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In this article, we determine modular identities on Ramanujan's product of theta-functions ψ(−q) and f(q) which is similar to ai,j and their explicit evaluations. [ABSTRACT FROM AUTHOR]

MoS2 nanostructure was successfully synthesized by employing one step solvothermal route for electrochemical water splitting applications. Generally, MoS2 nanostructures played a very important role in electrochemical energy field due to its unique physical and chemical properties [1]. In the present study, bare and Ni incorporated MoS2 nanostructures were synthesized via solvothermal route and the rhombohedral phase formation for bare and 5% Ni doped MoS2 was confirmed by X-ray diffraction (XRD) study. On further increasing the dopant concentration as 10%, the phase transformation was strongly influenced and thereby the rhombohedral phase was turned as monoclinic Mo2S3 phase and was evidenced by strong diffraction peak of plane (-101). The phase changing mechanism of Ni dopant on MoS2 nanostructures was also revealed. The luminescent nature of the synthesized nanostructures was studied by photoluminescence (PL) spectra. FTIR result clearly demonstrated the Mo-S vibration of two different phases. SEM images clearly revealed the clumsy growth of nanorods for both the phases of nanostructures. The electrochemical water splitting efficiency of different phase molybdenum sulfides have been explored by cyclic voltammetry (CV), linear sweep voltammetry (LSV), electrochemical impedance spectroscopy (EIS) and chronoampherometry (CA) studies. The best efficient 10% Ni doped Mo2S3 electrode governed the specific capacitance of 1207 F/g at 10 mV/s scan rate with higher current density of 193 mA/g with good conductivity. Moreover, the very good electrochemical stability was reported for the efficient electrode for 18 h with zero percent decay of its activity even after 18 h of excellent electrochemical water oxidation process. Mechanism of dopant and phase nature on electrochemical performance of the electrode was revealed. Hence, the favorable phase, dopant and morphology of molybdenum sulfide nanostructures for electrochemical water splitting applications were explored in this study. [ABSTRACT FROM AUTHOR]

Novel PVP supported multi-phase nanocomposite electrocatalysts has been synthesized by one step solvothermal route. Successful attempting of achieving multi-phase CuBi2O4@CuO@α-Bi2O3 nanocomposite electrocatalyst has been confirmed by well-built diffraction peaks obtained through XRD. Phonon vibration modes, oxygen defects and metal-oxygen vibrations present in the nanocomposite has been confirmed by Raman, PL and FTIR studies. The estimation of optical band gap for CuBi2O4@CuO@α-Bi2O3 nanocomposite was 1.77 eV. The rice like nanoparticle morphology has been examined by SEM images. The multi-phase formation and growth mechanism achieved by PVP linkaging agent has been discussed. The maximum oxygen evolution reaction (OER) activity of CuBi2O4@CuO@α-Bi2O3 nanocomposite achieved as 0.14 mA/g with lowest over potential of 135 mV/decade and the excellent stability over 3h with 0.2 mA/g current density. From this report, we have strongly recommended that PVP capping agent is the most suitable surfactant for highly active multiphase nanocomposite electrocatalyst rather than single phase binary metal oxides for electrochemical water splitting application. [ABSTRACT FROM AUTHOR]

In this work, synthesis of β-V2O5 nanorods by solvothermal method was adopted at optimum experimental conditions by varying the concentration of NaOH as 0.5M, 1M, 1.5M and 2M. The obtained products were characterization by following techniques, XRD, RAMAN, FTIR, and FESEM. The XRD results reveal the formation of β-V2O5 nanorods and its crystalline nature was confirmed by its lattice parameters. The Raman analysis shows a peak at 485, 770 and 998 cm−1 corresponds to the vibration of O-V-O bonds. Similarly the FITR peaks appeared at the 530 and 786 cm−1 can be attributed to the symmetric stretching of Metal Oxide (V-O). The morphology and its structure of β-V2O5 nanorods can be analysized by the FESEM techniques and its images shows the formation of β-V2O5 nanorods with different dimensions. The role of concentration of NaOH can be studied by comparing the FESEM micrographs. It is clearly evident from FESEM images as the concentration of NaOH increases from 0.5 M to 2M, the shape and size of the change rapidly and the surface effect results in the mesoporous features on the surface of nanorods. Its note worthy as the concentration of NaOH increases results in the flattening of nanorods could be observed due more of interaction of NaOH precursor solution. [ABSTRACT FROM AUTHOR]

The surfactant free SnO2 nanostructure was successfully synthesized by simple one pot hydrothermal route and its physico-chemical properties were investigated. XRD result confirmed the formation of tetragonal SnO2 nanostructure. Raman spectrum revealed two Raman active modes (Eg +A2u) of SnO2 nanostructure. SEM images revealed nanoplate array formation of SnO2. The well defined metal oxygen vibration band (O-Sn-O) at 609 cm−1 was confirmed through FTIR spectrum. The electrochemical properties of the sample were examined by employing four different electrolytes such KCl, KOH, Na2SO4 and NaOH respectively. The highest specific capacitance of about 120.41 F/g for 5 mV/s and good conductivity was observed for the electrolyte KCl by cyclic voltammogram (CV) and electrochemical impedance spectroscopy (EIS) studies. [ABSTRACT FROM AUTHOR]

An attempt was made to synthesis the copper doped tin oxide (Cu-SnO2) nanoparticles by adopting different chelating agents (NaOH, KOH and C2H2O4) by Sol-gel process. The synthesized products were characterized by XRD, Photoluminescence (PL), Infra- Red (FTIR) and SEM analysis. The XRD confirms the formation of Cu-SnO2 shows the maximum peak at 33.8° with lattice plane (101). The PL peak at 361 and 382 nm due to the recombination of electron in conduction band to valence band infers the optical properties. The IR spectra correspond to the peak at 551 and 620 cm−1 attributed to the characteristics peak for Cu-SnO2 nanoparticles. The SEM images for all three Cu-SnO2 nanoparticles formed by three chelating agent (NaOH, KOH and C2H2O4) facilitates the formation mechanism and the chelating agent Oxalic acid results in formation of nano flowers with diverse layers orientated in random direction. Further SEM studies reveal that, the Cu-SnO2 nanoparticles formed by oxalic acid could posses high surface area with large number layered structured enables the better electrochemical properties and its applications. [ABSTRACT FROM AUTHOR]

Facile and economically viable one step hydrothermal route was adapted to synthesis SnO2/α-Fe2O3 nanocomposite with and without hexamine (HMT) as surfactant successfully. The formation of SnO2/α-Fe2O3 nanocomposite was confirmed through XRD, Raman, PL and FTIR studies. The presence of well defined XRD diffraction peaks of both SnO2 and α-Fe2O3 revealed the formation SnO2/α-Fe2O3 nanocomposite. The obtained characteristic Raman active (Eg+Eg+Eu+A2u) mode of vibrations confirmed the formation of SnO2/α-Fe2O3 nanocomposite. Photoluminescence study revealed the emission behavior of the product. Metal oxygen vibrations of Fe-O in both octahedral, tetrahedral sites and Sn-O were confirmed by the bands located at 466, 580 and 673 cm−1 respectively through FTIR. The spherical morphology of the product synthesized with and without the surfactant HMT has been revealed by SEM images. The electrochemical behavior of the product was investigated through CV and EIS studies in 1M Na2SO4 electrolyte solution and obtained the highest specific capacitance of 211.25 F/g at 5 mV for the surfactant assisted product. [ABSTRACT FROM AUTHOR]

High quality Ni-doped CeO2 (CeO2:Ni) thin films were deposited on glass substrates at room temperature by using radiofrequency magnetron sputtering. The effect of annealing temperature on structural and optical properties of the CeO2:Ni films was investigated. The structural, optical and vibrational properties of the films were determined using X-ray diffraction (XRD), photoluminescence spectrometer (PL) and Raman spectrometer. It was found that the as-deposited film has a fluonte cubic structure. By increasing annealing temperature from 100°C to 300°C, the crystalline quality of the thin films could be improved. The UV and visible band emissions were observed in the photoluminescence spectra, due to exciton, defect related emissions respectively. The micro-Raman results show the characteristic peak of CeO2 F2g at 465 cm-1 and 2LO at 1142 cm-1. Defect peaks like D and O bands were observed at 641 cm-1 and 548 cm-1 respectively. It is found from the spectra that the peak intensity of the films increased with increase of annealing temperature. [ABSTRACT FROM AUTHOR]

We report systematic studies of the magnetic properties of Ni and Mn co-doped ZnO nanoparticles prepared by co-precipitation method. Structural characterization reveals that Ni and Mn ions substituted into ZnO lattices without any secondary phases formation. Photoluminescence and Raman spectra shows that the Ni/Mn were doped into the ZnO lattice resulting slight shift in near-band-edge emission. Moreover, the novel Raman peak at 586 cm-1 indicates two kinds of cations via doping that could affect the local polarizability. Magnetic measurements of the nanoparticles exhibits ferromagnetic behavior at room-temperature. [ABSTRACT FROM AUTHOR]