Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Hybrid graphene and graphitic carbon nitride nanocomposite : gap opening, electron–hole puddle, interfacial charge transfer, and enhanced visible light response

Opening up a band gap and finding a suitable substrate material are two big challenges for building graphene-based nanodevices. Using state-of-the-art hybrid density functional theory incorporating long range dispersion corrections, we investigate the interface between optically active graphitic carbon nitride (g-C3N4) and electronically active graphene. We find an inhomogeneous planar substrate (g-C3N4) promotes electronrich and hole-rich regions, i.e., forming a well-defined electron−hole puddle, on the supported graphene layer. The composite displays significant charge transfer from graphene to the g-C3N4 substrate, which alters the electronic properties of both components. In particular, the strong electronic coupling at the graphene/g-C3N4 interface opens a 70 meV gap in g-C3N4-supported graphene, a feature that can potentially allow overcoming the graphene’s band gap hurdle in constructing field effect transistors. Additionally, the 2-D planar structure of g-C3N4 is free of dangling bonds, providing an ideal substrate for graphene to sit on. Furthermore, when compared to a pure g-C3N4 monolayer, the hybrid graphene/g-C3N4 complex displays an enhanced optical absorption in the visible region, a promising feature for novel photovoltaic and photocatalytic applications.

Comparison of functionals for metal hexaboride band structure calculations

Density functional calculations of the electronic band structure for superconducting and semi-conducting metal hexaborides are compared using a consistent suite of assumptions and with emphasis on the physical implications of computed models. Spin polarization enhances mathematical accuracy of the functional approximations and adds significant physical meaning to model interpretation. For YB6 and LaB6, differences in alpha and beta projections occur near the Fermi energy. These differences are pronounced for superconducting hexaborides but do not occur for other metal hexaborides.

Neutral and charged boron-doped fullerenes for CO2 adsorption

Recently, the capture and storage of CO2 have attracted research interest as a strategy to reduce the global emissions of greenhouse gases. It is crucial to find suitable materials to achieve an efficient CO2 capture. Here we report our study of CO2 adsorption on boron-doped C60 fullerene in the neutral state and in the 1e−-charged state. We use first principle density functional calculations to simulate the CO2 adsorption. The results show that CO2 can form weak interactions with the BC59 cage in its neutral state and the interactions can be enhanced significantly by introducing an extra electron to the system.

Catalytic role of pre-adsorbed CO in platinum-based catalysts : the reduction of SO 2 by CO on Pt l Au m (CO) n

Using density functional theory, we have investigated the catalytic properties of bimetallic complex catalysts PtlAum(CO)n (l + m = 2, n = 1–3) in the reduction of SO2 by CO. Due to the strong coupling between the C-2p and metal 5d orbitals, pre-adsorption of CO molecules on the PtlAum is found to be very effective in not only reducing the activation energy, but also preventing poisoning by sulfur. As result of the coupling, the metal 5d band is broadened and down-shifted, and charge is transferred from the CO molecules to the PtlAum. As SO2 is adsorbed on the catalyst, partial charge moves to the anti-σ bonding orbitals between S and O in SO2, weakening the S–O bond strength. This effect is enhanced by pre-adsorbing up to three CO molecules, therefore the S–O bonds become vulnerable. Our results revealed the mechanism of the excellent catalytic properties of the bimetallic complex catalysts.

Coherent phonon decay and the boron isotope effect for MgB2

Ab-initio DFT calculations for the phonon dispersion (PD) and the Phonon Density Of States (PDOS) of the two isotopic forms (10B and 11B) of MgB2 demonstrate that use of a reduced symmetry super-lattice provides an improved approximation to the dynamical, phonon-distorted P6/mmm crystal structure. Construction of phonon frequency plots using calculated values for these isotopic forms gives linear trends with integer multiples of a base frequency that change in slope in a manner consistent with the isotope effect (IE). Spectral parameters inferred from this method are similar to that determined experimentally for the pure isotopic forms of MgB2. Comparison with AlB2 demonstrates that a coherent phonon decay down to acoustic modes is not possible for this metal. Coherent acoustic phonon decay may be an important contributor to superconductivity for MgB2.

Phonon anomalies predict superconducting Tc for AlB2-type structures

We show that the well-known Kohn anomaly predicts Tc for ordered AlB2-type structures. We use ab initio Density Functional Theory to calculate phonon dispersions for Mg1-xAlxB2 compositions and identify a phonon anomaly with magnitude that predicts experimental values of Tc for all x. Key features of these anomalies correlate with the electronic structure of Mg1-xAlxB2. This approach predicts Tc for other known AlB2-type structures as well as new compositions. We predict that Mg0.5Ba0.5B2 will show Tc = 63.6 ± 6.6 K. Other forms of the Mg1-xBaxB2 series will also be superconductors when successfully synthesised. Our calculations predict that the end-member composition, BaB2, is likely to show a Tc significantly higher than currently achieved by other diborides although an applied pressure ~16 GPa may be required to stabilise the structure.

Electronic structure studies and photocatalytic properties of cubic Bi1.5ZnNb1.5O7

The photocatalytic ability of cubic Bi1.5ZnNb1.5O7 (BZN) pyrochlore for the decolorization of an acid orange 7 (AO7) azo dye in aqueous solution under ultraviolet (UV) irradiation has been investigated for the first time. BZN catalyst powders prepared using low temperature sol-gel and higher temperature solid-state methods have been evaluated and their reaction rates have been compared.The experimental band gap energy has been estimated from the optical absorption edge and has been used as reference for theoretical calculations. The electronic band structure of BZN has been investigated using first-principles density functional theory (DFT) calculations for random, completely and partially ordered solid solutions of Zn cations in both the A and B sites of the pyrochlore structure.The nature of the orbitals in the valence band (VB) and the conduction band (CB) has been identified and the theoretical band gap energy has been discussed in terms of the DFT model approximations.

Synthesis, characterization, and electronic structure studies of cubic Bi1.5ZnTa1.5O7 for photocatalytic applications

Bi1.5ZnTa1.5O7 (BZT) has been synthesized using an alkoxide based sol-gel reaction route. The evolution of the phases produced from the alkoxide precursors and their properties have been characterized as function of temperature using a combination of thermogravimetric analysis (TGA) coupled with mass spectrometry (MS), infrared emission spectrometry (IES), X-ray diffraction (XRD), ultraviolet and visible (UV-Vis) spectroscopy, Raman spectroscopy, and N2 adsorption/desorption isotherms. The lowest sintering temperature (600∘C) to obtain phase pure BZT powders with high surface area (14.5m2/g) has been determined from the thermal decomposition and phase analyses.The photocatalytic activity of the BZT powders has been tested for the decolorization of organic azo-dye and found to be photoactive under UV irradiation.The electronic band structure of the BZT has been investigated using density functional theory (DFT) calculations to determine the band gap energy (3.12 eV) and to compare it with experimental band gap (3.02 eV at 800∘C) from optical absorptionmeasurements. An excellent match is obtained for an assumption of Zn cation substitutions at specifically ordered sites in the BZT structure.

Computational fluid dynamics analysis of a flat plate photocatalytic reactor for storm and wastewater reuse

A computational fluid dynamics (CFD) analysis has been performed for a flat plate photocatalytic reactor using CFD code FLUENT. Under the simulated conditions (Reynolds number, Re around 2650), a detailed time accurate computation shows the different stages of flow evolution and the effects of finite length of the reactor in creating flow instability, which is important to improve the performance of the reactor for storm and wastewater reuse. The efficiency of a photocatalytic reactor for pollutant decontamination depends on reactor hydrodynamics and configurations. This study aims to investigate the role of different parameters on the optimization of the reactor design for its improved performance. In this regard, more modelling and experimental efforts are ongoing to better understand the interplay of the parameters that influence the performance of the flat plate photocatalytic reactor.

Computational design of cyclic nitroxides as efficient redox mediators for dye-sensitized solar cells

Cyclic nitroxide radicals represent promising alternatives to the iodine-based redox mediator commonly used in dye-sensitized solar cells (DSSCs). To date DSSCs with nitroxide-based redox mediators have achieved energy conversion efficiencies of just over 5 % but efficiencies of over 15 % might be achievable, given an appropriate mediator. The efficacy of the mediator depends upon two main factors: it must reversibly undergo one-electron oxidation and it must possess an oxidation potential in a range of 0.600-0.850 V (vs. a standard hydrogen electrode (SHE) in acetonitrile at 25 °C). Herein, we have examined the effect that structural modifications have on the value of the oxidation potential of cyclic nitroxides as well as the reversibility of the oxidation process. These included alterations to the N-containing skeleton (pyrrolidine, piperidine, isoindoline, azaphenalene, etc.), as well as the introduction of different substituents (alkyl-, methoxy-, amino-, carboxy-, etc.) to the ring. Standard oxidation potentials were calculated using high-level ab initio methodology that was demonstrated to be very accurate (with a mean absolute deviation from experimental values of only 16 mV). An optimal value of 1.45 for the electrostatic scaling factor for UAKS radii in acetonitrile solution was obtained. Established trends in the values of oxidation potentials were used to guide molecular design of stable nitroxides with desired E° ox and a number of compounds were suggested for potential use as enhanced redox mediators in DSSCs. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.