Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Preparation and characterization of TiO2/acid leached serpentinite tailings composites and their photocatalytic reduction of Chromium(VI)

Composite TiO2/acid leached serpentine tailings (AST) were synthesized through the hydrolysis–deposition method and characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), energydispersive X-ray spectrometry (EDS), Fourier-transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), and surface area measurement (BET). The XRD analysis showed that TiO2 coated on the surface of acid leached serpentine tailings was mixed crystal phases of rutile and anatase, the grain size of which is 10–30 nm. SEM, TEM, and EDS analysis exhibited that nano-TiO2 particles were deposited on the surface and internal cavities of acid leaching serpentine tailings. The XPS and FT-IR analysis demonstrated that the coating process of TiO2 on AST was a physical adsorption process. The large specific surface area, porous structure, and plentiful surface hydroxyl group of TiO2/AST composite resulted in the high adsorption capacity of Cr(VI). The experimental results demonstrated that initial concentration of Cr(VI), the amount of the catalyst, and pH greatly influenced the removal efficiency of Cr(VI). The removal kinetics of Cr(VI) at a relative low initial concentration was fitted well with Langmuir–Hinshelwood kinetics model with R2 value of about unity. The asprepared composites exhibited strong adsorption and photocatalytic capacity for the removal of Cr(VI), and the possible photocatalytic reduction mechanism was studied. The photodecomposition of Cr(VI) was as high as 95% within 2 h, and the reusability of the photocatalysis was proven.

Importance of bearing porosity in engineering and natural lubrication

The multilamellar structure of phospholipids, i.e. the surface amorphous layer (SAL) that covers the natural surface of articular cartilage, and hexagonal boron nitride (h-BN) on the surface of metal porous bearings are two prominent examples of the family of layered materials that possess the ability to deliver lamellar lubrication. This chapter presents the friction study that was conducted on the surfaces of cartilage and the metal porous bearing impregnated with oil (first generation) and with oil + h-BN (second generation). The porosity of cartilage is around 75% and those of metal porous bearings were 15–28 wt%. It is concluded that porosity is a critical factor in facilitating the excellent tribological properties of both articular cartilage and the porous metal bearings studied.

Modelling sea water intrusion in coastal aquifers using heterogeneous computing

The objective of this PhD research program is to investigate numerical methods for simulating variably-saturated flow and sea water intrusion in coastal aquifers in a high-performance computing environment. The work is divided into three overlapping tasks: to develop an accurate and stable finite volume discretisation and numerical solution strategy for the variably-saturated flow and salt transport equations; to implement the chosen approach in a high performance computing environment that may have multiple GPUs or CPU cores; and to verify and test the implementation. The geological description of aquifers is often complex, with porous materials possessing highly variable properties, that are best described using unstructured meshes. The finite volume method is a popular method for the solution of the conservation laws that describe sea water intrusion, and is well-suited to unstructured meshes. In this work we apply a control volume-finite element (CV-FE) method to an extension of a recently proposed formulation (Kees and Miller, 2002) for variably saturated groundwater flow. The CV-FE method evaluates fluxes at points where material properties and gradients in pressure and concentration are consistently defined, making it both suitable for heterogeneous media and mass conservative. Using the method of lines, the CV-FE discretisation gives a set of differential algebraic equations (DAEs) amenable to solution using higher-order implicit solvers. Heterogeneous computer systems that use a combination of computational hardware such as CPUs and GPUs, are attractive for scientific computing due to the potential advantages offered by GPUs for accelerating data-parallel operations. We present a C++ library that implements data-parallel methods on both CPU and GPUs. The finite volume discretisation is expressed in terms of these data-parallel operations, which gives an efficient implementation of the nonlinear residual function. This makes the implicit solution of the DAE system possible on the GPU, because the inexact Newton-Krylov method used by the implicit time stepping scheme can approximate the action of a matrix on a vector using residual evaluations. We also propose preconditioning strategies that are amenable to GPU implementation, so that all computationally-intensive aspects of the implicit time stepping scheme are implemented on the GPU. Results are presented that demonstrate the efficiency and accuracy of the proposed numeric methods and formulation. The formulation offers excellent conservation of mass, and higher-order temporal integration increases both numeric efficiency and accuracy of the solutions. Flux limiting produces accurate, oscillation-free solutions on coarse meshes, where much finer meshes are required to obtain solutions with equivalent accuracy using upstream weighting. The computational efficiency of the software is investigated using CPUs and GPUs on a high-performance workstation. The GPU version offers considerable speedup over the CPU version, with one GPU giving speedup factor of 3 over the eight-core CPU implementation.

Memory effect in the deposition of C20 fullerenes on a diamond surface

In this paper, the deposition of C-20 fullerenes on a diamond (001)-(2x1) surface and the fabrication of C-20 thin film at 100 K were investigated by a molecular dynamics (MD) simulation using the many-body Brenner bond order potential. First, we found that the collision dynamic of a single C-20 fullerene on a diamond surface was strongly dependent on its impact energy. Within the energy range 10-45 eV, the C-20 fullerene chemisorbed on the surface retained its free cage structure. This is consistent with the experimental observation, where it was called the memory effect in "C-20-type" films [P. Melion , Int. J. Mod. B 9, 339 (1995); P. Milani , Cluster Beam Synthesis of Nanostructured Materials (Springer, Berlin, 1999)]. Next, more than one hundred C-20 (10-25 eV) were deposited one after the other onto the surface. The initial growth stage of C-20 thin film was observed to be in the three-dimensional island mode. The randomly deposited C-20 fullerenes stacked on diamond surface and acted as building blocks forming a polymerlike structure. The assembled film was also highly porous due to cluster-cluster interaction. The bond angle distribution and the neighbor-atom-number distribution of the film presented a well-defined local order, which is of sp(3) hybridization character, the same as that of a free C-20 cage. These simulation results are again in good agreement with the experimental observation. Finally, the deposited C-20 film showed high stability even when the temperature was raised up to 1500 K.

Transnational organised environmental crime

Transnational environmental crime must become a government priority, as organised criminal networks continue to exploit the environment with unprecedented profits. Such earnings come at a substantial social, economic and environmental expense for communities and their livelihoods. Indeed, organised environmental crime is identified by the United Nations as a key factor in the impoverishment, displacement and violent conflicts affecting millions of people — notably in developing societies.2 It is widely recognised that organised environmental crime syndicates, motivated by substantial financial rewards, continue to flourish and expand in disadvantaged societies with porous borders, where corruption is widespread and regulation is poor. The theft of biodiversity and the demise of animal species and habitats have resulted not only in financial loss, but also in an increase in “environmental refugees” — people dislocated and forced to migrate due to loss of livelihoods.

How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem. Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.

Development of an ultra-thin fibroin membrane for RPE cell transplantation

Purpose: One of the challenges associated with cell-based therapies for repairing the retina is the development of suitable materials on which to grow and transplant retinal cells. Using the ARPE-19 cell line, we have previously demonstrated the feasibility of growing RPE-derived cells on membranes prepared from the silk protein fibroin. The present study was aimed at developing a porous, ultra-thin fibroin membrane that might better support development of apical-basal polarity in culture, and to extend this work to primary cultures of human RPE cells. Methods: Ultra-thin fibroin membranes were prepared using a highly polished casting table coated with Topas® (a cyclic olefin copolymer) and a 1:0.03 aqueous solution of fibroin and PEO (Mv 900 000 g/mol). Following drying, the membranes were water annealed to make them water-stable, washed in water to remove PEO, sterilised by treatment with 95% ethanol, and washed extensively in saline. Primary cultures containing human RPE cells were established from donor posterior eye cups and maintained in DMEM/F12 medium supplemented with 10% fetal bovine serum and antibiotics. First passage cultures were seeded onto fibroin membranes pre-coated with vitronectin and grown for 6 weeks in medium supplemented with 1% serum. Comparative cultures were established on porous 1.0 µm pore PET membrane (Millipore) and using ARPE-19 cells. Results: The fibroin membranes displayed an average thickness of 3 µm and contained numerous dimples/pore-like structures of up to 3-5 µm in diameter. The primary cultures predominantly contained pigmented epithelial cells, but mesenchymal cells (presumed fibroblasts) were also often present. Passaged cultures appeared to attach equally well to either fibroin or PET membranes. Over time cells on either material adopted a more cobblestoned morphology. Conclusions: Progress has been made towards developing a porous ultra-thin fibroin membrane that supports cultivation of RPE cells. Further studies are required to determine the degree of membrane permeability and RPE polarity.

Encapsulation of transition metal species into zeolites and molecular sieves as redox catalysts: Part I-preparation and characterisation of nanosized TiO2, CdO and ZnO semiconductor particles anchored in NaY zeolite

In this paper, we report the preparation and characterisation of nanometer-sized TiO2, CdO, and ZnO semiconductor particles trapped in zeolite NaY. Preparation of these particles was carried out via the traditional ion exchange method and subsequent calcination procedure. It was found that the smaller cations, i.e., Cd2+ and Zn2+ could be readily introduced into the SI′ and SII′ sites located in the sodalite cages, through ion exchange; while this is not the case for the larger Ti species, i.e., Ti monomer [TiO]2+ or dimer [Ti2O3]2+ which were predominantly dispersed on the external surface of zeolite NaY. The subsequent calcination procedure promoted these Ti species to migrate into the internal surface of the supercages. These semiconductor particles confined in NaY zeolite host exhibited a significant blue shift in the UV-VIS absorption spectra, in contrast to the respective bulk semiconductor materials, due to the quantum size effect (QSE). The particle sizes calculated from the UV-VIS optical absorption spectra using the effective mass approximation model are in good agreement with the atomic absorption data.

Composites for delivery of therapeutics : combining melt electrospun scaffolds with loaded electrosprayed microparticles

A novel strategy is reported to produce biodegradable microfiber-scaffolds layered with high densities of microparticles encapsulating a model protein. Direct electrospraying on highly porous melt electrospun scaffolds provides a reproducible scaffold coating throughout the entire architecture. The burst release of protein is significantly reduced due to the immobilization of microparticles on the surface of the scaffold and release mechanisms are dependent on protein-polymer interactions. The composite scaffolds have a positive biological effect in contact with precursor osteoblast cells up to 18 days in culture. The scaffold design achieved with the techniques presented here endorses these new composite scaffolds as promising templates for growth factor delivery.

Melt-electrospun polycaprolactone-strontium substituted bioactive glass scaffolds for bone regeneration

Polycaprolactone (PCL) is a resorbable polymer used extensively in bone tissue engineering owing to good structural properties and processability. Strontium substituted bioactive glass (SrBG) has the ability to promote osteogenesis and may be incorporated into scaffolds intended for bone repair. Here we describe for the first time, the development of a PCL-SrBG composite scaffold incorporating 10% (weight) of SrBG particles into PCL bulk, produced by the technique of melt-electrospinning. We show that we are able to reproducibly manufacture composite scaffolds with an interconnected porous structure and, furthermore, these scaffolds were demonstrated to be non-cytotoxic in vitro. Ions present in the SrBG component were shown to dissolve into cell culture media and promoted precipitation of a calcium phosphate layer on the scaffold surface which in turn led to noticeably enhanced alkaline phosphatase activity in MC3T3-E1 cells compared to PLC-only scaffolds. These results suggest that melt-electrospun PCL-SrBG composite scaffolds show potential to become effective bone graft substitutes.

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.

Electrospinning and crosslinking of low-molecular-weight poly(trimethylene carbonate-co-L-lactide) as an elastomeric scaffold for vascular engineering

The growth of suitable tissue to replace natural blood vessels requires a degradable scaffold material that is processable into porous structures with appropriate mechanical and cell growth properties. This study investigates the fabrication of degradable, crosslinkable prepolymers of l-lactide-co-trimethylene carbonate into porous scaffolds by electrospinning. After crosslinking by γ-radiation, dimensionally stable scaffolds were obtained with up to 56% trimethylene carbonate incorporation. The fibrous mats showed Young’s moduli closely matching human arteries (0.4–0.8 MPa). Repeated cyclic extension yielded negligible change in mechanical properties, demonstrating the potential for use under dynamic physiological conditions. The scaffolds remained elastic and resilient at 30% strain after 84 days of degradation in phosphate buffer, while the modulus and ultimate stress and strain progressively decreased. The electrospun mats are mechanically superior to solid films of the same materials. In vitro, human mesenchymal stem cells adhered to and readily proliferated on the three-dimensional fiber network, demonstrating that these polymers may find use in growing artificial blood vessels in vivo.

Optimal catalyst thickness in titanium dioxide fixed film reactors: Mathematical modelling and experimental validation

The use of immobilised TiO2 for the purification of polluted water streams introduces the necessity to evaluate the effect of mechanisms such as the transport of pollutants from the bulk of the liquid to the catalyst surface and the transport phenomena inside the porous film. Experimental results of the effects of film thickness on the observed reaction rate for both liquid-side and support-side illumination are here compared with the predictions of a one-dimensional mathematical model of the porous photocatalytic slab. Good agreement was observed between the experimentally obtained photodegradation of phenol and its by-products, and the corresponding model predictions. The results have confirmed that an optimal catalyst thickness exists and, for the films employed here, is 5 μm. Furthermore, the modelling results have highlighted the fact that porosity, together with the intrinsic reaction kinetics are the parameters controlling the photocatalytic activity of the film. The former by influencing transport phenomena and light absorption characteristics, the latter by naturally dictating the rate of reaction.

Modified alumina nanofiber membranes for protein separation

Large-scale purification/separation of bio-substances is a key technology required for rapid production of biological substances in bioengineering. Membrane filtration is a new separation process and has potential to be used for concentration (removal of solvent), desalting (removal of low molecular weight compounds), clarification (removal of particles), and fractionation (protein-protein separation). In this study, we developed an efficient membrane for protein separation based on ceramic nanofibers. Alumina nanofibers were prepared on a porous support and formed large flow passages. The radical changes in membrane structure provided new ceramic membranes with a large porosity (more than 70%) due to the replacement of bulk particles with fine fibers as building components. The pore size had an average of 11 nm and pure water flux was approximately 360 L•h-1•m-2•bar-1. Further surface modification with a self-assembled monolayer of (3-aminopropyl) triethoxysilane enhanced the membrane filtration properties. Characterization with SEM, FTIR, contact angle, and proteins separation tests indicated that the fibril layers uniformly spread on the surface of the porous support. Moreover, the membrane surface was changed from hydrophilic to hydrophobic after silane groups were grafted. It demonstrated that the silane-grafted alumina fiber membrane can reject 100% BSA protein and 92% cellulase protein. It was also able to retain 75% trypsin protein while maintaining a permeation flux of 48 L•h-1•m-2•bar-1.