Predicting active material utilisation in LiFePO4 electrodes using a multi-scale mathematical model

A mathematical model is developed to simulate the discharge of a LiFePO4 cathode. This model contains 3 size scales, which match with experimental observations present in the literature on the multi-scale nature of LiFePO4 material. A shrinking-core is used on the smallest scale to represent the phase-transition of LiFePO4 during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilisation. Specifically the size and composition of agglomerates of LiFePO4 crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilisation. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.

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.

Low-pressure planar magnetron discharge for surface deposition and nanofabrication

Current-voltage characteristics of the planar magnetron are studied experimentally and by numerical simulation. Based on the measured current-voltage characteristics, a model of the planar magnetron discharge is developed with the background gas pressure and magnetic field used as parameters. The discharge pressure was varied in a range of 0.7-1.7 Pa, the magnetic field of the magnetron was of 0.033-0.12 T near the cathode surface, the discharge current was from 1 to 25 A, and the magnetic field lines were tangential to the substrate surface in the region of the magnetron discharge ignition. The discharge model describes the motion of energetic secondary electrons that gain energy by passing the cathode sheath across the magnetic field, and the power required to sustain the plasma generation in the bulk. The plasma electrons, in turn, are accelerated in the electric field and ionize effectively the background gas species. The model is based on the assumption about the prevailing Bohm mechanism of electron conductivity across the magnetic field. A criterion of the self-sustained discharge ignition is used to establish the dependence of the discharge voltage on the discharge current. The dependence of the background gas density on the current is also observed from the experiment. The model is consistent with the experimental results. © 2010 American Institute of Physics.

Discharge parameters and dominant electron conductivity mechanism in a low-pressure planar magnetron discharge

Parameters of a discharge sustained in a planar magnetron configuration with crossed electric and magnetic fields are studied experimentally and numerically. By comparing the data obtained in the experiment with the results of calculations made using the proposed theoretical model, conclusion was made about the leading role of the turbulence-driven Bohm electron conductivity in the low-pressure operation mode (up to 1 Pa) of the discharge in crossed electric and magnetic fields. A strong dependence of the width of the cathode sputter trench, associated with the ionization region of the magnetron discharge, on the discharge parameters was observed in the experiments. The experimental data were used as input parameters in the discharge model that describes the motion of secondary electrons across the magnetic field in the ionization region and takes into account the classical, near-wall, and Bohm mechanisms of electron conductivity.

Measurement of contact voltage drop and resistance in organic solar cells

Bulk heterojunction organic solar cells based on poly[4,7-bis(3- dodecylthiophene-2-yl) benzothiadiazole-co-benzothiadiazole] and [6,6]-phenyl C71-butyric acid methyl ester are investigated. A prominent kink is observed in the fourth quadrant of the current density-voltage (J-V) response. Annealing the active layer prior to cathode deposition eliminates the kink. The kink is attributed to an extraction barrier. The J-V response in these devices is well described by a power law. This behavior is attributed to an imbalance in charge carrier mobility. An expected photocurrent for the device displaying a kink in the J-V response is determined by fitting to a power law. The difference between the expected and measured photocurrent allows for the determination of a voltage drop within the device. Under simulated 1 sun irradiance, the peak voltage drop and contact resistance at short circuit are 0.14 V and 90 Ω, respectively. © 2012 American Institute of Physics.

Multifunctional SA-PProDOT binder for lithium ion batteries

An environmentally benign, highly conductive, and mechanically strong binder system can overcome the dilemma of low conductivity and insufficient mechanical stability of the electrodes to achieve high performance lithium ion batteries (LIBs) at a low cost and in a sustainable way. In this work, the naturally occurring binder sodium alginate (SA) is functionalized with 3,4-propylenedioxythiophene-2,5-dicarboxylic acid (ProDOT) via a one-step esterification reaction in a cyclohexane/dodecyl benzenesulfonic acid (DBSA)/water microemulsion system, resulting in a multifunctional polymer binder, that is, SA-PProDOT. With the synergetic effects of the functional groups (e.g., carboxyl, hydroxyl, and ester groups), the resultant SA-PProDOT polymer not only maintains the outstanding binding capabilities of sodium alginate but also enhances the mechanical integrity and lithium ion diffusion coefficient in the LiFePO4 (LFP) electrode during the operation of the batteries. Because of the conjugated network of the PProDOT and the lithium doping under the battery environment, the SA-PProDOT becomes conductive and matches the conductivity needed for LiFePO4 LIBs. Without the need of conductive additives such as carbon black, the resultant batteries have achieved the theoretical specific capacity of LiFePO4 cathode (ca. 170 mAh/g) at C/10 and ca. 120 mAh/g at 1C for more than 400 cycles.

Microporous bamboo biochar for lithium-sulfur batteries

Being simple, inexpensive, scalable and environmentally friendly, microporous biomass biochars have been attracting enthusiastic attention for application in lithium-sulfur (Li-S) batteries. Herein, porous bamboo biochar is activated via a KOH/annealing process that creates a microporous structure, boosts surface area and enhances electronic conductivity. The treated sample is used to encapsulate sulfur to prepare a microporous bamboo carbon-sulfur (BC-S) nanocomposite for use as the cathode for Li-S batteries for the first time. The BC-S nanocomposite with 50 wt.% sulfur content delivers a high initial capacity of 1,295 mA·h/g at a low discharge rate of 160 mA/g and high capacity retention of 550 mA·h/g after 150 cycles at a high discharge rate of 800 mA/g with excellent coulombic efficiency (⩾95%). This suggests that the BC-S nanocomposite could be a promising cathode material for Li-S batteries.

Simultaneous Electrodeposition of MnO2 and Mn(OH)(2) for Supercapacitor Studies

Among the various Mn compounds, both MnO2 and Mn(OH)2 are electrochemically active in supercapacitor studies. MnO2 and Mn(OH)2 are simultaneously deposited, through a one-pot method, on the anode and cathode, respectively, of a galvanostatic electrolysis cell consisting of aqueous Mn(NO3)2 electrolyte. MnO2 and Mn(OH)2 coated stainless steel (SS) electrodes are found to exhibit a capacitive behavior with a high specific capacitance. MnO2/SS and Mn(OH)2/SS electrodes are used as the negative and positive electrodes, respectively, in assembling nonsymmetrical capacitors and testing. The results indicate that both Mn-based electrodes prepared simultaneously in a single electrolysis possess interesting electrochemical properties for supercapacitor application.

Digital color reproduction on color television monitors

Color displays used in image processing systems consist of a refresh memory buffer storing digital image data which are converted into analog signals to display an image by driving the primary color channels (red, green, and blue) of a color television monitor. The color cathode ray tube (CRT) of the monitor is unable to reproduce colors exactly due to phosphor limitations, exponential luminance response of the tube to the applied signal, and limitations imposed by the digital-to-analog conversion. In this paper we describe some computer simulation studies (using the U*V*W* color space) carried out to measure these reproduction errors. Further, a procedure to correct for color reproduction error due to the exponential luminance response (gamma) of the picture tube is proposed, using a video-lookup-table and a higher resolution digital-to-analog converter. It is found, on the basis of computer simulation studies, that the proposed gamma correction scheme is effective and robust with respect to variations in the assumed value of the gamma.

Synthesis and Characterization of Carbon-Coated LiNi1/3Co1/3Mn1/3O2 in a Single Step by an Inverse Microemulsion Route

Layered LiNi1/3Co1/3Mn1/3O2, which is isostructural to LiCoO2, is considered as a potential cathode material. A layer of carbon coated on the particles improves the electrode performance, Which is attributed to an increase of the grain connectivity and also to protection of metal oxide from chemical reaction. The present work involves in situ synthesis of carbon-coated submicrometer-sized particles of LiNi1/3Co1/3Mn1/3O2 in an inverse microemulsion medium in the presence of glucose. The precursor obtained from the reaction is heated in air at 900 degrees C for 6 h to get crystalline LiNi1/3Co1/3Mn1/3O2. The carbon coating is found to impart porosity as well as higher surface area in relation to bare samples of the compound. The electrochemical characterization studies provide that carbon-coated LiNi1/3Co1/3Mn1/3O2 samples exhibit improved rate capability and cycling performance. The carbon coatings are shown to suppress the capacity fade, which is normally observed for the bare compound. Impedance spectroscopy data provide additional evidence for the beneficial effect of a carbon coating on LiNi1/3Co1/3Mn1/3O2 particles.

Quest for new materials: Inorganic chemistry plays a crucial role

There is an endless quest for new materials to meet the demands of advancing technology. Thus, we need new magnetic and metallic/semiconducting materials for spintronics, new low-loss dielectrics for telecommunication, new multi-ferroic materials that combine both ferroelectricity and ferromagnetism for memory devices, new piezoelectrics that do not contain lead, new lithium containing solids for application as cathode/anode/electrolyte in lithium batteries, hydrogen storage materials for mobile/transport applications and catalyst materials that can convert, for example, methane to higher hydrocarbons, and the list is endless! Fortunately for us, chemistry - inorganic chemistry in particular - plays a crucial role in this quest. Most of the functional materials mentioned above are inorganic non-molecular solids, while much of the conventional inorganic chemistry deals with isolated molecules or molecular solids. Even so, the basic concepts that we learn in inorganic chemistry, for example, acidity/basicity, oxidation/reduction (potentials), crystal field theory, low spin-high spin/inner sphere-outer sphere complexes, role of d-electrons in transition metal chemistry, electron-transfer reactions, coordination geometries around metal atoms, Jahn-Teller distortion, metal-metal bonds, cation-anion (metal-nonmetal) redox competition in the stabilization of oxidation states - all find crucial application in the design and synthesis of inorganic solids possessing technologically important properties. An attempt has been made here to illustrate the role of inorganic chemistry in this endeavour, drawing examples from the literature its well as from the research work of my group.

Mordenite-incorporated PVA-PSSA membranes as electrolytes for DMFCs

Composite membranes with mordenite (MOR) incorporated in poly vinyl alcohol (PVA)–polystyrene sulfonic acid (PSSA) blend tailored with varying degree of sulfonation are reported. Such a membrane comprises a dispersed phase of mordenite and a continuous phase of the polymer that help tuning the flow of methanol and water across it. The membranes on prolonged testing in a direct methanol fuel cell (DMFC) exhibit mitigated methanol cross-over from anode to the cathode. The membranes have been tested for their sorption behaviour, ion-exchange capacity, electrochemical selectivity and mechanical strength as also characterized by Fourier transform infrared spectroscopy and thermogravimetric analysis. Water release kinetics has been measured by magnetic resonance imaging (NMR imaging) and is found to be in agreement with the sorption data. Similarly, methanol release kinetics studied by volume-localized NMR spectroscopy (point resolved spectroscopy, PRESS) clearly demonstrates that the dispersion of mordenite in PVA–PSSA retards the methanol release kinetics considerably. A peak power-density of 74 mW/cm2 is achieved for the DMFC using a PVA–PSSA membrane electrolyte with 50% degree of sulfonation and 10 wt.% dispersed mordenite phase. A methanol cross-over current as low as 7.5 mA/cm2 with 2 M methanol feed at the DMFC anode is observed while using the optimized composite membrane as electrolyte in the DMFC, which is about 60% and 46% lower than Nafion-117 and PVA–PSSA membranes, respectively, when tested under identical conditions.

A new magnesium-air cell for long-life applications

A novel type of magnesium-air primary cell has been evolved which employs non-polluting and abundantly available materials. The cell is based on the scheme Mg/Mg(NO3)2, NaNO2, H20/Q(C). The magnesium anode utilization is about 90% at a current density of 20 mAcm -2. The anode has been shown to exhibit a low open-circuit corrosion, a relatively uniform pattern of corrosion and a low negative difference effect in the electrolyte developed above as compared to the conventional halide or perchlorate electrolytes. In the usual air-depolarized mode of operation, the cell has been found to be capable of continuous discharge over several months at a constant cell voltage of about 1 V and a current density of 1 mAcm -2 at the cathode. The long service-life capability arises from the formation of a protective film on the porous carbon cathode and fast sedimentation of the anodic product (magnesium hydroxide) in the electrolyte. The cell has a shelf-life in the activated state of about a year due to the low open-circuit corrosion of the anode. These favourable features suggest the practical feasibility of developing economical, long-life, non-reserve magnesium-air ceils for diverse applications using magnesium anodes with a high surface area and porous carbon-air electrodes.

Excellent field emission from semialigned carbon nanofibers grown on cylindrical copper surface

We report the field emission from carbon nanofibers (CNFs) grown directly on cylindrical copper by a simple pyrolysis technique. The turn-on field is 0.17 V/µm and the emission current density is 0.9 mA/cm2 at 0.35 V/µm. The emission current is stable at a field of 0.35 V/µm and 6.5×10−6 Torr. The excellent field emission behavior is attributed to the sp2 phase in CNFs and the stable emission is due to the direct growth. The direct growth on cylindrical cathode is advantageous for field emission. ©2009 American Institute of Physics.