferromagnetic nearest- and next-nearest-neighbor exchange (J = -4.0 K and J' = -0.15 K; using the spin Hamiltonian H(HDvV) = -2J(S(1)S(2) + S(2)S(3)) - 2J'S(1)S(3)). In contrast, the (s = 1)(3) L(2)(Ni(II))(3) derivative, 5, displays ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions (J = 4.43 K and J' = -0.28 K; H = H(HDvV)+ S(1)DS(1) + S(2)DS(2)+ S(3)DS(3)). The magnetic behavior of the L(2)(Co(II))(3) derivative, 4, reveals only antiferromagnetic exchange analogous to 3 (J = -4.5, J' = -1.4; same Hamiltonian as for 3).     

Synthesis of lateral macrobicyclic compartmental ligands: structural,magnetic, electrochemical,and catalytic studies of mono- and binuclear copper(II) complexes

A series of putative mono- and binuclear copper(II) complexes, of general formulas [CuL](ClO(4)) and [Cu(2)L](ClO(4))(2), respectively, have been synthesized from lateral macrocyclic ligands that have different compartments, originated from their corresponding precursor compounds (PC-1, 3,4:9,10-dibenzo-1,12-[N,N'-bis[(3-formyl-2-hydroxy-5-methyl)benzyl]diaza]-5,8-dioxacyclotetradecane; and PC-2, 3,4:9,10-dibenzo-1,12-[N,N'-bis[(3-formyl-2-hydroxy-5-methyl)benzyl]diaza]-5,8-dioxacyclopentadecane). The precursor compound PC-1 crystallized in the triclinic system with space group P(-)1. The mononuclear copper(II) complex [CuL(1a)](ClO(4)) is crystallized in the monoclinic system with space group P2(1)/c. The binuclear copper(II) complex [Cu(2)L(2c)](ClO(4))(2) is crystallized in the triclinic system with space group P(-)1; the two Cu ions have two different geometries. Electrochemical studies evidenced that one quasi-reversible reduction wave (E(pc) = -0.78 to -0.87 V) for mononuclear complexes and two quasi-reversible one-electron-transfer reduction waves (E(1)(pc) = -0.83 to -0.92 V, E(2)(pc) = -1.07 to -1.38 V) for binuclear complexes are obtained in the cathodic region. Room-temperature magnetic-moment studies convey the presence of antiferromagnetic coupling in binuclear complexes [mu(eff) = (1.45-1.55)mu(B)], which is also suggested from the broad ESR spectra with g = 2.10-2.11, whereas mononuclear complexes show hyperfine splitting in ESR spectra and they have magnetic-moment values that are similar to the spin-only value [mu(eff) = (1.69-1.72)mu(B)]. Variable-temperature magnetic susceptibility study of the complex shows that the observed -2J value for the binuclear complex [Cu(2)L(1b)](ClO(4))(2) is 214 cm(-1). The observed initial rate-constant values of catechol oxidation, using complexes as catalysts, range from 4.89 x 10(-3) to 5.32 x 10(-2) min(-1) and the values are found to be higher for binuclear complexes than for the corresponding mononuclear complexes.     

Novel photosensitizer for dye-sensitized solar cell based on ionic liquid–doped blend polymer electrolyte

The existing energy situation demands not only the huge energy in a short time but also clean energy. In this regard, an integrated photo-supercapacitor device has been fabricated in which photoelectric conversion and energy storage are achieved simultaneously. A novel carbazole-based dye is synthesized and characterized for photosensitizer. The silver-doped titanium dioxide (Ag-TiO₂) is synthesized, and it is used as photoanode material. Different concentrations of tetrabutylammonium iodide (TBAI)-doped polyvinyl alcohol–polyvinylpyrrolidone (PVA-PVP) blend polymer electrolytes are prepared, and their conductivity and dielectric properties were studied. Reduced graphene oxide (r-GO) is synthesized by a one-pot synthesis method and confirmed using Raman spectroscopy for counter electrode material in dye-sensitized solar cell (DSSC) and supercapacitor electrodes. The DSSC having 4% Ag-TiO₂–based photoanode showed the highest efficiency of 1.06% (among r-GO counter electrodes) and 2.37% (among platinum counter electrodes). The supercapacitor before integration and after integration exhibits specific capacitance of 1.72 Fg⁻¹ and 1.327 Fg⁻¹, respectively.

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