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.

Generation of active surface states of gold and the role of such states in electrocatalysis

The cyclic voltammetry behaviour of gold in aqueous media is often regarded in very simple terms as a combination of two distinct processes, double layer charging/discharging and monolayer oxide formation/removal. This view is questioned here on the basis of both the present results and earlier independent data by other authors. It was demonstrated in the present case that both severe cathodization or thermal pretreatment of polycrystalline gold in acid solution resulted in the appearance of substantial Faradaic responses in the double layer region. Such anamolous behaviour, as outlined recently also for other metals, is rationalized in terms of the presence of active metal atoms (which undergo premonolayer oxidation) at the electrode surface. Such behaviour, which is also assumed to correspond to that of active sites on conventional gold surfaces, is assumed to be of vital importance in electrocatalysis; in many instances the latter process is also quite marked in the double layer region.

Auto-inhibition of hydrogen gas evolution on gold in aqueous acid solution

It was demonstrated recently that dramatic changes in the redox behaviour of gold/aqueous solution interfaces may be observed following either cathodic or thermal electrode pretreatment. Further work on the cathodic pretreatment of gold in acid solution revealed that as the activity of the gold surface was increased, its performance as a substrate for hydrogen gas evolution under constant potential conditions deteriorated. The change in activity of the gold atoms at the interface, which was attributed to a hydrogen embrittlement process (the occurrence of the latter was subsequently checked by surface microscopy), was confirmed, as in earlier work, by the appearance of a substantial anodic peak at ca. 0.5 V (RHE) in a post-activation positive sweep. Changes in the catalytic activity of a metal surface reflect the fact that the structure (or topography), thermodynamic activity and electronic properties of a surface are dependent not only on pretreatment but also, in the case of the hydrogen evolution reaction, vary with time during the course of reaction. As will be reported shortly, similar (and often more dramatic) time-dependent behaviour was observed for hydrogen gas evolution on other metal electrodes.

Shape dependent electrocatalytic behaviour of silver nanoparticles

The electrochemical and electrocatalytic behaviour of silver nanoprisms, nanospheres and nanocubes of comparable size in an alkaline medium have been investigated to ascertain the shape dependent behaviour of silver nanoparticles, which are an extensively studied nanomaterial. The nanomaterials were synthesised using chemical methods and characterised with UV-visible spectroscopy, transmission electron microscopy and X-ray diffraction. The nanomaterials were immobilised on a substrate glassy carbon electrode and characterised by cyclic voltammetry for their surface oxide electrochemistry. The electrocatalytic oxidation of hydrazine and formaldehyde and the reduction of hydrogen peroxide were studied by performing cyclic voltammetric and chronoamperometric experiments for both the nanomaterials and a smooth polycrystalline macrosized silver electrode. In all cases the nanomaterials showed enhanced electrocatalytic activity over the macro-silver electrode. Significantly, the silver nanoprisms that are rich in hcp lamellar defects showed greater activity than nanospheres and nanocubes for all reactions studied.

The role of defects, or active states, in surface electrochemistry with particular reference to gold in neutral solution

Metastable, active, or nonequilibrium states due to the presence of abnormal structures and various types of defects are well known in metallurgy. The role of such states at gold surfaces in neutral aqueous media (an important electrode system in the microsensor area) was explored using cyclic voltammetry. It was demonstrated that, as postulated in earlier work from this laboratory, there is a close relationship between premonolayer oxidation, multilayer hydrous oxide reduction and electrocatalytic behaviour in the case of this and other metal electrode systems. Some of the most active, and therefore most important, entities at surfaces (e.g., metal adatoms) are not readily imageable or detectable by high resolution surface microscopy techniques. Cyclic voltammetry, however, provides significant, though not highly specific, information about such species. The main conclusion is that further practical and theoretical work on active states of metal surfaces is highly desirable as their behaviour is not simple and is of major importance in many electrocatalytic processes.

AFM study of morphological changes associated with electrochemical solid--solid transformation of three-dimensional crystals of TCNQ to metal derivatives (metal= Cu, Co, Ni; TCNQ= tetracyanoquinodimethane)

In situ atomic force microscopy (AFM) allows images from the upper face and sides of TCNQ crystals to be monitored during the course of the electrochemical solid–solid state conversion of 50 × 50 μm2 three-dimensional drop cast crystals of TCNQ to CuTCNQ or M[TCNQ]2(H2O)2 (M = Co, Ni). Ex situ images obtained by scanning electron microscopy (SEM) also allow the bottom face of the TCNQ crystals, in contact with the indium tin oxide or gold electrode surface and aqueous metal electrolyte solution, to be examined. Results show that by carefully controlling the reaction conditions, nearly mono-dispersed, rod-like phase I CuTCNQ or M[TCNQ]2(H2O)2 can be achieved on all faces. However, CuTCNQ has two different phases, and the transformation of rod-like phase 1 to rhombic-like phase 2 achieved under conditions of cyclic voltammetry was monitored in situ by AFM. The similarity of in situ AFM results with ex situ SEM studies accomplished previously implies that the morphology of the samples remains unchanged when the solvent environment is removed. In the process of crystal transformation, the triple phase solid∣electrode∣electrolyte junction is confirmed to be the initial nucleation site. Raman spectra and AFM images suggest that 100% interconversion is not always achieved, even after extended electrolysis of large 50 × 50 μm2 TCNQ crystals.

Electrochemical detection of dopamine and cytochrome c at a nanostructured gold electrode

A nanostructured gold surface consisting of closely packed outwardly growing spikes is investigated for the electrochemical detection of dopamine and cytochrome c. A significant electrocatalytic effect for the electrooxidation of both dopamine and ascorbic acid at the nanostructured electrode was found due to the presence of surface active sites which allowed the detection of dopamine in the presence of excess ascorbic acid to be achieved by differential pulse voltammetry. By simple modification with a layer of Nafion, the enhanced electrocatalytic properties of the nanostructured surface was maintained while increasing the selectivity of dopamine detection in the presence of interfering species such as excess ascorbic and uric acids. Also, upon modification of the nanostructured surface with a monolayer of cysteine, the electrochemical response of immobilised cytochrome c in two distinct conformations was observed. This opens up the possibility of using such a nanostructured surface for the characterisation of other biomolecules and in bio-electroanalytical applications.

An investigation of silver electrodeposition from ionic liquids : influence of atmospheric water uptake on the silver electrodeposition mechanism and film morphology

The electrodeposition of silver from two ionic liquids, 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIm][BF4]) and N-butyl-N-methyl-pyrrolidinium bis(trifluoromethanesulfonyl)imide ([C4mPyr][TFSI]), and an aqueous KNO3 solution on a glassy carbon electrode was undertaken. It was found by cyclic voltammetry that the electrodeposition of silver proceeds through nucleation–growth kinetics. Analysis of chronoamperometric data indicated that the nucleation–growth mechanism is instantaneous at all potentials in the case of [BMIm][BF4] and [C4mPyr][TFSI], and instantaneous at low overpotentials tending to progressive at high overpotentials for KNO3. Significantly, under ambient conditions, the silver electrodeposition mechanism changes to progressive nucleation and growth in [C4mPyr][TFSI], which is attributed to the uptake of atmospheric water in the IL. It was found that these differences in the growth mechanism impact significantly on the morphology of the resultant electrodeposit which is characterised ex situ by scanning electron microscopy and X-ray diffraction.

The facile formation of silver dendritic structures in the absence of surfactants and their electrochemical and SERS properties

In this work a simple approach to the creation of highly dispersed electrocatalytically active silver microstructured dendrites on indium tin oxide in the absence of any surface modification or surfactant is presented. It is found that the addition of low concentrations of supporting electrolyte to the AgNO3 solution dramatically influences the morphology of electrodeposited silver which is independent of both the anion and the cation employed. The silver dendrites are characterized by SEM, XRD, XPS as well as by cyclic voltammetry under alkaline conditions. It is found that the surface oxide formation and removal processes are significantly influenced by the microstructured morphology of the silver electrodeposits compared to a smooth macrosized silver electrode. The facile formation of dendritic silver microstructures is also shown to be beneficial for the electrocatalytic oxidation of both formaldehyde and hydrazine and oxygen reduction. The formation of a continuous film of dendritic silver is also investigated for its SERS activity where the connectivity between the individual dendrites is found to be particularly important.

Electrodeposited α- and β-phase MoO3 films and investigation of their gasochromic properties

α- and β-Phase MoO3 are synthesized using an electrodeposition method on fluorine-doped tin oxide (FTO) glass substrates from sodium-molybdate (Na2MoO4) solutions. We show that it is possible to obtain both α- and β-MoO3 by manipulating the cyclic voltammetry (CV) parameters during electrodeposition. Raman spectroscopy, X-ray diffraction, and scanning electron microscopy indicate that the applied potential range and sweep rate are strongly influential on the phase obtained and the surface morphology of the electrodeposited thin films. Gasochromic measurements were carried out on the annealed samples by exposing them to H2 gas. It was revealed that α-MoO3 thin films provided better response to H2 interaction than β-MoO3 films did. Additionally, porous films provided significantly larger responses than smooth films.

The electrochemical corrosion behaviour of quaternary gold alloys when exposed to 3.5% NaCl solution

Lower carat gold alloys, specifically 9 carat gold alloys, containing less than 40 % gold, and alloying additions of silver, copper and zinc, are commonly used in many jewellery applications, to offset high costs and poor mechanical properties associated with pure gold. While gold is considered to be chemically inert, the presence of active alloying additions raises concerns about certain forms of corrosion, particularly selective dissolution of these alloys. The purpose of this study was to systematically study the corrosion behaviour of a series of quaternary gold–silver–copper–zinc alloys using dc potentiodynamic scanning in saline (3.5 % NaCl) environment. Full anodic/cathodic scans were conducted to determine the overall corrosion characteristics of the alloy, followed by selective anodic scans and subsequent morphological and compositional analysis of the alloy surface and corroding media to determine the extent of selective dissolution. Varying degrees of selective dissolution and associated corrosion rates were observed after anodic polarisation in 3.5 % NaCl, depending on the alloy composition. The corrosion behaviour of the alloys was determined by the extent of anodic reactions which induce (1) formation of oxide scales on the alloy surface and or (2) dissolution of Zn and Cu species. In general, the improved corrosion characteristics of alloy #3 was attributed to the composition of Zn/Cu in the alloy and thus favourable microstructure promoting the formation of protective oxide/chloride scales and reducing the extent of Cu and Zn dissolution.

Direct electrochemical formation of alloyed AuPt nanostructured electrocatalysts for the oxidation of formic acid

The formation of highly anisotropic AuPt alloys has been achieved via a simple electrochemical approach without the need for organic surfactants to direct the growth process. The surface and bulk properties of these materials were characterised by scanning electron microscopy (SEM), X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX) and electrochemically by cyclic voltammetry to confirm alloy formation. It was found that AuPt materials are highly active for both the model hydrogen evolution reaction and the fuel cell relevant formic acid oxidation reaction. In particular for the latter case the preferred dehydrogenation pathway was observed at AuPt compared to nanostructured Pt prepared under identical electrochemical conditions which demonstrated the less preferred dehydration pathway. The enhanced performance is attributed to both the ensemble effect which facilitates CO(ads) removal from the surface as well as the highly anisotropic nanostructure of AuPt.

From single crystal surfaces to single atoms : investigating active sites in electrocatalysis

Electrocatalytic processes will undoubtedly be at the heart of energising future transportation and technology with the added importance of being able to create the necessary fuels required to do so in an environmentally friendly and cost effective manner. For this to be successful two almost mutually exclusive surface properties need to be reconciled, namely producing highly active/reactive surface sites that exhibit long term stability. This article reviews the various approaches which have been undertaken to study the elusive nature of these active sites on metal surfaces which are considered as adatoms or clusters of adatoms with low coordination number. This includes the pioneering studies at extended well defined stepped single crystal surfaces using cyclic voltammetry up to the highly sophisticated in situ electrochemical imaging techniques used to study chemically synthesised nanomaterials. By combining the information attained from single crystal surfaces, individual nanoparticles of defined size and shape, density functional theory calculations and new concepts such as mesoporous multimetallic thin films and single atom electrocatalysts new insights into the design and fabrication of materials with highly active but stable active sites can be achieved. The area of electrocatalysis is therefore not only a fascinating and exciting field in terms of realistic technological and economical benefits but also from the fundamental understanding that can be acquired by studying such an array of interesting materials.

Voltammetric, spectroscopic, and microscopic investigations of electrocrystallized forms of semiconducting AgTCNQ (TCNQ=7,7,8,8-tetracyanoquinodimethane) exhibiting different morphologies and colors

Chemically synthesized AgTCNQ exists in two forms that differ in their morphologies (needles and microcrystals) and colors (red and blue). It is now shown that both forms exhibit essentially indistinguishable X-ray diffraction, spectroscopic, and thermochemical data, implying that they are not separate phases, as implied in some literature. Electrochemical reduction of TCNQ((MeCN)) in the presence of Ag+((MeCN)) generates both red and blue AgTCNQ. On glassy carbon, platinum, or indium tin oxide electrodes and at relatively positive deposition potentials, slow growth of high aspect ratio, red needle AgTCNQ crystals occurs. After longer times and at more negative deposition potentials, blue microcrystalline AgTCNQ thin films are favored. Blue AgTCNQ is postulated to be generated via reduction of a Ag+\[(TCNQ(center dot-))(TCNQ)]((MeCN)) intermediate. At even more negative potentials, Ag-(metal) formation inhibits further growth of AgTCNQ. On a gold electrode, Ag-(metal)) deposition occurs at more positive potentials than on the other electrode materials examined. However, surface plasmon resonance data indicate (hat a small potential region is available between the stripping of Ag-(metal)) and the oxidation of TCNQ(center dot-)(MeCN) back to TCNQ(MeCN) where AgTCNQ may form. AgTCNQ in both the red and blue forms also can be prepared electrochemically on a TCNQ((s)) modified electrode in -0.1 M AgNO3(aq) where deposition of Ag(m,,,I) onto the TCNQ((s)) crystals allows a charge transfer process to occur. However, the morphology formed in this solid-solid phase transformation is more difficult to control.