Spectral approximations to the fractional integral and derivative

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Theoretical study of two states reactivity of methane activation on iron atom and iron dimer

Density functional theory (DFT) calculations have been carried out to explore the catalytic activation of C–H bonds in methane by the iron atom, Fe, and the iron dimer, Fe2. For methane activation on an Fe atom, the calculations suggest that the activation of the first C–H bond is mediated via the triplet excited-state potential energy surface (PES), with initial excitation of Fe to the triplet state being necessary for the reaction to be energetically feasible. Compared with the breaking of the first C–H bond, the cleavage of the second C–H bond is predicted to involve a significantly higher barrier, which could explain experimental observations of the HFeCH3 complex rather than CH2FeH2 in the activation of methane by an Fe atom. For methane activation on an iron dimer, the cleavage of the first C–H bond is quite facile with a barrier only 11.2, 15.8 and 8.4 kcal/mol on the septet state energy surface at the B3LYP/6-311+G(2df,2dp), BPW91/6-311+G(2df,2dp) and M06/B3LYP level, respectively. Cleavage of the second C–H bond from HFe2CH3 involves a barrier calculated respectively as 18.0, 10.7 and 12.4 kcal/mol at the three levels. The results suggest that the elimination of hydrogen from the dihydrogen complex is a rate-determining step. Overall, our results indicate that the iron dimer Fe2 has a stronger catalytic effect on the activation of methane than the iron atom.

Iron nodules in ferric soils of the Fraser Coast, Australia : relicts of laterisation or features of contemporary weathering and pedogenesis?

The genesis of ferruginous nodules and pisoliths in soils and weathering profiles of coastal southern and eastern Australia has long been debated. It is not clear whether iron (Fe) nodules are redox accumulations, residues of Miocene laterite duricrust, or the products of contemporary weathering of Fe-rich sedimentary rocks. This study combines a catchment-wide survey of Fe nodule distribution in Poona Creek catchment (Fraser Coast, Queensland) with detailed investigations of a representative ferric soil profile to show that Fe nodules are derived from Fe-rich sandstones. Where these crop out, they are broken down, transported downslope by colluvial processes, and redeposited. Chemical and physical weathering transforms these eroded rock fragments into non-magnetic Fe nodules. Major features of this transformation include lower hematite/goethite and kaolinite/gibbsite ratios, increased porosity, etching of quartz grains, and development of rounded morphology and a smooth outer cortex. Iron nodules are commonly concentrated in ferric horizons. We show that these horizons form as the result of differential biological mixing of the soil. Bioturbation gradually buries nodules and rock fragments deposited at the surface of the soil, resulting in a largely nodule-free 'biomantle' over a ferric 'stone line'. Maghemite-rich magnetic nodules are a prominent feature of the upper half of the profile. These are most likely formed by the thermal alteration of non-magnetic nodules located at the top of the profile during severe bushfires. They are subsequently redistributed through the soil profile by bioturbation. Iron nodules occurring in the study area are products of contemporary weathering of Fe-rich rock units. They are not laterite duricrust residues nor are they redox accumulations, although redox-controlled dissolution/re-precipitation is an important component of post-depositional modification of these Fe nodules.

Application of kaolin amorphous derivative as a nitrogen carrier

Sandy soils have low nutrient holding capacity and high water conductivity. Consequently, nutrients applied as highly soluble chemical fertilisers are prone to leaching, particularly in heavily irrigated environments such as horticultural soils and golf courses. Amorphous derivatives of kaolin with high cation exchange capacity may be loaded with desired nutrients and applied as controlledrelease fertilisers. Kaolin is an abundant mineral, which can be converted to a meso-porous amorphous derivative (KAD) using facile chemical processes. KAD is currently being used to sequester ammonium from digester effluent in sewage treatment plants in a commercial environment. This material is also known in Australia by the trade name MesoLite. The ammonium-saturated form of KAD may be applied to soils as a nitrogen fertiliser. Up to 7% N can be loaded onto KAD by contacting it with high-ammonia concentration wastewater from sewerage treatment plants. This poster paper demonstrates plant uptake of nitrogen from KAD and compares its efficiency as a fertiliser with NH4SO4. Rye grass was grown in 1kg pots in a glass-house. Nitrogen was applied at a range of rates using NH4SO4 and two KAD materials carrying 7% and 3% nitrogen, respectively. All other nutrients were applied in adequate amounts. All treatments were replicated three times. Plants were harvested after four weeks. Dry mass and N concentrations were determined by standard methods. At all N application rates, ammonium-loaded KAD produced significantly higher plant mass than for NH4SO4. The lower fertiliser effectiveness of NH4SO4 is attributed to possible loss of some N through volatilisation. Of the two KAD types, the material with lower CEC value supported slightly higher plant yields. The KAD materials did not show any adverse effect on availability of trace elements, as evidenced by lack of deficiency symptoms and plant analyses. Clearly, nitrogen loaded on to KAD in the form of ammonium is likely to be protected from leaching, but is still available to plants. These data suggest that KAD-based fertilisers may be suitable substitutes for water soluble N, K and other cation fertilisers for leaching soils.

Electrochemical properties of galvanically replaced iron nanocubes with gold and palladium

The galvanic replacement reaction has received considerable interest due to the creation of novel bimetallic nanomaterials that minimise the use of expensive metals while maintaining enhanced electrocatalytic properties for certain reactions. In this work we investigate the galvanic replacement of electrochemically synthesised iron nanocubes on glassy carbon, with gold and palladium. The resultant nanomaterials demonstrate quite a difference in morphology; the original cuboid like template is maintained in the case of gold but destroyed when palladium is used. The electrochemical and electrocatalytic behaviours of these materials are reported for reactions such as methanol oxidation, hydrogen evolution and oxygen reduction.

Degradation of simazine from aqueous solutions by diatomite-supported nanosized zero-valent iron composite materials

A novel composite material based on deposition of nanosized zero-valent iron (nZVI) particles on acid-leached diatomite was synthesised for the removal of a chlorinated contaminant in water. The nZVI /diatomite composites were characterized by X-ray diffraction, scanning electron microscopy, elemental analysis, transmission electron microscopy and X-ray photoelectron spectroscopy. Compared with the pure nZVI particles, better dispersion of nZVI particles on the surface or inside the pores of diatom shells was observed. The herbicide simazine was selected as the model chlorinated contaminant and the removal efficiency by nZVI /diatomite composite was compared with that of the pristine nZVI and commercial iron powder. It was found that the diatomite supported nZVI composite material prepared by centrifugation exhibits relatively better efficient activity in decomposition of simazine than commercial Fe, lab synthesized nZVI and composite material prepared via rotary evaporation, and the optimum experimental conditions were obtained based on a series of batch experiments. This study on immobilizing nZVI particles onto diatomite opens a new avenue for the practical application of nZVI and the diatomite-supported nanosized zero-valent iron composite materials have potential applications in environmental remediation.

Bisphenol A degradation enhanced by air bubbles via advanced oxidation using in situ generated ferrous ions from nano zero-valent iron/palygorskite composite materials

Novel nano zero-valent iron/palygorskite composite materials prepared by evaporative and centrifuge methods are tested for the degradation of bisphenol A in an aqueous medium. A systematic study is presented which showed that nano zero-valent iron material has little effect on bisphenol A degradation. When hydrogen peroxide was added to initiate the reaction, some percentage of bisphenol A removal (∼20%) was achieved; however, with the aid of air bubbles, the percentage removal can be significantly increased to ∼99%. Compared with pristine nano zero-valent iron and commercial iron powder, nano zero-valent iron/palygorskite composite materials have much higher reactivity towards bisphenol A and these materials are superior as they have little impact on the solution pH. However, for pristine nano zero-valent iron, it is difficult to maintain the reaction system at a favourable low pH which is a key factor in maintaining high bisphenol A removal. All materials were characterized by X-ray diffraction, scanning electron microscopy, elemental analysis, transmission electron microscopy and X-ray photoelectron spectroscopy. The optimum conditions were obtained based on a series of batch experiments. This study has extended the application of nano zero-valent iron/palygorskite composites as effective materials for the removal of phenolic compounds from the environment.

Control of morphology and nucleation density of iron oxide nanostructures by electric conditions on iron surfaces exposed to reactive oxygen plasmas

The possibility to control the morphology and nucleation density of quasi-one-dimensional, single-crystalline α -Fe2 O3 nanostructures by varying the electric potential of iron surfaces exposed to reactive oxygen plasmas is demonstrated experimentally. A systematic increase in the oxygen ion flux through rf biasing of otherwise floating substrates and then an additional increase of the ion/neutral density resulted in remarkable structural transformations of straight nanoneedles into nanowires with controlled tapering/aspect ratio and also in larger nucleation densities. Multiscale numerical simulations relate the microscopic ion flux topographies to the nanostructure nucleation and morphological evolution. This approach is applicable to other metal-oxide nanostructures.

Deterministic surface growth of single-crystalline iron oxide nanostructures in nonequilibrium plasma

An innovative approach to precise tailoring of surface density, shapes, and sizes of single-crystalline α-Fe 2O 3 nanowires and nanobelts by controlling interactions of reactive oxygen plasma-generated species with the Fe surface is proposed. This strongly nonequilibrium, rapid, almost incubation-free, high-rate growth directly from the solid-solid interface can also be applied to other oxide materials and is based on deterministic control of the density of oxygen species and the surface conditions, which determine the nanostructure nucleation and growth.

Reduction and adsorption of Pb2+ in aqueous solution by nano zero-valent iron : a SEM, TEM and XPS study

This study reports the synthesis, characterization and application of nano zero-valent iron (nZVI). The nZVI was produced by a reduction method and compared with commercial available ZVI powder for Pb2+ removal from aqueous phase. Comparing with commercial ZVI, the laboratory made nZVI powder has a much higher specific surface area. XRD patterns have revealed zero valent iron phases in two ZVI materials. Different morphologies have been observed using SEM and TEM techniques. EDX spectrums revealed even distribution of Pb on surface after reaction. The XPS analysis has confirmed that immobilized lead was present in its zero-valent and bivalent forms. ‘Core-shell’ structure of prepared ZVI was revealed based on combination of XRD and XPS characterizations. In addition, comparing with Fluka ZVI, this lab made nZVI has much higher reactivity towards Pb2+ and within just 15 mins 99.9% removal can be reached. This synthesized nano ZVI material has shown great potential for heavy metal immobilization from waste water.

Dispersion of zero valent iron nanoparticles onto bentonites and the decolourization of orange II

Nano Zero valent iron (Fe0) were reported as an effective material for azo dye removal, however, similar to other nano-materials, ultra-fine powder has a strong tendency to agglomerate into larger particles, resulting in an adverse effect on both effective surface area and catalyst performance. Here we report nano sized Fe0 particles dispersed onto the surface of natural bentonites. X-ray diffraction was used to study the sample phases. Scanning electron microscopy and transmission electron microscopy were applied to study the morphology and morphological changes. Spherical individual Fe0 particles were observed after dispersion onto bentonites, and these samples were used for orange II (OII) decolourization with wide working pH range. Higher reactivity is attributed to good dispersion of Fe0 particles on clay minerals’ surface. This study is significant for providing novel modified clay based catalyst materials for the decolourization of azo dye contaminants from wastewater.

Iron(II) spin transition complexes with dendritic ligands, Part I

The ligands G1- and G2-oligo (benzyl ether) (PBE) dendrons and their iron(II) complexes [Fe(Gn-PBE)3]A2·xH2O (with n = 1, 2 and A = triflate, tosylate) were prepared. The magnetic properties of the complexes were investigated by a SQUID magnetometer. All complexes exhibit gradual spin transition below room temperature. At very low temperatures the magnetic behaviour reflects zero-field splitting (ZFS) effects. 57Fe-Mössbauer spectroscopy was performed to distinguish between ZFS of high spin species and spin state conversion into the low spin state. Further characterisation was carried out by thermogravimetric analysis (TGA) and FT-IR spectroscopy. Structural features have been determined by powder XRD measurements.

Iron(II) spin-transition complexes with dendritic ligands, part II

The dendritic triazole-based complexes \[Fe(G1-BOC)3](triflate) 2·xH2O (1; G1-BOC = tert-butyl {3-\[3-(3-tert- butoxycarbonylaminopropyl)-5-(\[1,2,4]triazol-4-ylcarbamoyl)-phenyl]propyl} carbamate, triflate = CF3SO3-), \[Fe(G1-BOC) 3]-(tosylate)2·xH2O(2;tosylate = p-CH3PhSO3-),\[Fe(G1-DPBE)3]-(triflate) 2·xH2O {3; G1-DPBE = 3,5-bis(3,5- didodecaoxybenzyloxy)-N-\[1,2,4]triazol-4-ylbenzamide}, \[Fe(G1-DPBE) 3]-(tosylate)2·xH2O (4) and \[Fe(G1-DPBE)3](BF4)2·xH2O (5) were designed and synthesized. Magnetic and thermal properties of these novel complexes were characterized by magnetic susceptibility measurements, 57Fe Mössbauer spectroscopy and thermogravimetric analysis or differential scanning calorimetry, respectively. All dendritic complexes under study show different spin-transition behaviour with respect to the nature of different dendritic ligands and counteranions. Complexes 1 and 2 have pronounced effects of a spin-state change during the first heating process and gradual spintransition properties for further temperature treatments, whereas 3 and 4 exhibited a very sharp spin-state change in the first heating procedures. Complex 5 showed a gradual spin-transition curve. In this paper, we report how the magnetic properties of these complexes are correlated with noncoordinated water molecules and their effects on spin states.

Changes in environmentally sensitive productivity and technological modernization in China's iron and steel industry in the 1990s

Technological modernization is widely believed to contribute positively both to economic development and to environmental and resource conservation, through improvements in productivity and strengthening of business competitiveness. However, this may not always be true, particularly in the short term, as it requires substantial investments and may impose financial burdens on firms undertaking such investments. This study empirically examines the effects of technological modernization in China's iron and steel industry in the 1990s on conventional economic productivity (CEP) and environmentally sensitive productivities (ESPs). We employ a directional distance function that can handle multiple inputs and outputs to compute relative production efficiencies. We apply these models to the data covering 27 iron and steel firms in China between 1990 and 1999-a period when the Chinese iron and steel industry modernized rapidly. We find that ESPs have continuously improved, even in the period when the CEP declined.