1 An Experimental Study on the Structure-Property Relationship of Composite Fluid Electrodes for Use In High Energy Density Semi-Solid Flow Cells. by Bryan Y. Ho A.B., Harvard University (2006) ARCHIVES Submitted to the Department of Materials Science and Engineering in Partial Fulfillment of the Requirements for the Degree of MASSACHUSETTS INSTITUTE OF TECHNOLOGY Doctor of Philosophy at the NOV 10 2015 MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2012 LIBRARIES 2011 Massachusetts Institute of Technology. All rights reserved Signature of Author ....................................................... Signature redacted Department dciraterials Science and Engineering October 3, 2011 Signature redacted Certified by ......................................................................... W. Craig Carter Professor of Materials Science and Engineering Thesis Co-Advisor Certified by ......................................................................... .............. Signature redacted 1 Professor o Yet-Ming Chiang terials Science and Engineering Thesil Co-Advisor Certified by ........................................................................... S ig nature redacted John B. Vander Sande Professor Emeritus of Materials Science and Engineering Thesi5 Co-Advisor Signature redacted Acce p te d by .............................................................................................................................................................. Christopher Schuh Chair, Department Committee on Graduate Students 2 An Experimental Study on the Structure-Property Relationship of Composite Fluid Electrodes for Use In High Energy Density Semi-Solid Flow Cells. by Bryan Y. Ho Submitted to the Department of Materials Science and Engineering on October 3, 2011 in Partial fulfillment of the Requirements for the Degree of Doctor of Philosophy in Materials Science and Engineering ABSTRACT - A novel electrochemical energy storage device, the semi-solid flow cell (SSFC), has recently been demonstrated. The device features a complex fluid composite as its anode and cathode. Both electrodes incorporate particles of a lithium storage compound suspended in a carbon black electrolyte gel. This design of a mixed conductor gel host and electrochemically active filler allows for fluid electrodes to be pumped, from storage tanks, through reaction cells. The de-coupling of energy and power capacity in a high energy density device opens up new opportunities for low cost, high performance energy storage. This thesis explores the microstructure of these fluid composites and establishes links to macroscopic properties that determine the device's energy and power density, efficiency, and cycle life. The rapid agglomeration of colloidal carbon black aggregates leads to gelation by diffusion limited cluster aggregation. The low density, percolating network of carbon provides conduction paths for both ions and electrons. The gel's yield stress stably suspends density mismatched particles of lithium storage compounds, which can readily access the electrochemical reactants via the gel matrix. Application of shear reversibly destroys the gel network, allowing for flow. Flow-induced heterogeneities are also investigated and methods of maintaining macroscopic homogeneity are presented. Thesis Supervisors: W. Craig Carter, Yet-Ming Chiang, John B. Vander Sande 3 Table of Contents of Figures ........................................................................................................................................................ 4 Acknow ledgem ents ................................................................................................................................................. 7 Preface ....................................................................................................................................................................... 8 In dex 14 Chapter 1 ................................................................................................................................................................. Demonstrating SSFC Electrodes and Identifying Microstructure Characterization as a Research Priority Chapter 2 ................................................................................................................................................................. 39 Structure-Property Relationship of DLCA Carbon Black Gels Chapter 3 ................................................................................................................................................................. 78 Stable Suspensions of Lithium Cobalt Oxide in a Carbon Black Gel as Semi-solid Electrodes Chapter 4 .............................................................................................................................................................. 113 Flow-induced Segregation in Semi-solid Electrodes Chapter 5 .............................................................................................................................................................. 149 Conclusions and Future Work Supplem ental Inform ation ................................................................................................................................. 161 4 Index of Figures 1.1 SSFC schematic 16 1.2a 1.2b 1.3 1.4 1.5 1.6 1.7a 1.7b 1.8 1.9 1.10a 1.10b 1.11 1.12a 1.12b 1.12c 2.1a 2.1b 2.2a 2.2b 2.2c 2.3 2.4 2.5a 2.5b 2.6a 2.6b 2.7 2.8a 2.8b 2.9 2.10a 2.10b 2.10c 2.11 2.12 2.13 2.14a 2.14b 2.14c 2.14d 3.1 Photograph of a laboratory SSFC Rendered drawing of a laboratory SSFC Flow cell channel geometry drawing Static cell schematic Equivalent circuit model for the electrode's complex impedance response Galvanostatic charge and discharge curve of a LCO electrode under constant flow Potentiostatic charge and discharge curve of a 30 vol% LCO electrode at rest Potentiostatic charge and discharge curve of a 40 vol% LCO electrode at rest Summary of specific capacities from 1.7a and 1.7b Nyquist plot of impedance response of 30 vol% LCO electrodes with varied Ketjenblack Flow curves of 30 vol% LCO with 4 different Ketjenblack loadings Flow curves of 40 vol% LCO with 4 different Ketjenblack loadings Viscoelastic response of a LCO electrode under a stress sweep LTO static half cell cycling data LCO static half cell cycling data LMNO static half cell cycling data TEM micrograph of acetylene black Digitally modified version of 2.1a TEM micrograph of TIMCAL C45 TEM micrograph of Chevron Shawinigan black TEM micrograph of Ketjenblack EC-600JD Schematic of parallel plate conductivity measurement apparatus Interpretation of stress amplitude sweep viscoelasticity data Power-law scaling of the elastic modulus with carbon black volume fraction Power-law scaling of the strain limit of linearity with carbon black volume fraction Gel point study -elastic modulus Gel point study - yield stress Effect of electrolyte salt concentration on viscoelastic moduli Optical micrograph of Ketjenblack clusters SEM micrograph of Ketjenblack clusters Electronic conductivities as a function of weight percent for various carbon blacks Correlation of yield stress and electronic conductivity in carbon black gels Correlation of elastic modulus and electronic conductivity in carbon black gels Correlation of 1 1/s shear viscosity and electronic conductivity in carbon black gels Shear thickening flow curve of Ketjenblack gel Time-resolved viscoelastic response of Shawinigan black gel after pre-shear TEM micrographs of DLCA and RLCA structures Reproduction of Osuji's data on shear thickening of carbon black dispersions TEM micrograph of Vulcan XC-72R TEM micrograph of Ketjenblack Reproduction of 2.11 Photograph of X-ray tomography fluid sample holder 20 20 21 22 23 25 26 26 27 28 29 29 30 31 31 31 42 42 43 43 43 47 51 52 52 53 53 54 55 55 56 57 57 57 58 59 65 70 70 70 70 85 5 3.2 3.3 Time-resolved viscoelastic response of LCO in electrolyte Stress sweep viscoelastic response of Shawinigan black gel with and without LCO 87 89 3.4 X-ray microtomography compilation displaying vertically resolved LCO concentrations 91 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 4.1 4.2 4.3a 4.3b 4.4 4.5 4.6 4.7 4.8 4.9a 4.9b 4.10a 4.10b 4.11a 4.11b 4.12 4.13 4.14a 4.14b 4.14c 4.14d 4.15a 4.15b 4.15c 4.15d 4.16a 4.16b 4.17 4.18 5.1 5.2 5.3 5.4 5.5a 3D tomographic reconstruction with colored LCO clusters Cluster size histrogram of data in 3.5 Wet-SEM micrograph of LCO electrode - low magnification Wet-SEM micrograph of LCO electrode - high magnification Electronic conductivities of Shawinigan black gels with and without LCO Effect of LCO bulk conductivity and volume percent on electrode electronic conductivity Effect of LCO specific surface area on electronic conductivity Effect of LCO total surface area on electronic conductivity Schematic of confinement effect of smaller particles Melting point of an ethylene carbonate based electrode Schematic drawing of a flow-conductivity cell Confocal microscope height map of smooth SS316 electrodes Confocal microscope height map of rough SS316 electrodes Schematic of pumping protocol in flow-conductivity experiments Photograph of a flow-conductivity cell in a ultra-sonic bath Schematic drawing of conductivity measurements parallel to flow Schematic of the half-plane SEM imaging method of flowed electrodes Herschel-Bulkley fitting to a measured electrode flow curve Normalized radial flow velocity profiles for computed pipe flow results Normalized radial shear rate profiles for computed pipe flow results Yield radius map based on computed pipe flow results Maximum shear rate map based on computed pipe flow results Galvanostatic charge and discharge of smooth and rough electrodes. V(t) Galvanostatic charge and discharge of smooth and rough electrodes. V(Q) Summary of DC cell impedances for 4.11 calculated from intermittent current interrupts Evolution of electronic conductivities under intermittent flow Backscattered electron SEM image of as-prepared electrodes, low magnification Backscattered electron SEM image of 2.8 cm/s flow, low magnification Backscattered electron SEM image of 0.28 cm/s flow, low magnification Backscattered electron SEM image of sonicated 0.28 cm/s flow, low magnification Backscattered electron SEM image of as-prepared electrodes, high magnification Backscattered electron SEM image of 2.8 cm/s flow, high magnification Backscattered electron SEM image of 0.28 cm/s flow, high magnification Backscattered electron SEM image of sonicated 0.28 cm/s flow, high magnification Galvanostatic charge and discharge of direct and tube injected electrodes. V(t) Galvanostatic charge and discharge of direct and tube injected electrodes. V(Q) Summary of DC cell impedances for 4.16 calculated from intermittent current interrupts Schematic drawing of series interface resistances SEM micrograph of NanoAmor MWCNT Reproduction of 2.10 with data for NanoAmor MWCNTs included Secondary electron SEM of MWCNT electrodes Backscattered electron SEM of MWCNT electrodes Commercial in-line static mixer produced by StatMixCo 93 94 95 95 96 97 99 106 107 116 118 119 119 121 121 122 123 125 126 126 127 127 129 129 130 131 133 133 134 134 134 134 135 135 136 136 136 140 154 155 156 157 158 6 5.5b S.1 S.2a S.2b S.3 S.4 S.5 S.6 Commercial in-line static mixer produced by StatMixCo Schematic drawing of cell impedance contributions TEM micrograph of acetylene black TEM micrograph of Ketjenblack Reproduced figure of DLVO interaction energies Flow curve of LCO electrodes under multiple cycles Stress amplitude sweep viscoelastic response of an electrode before and after pre-shear Schematic drawing of nearest neighbor voxels used in tomographic data analysis 158 163 165 165 170 175 176 178 7 Acknowedgements This work would not have been possible without the support of my professional colleagues, friends, and family. I thank my research advisors, Prof. Craig Carter and Prof. Yet-Ming Chiang, for allowing me to be part of this dynamic project and for guiding me in my professional development as a scientist and engineer. I am also grateful to Prof. John Vander Sande for his mentorship and help in translating my results into a cohesive thesis. I had the good fortune of having a very involved thesis committee who helped to introduce me to the field of rheology - I appreciate the time and commitment of Prof Gareth McKinley and Prof Robert Armstrong. My fellow researchers in the Chiang and Carter groups were patient and helpful, both for academic pursuits and also for a good laugh over coffee breaks. I have to thank Billy, Pimpa, Mishu, Nir, Rae, Vanessa, Yajie, David, Can, Tim, and Wei for their help and company over the past five years. While the majority of the results here were produced within our own laboratories, some relied greatly on external collaborations. In particular, Prof. Vanessa Wood and Dr. Federica Marone were crucial in our X-ray microtomography studies. Finally, I am thankful to my friends and family for their support. I could not have made it through my studies without the lunches, dinners, beers, trips, phone calls, and laughs that they shared. I need to point out in particular, Christina and my parents, for their love and grace. This work was enabled by the generous funding provided by the Defense Advanced Research Projects Agency (DARPA) under contract number FA8650-09-D-5037 and by the Advanced Research Projects Agency - Energy (ARPA-E) under award number DE-AR0000065. 8 Preface Over the past decade, concerns over the cost and environmental impact of oil as a transport fuel have motivated a surge of research into energy storage technologies for all-electric vehicles. Desires to build a more robust electrical grid, able to incorporate variable generation sources such as solar and wind power, have also spurred research in the field of energy storage. A solution for either problem, able to meet both the performance and cost requirements, has yet to emerge. All-electric transport requires system-level energy densities in excess of 300 Wh/L and costs below $250/kWh [1]. Grid-level energy storage has less stringent energy density requirements, but more aggressive cost requirements of $100/kWh [2]. Decades of research in modern electrochemical energy storage materials, particularly in lithiumion chemistries, have produced materials that continually push the boundaries of energy density and cost. High energy-density lithium-ion cells storing over 600 Wh/L are commercially available. Even factoring in an approximate, 2-fold decrease in energy density at the system level, the technical requirements for motive applications is within reach. The major hurdle is cost; at over $500/kWh at the cell level, significant breakthroughs are needed to bring all-electric vehicles to the masses. Both energy density and cost metrics are hampered by the volume and expense of packaging present in a wound or prismatic cell. Another type of electrochemical energy storage device, the aqueous redox flow cell, is gaining interest as a low-cost technology with possible applications in stationary, grid-level storage. Its attractive cost comes from the device design, which decouples the power capacity of the cell from the energy capacity. The reaction stack is sized for power and the fluid storage tanks are sized for energy. As the power to energy ratio decreases, the energy-specific cost of the system approaches that of the 9 aqueous fluid. Some drawbacks of this technology are the low energy density of the electrochemically active solutions, ca. 40 Wh/L, and the large parasitic losses that result from the high pumping rates required to operate the device. A semi-solid flow cell (SSFC) is a novel energy storage device that combines the advantages of solid electrochemical storage compounds found in traditional lithium-ion batteries with the operational flexibility of a flow cell [3][4]. Lithium storage compounds are suspended in a mixed conductor fluid and pumped from storage tanks through a reaction stack, in a similar fashion to redox flow batteries. This approach is advantageous to traditional wound or prismatic cells, in that cost and volume of many packaging components are translated to the reaction stack; the storage tanks may be scaled independently, and the cost per kilowatt-hour decreased. The semi-solid electrodes of a SSFC can exceed the energy densities of aqueous storage fluids by a factor of 10-50, given the molar equivalent of 20-90 mol/L possible for storage in solid compounds. This thesis study began with the development of the idea of an SSFC device into a physical demonstration in the laboratory. Many of the defining characteristics and key limitations of the SSFC device were surveyed during this development work. For example, electrodes of the desired energy density could not be synthesized without incurring prohibitive increases in fluid viscosity. The basic composition of a semi-solid electrode is formulated as a composite of a micron-scale lithium storage compound, a sub-micron scale conductive carbon additive, and a non-aqueous liquid electrolyte. The research topics on the further development of SSFC devices, past the proof-of-concept stage, can be classified into the three categories of electrode chemistry development, electrode microstructure engineering, and device engineering. The first topic of chemistry research seeks to maximize the performance of each individual component of the composite semi-solid electrode. For example, improving the energy density of the cathode or anode compound will enable higher energy 10 density semi-solid electrodes. The second topic takes the bulk chemical properties of the electrode components as given, and aims to improve electrode performance by tailoring the composite microstructure. For example, introducing polydispersity into the particle size distribution of the lithium storage compound can enable lower viscosity electrodes. Finally, device engineering addresses designs of the SSFC cell geometries and operating conditions that maximize performance for a given semi-solid electrode. For example, flow channel geometries need to minimize the transport lengths through the electrode for ions and electrons to enable high power output. Electrode microstructure is selected as the focus of this thesis for a few reasons. As a study in materials science, the study of flow cell device design is not the most appropriate area of research. Furthermore, many features of device design will grow to accommodate the materials limitations, once they are more clearly defined. Between studying the chemistry and microstructure of the semi-solid electrodes, the latter is chosen because a better understanding of the structure-property relationships informs materials engineering approaches that can be applied across a whole family of current and future chemical compounds. Lithium cobalt oxide will be used as a model lithium storage compound because its properties are widely studied and understood, due to its widespread commercial deployment. A variety of experimental techniques were employed in this study of SSFC electrodes. So much so, that combining all of the results into a single chapter seemed unwieldy at best. Instead, this thesis is organized into 4 results-driven chapters, by topic. Each chapter is structured as a free-standing article, with its own abstract, introduction, methods, results, discussion, conclusion, and references sections. In addition, there is a concluding chapter that summarizes the important lessons of electrode microstructure engineering and outlines areas for future work. A supplemental information section at 11 the end of the document, with section indices preceded by an S, is called upon in the general text as needed. Chapter 1 is entitled Demonstrating SSFC Electrodes and Identifying Microstructure Characterization as a Research Priority. Prototype results on the SSFC concept introduced in this Preface motivate a discussion on how the semi-solid electrodes may be engineered to improve upon the SSFC device's energy and power densities, efficiency, and cycle life. Each area for improvement is analyzed within the framework of the three research categories defined above: advances in chemistry, electrode microstructure, and device features. The conclusions of this chapter will identify the conductive carbon black additive as a first topic of study to understand how the particulate gel's structure affects electronic and rheological properties of the electrode. Chapter 2, Structure-Property Relationship of DLCA Carbon Black Gels, will therefore investigate the role of carbon black in semi-solid electrodes. Carbon black is shown in Chapter 1 to be crucial to wiring the electrode for effective capacity utilization and for low impedance devices. In addition to its role as an electrochemical additive, carbon black is seen to significantly increase the viscosity of the electrodes and impart a yield stress behavior. It will be demonstrated that carbon blacks form DLCA gels in the organic electrolytes studied here. The spanning agglomerates form a network that supports both mechanical stresses (yield stress) and electron transport (conductivity). The open gel structure and low occupied volume leaves ample, continuous porosity for ion transport. In Cha pter 3, Stable Suspensions of Lithium Cobalt Oxide in a Carbon Black Gel as Semi-solid Electrodes, lithium cobalt oxide (LCO) particles are added to the carbon black gel to form a complete semi-solid electrode. The LCO particles are found to form a stable suspension in a mixed conductor carbon black gel. The carbon black phase occupies the interstices of the LCO phase and creates a mechanically supporting structure to stabilize the density-mismatched particles. The proposed van der 12 Waals attraction of the carbon black and LCO integrates the two electronically, allowing for charge transfer from the gel and onto the particles. This filled gel interpretation predicts that solid phase loadings can be increased closer to theoretical limits of particulate suspensions if the carbon black content is tuned to retain a constant gel composition. Chapter 4, Flow-induced Segregation in Semi-solid Electrodes, will investigate the effect of flow on semi-solid electrodes to address the issue of cycle life. It is found that without intervention, prolonged flow causes segregation of the carbon black and LCO particle phases, with an associated drop in electronic conductivity. As high rate, high efficiency electrodes require low impedance materials, the drop in electronic conductivity is detrimental to device performance. Device modifications - roughened current collectors and ultra-sonic disruption - are identified as avenues for extending the cycle life of semi-solid electrodes against mechanical degradation. While efforts have been made to address the most pressing questions of electrode structure and performance, there are many open research topics. A final chapter of this thesis will summarize the main conclusions of the thesis and address areas of research for future work. The goal of this work is to develop the basic framework for analyzing the components of a semi-solid electrode for future researchers. 13 Preface References [1] "ARPA-E BEEST FOA.". [2] "ARPA-E GRIDS FOA.". [3] M. Duduta et al., "Semi-Solid Lithium Rechargeable Flow Battery," Advanced Energy Materials, vol. 1, no. 4, pp. 511-516, Jul. 2011. Yet-Ming Chiang, W. Craig Carter, Bryan Ho, and Mihai Duduta, "High Energy Density Redox [41 Flow Device," U.S. Patent US 2010/0047671 Al. [5] P. B. Balbuena and Y. Wang, Lithium-Ion Batteries: Solid-Electrolyte Interphase. London: World Scientific Publishing Company, 2004. 14 Chapter 1 Demonstrating SSFC Electrodes and Identifying Microstructural Characterization as a Research Priority Abstract The recently introduced concept of a semi-solid flow cell (SSFC)is reviewed alongside experimental results demonstrating the electrochemical and rheological properties of the novel fluid electrodes [1]. These semi-solid electrodes are composed of a lithium storage compound, carbon black, and a liquid electrolyte. The resulting composite is shown to charge and discharge under continuous flow and stationary conditions. Systematic variation of the carbon black phase demonstrates its role in electrically wiring the semi-solid electrode; increasing the carbon black loading from near 1 wt% to over 2 wt% leads to increases in the reversible electrode storage capacity from nearly 0% to 87% of its theoretical value. Electrochemical cell impedances are also shown to drop by over a factor of 2. The electrodes exhibit dynamic viscosities well above 1000 cP at moderate shear rates and increasing the lithium compound loading and carbon black content to achieve higher energy densities and lower impedances are shown to raise that viscosity. These combined observations will be related to performance metrics of electrochemical energy storage devices, such as energy density, power density, efficiency, and cycle life, to motivate the further study of the structure-property relationship in semisolid electrodes. 1.1 Introduction The device innovation of a semi-solid flow sell (SSFC) enables electrochemical energy storage in a high energy density fluid medium. The separation of energy storage and power extraction in a SSFC 15 (Figure 1.1) lends to a flexible storage architecture. At the heart of this novel device is a material innovation, in the form of the semi-solid electrode. Composed of a solid lithium intercalation compound and conductive carbon additive dispersed in a liquid electrolyte, these electrodes are engineered to flow as a fluid, while possessing the electrochemical properties of conventional, all-solid electrodes. This chapter presents a survey of the basic rheological and electrochemical properties of the semi-solid electrodes studied in this thesis. Shear viscometry studies demonstrate that the electrodes flow under applied shear stresses, exhibiting complex fluid behaviors such as a yield stress and shearthinning viscosity. The electrodes also behave similarly to conventional lithium-ion electrodes under charging and discharging; all of the electrochemical techniques and physical models used to characterize conventional electrodes may be applied to these semi-solid electrodes. Prototype SSFC devices are presented for three electrode chemistries, and solid loadings of up to 40 vol% are achieved for lithium cobalt oxide. Electrochemical impedance studies show that the loading of carbon black plays a dominant role in determining the cell impedance, thereby defining the rate capabilities of the device. Carbon black is also shown to be a determining factor in the accessing the capacity of the lithium storage compounds; up to 87% of the theoretical capacity is recovered during discharge with a 40 vol% LCO electrode. These results will be discussed in light of the quantitative metrics of battery performance, the energy density, power density, energy efficiency, and cycle life. The discussion will outline how the three target areas of SSFC research, chemistry development, microstructure engineering, and device engineering, apply to each of these metrics. The study of the semi-solid electrode microstructure and its relationship to macroscopic properties is selected as a primary focus for this thesis, as it provides a materials engineering framework for the incorporation of future developments in component chemistries. 16 B nhO Figure 1.1. A schematic illustration of a semi-solid flow cell (SSFC) device. Fluid electrodes, comprised of solid electrochemical energy storage compounds in suspension, are flowed through a device architecture similar to redox flow cells. A reaction stack (center) is scaled to achieve the desired power output. Fluid storage tanks (left and right) are scaled for the desired energy capacity. As an added functional advantage, tanks of spent fluid may be exchanged for charged fluid, greatly accelerating the charging process. 1.2 Methods This section details the synthesis of semi-solid electrodes and the methods used to conduct electrochemical and rheological measurements. The electrodes are fluid composites composed of commercially available components. These materials are tested in two types of electrochemical cells, one where the electrode slurry is flowed through the cell (flow cell) and another where the slurry is 17 spatula-loaded into a stationary well (static cell). Rheological characterization is performed in two manners as well, one is a Couette geometry in a rate-controlled viscometer and the other is a parallel plate geometry in a stress-controlled rheometer. Together, these measurements provide an overview of the semi-solid electrode behavior and identify the electronic conductivity and dynamic viscosity as properties to maximize and minimize, respectively. 1.2.1 Materials Samples consist of three components, a lithium storage compound powder, carbon black, and electrolyte. Three lithium compounds are featured in this chapter, lithium cobalt oxide (LiCoO 2, LCO), lithium titanate (LiJi01 , LTO), and lithium manganese nickel oxide (LiMn1.5Nio.s0 4, LMNO). The lithium cobalt oxide is from the AGC Seimi Chemical Company, Ltd. The LCO is jetmilled with a grinding air pressure of 60 PSI and classified at 15,000 RPM to reduce the particle size distribution. The distribution data for the original material and jet-milled material is summarized in Table 1.1. Both the LMNO spinel and the LTO are produced by the NEI Corporation. The two carbon blacks studied here are Ketjenblack EC-600JD (Akzo Nobel Polymer Chemicals, LLC) and Chevron Shawinigan black (Chevron Corporation). Finally, two electrolytes are used. SSDE is a proprietary solution of 1.3 M LiPF 6 in a blend cyclic and linear alkyl carbonates produced by Novolyte Technologies. An electrolyte composed of 1.0 M LiPF 6 in a 1:1 volume blend of ethylene carbonate (EC) and dimethyl carbonate (DMC) is synthesized from materials purchased from the Sigma Aldrich Corporation, and is referred to as an EC:DMC electrolyte in this work. Electrochemical testing is performed in flow cells machined out of alloy 6061 on the cathode current collector and alloy 101 copper on the anode current collector. The aluminum is then sputtered with a 2 um layer of gold using a Pelco SC-7 sputtering system. Static cell testing is performed with alloy 316 stainless steel current collectors on both the anode and cathode. The lithium metal counter- 18 electrode is separated from the semi-solid working electrode in all cells by Tonen microporous polymer separator produced by the Toray Tonen Specialty Separator Godo Kaisha. Material Original Seimi LCO Jet-milled Seimi LCO d(0.1) 4.66 um 1.66 um d(0.5) 12.14 um 2.94 urm d(0.9) 28.97 um 5.12 um Specific Surface Area (N 2 BET) 0.43 m 2/g 2.02 m 2/g Table 1.1. Particle size distribution information for the as-received LCO and the jet-milled product. 1.2.2 Experimental Semi-solid electrode synthesis protocol begins with a consistent method for reporting the composition of the three-component fluid composites. All samples are reported with a volume percentage of lithium storage compound. The rationale for expressing the lithium compound content as a volume percentage is that it provides a reference within the well studied field of suspension rheology for the degree of loading. In order to maximize the energy density of the semi-solid electrode, the loading of the lithium storage compound must be likewise maximized. The volume fractions tested can be easily benchmarked against target references such as the glass-transition phase fraction of 58 vol% for monodisperse spheres. i~Compoun= VLiCompound VLiCompound + Vcarbon + VelectroLyte Equation 1.1. The definition of the phase volume fraction of lithium compound in a 3-component slurry. Results shown in Chapter 3 will support a hypothesis of a microstructure where the lithium compound fills a carbon black-electrolyte gel matrix; the carbon black and electrolyte are therefore coarse-grained into a single host phase into which the lithium storage particles are introduced. The carbon black content is reported as a weight fraction of this carbon black-electrolyte gel phase. Excluding the mass of the lithium storage phase allows for the independent control of the gel matrix 19 composition. A weight fraction is used instead of a volume fraction because of the ambiguous definition of a solid density for the various grades of carbon black. Results from Chapter 2 on the scaling of electronic conductivity with weight fraction of carbon black indicate that the effective density of Ketjenblack and Shawinigan black differ by over a factor of 3. The varying degrees of graphitic versus amorphous carbon content, presence of meso and micro porosity, and fractal structure (see section S.3) all make for the use of a weight fraction a more accurate comparison across carbon black grades. Scarbon = Mcarbon Mcarbon + Meiectrolyte Equation 1.2. The definition of the phase weight fraction of carbon black in a carbon black-electrolyte gel. As an example of a SSE formulation, a commonly used composition is 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC electrolyte gel. In this case, 30 volume percent of the total slurry volume is LCO. The remaining 70 volume percent is a carbon black-electrolyte gel phase consisting of 7 weight percent Shawinigan black and 93 weight percent EC:DMC electrolyte. Once the electrode composition is determined, the solid components are weighed out on a milligram accuracy analytical balance (Sartorius Model ED143-CW). The solids are hand-mixed in a 20 mL scintillation vial and then combined with the liquid electrolyte, which is dispensed by Eppendorf pipet. The complete electrode is hand mixed and sealed in the vial under an argon atmosphere, then placed in a bath sonicator (Cole Parmer Model 8890) for 1 hour. The laboratory flow cell consists of two blocks of machined metal - aluminum on the cathode and copper on the anode. Each half has a 1.6 mm diameter entry and exit port coupled to either a barbed tip or Luer Lock polyvinylidene fluoride (PVDF) connector. The two ports feed into a reaction channel, measuring 1.6 mm wide and 1.4 mm deep (Figure 1.3). The anode and cathode channels are 20 vertically aligned and separated by a microporous Tonen separator film. In the experiments conducted here, the anode channel hosts a strip of lithium metal flooded under electrolyte, rather than an anode slurry. The lithium metal reference electrode seen in Figures 1.2a and 1.2b is not used. Flow in the system is driven by a peristaltic pump (Masterflex L/S Digital 600 RPM Drive with a Masterflex L/S Easy-Load pump head). The peristaltic pump eliminates contamination of the sample from the pump head and contains the slurry in a closed system, mitigating solvent loss. Masterflex Chem-Durance flexible tubing (1.6 mm inner diameter) is used for lengths exceeding 20 cm because of its combination of flexibility, chemical compatibility, and low cost. The Chem-Durance tubing is not sufficiently mechanically resilient for use in the peristaltic pump head. Short, 15 cm sections of the fluoro-elastomer Chem-Sure tubing (W.L. Gore and Associates, 1.6 mm inner diameter) are inserted into the pump head and coupled to the Chem-Durance tubing by PTFE barbed connectors. The ChemDurance tubing is then coupled to the flow cell channels via the PVDF barbed connectors described above. In other experiments where semi-solid electrodes are tested in the flow cell under stationary conditions, the electrodes are delivered into the channel by a syringe directly coupled to the PVDF Luer Lock connectors described above. reflon plates 21 Figure 1.2a (left) and 1.2b (right). A photograph and a rendered, exploded view of the laboratory flow cell. A gold-coated aluminum channel acts as the cathode current collector. A copper channel acts as the anode current collector. The two are separated by PTFE insulating plates and a microporous Tonen polymer separator. A reference electrode is optional, and is not used in these studies, where the anode is a lithium metal counter electrode. 1.6 mm 1.6 mm m_ m 3 Area = 2.0 mm 2 Figure 1.3. The cross-sectional view of the flow cell channel (right). The channel is near-tubular and is intended to replicate a 1.6 mm diameter tube (left). Both have a cross sectional area of 2.0 mm 2, but the flow cell channel is truncated at its top, where the separator film lies. Electrochemical measurements are also made in a static cell configuration. A stainless steel current collector hosts the semi-solid electrode in a shallow, cylindrical well measuring 500 um in depth and 6.4 mm in diameter. Semi-solid electrodes are spatula loaded into the well and covered with a circular piece of separator film. A circular film of lithium metal, attached to a stainless steel current collector, is pushed against the well by light spring force, as shown in Figure 1.4. The entire assembly is flooded under electrolyte and sealed inside of a Swagelok cell (Swagelok Co.). The cell bodies are fabricated from either polytetrafluoroethylene (PTFE) or PVDF. Impedance measurements involve an additional lithium metal reference electrode, which is introduced laterally in a T-junction style Swagelok cell. 22 -CE - SS316 - - Spring SS316 Lithium metal Separator Electrode Well SS316 +WE Figure 1.4. A schematic illustration of the static cell measurement system. The semi-solid electrode is loaded into a 500 urn deep, 6.4 mm diameter cylindrical well by spatula. A circular film on lithium metal acts as the counter-electrode and is lightly compressed against the well by spring force. A microporous separator film separates the working and counter electrodes. All parts are flooded under electrolyte and hermetically sealed within a PTFE or PVDF Swagelok body. Both flow cell and static cell experiments are conducted with a Solartron 1400 Cell Test potentiostat (AM ETEK Inc.). All tests other than the electrochemical impedance spectroscopy (EIS) experiments use a 2 electrode system. The working electrode (semi-solid electrode) potential is set and measured relative to the counter-electrode (lithium metal). Voltage limits and current values are reported with the results. The EIS measurements combine the Solartron 1400 system with a Solartron 1455 frequency response analyzer. Sinusoidal voltage oscillations of 10 mV amplitude are applied about the cell's open circuit voltage, between a reference electrode and the working electrode, while the current response is monitored between the lithium counter electrode and working electrode. Oscillation frequencies are swept logarithmically from 0.1 Hz to 100 kHz. Fits to the complex impedance 23 response are made with a modified version of an equivalent circuit model proposed by Atebamba and colleagues [2]. The equivalent circuit model is shown below in Figure 1.5. L Rs CM Rm Csei Rsei CdI Rct W Figure 1.5. The equivalent circuit model used to fit the complex impedance response of LCO semi-solid electrodes. Working from the top-left to the bottom-right, the circuit elements refer to, the test lead inductance, electrolyte resistance, current collector-electrode double layer capacitance, current collector-electrode electron transfer resistance, solid electrolyte interphase capacitance, solid electrolyte interphase resistance, electrode double layer capacitance, charge transfer resistance, solid state mass transport Warburg element. Viscosity measurements were made in a Couette geometry in a Brookfield Engineering Model RVDV-ll+Pro viscometer. The inner spindle was a SC4-15 geometry, with a 9.55 mm diameter and 17.12 mm side wall height. The outer cylinder was a model SC4-7R chamber with a 12.73 mm and 44.32 mm depth. Each shear rate was held for one minute and shear rates were stepped downwards from 95 1/s to 0.1 1/s. Viscoelastic response measurements were conducted in a 20 mm diameter parallel plate geometry in a Malvern Kinexus Pro rheometer. P220 grit sandpaper, with an average particle size of 68 um, was adhered to the plate surfaces with Krazy Glue. Measurements were made across a 1 mm gap, at a 1 Hz frequency, as the oscillation stress amplitude was increased from 0.1 Pa to 1000 Pa. A solvent trap was used to minimize solvent loss. Both viscosity and viscoelasticity measurements were performed under an argon atmosphere in a MBRAUN Labmaster glovebox. 24 1.3 Results This chapter's results provide an overview of the electrochemical properties and rheological behavior of prototype SSFC cathodes based on lithium cobalt oxide. SSFC electrodes behave similarly to conventional electrodes when charged and discharged under rapid, constant flow and stationary conditions. Carbon black is shown to be a necessary conductive additive for full storage capacity utilization under potentiostatic testing. Electrochemical impedance spectroscopy confirms that carbon black acts as a fluid wiring and reduces the cell impedance significantly. Along with providing path for electron conduction in the electrode, carbon black also increases the fluid's dynamic viscosity. Meanwhile, visoelasticity measurements show that the term "semi-solid" not only refers to the solid components of the fluid electrode, but also to the macroscopic, solid-like properties of the electrode at rest. Both the yield behavior and high viscosity will be considerations when considering pumping losses and flow profiles in a reaction stack. This section finishes with the semi-solid electrode concept shown to translate to different commercial Li-ion chemistries. A semi-solid electrode of 22 vol% LCO in a 1.5 wt% Ketjenblack-SSDE matrix is demonstrated to galvanostatically charge and discharge in a laboratory SSFC device under continuous flow (Figure 1.6). Operated in a rapid, continuous manner similar to a conventional redox flow cell, the semi-solid electrode is driven around a loop by a peristaltic pump at an area-averaged linear velocity of 16 cm/s. At this rate, the slurry makes a pass through the reaction cell 24 times per minute, undergoing an incremental charge or discharge in every pass. The galvanostatic current density of 1.5 mA/cm 2 corresponds to a c-rate of C/11 and C/97 when measured against the capacity within the reaction cell and entire loop, respectively. Charging is terminated when the theoretical capacity is attained; discharging is terminated at a IV potential cutoff. An experimentally measured potential profile for a 25 conventional, composite LCO electrode is included for reference. While the polarization is larger, particularly during discharge, the behavior of this flowing electrode is indicative of a LCO half-cell, and over 80% of charge is recovered during discharge. Charge and Discharge of a Suspension Cathode Under Continuous Flow -a .Y: 'V 100 - 0 0U CL50, C77M Discharge Charge 5 Composite Cathode 0 I 3 2 > uspension Cathode 1* 0 0 50 100 150 200 Time (hours) Figure 1.6. One galvanostatic charge-discharge cycle of a semi-solid LiCoO 2 cathode, under continuous flow in a closed loop. An electrode composed of 22 vol% LCO in a 1.5 wt% Ketjenblack-SSDE matrix is flowed at an area-averaged linear velocity of 16 cm/s through a 1.6 mm, gold sputtered flow channel. The galvanostatic current density of 1.5 mA/cm 2 corresponds to a c-rate of C/11 for material in the channel and C/97 for all of the material in the closed loop. An experimentally measured voltage profile from a conventional, composite LiCoO 2 is included (dotted line) for reference. Semi-solid LCO cathodes are pumped into a reaction cell by syringe and tested at rest by potentiostatic charge and discharge. This type of testing, where flow and electrochemical cycling are applied at different times, is indicative of an intermittent mode of operation. 4 different carbon black loadings are studied for 30 vol% LCO (Figure 1.7a) and 40 vol% LCO (Figure 1.7b) compositions. 26 Electrodes are pumped into a 1.6 mm, near-tubular, gold-coated channel. The metallic channel acts as a current collector, and is held at +4.2V and +3.7V versus a lithium metal counter electrode for charging and discharging, respectively. The current response is plotted as a function of specific charge capacity to highlight the effect that carbon black loadings have on the utilization of the LCO storage capacity. Positive current densities correspond to charging and negative current densities reflect the discharge reaction. With a cutoff condition of a C/100 charge or discharge rate, below which the reaction rate is considered negligible, the effective utilization varies from just above 0 mAh/g to values approaching the theoretical capacity of 135 mAh/g. Figure 1.8 summarizes these storage capacities and shows a steep increase in the utilization of the electrode capacity as the carbon black content is increased from 1 wt% to 2 wt%. This transition occurs at a higher composition of carbon black for the 40 vol% LCO electrodes, as compared to the 30 vol% samples. 40 vol% LCO 30 vol% LCO A A) 1.0 wt% Kejenblack in SSDE B) 1.4 wt% Ketjenblack in SSDE 7 1 wt% Ketjenblack in SSDE B) 1.7 wt% Ketjenbiack in SSDE D) 2.8 wt% Ketjenblack in SSDE C) 2.2 wt% Ketjenblack in SSDE 5 D) 2.4 wt% Ketjenblack in SSDE C) 1.9 wt% Ketenblack in SSDE 4 4 C) 1.9 8)l14 wt% Ketjenblack in SSDE -5 A) 1 S10 D) 2.wt% Ketjenblack in SSDE SSDE wt% Ketjenblack in 0wt% KetjenbackinSSDE 20 30 40 50 60 70 80 90 100 110 120 Specific Capacity (nAh/g) 130 6 D) 2 8wt% Ketjenblacn SSDE C) 22 wt% Ketjenblack in SSDE 8)1 .7 wt% Ketjenbiackc in SSOE SSDE A) 11wtKet ncin 10 20 30 40 50 60 70 80 90 100 110 120 130 Specific Capacity (mAh/g) Figure 1.7a (left) and 1.7b (right). Figures 1.7a and 1.7b are potentiostatic charge and discharge curves for 30 vol% LCO and 40 vol% LCO electrodes. The electrodes are flowed into a reaction cell and then cycled at rest. Each figure plots the charge (positive current density) at 4.2V and discharge (negative current density) at 3.7V of four, different Ketjenblack compositions. Curves are terminated at a current density equivalent to a C/100 rate. to Increased amounts of carbon, particularly from 1 wt% to 2 wt% lead large increases in the storage capacity. 27 140 ~ 120 -- 100 30 vol% LCO Discharging -- 80 60 rgV 30 vol% LCO Charging - - L 0~- Discharging 40 - 20 40 vol% LCO Charging 0 0.5 2.5 2 1.5 1 Weight Percent of Ketjen Black in Electrolyte (%) 3 Figure 1.8. A summary of the charge and discharge capacities obtained under potentiostatic conditions from Figures 1.7a and 1.7b. Sharp increases in charge capacity accompany the increase in Ketjenblack loading from 1 wt% to 2 wt%. The transition occurs at a higher Ketjenblack loading for the 40 vol% LCO electrodes (open symbols), as compared to the 30 vol% LCO samples (filled symbols). Electrochemical impedance spectroscopy (EIS), performed by Nir Baram, demonstrates that carbon black lowers the cell impedance and mass transport of ions in the liquid electrolyte is not rate limiting. Semi-solid, 30 vol% cathodes are combined with a Ketjenblack-SSDE matrix with 3 different loadings of Ketjenblack. Experiments are conducted in a three-electrode Swagelok cell under static conditions with lithium metal counter and reference electrodes. Impedance models are fit (solid lines) to impedance data (open symbols) taken over a frequency range of 0.1 Hz to 100 kHz. Model parameters show that the overall cell impedance decreases with increasing Ketjenblack. The electrolyte mass transport impedance remains nearly constant, and is a small contributor to the total cell impedance. 28 80 25 - 1 kHz 2.5 wt% Ketjenblack 0.1 E 0 70 Hz 20 - 60 Other Contributions C To Cell Impedance i & E 0 o 1 15 Electrolyte Mass 4 4Transport 10-3 10 Hz Hz 1010 0.1 Hz 2.0 wt% Ketjenblack 1.7 wt%/o Ketjenblack -5 10 100 kHz 20 30 40 50 60 70 Impedance Real Component (Ohm) Impedance a 80 90 10 1.7 2 2.5 Weight Percent Ketjenblack Figure 1.9. Electrochemical Impedance Spectroscopy (EIS) experiments, conducted by Nir Baram, on the effect of Ketjenblack loading on the cell impedance. Semi-solid LCO cathodes are tested against lithium metal in a three electrode, Swagelok cell in static conditions. Nyquist plots of the complex impedance response data (open symbols) are provided alongside impedance model fits (solid lines). The model separates the ionic contribution from the total cell impedance. Ion transport in the liquid electrolyte contributes minimally to the overall impedance. Increasing the Ketjenblack content from 1.7 wt% to 2.5 wt% more than halves the total cell impedance. The rheological characteristics of the semi-solid electrodes are described by a shear thinning behavior and a yield stress. The viscosity measurements under a downward shear rate ramp, from 95 1/s to 0.1 1/s, are shown for 4 different Ketjenblack loadings in 30 vol% LCO electrodes (Figure 1.10a) and 40 vol% LCO electrodes (Figure 1.10b). The electrode compositions are the same as those tested electrochemically under potentiostatic conditions. A power law shear thinning behavior is observed for shear rates above 5 1/s. Data below 5 1/s is affected by both the non-continuum behavior of the semisolid electrode and by the torque accuracy of the viscometer. Even at low loadings - as a volume fraction of the total slurry, these samples' Ketjenblack content fall between 0.4 vol% and 1.0 vol% - the increasing amounts of Ketjenblack increase the dynamic viscosity by a factor of 2-4. 29 In addition to a non-Newtonian viscosity, the electrodes demonstrate other complex fluid behavior such as a yield stress. The viscoelastic response of an LCO semi-solid electrode, with Shawinigan black as the carbon black additive, is shown in Figure 1.11. The stress amplitude of a 1 Hz oscillation is increased logarithmically from 0.1 Pa to 1000 Pa in a parallel plate geometry with roughened surfaces. The elastic modulus exceeds the viscous modulus until the 650 Pa yield stress, where the solid-like behavior becomes liquid. The linear response breaks down after applied stresses exceed 10 Pa, corresponding to a 0.019% strain. 30 vol% LCO 100 40 vol% LCO 100 2.8 wt% Ketienblack 2.2 wt% Kejenblack 2.4 wt% Ketjenblack 1.9 wt6 Ketjenblack, 10 0 a eteb %K t...... 10 .... 0. 0. 1.4 wt Ketjenblack 1.0 wt% Ketenblack 1.7 wt% Ketjenblack 1.1 wto Ketjenblack 0.1 0.1 0.1 1 10 Shear Rate (1/s) 100 0.1 1 10 Shear Rate (1/s) 100 Figure 1.10a (left) and 1.10b (right). Flow curves of 4 carbon black compositions for 30 vol% LCO and 40 vol% LCO electrodes. The compositions are the same as used in the potentiostatic experiments (Figures 1.7a and 1.7b). Measurements are made in a Couette geometry and the shear rates are stepped down from 95 1/s to 0.1 1/s. Shear rates above 5 1/s show a power-law shear thinning behavior. Measurements below 5 1/s are complicated by non-continuum behavior of the particulate gel and the torque accuracy of the viscometer. 30 100000 - A Md-~h&za Modulus 100000 -Elastic - 10000 Viscous Modulus 0 0 1000 0 100 10 0.01 0.1 1 10 100 1000 10000 Stress Amplitude (Pa) Figure 1.11. Viscoelastic moduli of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC matrix under a stress amplitude sweep oscillation a 1 Hz. The electrode exhibits solid-like behavior, with an elastic modulus greater than the viscous modulus, up until a yield stress of 650 Pa. The elastic modulus of 60,000 Pa decreases after the limit of linear behavior is reach at a 10 Pa applied stress and a 0.019% strain. While the results of this study use LCO as a model chemistry, the semi-solid electrode concept has been shown to apply to many Li-ion chemistries. Figures 1.12a, 1.12b, and 1.12c present previously published cycling data for galvanostatic charge and discharge experiments performed by Mihai Duduta [1]. Three different electrode chemistries, all composed of a lithium storage compound, carbon black, and electrolyte, are cycled under stationary conditions against a lithium metal counter-electrode. Data for Li4 TisO 2 (LTO), LiCoO 2 (LCO), and LiMn1.NiO. 50 4 (LMNO), show stable voltage profiles over multiple cycles. LTO, LCO, and LMNO are expected to display lithium intercalation voltages on or about 1.55V, 4V, and 4.7V, respectively. The voltage hysteresis is indicative of the over-potential required to drive the charge and discharge reactions at the rates indicated below the curves. 31 En 20 vol% LiMn 1, 5NiO.50 4 in a 5.1 wt % carbon black-electrolyte matrix 26 vol% LiCoO 2 in a 1.8 wt% Ketjenblack-electrolyte matrix 1.8 wt/ Ketjenblack-electrolyte matrix ( 3. 2 . i502in a 25 vol% Li 4 2.5 4 1.5 C/3 Rate 6u). Specific Capacity (mAh/g) C/3.2 Rate 0 120 so120 180 > 1850 120> C/5 Rate 30t so9120 1s Specific Capacity (mAh/g) Specific Capacity (mAh/g) Figures 1.12a (left), 1.12b (center), and 1.12c (right). Semi-solid electrodes of three different lithium storage compound chemistries shown to cycle in a similar manner to conventional electrodes. The charge rates are given in the figure. Li 4Ti 5O12 (LTO, Figure 1.12a) is an anode compound with a lithium intercalation voltage of 1.55V. LiCoO 2 (LCO, Figure 1.12b) is a cathode compound with a lithium intercalation voltage centered about 4V. LiMn1.5NiO.504 (LMNO, Figure 1.12c) is a cathode compound with a lithium intercalation voltage of 4.7V. All voltages are against a Li/Li+ couple. 1.4 Discussion The SSFC concept aims to combine the energy density of solid energy storage compounds with the operational flexibility of a flow cell device. The material innovation of a composite fluid electrode comprised of a solid storage compound, conductive additive, and liquid electrolyte may be extended to a host of current and future electrochemical systems. Lithium ion chemistry is the basis for prototype semi-solid electrodes as it is today's leading edge in commercial, high energy density energy storage. Based on results presented in this chapter on prototype materials, the link of electrode microstructure to performance metrics is singled out as a research priority, as it will identify paths toward material optimization which are universal across the semi-solid electrode platform. There are several quantitative metrics by which energy storage devices are gauged, pertaining to energy density, power density, efficiency, cycle life, cost, and safety. The energy and power density 32 metrics are particularly stringent for motive applications, but are also relevant for citing energy storage in urban environments. Efficiency affects the operating costs of a device, as low efficiency leads to the loss of refined input energy as heat and entropy. Cost and safety are often overlooked in laboratory research - and in fact, will not be a primary concern in this work - but are nonetheless critical for the commercial viability of a technology. Energy density is measured in mass and volume terms, typically reported as watt-hours per kilogram (Wh/kg) and watt-hours per liter (Wh/L). Factors affecting the energy density of a SSFC are chemistry, microstructure, and device dependent. Chemistry dependent factors include the cell voltage and the bulk specific charge capacity of the anode and cathode compounds. As the difference in lithium intercalation potentials between the cathode and anode defines the cell voltage, it is desirable to have a high voltage cathode and low voltage anode. A high voltage cathode, such as LiNi 0 .5 MnI. 5O 4 (4.7V vs. Li, Figure 1.12C), and low voltage anode, such as graphite (0.1V vs. Li) can create a 4.6V couple. Constraints exist on the voltage, particularly at the anode, in a SSFC. Organic solvents in the electrolyte are reduced at the anode, producing an electrically insulating solid electrolyte interphase (SEI, see section S.1). Coating of particles and current collector with this insulating layer prevents delivery of electrons to redox reaction sites. As a result, higher voltage anodes such as Li 4 Ti 5O12 (1.55 V vs Li, Figure 1.12a) are required to prevent SEI formation, awaiting the development of SEI resistant electrolytes. Battery materials with high specific charge capacities, reported as milliamp-hours per gram (mAh/g) or milliamp-hours per milliliter (mAh/mL), are desirable for a high energy density. Microstructure dependent factors for energy density are the loading fraction of the charge storage compounds and the accessibility of the theoretical charge capacity. Loadings of solid compounds at 40 vol% are shown to produce flowable electrodes (Figure 1.10b) that can be charged and discharged (Figure 1.7b). Higher loadings should be accessible; the transition to a jammed glass 33 occurs at 58 vol% for monodisperse spheres and polydisperse suspensions have been shown to be fluid up to 75 vol% [3]. Yet even the highest loadings of storage compounds are of little use if the battery cannot usefully access that storage capacity. Figure 1.8 demonstrates that the accessible capacity is highly dependent on the amount of conductive additive present in the semi-solid electrode. Device dependent factors include the size of cell components such as the stack, tank, and pump. Power densities for flow batteries are typically expressed as power per unit of stack area, such as watts per square meter (W/m 2 ). As the power density is a product of the current density and operating voltage (Equation 1.3), achieving a high power density requires a retaining a large operating voltage at high current density. There are two approaches to a large operating voltage - a large equilibrium voltage, Veg, and a low over-potential, rq. The former approach is a function of the cathode and anode chemistry, discussed earlier. The latter requires the engineering of a low impedance battery. P I A = A (Veqfl Equation 1.3. The power density is given by the product of the current per unit area, 1/A, and the operating voltage. The operating voltage is the equilibrium cell voltage, Veq, less the over-potential, r. Contributions to a battery's impedance come from multiple mechanisms, which are reviewed in section S.2. Again, these contributions can be classified as chemistry, microstructure, or device dependent. Chemistry dependent mechanisms are the interfacial reaction rate, solid state lithium diffusion, ion transport across the composite, and the electron transport across the composite. These are in turn determined chemically by the area-specific interfacial reaction rate, the lithium diffusivity in the lithium storage compound, the bulk ionic conductivity of electrolyte, and the bulk electronic conductivities of the conductive additive and lithium storage compound. 34 The microstructure of the semi-solid electrode will affect the very same sources of impedance. Use of smaller particles of lithium storage compounds increases the specific surface area, increasing the total interfacial reaction rate. Smaller particles also shorten the diffusion path of lithium in the particles, reducing kinetic limitations from solid phase mass transport. The connectivity of the conductive additives will determine how bulk electronic conductivities translate into effective conductivities in for the fluid composite. For example, it will be shown that the effective electronic conductivities of the fluid composite, on the order of 1 mS/cm, are orders of magnitude below the bulk conductivity of carbon black, which is on the order of 10 S/cm. The liquid electrolyte connectivity similarly affects the effective ionic conductivity of the composite. Device geometry affects how material resistivities translate to cell impedances. In general, smaller electrode dimensions will lower the cell impedance. Furthermore, device factors often affect microstructural features and affect cell impedances indirectly through the microstructure. Chapter 4 will provide two examples of such effects, particle depletion at the walls and shear induced segregation in the bulk. Understanding what mechanisms are rate limiting, and how chemistry, microstructure, and device features influence those properties, will help answer questions such as why the discharge polarization in Figure 1.6 is so much higher than the charge polarization or why increasing the Ketjenblack loading in Figure 1.9 has such a large impact on the cell impedance. Round trip system-level efficiency, measured as a percentage of the input charge energy that is recovered during discharge, determines the amount, and cost, of refined energy that is irreversibly lost during operation. Sources of inefficiency are again attributed to chemical, microstructural, or device origins. A potential cause for inefficiency is the reaction over-potential. As seen in Figures 1.12a-1.12c, the over-potential leads to a voltage hysteresis between charge and discharge. Integrating the area in the hysteretic loop translates to the absolute energetic inefficiency, and its area relative to the total 35 area under the charge curve translates to a fractional inefficiency. The previous discussion on sources of impedance already attributed the origins of this over-potential to all three categories. Coulombic inefficiency is another form of input energy loss, and is usually entirely chemical in origin. Discharge curves in Figures 1.7a and 1.7b release less charge (here, measured in mAh/g) than initially inserted during charge. This irrecoverable charge, locked up in irreversible chemical reactions, is the source of Coulombic inefficiency. Pumping losses are a potentially significant contribution to system-level inefficiencies, and are a function of both the electrode microstructure and device parameters. The electrode's dynamic viscosity determines the pumping losses for a given flow rate through a given channel geometry. Figures 1.10a and 1.10b show that the dynamic viscosities of the tested electrodes are well above 1 Pa*s (1000 cP) at moderate shear rates of 10 1/s. Increasing the carbon black content to decrease the cell impedance or increasing the LCO volume fraction to increase the electrode's energy density will only push these viscosities up further, compounding the pumping losses. Conversely, for a given fluid behavior, device parameters such as the flow rate and channel geometry can be tuned to minimize pumping losses. Prior calculations have shown that operating a SSFC under rapid, continuous flow as seen in Figure 1.6 results in pumping losses of 22% [1]. Other modes of SSFC operation, such as stoichiometric flow and intermittent flow, are preferred for reducing pumping losses. In stoichiometric flow, the electrode is pumped slowly through a reaction stack at a rate which allows the electrode to fully charge or discharge in a single pass. In intermittent flow, a slug of electrode is pumped into the stack and charged or discharged under stationary conditions, before being replaced with a new slug. Either of these operating modes is predicted to lower pumping losses below 1% [1]. The cycle life of a battery is measured as the number of charge and discharge cycles that occur before the usable capacity drops by a given amount, for example 30%. Depending upon the chemistry 36 and operating conditions, commercial lithium-ion cells may have cycle lives ranging from hundreds to thousands of cycles. A SSFC faces the same chemical factors affecting traditional batteries' cycle lives. There are additional sources of degradation that can be attributed to microstructure and device features. Sedimentation of the suspended lithium storage compounds can lead to gravitationally driven phase separation. Other forms of microstructural segregation, induced by shearing flow can also detrimentally affect the electrode's cycle life. The conditions of shear present on a semi-solid electrode are determined by device parameters such as the flow rate and channel geometry. Other features of the device can lead to a shortened cycle life of the device, such as pump failure, abrasion-induced degradation of the reaction stack, or contamination of the electrodes. 1.5 Conclusion This chapter presented results that demonstrate a novel composite, fluid electrode that can be engineered to host multiple lithium compound chemistries. In order for SSFC devices to be viable for transportation or grid-scale energy storage, significant improvements must be made to the electrode properties. Understanding and engineering the composite microstructure holds part of the solution to this challenge. The energy density must be improved, requiring higher volume loadings of lithium storage compounds while keeping the electrode's ability to flow. The electrochemical impedance of the electrode must be lowered by increasing the electronic conductivity without excluding the lithium storage compound and without sacrificing the fluid properties. Improvements in impedance will benefit both the power density and efficiency. The electrodes need to demonstrate consistent performance in the face of hundreds of electrochemical cycles and flow events. Tackling the structure-property relationship will be handled incrementally. The first step is to understand the properties of carbon black-electrolyte gels. This chapter demonstrated that the carbon 37 black phase is important to the cell impedance (Figure 1.9), storage capacity utilization (Figure 1.8), and viscosity (Figure 1.10a,b). The next chapter will focus on how knowledge of the gel formation process and structure can explain the origins of these properties. 38 Chapter 1 References M. Duduta et al., "Semi-Solid Lithium Rechargeable Flow Battery," Advanced Energy Materials, [1] vol. 1, no. 4, pp. 511-516, Jul. 2011. [2] J.-M. Atebamba, J. Moskon, S. Pejovnik, and M. Gaberscek, "On the Interpretation of Measured Impedance Spectra of Insertion Cathodes for Lithium-Ion Batteries," Journal of The Electrochemical Society, vol. 157, no. 11, p. A1218-A1228, Nov. 2010. [3] H. A. Barnes, J. F. Hutton, and K. Walters, An Introduction to Rheology. Elsevier Science, 1993. 39 Chapter 2 Structure-Property Relationship of DLCA Carbon Black Gels Abstract Chapter 2 focuses on the properties of carbon blacks dispersed in organic lithium-ion battery electrolytes. Carbon black is shown to be an essential conductive additive in a semi-solid electrode (SSE), allowing for the transport of charge between the device current collector and the redox reaction sites on the suspended lithium storage compounds. Diffusion limited cluster agglomeration' (DLCA) forms thermally irreversible inter-aggregate bonds, which in turn are the building blocks for a spanning, carbon black gel structure. Agglomeration by van der Waals attraction is the source of both the gel's solid-like yield stress behavior and its electrical conductivity, and it imparts additional, key electronic and rheological properties to the carbon gels. In particular, conductive gels are formed at volume fractions that are two orders of magnitude below what is predicted by standard percolation theory, and these conductive structures may be reversibly deconstructed under a shearing force. 2.1 Introduction The semi-solid flow cell (SSFC) electrode must be engineered to balance multiple requirements. The electrode must be a good mixed conductor in order to supply electrons and ions to the redox reaction sites on the surfaces of the dispersed lithium storage compound. It must also stably suspend a 1The acronym DLCA refers to Diffusion Limited Cluster Aggregation in the literature. The presence of carbon black aggregates may cause confusion in terminology, as the term aggregate is used to describe two distinct structures. Therefore the agglomeration of carbon black aggregates into flocs by a diffusion limited cluster mechanism will be renamed Diffusion Limited Cluster Agglomeration in this work. 40 high concentration of that same compound. Finally, it must flow as a fluid under the action of a pumping force. Chapter 1 demonstrates that these properties can be engineered into a complex fluid electrode composed of a lithium storage compound and carbon black incorporated into a liquid electrolyte host. Figure 1.8 demonstrates the critical nature of the carbon black in electronically wiring the semi-solid electrode, allowing the delivery of current to and from the redox reaction sites. Using very low volume fractions of carbon black maintains the high ionic conductivity found in the pure electrolyte. The semisolid electrode demonstrates its ability to flow as a non-Newtonian fluid in Figures 1.10a and 1.10b. Adding carbon black significantly increases the dynamic viscosity, thereby increasing the energy required to maintain a shearing flow. While an increased loading of carbon black enhances the electronic conductivity of a SSE, it incurs the penalty of a higher viscosity. This chapter's study of the behavior of carbon black in electrolyte is driven by the desire to optimize the balance of electronic and rheological properties of these particulate gels. Results are presented in support of a DLCA gel microstructure. The power-law scaling of the elastic constant and of the limit of linearity in oscillatory strain lead to a fractal dimension of 1.8, which is consistent with a DLCA-mode of gel formation. Optical and electron microscopy images demonstrate a cluster-based structure across two length scales, separated by two orders of magnitude. The presence of salt in the electrolyte is shown to develop gels with more solid-like mechanical properties, in line with the theory that rapid, irreversible, van der Waals agglomeration results from the screening of repulsive electrostatic interactions between colloidal carbon black aggregates. Electronic and rheological properties of carbon black gels will also be presented, followed by an analysis of how the DLCA mechanism provides a uniform framework for understanding these physical properties. Attractive van der Waals forces lead to the agglomeration of carbon black aggregates into a spanning gel. The agglomerate structure leads to both solid-like rheological properties and high 41 electronic conductivities. The same inter-aggregate bonds that give rise to a mechanical gel provide the tunneling junctions that create a high conductivity network. 2.2 Methods 2.2.1 Materials There are a variety of conventions used in discussing aggregated and agglomerated structures. This work follows the system laid out by Donnet, where three levels of structural hierarchy are present in a carbon black composite [1]. The term particle refers to a carbonaceous sphere formed by the growth of a nucleus during manufacturing; particles generally are tens of nanometers in diameter. These particles are further fused into an aggregate during the hot carbon black manufacturing process; aggregates are hundreds of nanometers in diameter. An aggregate cannot be subdivided without irreversible fracture. Aggregates may further agglomerate in a host medium. Bulk and surface forces can create net-attractive interactions where aggregates combine into chemically discontinuous agglomerates. Carbon blacks are a class of material produced from the partial combustion or thermal decomposition of a hydrocarbon feedstock. While a vast diversity of specific properties exist for the numerous grades of carbon black available, they are typically sub-micron in size and have fractal microstructures composed of roughly spherical particles, of mixed graphitic and amorphous carbon content, fused into aggregates. A transmission electron microscope (TEM) image of a typical carbon black aggregate structure, as measured by Ehrburger-Dolle and colleagues, is presented in Figure 2.2a [2]. This fractal aggregate structure sets carbon black apart from other types of conductive additives such as carbon nanotubes, carbon fibers, graphene sheets, or graphite powder. A detailed description 42 of the defining characteristics of carbon black, and how they affect the properties of carbon black / - composites, is presented in section S.3. / I of Figure 2.1a (left) and 2.1b (right). Figure 2.1a is a TEM image of an electro-conductive grade acetylene black produced by the Denka Corporation. The image was taken at a 30,000 fold 2.1b is a magnification, and is borrowed from the work of Ehrburger-Dolle and colleagues [2]. Figure Spherical modified image produced by this author to highlight the structural features of the aggregate. particles aggregate into an open structure with a large occluded volume. 43 Figures 2.2a-2.2c. Micrographs of the three carbon blacks used in this study with original references noted. a) TEM image of TIMCAL C45 [3]. b) TEM image of Chevron Shawinigan [4]. c) TEM image of Ketjenblack EC-600JD. The carbon blacks have a qualitatively similar microstructure, composed of particles fused into open aggregates. The work in this chapter employs three carbon blacks, intended to sample a diversity of grades. TIMCAL C45, produced by TIMCAL Graphite and Carbon, is a furnace black with a BET specific surface area of 45 m 2/g; a TEM image of TIMCAL C45 is shown in Figure 2.2a [3]. A second carbon black is an acetylene black produced by the Chevron Corporation, with the trade name Shawinigan Black. Its TEM micrograph is included as Figure 2.2b, and it has a measured BET specific surface area of 60 m 2/g [4]. A third carbon black is in a unique class of its own - Ketjenblack ECP600JD is a grade of carbon black produced by Akzo Nobel Polymer Chemicals, LLC. that does not fit into the standard manufacturing process classification. Ketjenblack has an abundance of micro and mesoporosity, lending to a high BET measurement of 1453 m 2/g [5]. A TEM image of Ketjenblack is shown in Figure 2.2c [4]. All three carbon blacks are considered high structure carbon blacks suitable as an electro-conductive additive. A summary of cited BET measurements included in Table 2.1. 44 Carbon Additive TIMCAL C45 Type BET SSA (m 2/g) Furnace Black Chevron Shawinigan Acetylene Black Ketjenblack EC600JD Other Carbon Black 45 [3] 60 [4] 1453 [5] Table 2.1. A summary of carbon additives used in this study. The high BET derived surface area of Ketjenblack is attributed to its significant meso and microporosity. The redox reactions occurring at the surface of the suspended lithium storage compound in a SSE require the delivery of both electrons and ions. As such, the simplest vehicle to host the solid SSE components is a standard, liquid lithium-ion electrolyte, to guarantee the facile delivery of ions; the electrolyte acts as the unnamed, 'semi-liquid', portion of the semi-solid electrode. Lithium-ion secondary battery electrolytes are carefully engineered blends of solvents, salts, and additives that are optimized for the stable, long term performance of an electrochemical cell. The roles of the electrolyte components are laid out in section S.4 as background material. This work employs two, different electrolyte systems. The first is a proprietary, commercial research electrolyte produced by Novolyte Inc., referred to as a small-scale developmental electrolyte (SSDE). It is a blend of alkyl carbonate solvents and stabilizing additives with a 1.3 molar lithium hexafluorophosphate (LiPF 6) salt concentration. The second electrolyte is a one to one (by volume) blend of ethylene carbonate (EC) and dimethyl carbonate (DMC), with a 1.0 molar concentration of LiPF 6. The EC:DMC electrolyte is intended to be a simplified analogue to SSDE in terms of composition and physical properties. 45 Abbreviated Electrolyte Name LiPF 6 Concentration Solvent SSDE 1.3 Proprietary mix of alkyl carbonates EC:DMC 1.0 1:1 volume ratio of ethylene carbonate and dimethyl carbonate Table 2.2. Summary of properties of the two electrolytes used in this study. The EC:DMC electrolyte is formulated as a simplified analogue to SSDE. 2.2.2 Experimental Multiple terms can describe the solid-liquid composite of carbon black and electrolyte. Here, the term composite most generally describes the two-phase combination without any specificity on how the two phases are structured. Carbon black dispersed in electrolyte, or a carbon black-electrolyte dispersion, is a more specific description of a system where the carbon black is homogenously distributed as a colloidal solid phase in a liquid matrix. If the distribution of carbon black leads to a spanning network through attractive interactions, the dispersion is termed a gel. The carbon black content in a gel is calculated as a weight percent of carbon black in the carbonelectrolyte composite. As mentioned earlier in this chapter, various carbon black grades differ in microporosity, mesoporosity, graphitic content, and structure. Therefore the concept of a material density is somewhat ambiguous and can differ dramatically across different carbon black grades. Reporting a weight fraction removes this element of interpretive ambiguity. Where necessary, this weight percentage will be converted to a volume percentage by using the densities tabulated in Table 2.3. Material Density (g/mL) All Carbon Additives 2.16 SSDE 1.31 EC:DMC 1.29 46 Table 2.3. Standard density values used to convert weight percentages into volume percentages. The electrolyte densities are measured values. The carbon density is an assumption, attributing a common, graphitic density to all carbon additives. The sensitivity of gel properties to its composition calls for a mixing protocol that maximizes homogeneity and reproducibility. As such, gel synthesis is a three step process. In the first step, a milligram accuracy analytical balance (Sartorius Model ED153-CW) is used to weigh a calculated mass of carbon black in a 20 mL glass scintillation vial. Depending upon the carbon black, the raw material may be in a pelletized form or in a 'fluffy' state. In the former case, the pellets are initially crushed in a vial to promote its dispersability in the following step. A calculated volume of electrolyte is added with an Eppendorf pipet. The measured densities of 1.31 g/mL and 1.29 g/mL for SSDE and EC:DMC are used to convert between masses and volumes of the electrolytes. All of the carbon blacks used in this study, pelletized or not, are agglomerated in their dry state and it is therefore necessary to use a rotor-stator shear mixer to homogenize the solid-liquid mixture in a second step. A PRO Scientific Bio-Gen PRO200 homogenizer on its low power setting is applied to the sample in its glass vial for 10 to 30 seconds, with longer times required for higher solid loadings, as the formation of a gel reduces the efficiency of the homogenizer. In the final step, the sample vial is sealed and immersed in an ultrasonic water bath sonicator (Cole Parmer Model 8890) for one hour. The intense, localized application of power by bubble cavitation present in the 42 kHz sonicator allows the carbon black gels to relax into a lower energy state, in what may be considered an accelerated aging. 47 Top Electrode Sample Well -Bottom 0.9 cm Electrode 11cm Figure 2.3. Schematic of a parallel plate conductivity cell. Current is passed between two, ion-blocking, electron-conducting stainless steel plates across a cylindrical sample with the dimensions shown. The conductivity cell has a measured cell factor of 1.2 1/cm. Electronic conductivity measurements on the prepared gels are made in a two-probe parallel plate geometry, illustrated schematically in Figure 2.3. A cylindrical well in a PTFE housing is sealed on either end by polished, alloy 316 stainless steel plates. Electronic conductivities of the gels are highly shear history dependent, and therefore care is taken to minimize the application of shear on the samples during transfer into the well with a spatula. The two seals present around the sample, one a PTFE tape-lined threading and the other an Aflas o-ring seal, prevent solvent loss. Conductivity measurements are taken over the course of one to two hours. A Solartron Analytical model 1470 potentiostat and model 1455 frequency response analyzer are used to apply either a +/-10 mV DC or AC bias to the parallel plates. Both AC impedance measurements and DC measurements are made on the sample for completeness. The AC measurements are made with a 1 MHz to 0.01 Hz logarithmic frequency sweep, while the DC measurement is taken at a steady state value after a 5 minute hold. In most cases the low frequency extrapolation to a zero-frequency conductivity yields the same value as the measured DC conductivity. 48 In the low conductivity samples, typically below 1 mS/cm, the low frequency AC extrapolation can become ambiguous and the DC value is utilized exclusively. Resistances calculated from the data are converted to a conductivity by dividing the conductivity apparatus' cell factor by the resistance. The cell factors are calibrated to 1.2 1/cm with a 15 mS/cm conductivity standard produced by Oakton Instruments. Scanning Electron Microscope (SEM) images of carbon black dispersed in electrolyte were made by sealing the gels in a QX-102 capsule manufactured by QuantomiX. The gels were prepared as described above, and loaded into the capsule with a spatula. The sealed capsules were imaged in a FEI/Philips XL30 FEG ESEM. The accelerating voltage, spot size, and working distance were 15kV, 3, and 10mm, respectively. The QX-102 capsules feature a cover that is transparent to the electron beam, which is patterned with metallic current collectors. Despite the conductivity of the gel, it is necessary to do the majority of imaging in areas adjacent to these current collectors in order to obtain high resolution micrographs. Optical microscopy on the gels was carried out under a Nikon Eclipse ME600 microscope. The gels were placed between a slide and cover slip and imaged under ambient atmosphere. The imaging time was limited to avoid solvent loss. The images were taken at the fringe of the sample where the carbon content was lowest to achieve an adequate transmission of light. Imaging of the bulk was not possible due to the near complete absorption of light by the carbon black. The imaged areas do not have the same composition as bulk of the gel, therefore the reported carbon loading for the prepared sample does not accurately reflect the actual weight fraction in the imaged area. Rheological measurements were performed on a Malvern Kinexus Pro rheometer under an argon environment. Measurements on carbon black gels were made with a sandblasted, 40 mm diameter parallel plate geometry. Confocal microscope imagery of the sandblasted surface show 49 surface feature heights of 10 microns, much greater than the average carbon black aggregate diameter. Measurements were repeated at 700 micron and 500 micron gap heights to ensure that wall slip effects were not affecting the measured values. The parallel plate geometry inherently introduces a gradient in shear rates along the radial direction. The shear rate value at a distance Y4 of the radius of the plate is used to calculate shear rates and viscosities. While the application of a non-uniform shear rate is not ideal, the parallel plate geometry allows for the controlled variations in gap height and ready use of roughened surfaces. The gain in control over wall slip is preferred to the constant shear rate that cone and plate geometry provides. Once loaded into the rheometer, all samples are covered with a solvent trap to minimize solvent loss from the electrolyte. All samples are pre-sheared at 500 1/s for 5 minutes and then instantly quenched to a stop in order to remove variations in shear history introduced during sample loading. All measurements are made at 25*C, controlled to within 0.10 C. Stress amplitude sweeps are conducted logarithmically at an oscillation frequency of 1 Hz. The torque resolution of the rheometer sets the lower stress limit to 0.5 mPa. The upper stress limit is set to correspond to strain amplitudes exceed 1000/6. When conducting a frequency sweep experiment, a stress is chosen in the linear viscoelastic regime that is identified by a previous stress amplitude sweep. Frequencies from 0.01 Hz to 100 Hz are measured, although much of the data above 10 Hz is typically unusable due to inertial effects from the measuring geometry. Reported yield stresses are approximate values obtained from the stress amplitude sweep oscillation experiments. The stress at which the elastic modulus is exceeded by the viscous modulus, and therefore the material transitions from solid-like to fluid-like is reported as the yield stress. This measure of yield stress is arguably an approximation, with the more rigorous method being a succession 50 of creep experiments with increasing applied stress. The oscillation approach is employed out of considerations of expediency, particularly when doing surveys of a large parameter space. Flow curves are measured in the Kinexus Pro under a controlled shear rate schedule. Shear rates are incremented in logarithmic steps. Two minutes of equilibration time are allowed at each shear rate to account for thixotropic effects. The electrolytes in this study are water sensitive and all work where the electrolyte is exposed, including rheological measurements, is done in a MBRAUN Labmaster glovebox under an argon atmosphere. Oxygen levels are monitored and kept below 5 ppm. Water levels are kept below 0.1 ppm. The single exception is the optical microscopy experiment, where the sample is measured under ambient conditions. 2.3 Results The viscoelastic response of a carbon black gel under the varying parameters of solids loading, electrolyte salt concentration, and time after shear are measured to demonstrate that the carbon black agglomerates via a DLCA mechanism to form gels with a characteristic fractal dimension of 1.8. Those results are supported by direct observation of a multi-scale cluster-based microstructure. The correlation of electronic conductivity and rheology - particularly close to linear for conductivity and yield stress - is shown to demonstrate a common physical origin for the two macroscopic properties. The discussion, to follow, will argue that the inter-aggregate bonding via van der Waals forces defines the building block for mechanical properties via the bending, stretching, and breaking of those bonds. It also determines the origin of conductivity by defining the gap across which inter-aggregate electron tunneling occurs. 51 1E+3 Limi ofLinearity Yield Stres' A -I-: 0jg& -Ela~tic -Modulus1 A I.E+2 001 0 00 -- bI E+1 0icu~ouu _ 00 - I ~ ~~706boo I E+O _ 0 1E-4 1E-3 1E-2 1E-1 1E+O 1E+I1 1E+2 1E+3 Stress Amplitude (Pa) Figure 2.4. An sample dataset of the dynamic viscoelastic response to an oscillatory stress amplitude sweep experiment. Data for 1 wt% Ketjenblack in an EC:DMC electrolyte is shown. The Limit of Linearity, Yield Stress, Elastic Modulus, and Viscous Modulus are labeled for clarity. These four properties, and their scaling with composition, are used to describe the mechanical properties of a gel at rest. Figure 2.4 is a sample viscoelastic response of a 1 wt% Ketjenblack gel to an oscillation stress amplitude sweep conducted at 1 Hz. Four parameters are extracted from the viscoelastic moduli. The first two are the absolute values of the elastic and viscous moduli in the linear viscoelastic regime (LVER), where the moduli are independent of the applied stress amplitude. A gel will have an elastic modulus that is greater in value than its viscous modulus. The third parameter is the limit of linearity; this is the stress - and corresponding strain - at which the fluid's linear response breaks down and becomes a function of the applied stress [6]. The limit of linearity marks strain amplitudes that break, rather than stretch, bonds. The last is the yield stress, defined as the applied stress amplitude at which the elastic and viscous moduli cross over from a solid-like behavior to a liquid-like behavior. 52 Figures 2.5a and 2.5b plot the elastic moduli and limits of linearity for the three different carbon blacks studied here, as a function of the solids loading in an EC:DMC electrolyte. Here, the methodology developed by Shih is observed, and the carbon content is reported as a volume fraction [6]. A clusterbased gel microstructure will show a power law scaling of the elastic modulus and limit of linearity, and a fractal dimension is deduced from the two scaling exponents. Background on the methodology is provided in section S.7. Power law fits are shown for the Ketjenblack EC-600JD, Chevron Shawinigan, and Timcal C45, and the fit parameters are summarized in Table 2.4. All samples demonstrate an increasing elastic modulus with increasing solids loading; additional carbon creates stronger gels. With power law exponents of 3.3 - 3.6, the increase in elastic modulus is non-linear. The limit of linearity decreases with increasing solid loading for all samples. The gels become less compliant with increased carbon and the onset of bond breakage occurs at lower strains with carbon-rich gels. Calculated values of the gel structure's fractal dimension are also tabulated. 100000 - 10Ketjenblack Shawinigan 10000- C45 Ketjenblack 0 - 1000 _ 10. 0.1 - - 100 - C45 Shawinigan 1 0.01 0.1 1 Volume Fraction (%) 10 0.1 1 10 Volume Fraction (%) Figure 2.5a (left) and Figure 2.5b (right). Figure 2.5a shows the scaling of the gel elastic modulus with carbon loading for three carbon black samples. Figure 2.5b plots the limits of linearity for the same samples. Power law fits are shown as solid lines and the fit parameters are summarized separately. The three carbon blacks become stiffer and less compliant with increasing carbon content. 53 Sample Elastic Modulus Power Ketjenblack EC-600JD +3.3 Chevron Shawinigan +3.3 TIMCALC45 +3.6 -1.6 -1.6 -1.9 1.8 1.8 1.8 Law Exponent Limit of Linearity Power Law Exponent Fractal Dimension Table 2.4. Summary of Power Law fit exponents for data plotted in Figures 2.5a and 2.5b and the fractal dimension calculated from the fits. The values of 1.8 for the fractal dimension agree with expectations for a DLCA microstructure. Ketjenblack EC-600JD dispersions in EC:DMC electrolyte are examined in much lower values of solid content to determine the gel point. The elastic modulus and yield stress are shown as a function of weight fraction of Ketjenblack in Figure 2.6a and 2.6b. The two properties diverge toward values that are obscured by the rheometer torque resolution at loadings approaching 0.2 wt% (0.12 vol%). Ketjenblack forms mechanically percolating structures at 0.12 vol%. 1000 ~~.0 100- ~.0 100- 10- 0 10- 1 - 0. 03 0 0.1- 0.01 0.1 0 0.5 1 1.5 Weight Percent Ketjen EC-600JD in Electrolyte (%) 2 0 1.5 1 0.5 Weight Percent Ketjen EC-600JD in Electrolyte (%) 2 Figure 2.6a (left) and Figure 2.6b (right). Figure 2.6a shows the elastic modulus as a function of Ketjenblack EC-600JD loading in an EC:DMC electrolyte. Figure 2.7b shows the yield stresses for the same samples. Ketjenblack forms a gel at a solid content of 0.2 wt% (0.12 vol%). 54 According to DLVO theory (see section S.6), the high concentration of salt in the electrolyte will screen repulsive, electrostatic interactions between carbon black aggregates. If the carbon black particles develop surface charge in the electrolyte solvent, then removing the salt will reveal the presence of repulsive interactions. The EC:DMC electrolyte is formulated as a complete electrolyte, with a 1 molar LiPF 6 salt concentration, and as salt-less electrolyte with only the solvents present. While the formulation without salt is technically not an electrolyte, it will be referred to as a 0 molar electrolyte to avoid confusing terminology. Identical composition, 0.3 wt% Ketjenblack gels are formulated with the two electrolytes. Their viscoelastic responses to a stress amplitude sweep oscillation experiment are shown in Figure 2.7. The sample without any salt displays an elastic modulus of 1.0 Pa, lower than the value of 2.9 Pa obtained in the 1 molar electrolyte. The yield stress also decreases in the sample without salt, a value of 0.073 Pa compares to 0.32 Pa for a gel with salt included. 10 Elastic Modulus 1.0 A~~~~~~~~~ -~~~ - 0u P V Vscous Modulus PF6 M IiPFR - -aW 0.1 0 Viscous Modulus > AA A Aj 0.01 AA ' 0 AD A NoSalt 0 Elastic Modulus No Salt A A 0.001 i 0.001 0.01 0.1 Stress Amplitude (Pa) 1 10 Figure 2.7. The viscoelastic response to an oscillatory stress amplitude sweep for 0 and 1 molar electrolyte samples are plotted. A 0.3 wt% Ketjenblack solids loading is dispersed in a EC:DMC electrolyte, with and without a LiPF 6 salt. The sample without salt has a lower elastic modulus and yield stress than the sample with salt. 55 Figures 2.8a and 2.8b are optical and SEM micrographs, respectively, of a Ketjenblack sample in SSDE. Very similar, cluster-based microstructures are observed across two orders of magnitude, on the length scales of 100 ums and 1 um. In the optical micrograph, the light absorption by the carbon black results in the solid phase appearing as black. In the SEM micrograph, the emission of secondary electrons from the carbon black results in the solid phase appearing as white. While both are 2 wt% solids loading formulations, the imaged areas do not accurately reflect the bulk concentration. - 100 u Figure 2.8a (left) and 2.8b (right). Figure 2.8a is a transmission mode optical micrograph of a Ketjenblack gel in SSDE. Figure 2.8b is a secondary electron detector image of a Ketjenblack gel in SSDE. Similar, cluster-based structures are observed across length scales differing by 2 orders of magnitude. Carbon gel conductivities are measured in a parallel plate geometry and conductivities are reported as a function of solids loading in Figure 2.9. Increasing the carbon loading monotonically increases the gel conductivity. Lithium ion electrolytes typically have ionic conductivities of 5-10 mS/cm. The carbon gels are able to develop electronic conductivities of similar magnitudes at higher solids loadings. The curves are terminated at weight fractions at which the gels become too thick to transfer via spatula. The effect of shear history and the finite amount of shear necessarily applied in transferring 56 the gels via spatula impose an error bound of up to 50% on the measured values of conductivity presented. The conductivity values are paired with rheological data obtained in other experiments to plot the four carbons' correlation of electronic conductivities and rheological properties in Figure 2.10a, 2.10b, and 2.10c. The conductivity measurements are made in a different measuring apparatus from the rheological measurements; this is not an in-situ measurement. A clustering of the three carbon black samples can be seen. The clustering is especially strong in the correlation of yield stress with conductivity, where the data lie on a near linear trend. A linear trendline is included as a simple visual aid - it is not a fit to the data. 1E+0 E E' 1E-1 - KE-e black .:C-6 ~i 2 1E-2 0 I1E-3 0 Cl evron $hawinigan 1E-4 TIMcAL C45 1 E-54- 0 8 7 6 5 4 3 2 1 Weight Percent Carbon Filler in Electrolyte (%) 9 Figure 2.9. Static electronic conductivities, as a function of solids loading, for three grades of carbon black. Ionic conductivities in the liquid electrolyte are typically 0.005-0.01 S/cm. 57 N Timcal C45 0 Ketjenblack EC-600JD A Chevron Shawinigan 100 10 0.1 1E-6 1E-5 1E-4 1E-3 IE-2 1E-1 1E-2 IE-1 Conductivity (S/cm) 10000- a- 100 0 100 .2r 4 1 1E-6 1E-5 1E-4 1E-3 Conductivity (S/cm) 100000 _ S10000 1000 100 10 1E-6 1E-5 1E-3 1E-4 Conductivity (S/cm) 1E-2 1E-1 Figure 2.10a (top), Figure 2.10b (middle), and Figure 2.10c (bottom). Data on carbon gel conductivities are plotted against three rheological parameters, the yield stress, elastic modulus, and dynamic viscosity at 1 1/s. A reference line for a linear trend is included for visual orientation - it is not a fit to the data. 58 0.1 Fae n n 1 10 100 Shear Rate (1/s) 1000 Figure 2.11. A viscosity curve for a Ketjenblack gel sheared in a roughened parallel plate geometery. A power law shear thinning behavior is followed by a mild shear thickening above 100 1/s. A shear rate controlled flow curve for a 1.1 weight percent Ketjenblack sample in SSDE is shown in Figure 2.11. A slight shear thickening above 100 1/s is observed; a similar shear thickening was studied by Osuji on carbon black dispersions in tetradecane [7][8]. Electrostatic stabilization is absent in both the electrolyte and tetradecane systems. The shear thickening is attributed to the increase in the total carbon black hydrodynamic volume as high shears lead to de-flocculation. The transient viscoelastic behavior of a fluid reflects the structural rearrangement occurring in the system. A 7 wt% Chevron Shawinigan gel is sheared at 100 1/s and then brought to a halt in a fraction of a second under the rheometer's control. A constant stress amplitude oscillation at 1 Hz, with a stress amplitude previously determined to be in the gel's LVER, commences immediately and the viscoelastic response of the gel is plotted in Figure 2.12. The viscoelastic moduli develop into a stable, solid-like profile after a brief 2 second transient. The elastic modulus grows thereafter with a weak power law relation with time. 59 - 10000 Elastic Modulus - 1000 Viscous Modulus 100 0.1 1 100 10 1000 10000 Time (s) Figure 2.12. The time evolution of the viscoelastic moduli of a 7 wt% Chevron Shawinigan gel in an EC:DMC electrolyte upon cessation of a 100 1/s shear. The moduli show the gel quickly stabilizes into a solid-like material after a brief, 2 second transient. 2.4 Discussion Results have been presented demonstrating the scaling of rheological and electronic properties of carbon black gels with solids loading. The power law scaling of the elastic modulus and limit of linearity for all three carbon blacks lead to a calculated fractal dimension of 1.8. The dependence of the gel strength on salt concentration demonstrates that colloidal interparticle forces are determining the microstructure of the gel. The two observations are consistent with a gel formation mechanism driven by thermally irreversible, attractive DLVO forces leading to carbon black aggregates agglomerating into a DLCA gel. Direct microscopic observations confirm a cluster-cluster structure on the 1 micron and 100 micron scale. A DLCA structure provides a percolating pathway for electron conduction, with electrons tunneling across inter-aggregrate junctions. The linear relationship of the electronic conductivity with 60 the yield stress supports the microstructural connection between mechanical percolation and electronic percolation. A DLCA gel can be broken down and reformed after shear; one can therefore understand how these carbon black gels are ideal, conductive hosts in a SSE. In applying the DCLA model to a particulate gel, there are two, primary criteria. The first is that the particles must be colloidal, such that their motion is dominated by Brownian forces. The second is that the particle-particle interactions must be attractive, thermally irreversible, and lack barriers that are relevant on the energetic scale of thermal fluctuations [9]. A summary of the DLCA mechanism is provided in section S.5. Under the influence of a DLCA mechanism, there are unique structural features that should arise in a strongly attractive colloidal system. Unlike a random distribution of particles, where percolation requires a volume filling of 16%-18%, the attractive interactions in a DLCA system creates an ordered microstructure which achieves a spanning network at a much lower loading. In a cluster growth mechanism, larger space-filling clusters lead to lower percolation thresholds. DLCA clusters form the building blocks of a microstructure which includes voids on every length scale, from the particle scale up to the domain boundary scale. A particulate gel is formed if the clusters can agglomerate into a spanning structure before gravitational forces cause sedimentation. The properties of this gel will depend on the quality, density, and homogeneity of the inter-aggregate bonds formed in the DLCA process. Those in turn depend upon the inter-particle potential, solids loading, and processing conditions, respectively. A DLCA gel should maintain a stable, static structure at rest, although thermal relaxation and gravitational compaction may age the structure of the gel over an extended period of time Understanding of the mechanism of gel formation in the carbon black - electrolyte system allows for the explanation of many unique features of the material. Furthermore it allows us to posit 61 the engineering constraints present in the system and illuminate methods of material optimization. The following discussion ties together the known properties, and observed results, of carbon black gels with expectations of the DLCA model. Two fundamental prerequisites for DLCA structures are a set of particles (or aggregates) dominated by Brownian forces and thermally irreversible interparticle attractions, without any significant energetic barrier to approach. The former condition is examined by calculating the carbon blacks' Brownian diffusivity with the Einstein-Stokes equation. The result is used to approximate the characteristic time scale of diffusing one aggregate diameter (approximately 300 nm). We take the ratio of this with the time scale of Stokes settling over the same distance as a gravitational settling Peclet number, Peg. Values less than one indicate the dominance of Brownian forces. DB -6i kBT Equation 2.1. The Einstein-Stokes equation for the Brownian diffusion constant, DB, of a spherical particle or radius r in a liquid of viscosity r. gr? (p -Pr) 18TI Equation 2.2. The Stokes settling rate, V,, of a sphere of radius r and density p, in a fluid of viscosity r and density pf. L Vs 2 DB IL=3oonm rLgr 3 (p _ p) 6kbT L=300nm Equation 2.3. The gravitational settling Peclet number,Peg, to be evaluated on a characteristic length scale, L, of 500 nm. 62 The calculation is complicated by the aggregates' fractal nature. Combining the aggregate's bounding radius with a graphitic density would significantly overstate the aggregate's mass, due to the structure's high void content (Figure 2.1b). To calculate the Peclet number based upon a single particle in the aggregate would overestimate the diffusivity, as the particles are entrained in a fused aggregate. The two extremes are computed in Table 2.5 and an intermediate value leads to the reasonable expectation of Brownian behavior (Peg << 1). Parameter Fluid Viscosity Characteristic Length Upper Estimate of Brownian Diffusion Constant (30nm primary particle calculation) Lower Estimate of Brownian Diffusion Constant (300nm aggregate calculation) Lower Estimate of Peclet Number (30nm primary particle calculation) Upper Estimate of Peclet Number (300nm aggregate calculation) Value 0.01 Pa s 300 nm 1.5E-12 m 2/s 1.5E-13 m 2/s 1 900,000 1 900 Table 2.5. Calculations on the Brownian nature of the carbon black aggregates. With gravitational settling Peclet numbers much less than 1, the carbon black aggregates are considered colloidal particles. With respect to the second condition of an attractive potential, without significant repulsive barriers, an analytical framework is provided the theory of interparticle potentials developed by Derjaguin, Landau, Verwey, and Overbeek (DLVO, see section S.6). DLVO theory accounts for the combined effects of van der Waals attraction and electrostatic repulsion in a colloidal system. The van der Waals attraction is largely unaffected by the salt concentration. The electrostatic repulsion is screened by the presence of ions in solution and therefore its strength is highly dependent on the salt concentration. The length scale of repulsive interactions is set by the extent of the diffuse, charged double layer formed around a charged surface; this is also known as the Debye length. 63 n. 1 e Zi2 1 h i=Li+PF6 _ EEckT Equation 2.4. An expression for the Debye length of the diffuse electric double layer in an electrolyte. The bulk ion concentration, n., is 1.0 M. Both cation and anion are monovalent (z=1). The dielectric constant of the 1:1 EC:DMC mixture is assumed simply as a mean of the two dielectric constants of 95.3 and 3.1 for EC and DMC, respectively [10][11]. Using parameters from literature for the EC:DMC electrolyte, Equation 2.4 calculates that the double layer collapses to 1 nanometer. At such short length scales, short range "hard shell" repulsive interactions of the surface adsorbed ions and their solvation shells, constituting the Stern layer, dominate. In other words, there should be no long range energetic barrier to the van der Waals attraction, until they approach non-DLVO short range interactions. The second criterion of the DLCA mechanism is observed. The microscopic origins of the gel's macroscopic viscoelastic properties and yield stress lie in this DLVO interparticle attraction. Applying a small shear to the material causes an elastic response through the bending and stretching of bonds that are constrained by the three dimension connected network. Applying a much larger strain with a sufficient stress leads to the breaking of these bonds. Assuming the nature of the interparticle attractions are not affected by the solids loading, the effect of solids loading on developing the gel's mechanical properties is through the evolution of the microstructure to more densely connected forms. The viscoelastic properties of two EC:DMC electrolyte gels, with and without lithium salt, are compared to tested the importance of the electrolyte salt in enabling the DLCA mechanism. If the carbon black develops a surface charge in the polar solvent, then the sample absent of lithium salt will 64 develop a degree of electrostatic stabilization. A thermally surmountable barrier will shift the formation mechanism from a pure DLCA model to a RLCA model, described earlier in section S.5. In the RLCA mode, the aggregates form denser clusters, as they are able to interpenetrate to a greater extent (Figure 2.13). The experiment utilizes a 0.3 weight percent Ketjenblack sample, chosen just above the measured gelation threshold. With a limited carbon black mass dispersed in electrolyte, denser clusters must necessarily be more tenuously interconnected. Figure 2.7 shows that the sample without salt does indeed show less solid-like properties. Its elastic modulus and yield stress are both below the values of the standard electrolyte sample. In a similar vein, Schueler and colleagues utilized the addition of - copper chloride salt to lower the percolation threshold in their electrically conductive carbon black polymer composites [12]. The rapid, irreversible DLCA gel formation created spanning clusters at lower carbon black loadings. 65 RLCA DLCA 4 1, eGold Silica Potystyrene Simu ation Figure 2.13. TEM micrographs and simulation results of fractal structures assembled by DLCA and RLCA mechanisms. Figure borrowed from Lin and colleagues [13]. The fractal dimension is a quantitative measure of structure in the fractal geometry predicted in cluster agglomeration models. Extensive computational and experimental studies have attributed values of 1.8 and 2.1 for DLCA and RLCA, respectively [9]. While many researchers have observed a power law growth in elastic moduli, with increased solids loading, for colloidal gel systems, Shih devised a theoretical and experimental framework for relating this scaling behavior back the gel's fractal dimension [6][14][15][16]. Details on Shih's model are given in section S.7. 66 The fractal dimensions of the three carbon black gels are calculated from a power law fitting of the elastic modulus and limit of linearity (Table 2.4), according to Equation 0.2 and 0.3. The results of this calculation are re-tabulated in Table 2.6. The calculated fractal dimensions of 1.8 are in agreement with the theoretical prediction of 1.8 for the DLCA mechanism. Elastic backbone dimensions near 1 indicate the load bearing backbones in the clusters are essentially linear across the cluster. Carbon Black Grade Fractal Dimension Elastic Backbone Fractal Dimension Ketjenblack EC-600JD 1.8 1.0 TIMCAL C45 1.8 1.3 Chevron Shawinigan 1.8 1.0 Table 2.6. The fractal dimensions calculated from the scaling analysis of gel properties with solid loading. A fractal dimension of 1.8 is consistent with a DLCA gel. Elastic backbone dimensions of 1 indicate linear, load bearing backbones that span the cluster. One of the identifying properties of fractal geometry is the concept of self similarity. Geometric features repeat themselves on multiple length scales. In the DLCA mechanism, the carbon black aggregates should agglomerate into clusters of multiple aggregates, which in turn agglomerate into increasingly larger clusters. This mechanism develops internal void structures at every length scale, from the aggregate upwards, lending to the low fractal dimension. A cluster-based microstructure is visible, along with a preservation of that structure over the 1 um (Figure 2.8a) and 100 um Figure 2.8b) length scales. The attribution of a DLCA mechanism and microstructure to the carbon black gels allows for the understanding of gel's device-relevant properties. These properties are the gel's electronic and ionic conductivity, viscosity, yield stress, and stability. As the gel has been shown to be critical in wiring the SSFC electrode, its conductivity should be maximized to reduce ohmic losses during charge transport. Chapter 1 demonstrated that the ionic conductivity is not currently rate limiting. SSFC device imposes 67 shearing flow on the complex fluid, and the electrode viscosity should be minimized. Stability is important in retaining consistent properties over time. The presence of a large yield stress can be detrimental to the flow properties of the SSE, but a limited yield stress can be useful in stabilizing the lithium storage compound against sedimentation [17]. This last topic will be revisited in Chapter 3. Percolation is necessary for high conductivity charge transport over macroscopic length scales. The development of percolating structures of agglomerated aggregates gives rise to solid-like mechanical properties such as a yield stress. Above a certain solid content, spanning networks are established and a gel is formed. As will be argued later, there is a common physical origin to the mechanical and electronic properties of the gel. In Figure 2.6a and Figure 2.6b Ketjenblack EC-600JD gels are formed in an EC:DMC electrolyte and two metrics of solid-like behavior, the elastic modulus and yield stress, are seen to diverge to zero at a solid content of 0.2 wt% (0.12 vol%). This percolation threshold is over two orders of magnitude lower than observed in non-attractive systems. One reason for the low percolation threshold is that the Ketjenblack aggregates are highly porous; they contain porosity on every level - micro, meso, and macro. The fractal nature of the aggregate allows it to fill space much more broadly than expected from its solid content. The second factor in the low gel point is the important distinction in physical mechanism driving particle organization. In the DLCA model, microstructures are not random, strong attractive interactions lead to a ordering in the distribution of particles. Electronic conductivity shares a common physical origin as the elastic modulus and yield stress in the DLCA gels. Many researchers have studied the origins of electrical conductivity in carbon blackinsulator composites, particularly in polymer composites [18][19][1]. Conduction across neighboring aggregates is through a thermally activated tunneling process, with the high resistance tunneling junctions lending to the composite conductivities, typically 10-5-102 S/cm being much lower than the 68 approximate bulk conductivities of 10-100 S/cm of the carbon black [1]. The attractive van der Waals attraction, balanced by short range hard sphere repulsive interactions, sets the tunneling gap in the gel. The structure of the gel determines the number of junctions which must be surmounted and the quantity of parallel conduction paths available to electrons. Assuming the nature of this inter-aggregate bond is independent of the solids loading, the effect of increasing the carbon content of the gel is to produce a more interconnected structure. The impact of higher electronic conductivities on the electrochemical performance can be seen in Figure 1.9. As predicted in Chapter 1, electron transport is a significant rate limiting mechanism in the semi-solid electrodes. Increasing the electronic conductivity with a higher carbon black loading reduces the total cell impedance by over a factor of 2, allowing for higher power and higher efficiency electrodes. The high viscosity of polymer melts restrict the Brownian mobility of carbon black aggregates, and the polymer composites do not form via a DLCA mechanism. As such, the solids loading values of 15-35 vol%, typically employed in conductive polymer composites, exceeds the value of 1-5 vol% used here [19]. Even at these low loadings, the gels are typically well beyond their percolation threshold. As shown above for the Ketjenblack system, the percolation threshold exists at fractions of a volume percent. Even for the carbon blacks without micro/mesoporosity, the added density of the aggregates are not expected to raise the gelation threshold above 1 vol%. Evidence of the underlying relationship between electronic and mechanical behavior may also be found by examining how the properties correlate across multiple carbon fillers at various loading. Figure 2.10a and Figure 2.10b show that the three grades of carbon black fall on a family of points that correlate electronic conductivity roughly linearly with the yield stress and elastic modulus. 69 When the solid loading is not explicitly plotted as a variable a master curve appears in the electronic conductivity-yield stress property relationship. While deviations in conductivities appear when measured against the weight fraction, this arises mainly from the differences in density of the carbon black grades. As the bulk conductivity, which may be a function of the aggregate porosity, is eclipsed by the tunneling junction resistances, the conductivity of the carbon black gels is determined mainly by its agglomerate microstructure. All three carbon blacks are high structure carbon blacks with sub-micron aggregates and primary particle sizes of 30-50 nanometers. The common graphitic chemistry of the carbon blacks should lend to similar Hamaker constants and therefore a similar van der Waals attraction. The high salt concentration should mute any differences in electrostatic interactions that may arise from varying surface chemistries. Finally, the common fractal dimension of 1.8 has been demonstrated earlier. One can therefore predict that the geometric layout and quality of interaggregate bonds that determine the gel's mechanical properties will also determine its electronic conductivity. The strong correlation of the two sets of macroscopic properties supports such a conclusion. Conduction in these carbon gels occurs across an effectively static network of aggregates that are arrested in a thermally irreversible, percolating gel network. Thus far, the discussion of the DLCA model has been limited to the discussion of static properties. The model can also help to explain what occurs under shear flow. The microstructures that form under shear can be interpreted in light of competing forces. There is the combined effect of Brownian and attractive van der Waals forces, which favor the formation of a DLCA structure. Against this competes hydrodynamic forces that act to tear apart the DLCA flocs and order them into structures that minimize their hydrodynamic drag. At very low shear rates, where the Brownian diffusivity overwhelms the effects of shear (Shear Peclet number << 1, Equation 2.5), the constant breaking and 70 reforming of transient gel structures leads a very high viscous loss. Rajaram's work on the three dimensional imaging of sheared colloidal gels by confocal microscopy presents a clear visual picture of this phenomenon at play [20]. The gel behaves in a non-continuum manner, where the formation and destruction of the flocs defies a characterization of the material as a homogenous fluid. Measurement of rheological properties such as the dynamic viscosity in this shear rate regime leads to large degrees of irregularity. Shear rates below approximately 1 1/s lead to this behavior. .3 -r Peg = - P kbT Equation 2.5. The shear Peclet number, Pey, is the ratio of the timescale of diffusive motion to that of shear motion due to an applied shear rate, '. lota ld 0. VuClaXC72 10001200 ~00O0 0 00~ >' TEM Image a 00000 *010 TEM Image Kegjenblack EC-600JD + SSDE Vulcan XC-72R + tetradecane Used by Osuji 10 102 Shear rate (s 101 d Used by Ho 1 0.1 __ _ -F, N Shear Thinning Densified Clusters Shear Thickening Finely Dispersed of carbon Black Carbon Black 0.01 10 100 ShearRate(lis) 1000 71 Figure 2.14a (left), 2.14b (top right), 2.14c (top right), and 2.14d (bottom right). Figure 2.14a is data from Osuji's rheo-optical investigation of sheared carbon black microstructures [8]. TEM images of the two carbon black grades are borrowed from Denaro [4] (Figures 2.14b and 2.14c). Figure 2.14d is Figure 2.11a reproduced for ease of comparison. At intermediate shear rates, the hydrodynamic forces create vorticity aligned structures seen in Osuji's work [7]. Here, the arrangement of flocs into rolling logs under the increased dominance of hydrodynamic forces reduces the viscosity of the sheared fluid. For a 300nm aggregate in a 0.01 Pa s fluid, a shear rate of 15 1/s leads to a Peclet number of 1. Shear rates within an order of magnitude of 15 1/s will lead to the interplay of Brownian and hydrodynamic forces to create flocculated, shear aligned structures. Upon further increase in the shear rate, the hydrodynamic forces completely dominate the microstructure. Agglomerates are torn apart into smaller flocs approaching the primary aggregates. According to Osuji's analysis, this deflocculation increases the overall hydrodynamic volume fraction of solids; aggregates, which formerly interpenetrated to form flocs, occupy a larger hydrodynamic volume when separated. This in turn explains the observation of a shear thickening at high rates of shear. Figure 2.11 illustrate this same shear thickening effect in the system studied here. There are three practical ramifications of these shear induced microstructures. The first is that low and intermediate rates of shear will lead to unique shear-induced microstructures. Upon the cessation of shear, the nature of the thermally irreversible interaggregate bonding will prevent any significant relaxation of these structures. The gel microstructure is therefore strongly dependent on it shear history. The sensitivity of macroscopic properties, such as the yield stress and electronic conductivity, of the carbon black gels to its shear history can be rationalized through this effect. 72 The second is that hydrodynamic forces exerted on the flocs during intermediate to high rates of shear will act to break apart flocs, particularly in the dimension extending normal to the shear planes. The transfer of current perpendicular to shear will therefore no longer occur via long range percolation. Collisions between flocs will be necessary to transfer charge over macroscopic distances. Finally, the ability to disperse the flocculated structures via the application of high rates of shear enables the resetting of the gel microstructure. Any undesirable microstructure induced by a sample's shear history may be wiped clean by quenching the gel from an aggressive shear. The reformation of a DLCA gel upon quenching is immediate, as the Brownian aggregates are highly mobile and able to agglomerate rapidly. Figure 2.12 tracks the elastic modulus immediately upon cessation of a 500 1/s shear. The gel recovers its solid-like properties within 2 seconds and remains largely unchanged thereafter. Knowledge of the relationship between structure and properties in the existing carbon black gel system allows for the consideration of avenues to improve the gel properties within the engineering constraints present. The first question may be whether a DLCA gel is actually a desirable outcome. It creates a conductive gel at low carbon filler loadings, an advantageous trait in reducing the cost and mass of the SSE. The gel it creates is based upon van der Waals bonding, meaning the structure may be broken down under shear to enable flow. On the other hand, the relatively strong bonding leads to a high viscosity at low shear rates, as energy is dissipated in breaking and reforming bonds. Achieving a high electronic conductivity is arguably the more critical of the traits, given that charge transfer was demonstrated to be a rate limiting mechanism in Chapter 1. As such, the DLCA mechanism is a good starting point for optimization. To stay in the DLCA regime, attractive inter-aggregate potentials and Brownian behavior must be observed. Two particles (or aggregates) of the same chemistry will always feel an attractive van der 73 Waals attraction in the presence of an intermediary medium[21]. The need to keep electrolyte salt concentrations high for ionic conductivity's sake will serve the dual purpose of screening electrostatic repulsions so that approaching aggregates do not encounter an energetic barrier to agglomeration. As for the Brownian diffusivity of the conductive solid, the constraints can be understood by looking at the dependence of the gravitational Peclet number on material parameters (Equation 2.3). The effect of fluid viscosity actually drops out of the equation. In order to keep the Peclet number low, the particle or aggregate size should be kept small and the density mismatch between liquid and solid density should be minimized. In this sense, carbon black is a good choice for its relatively low solid density. One strategy may be to replace carbon black with a similar aggregate of a higher bulk conductivity, such as a metal. The potential pitfall with this approach is that the correlation of the carbon black gel conductivities with the mechanical properties has shown that the gel conductivity is dominated by the interaggregate tunneling junctions. The intrinsic resistance of a junction is largely controlled by the barrier height and width. The choice of conductor material will affect these parameters through the nature of the agglomerate bonds, but it does not directly relate to the bulk conductivity of that material. Thus one cannot strictly predict that a higher conductivity material will produce a higher conductivity gel. Thus far, it seems as if the current choice of carbon black dispersed in a liquid electrolyte is a fairly optimal system. There are some key points where the choice of materials may lead to improvements. As the inter-aggregate junctions are the limiting feature in conduction, it is advisable to limit the number of series junctions that must be surmounted when crossing a gel; this is achieved by incorporating larger particles or aggregates. The particles must remain colloidal to remain in the DLCA regime. Possible ways to sidestep these two constraints is to enlarge the effective span of the particle 74 without a concurrent increase in its overall mass. A higher structure carbon black could have a larger span without necessarily adding additional solid mass, due its fractal structure. Otherwise one could reduce the dimensionality of the conductive particles to one or two dimensions, with tubes or plates, respectively. The danger of lower dimensional structures is the known tendency of materials such as carbon nanotubes and graphene sheets to agglomerate into bundles or stacks. Typical strategies to stabilize these dispersions via steric or electrostatic stabilization would be detrimental to the transfer of charge between particles. In addition to tuning the number of inter-aggregate gaps, the resistance of the gaps may be engineered. Reducing the gap distance is a fairly unambiguous way of increasing the tunneling current. The gap is determined by repulsive solvation shell interactions. van der Waals attractions draw particles together until the hard sphere interactions prevent the further approach of the particles. For particles with adsorbed charged species, this hard sphere interaction takes place at the Stern layer. The thickness of this layer may be modified by choosing smaller ions or smaller solvent molecules. As both the choice of ions and solvents are constrained by other electrochemical considerations, this may not be a realistic avenue for optimization. 2.5 Conclusion Chapter 1 presented results demonstrating that carbon black plays a crucial role in wiring the lithium storage compounds to the device current collector. In order to understand the mechanism by which conduction occurs and to gain insight into possible avenues for optimizing the conductivity of the SSE, this chapter presented results that identify a DLCA microstructure as the foundation for a particulate gel network. Direct observation of the cluster-cluster carbon black microstructure and an interpretation of the scaling of the gels' elastic moduli and limits of linearity in strain both support a 75 DLCA agglomeration mechanism with a characteristic fractal dimension of 1.7. The driving force for rapid, thermally irreversible agglomeration is attributed, within a DLVO framework, to the screened electrostatic repulsions and attractive van der Waals interactions present in the electrolyte solution. An understanding of the mechanism for agglomeration and the structure of the resulting gel provides a base for rationalizing the intrinsic correlation present between the composite material's electronic conductivity and rheology. The common scaling of electronic conductivity and yield stress in these gels arises from their common origin in the inter-aggregate van der Waals bond, which transmits electrons and transfers stress [18][19][22]. While a yield stress is undesirable as a barrier to initiating flow, it is a necessary characteristic of a percolating, conductive filler. DLCA gels are remarkably well suited to function as conductive networks in a flowable electrode architecture. Utilizing the extensively studied fields of fractal growth mechanisms and colloidal science, we have investigated the physical constraints present in the gel system and possible avenues for optimization. The following chapter investigates how the microstructural picture of the semi-solid electrode is modified and complicated by the addition of the lithium storage compounds. The second solid phase, typically of a non-colloidal nature, will introduce an additional property of importance to the conductive gel - its yield stress and ability to stabilize the storage compound against sedimentation. The picture of the carbon black gel microstructure established in this chapter will largely carry over into the discussion of the complete electrode microstructure in the next chapter. 76 Chapter 2 References J.-B. Donnet, R. C. Bansal, and M.-J. Wang, Eds., Carbon Black: Science and Technology, 2nd ed. [1] New York: CRC Press, 1993. [2] F. Ehrburger-Dolle, S. Misono, and J. Lahaye, "Characterization of the aggregate void structure of carbon blacks by thermoporometry," Journal of Colloid and Interface Science, vol. 135, no. 2, pp. 468485, Mar. 1990. [3] M. E. Spahr, D. Goers, A. Leone, S. Stallone, and E. Grivei, "Development of carbon conductive additives for advanced lithium ion batteries," Journal of Power Sources, vol. In Press, Corrected Proof. [4] T. Denaro et al., "Investigation of low cost carbonaceous materials for application as counter electrode in dye-sensitized solar cells," Journal ofApplied Electrochemistry, vol. 39, no. 11, pp. 21732179, Nov. 2009. [5] M. Taniguchi, D. Tashima, and M. Otsubo, "Temperature dependence of capacitance in electrochemical super capacitor," in Electrical Insulation and Dielectric Phenomena, 2007. CEIDP 2007. Annual Report - Conference on, 2007, pp. 396-399. [6] W.-H. Shih, W. Y. Shih, S.-I. Kim, J. Liu, and 1. A. Aksay, "Scaling behavior of the elastic properties of colloidal gels," Physical Review A, vol. 42, no. 8, p. 4772, Oct. 1990. [7] C. 0. Osuji and D. A. Weitz, "Highly Anisotropic Vorticity Aligned Structures in a Shear Thickening Attractive Colloidal System," 0710.4336, Oct. 2007. C. 0. Osuji, C. Kim, and D. A. Weitz, "Shear thickening and scaling of the elastic modulus in a [8] fractal colloidal system with attractive interactions," Physical Review E, vol. 77, no. 6, p. 060402, Jun. 2008. [9] T. Vicsek, Fractal Growth Phenomena, 2nd ed. Singapore: World Scientific, 1992. [10] S. Tobishima, M. Arakawa, T. Hirai, and J. Yamaki, "Ethylene carbonate-based electrolytes for rechargeable lithium batteries," Journal of Power Sources, vol. 26, no. 3-4, pp. 449-454, May 1989. [11] P. Tundo and M. Selva, "The Chemistry of Dimethyl Carbonate," Accounts of Chemical Research, vol. 35, no. 9, pp. 706-716, 2002. [12] R. Schueler, J. Petermann, K. Schulte, and H.-P. Wentzel, "Agglomeration and electrical percolation behavior of carbon black dispersed in epoxy resin," Journal of Applied Polymer Science, vol. 63, no. 13, pp. 1741-1746, 1997. 77 [13] M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, and P. Meakin, "Universality in colloid aggregation," Nature, vol. 339, no. 6223, pp. 360-362, Jun. 1989. R. C. Sonntag and W. B. Russel, "Elastic properties of flocculated networks," Journal of Colloid [14] and Interface Science, vol. 116, no. 2, pp. 485-489, Apr. 1987. H. M. Wyss, A. M. Deliormanli, E. Tervoort, and L. J. Gauckler, "Influence of microstructure on [15] the rheological behavior of dense particle gels," AIChE Journal, vol. 51, no. 1, pp. 134-141, Jan. 2005. [16] R. Buscall, P. D. A. Mills, J. W. Goodwin, and D. W. Lawson, "Scaling behaviour of the rheology of aggregate networks formed from colloidal particles," Journal of the Chemical Society, Faraday Transactions 1, vol. 84, no. 12, p. 4249, 1988. [17] N. Roussel, "A Theoretical Frame to Study Stability of Fresh Concrete," Materials and Structures, vol. 39, no. 1, pp. 81-91, Mar. 2006. [18] M. T. Connor, S. Roy, T. A. Ezquerra, and F. J. BaltVCalleja, "Broadband ac conductivity of conductor-polymer composites," Physical Review B, vol. 57, no. 4, p. 2286, Jan. 1998. E. K. Sichel, Ed., Carbon Black-Polymer Composites: The Physics of Electrically Conducting [19] Composites. New York: Marcel Dekker Inc, 1982. [20] B. Rajaram and A. Mohraz, "Microstructural response of dilute colloidal gels to nonlinear shear deformation," Soft Matter, vol. 6, no. 10, p. 2246, 2010. [21] J. N. Israelachvili, Intermolecular and Surface Forces, Third Edition, 3rd ed. Oxford: Academic Press, 2010. [22] J. Mewis, L. M. De Groot, and J. A. Helsen, "Dielectric behaviour of flowing thixotropic suspensions," Colloids and Surfaces, vol. 22, no. 2, pp. 249-269, 1987. 78 Chapter 3 Stable Suspensions of Lithium Cobalt Oxide in a Carbon Black Gel as Semi-solid Electrodes Abstract This chapter investigates the microstructure-property relationship of a stationary semi-solid electrode (SSE), composed of lithium cobalt oxide (LCO) suspended in a carbon black-electrolyte gel. Previous results load a carbon black gel with micron-scale LCO particles, at up to 40 volume percent, to yield a complex fluid electrode that behaves like a conventional, composite Li-ion cathode (Chapter 1). The origin of the fluid and electrochemical properties of the SSE is attributed to a stably suspended dispersion of LCO particles, electrically and mechanically coupled into a mixed conductor carbon blackelectrolyte gel. Direct observations of microstructure with x-ray microtomography and electron microscopy shows small agglomerates of LCO particles arrested in a DLCA carbon black-electrolyte matrix. Elastic reinforcement of the gel by the LCO filler and cooperative electron conduction between the two phases explain the ability to transfer charge across the electrode and to the distributed lithium reaction sites. 3.1 Introduction Chapter 2 began the investigation of the structure-property relationship of the semi-solid electrodes (SSE) demonstrated in Chapter 1 by focusing on the carbon black-electrolyte gel. Gels were shown to form by diffusion limited cluster agglomeration mechanism, producing percolating, electronically conductive structures at below 1 vol%. The study is continued here by adding the lithium storage compound. Lithium cobalt oxide (LCO) is used as a model lithium storage compound because its 79 particle size may be tuned with jet-milling and its particle conductivity is tuned by selective chemical delithiation. These two variables will be used to investigate how the LCO particles interact with the carbon black gel. Experimental methods are reviewed first. The slurry preparation, rheological testing, electron microscopy, and electronic conductivity measurement protocol are similar to those used with the carbon black gels in Chapter 2. Any differences in methodology are highlighted. X-ray microtomography appears as a new characterization method in this chapter. Measurements on the 3-dimensional structure of the LCO phase, made at the Swiss Light Source, will supply a view through the optically opaque carbon black phase, into the slurry bulk, to enable a quantitative analysis on the degree of agglomeration present between the LCO particles. Results on the SSE microstructure are then presented. LCO particles are shown to be stably dispersed in 3-dimensions by x-ray microtomography. DLCA carbon black agglomerates, seen in Chapter 2, persist with the addition of LCO. The increase in elastic modulus accompanying the filling of a 7 weight percent Shawinigan black gel with 30 volume percent LCO is mechanically coupled to the gel matrix that it inhabits. This coupling is also electronic in nature, as shown by the consistent increase in slurry conductivity with the tuning the LCO particle conductivity by over 3 orders of magnitude. A decrease in the electronic conductivity with increasing surface area of the LCO phase will lead into a discussion on the interactions of the filler and gel phase. This chapter focuses mainly on the electronic conductivity, given the results of Chapter 1 that demonstrates its role as a significant rate limiting mechanism in SSE. Engineering tactics to optimize the conductivity will be discussed at the end of the chapter, alongside potential penalties that will arise in other transport mechanisms present in the SSFC. Electrode behavior under flow is discussed in Chapter 4. 80 3.2 Methods This section will outline the procedure for synthesizing semi-solid electrodes (SSE) and will describe the techniques used to characterize their rheological, electrical, and microstructural properties. The relative amounts and chemical identities of the three component phases (carbon black, LCO, and electrolyte) are varied to probe their roles, individually and cooperatively, in defining the slurry properties. Stress controlled oscillations probe the mechanical behavior of the slurries. DC conductivities measured in a parallel plate geometry characterize their electronic behavior. Direct observations of microstructure via x-ray microtomography and scanning electron microscopy will be correlated with observed macroscopic responses to demonstrate that the LCO particles are stably dispersed as a weakly agglomerating filler within a carbon black-electrolyte gel matrix. 3.2.1 Materials Samples consist of three components, lithium cobalt oxide, carbon black, and electrolyte. The lithium cobalt oxide described in detail in Chapter 1. Its particle size distribution data is reproduced here in Table 3.1. Two of the carbon blacks studied in the previous chapter return here, Ketjenblack EC600JD (Akzo Nobel Polymer Chemicals, LLC) and Chevron Shawinigan black (Chevron Corporation). Finally, the same two electrolytes seen in Chapter 2, are used. SSDE is a proprietary solution of 1.3 M LiPF6 in a blend cyclic and linear alkyl carbonates produced by Novolyte Technologies. An electrolyte composed of 1.0 M LiPF6 in a 1:1 volume blend of ethylene carbonate (EC) and dimethyl carbonate (DMC) is synthesized from materials purchased from the Sigma Aldrich Corporation, and is referred to as an EC:DMC electrolyte in this work. 81 Material d(0.1) d(O.5) d(0.9) Specific Surface Area (N 2 BET) Original Seimi LCO 4.66 um 12.14 um 28.97 um 0.43 m 2/g 2.02 m 2/g 1.66 um 2.94 um 5.12 urn Jet-milled Seimi LCO Table 3.1. Particle size distribution information for the as-received LCO and the jet-milled product. The conductivity of the LCO particles are tuned by chemical delithiation to investigate the role of the LCO particles in conducting electrons through the SSE. The electronic conductivity of Li-,CoO 2 increases with lithium extraction [1][2]. While the effect is observed most commonly during the electrochemical delithiation of a LCO cathode under charging, it can also be induced by the chemical delithiation of LCO with an oxidizing agent such as nitronium (NO 2') [2]. Chemical delithiation is preferred to prepare a stock of material without contamination from additives, such as binder and carbon black, required to build an electrochemical cell. The jet-milled LCO described above is treated to three different degrees of lithium extraction in identical, parallel processes. The only variable is the amount of NO 2BF 4 added; the nitronium salt is the limiting reactant in the delithiation process and its quantity is used to control the extent of the reaction. Three samples of LilCoO 2 are prepared by controlling the quantity of NO 2 BF 4 , where x equals 0, 0.02, and 0.16. For each reaction, a measured mass nitronium salt is dissolved in 250 mL of anhydrous acetonitrile under an argon atmosphere. Separately, 100 g of LCO is suspended in 250 mL of acetonitrile. The suspension is stirred in an Erlenmeyer flask, as argon is constantly bubbled through it. The solution of NO 2BF 4 is added to the LCO suspension and the mixture is allowed to react under an argon atmosphere for 12 hours. After the reaction is complete, the powder is retrieved by vacuum filtration and washed in acetonitrile by 5 repetitions of sonication and centrifuge. The final product is dried in under vacuum at 60 *C for 3 hours, and is returned to powder form with a mortar and pestle. The electronic conductivity of a sample of each of the three powders is measured in a twoelectrode parallel plate geometry, under uni-axial compression. The powder is sandwiched between 82 two, 3/8 inch, stainless steel 316 discs in a polyvinylidine fluoride (PVDF) die. The stainless steel discs act as parallel plate electrodes and the hollow PVDF cylinder provides an electrically insulating die casing. A pressure of 400 MPa is applied to the powder to compress it and its DC conductivity is extrapolated from the low frequency AC impedance response of the powder compact, as measured by a Solartron SI-1260 frequency response analyzer. The measured values of all three states of delithiation are in good agreement with the results of Molenda [1]. The chemical quantities and measured conductivites are summarized in Table 3.2. Sample Mass of LCO Reacted LiCoO 2 100.00 g LiO.98CoO 2 100.00 g LiO.84CoO 2 100.00 g Mass of NO 2 BF4 Reacted 0g 2.714 g 22.069 g Electronic Conductivity 0.00062 S/cm 0.054 S/cm 1.4 S/cm Table 3.2. Summary of quantities used to synthesize delithiated samples of Li 2aCoO 2 . The measured DC conductivities of the powders under uniaxial compression are also included. 3.2.2 Experimental SSE must be synthesized in a manner that maximizes reproducibility to probe the effects of systematic variations in their composition. The significant difference in density and particle size between the LCO and carbon black solid phases, as well as the strong shear-history dependence of the carbon black-electrolyte gels, calls for a specific protocol in preparing the slurry electrodes. Compositions of semi-solid electrodes are reported in the manner defined in Chapter 1. The LCO phase is reported a volume fraction of the total electrode, while the carbon black is reported as a weight fraction of the remaining carbon black-electrolyte gel matrix. With the composition of a slurry determined, the synthesis of the sample proceeds in three steps. The procedure of Chapter 1 is modified for improved reproducibility. In the first step, the dry 83 components (carbon black and LCO) are weighed and combined in a 20 mL scintillation vial under an argon atmosphere. The vial is sealed and loaded into a Schatz mixer, an 88 Mixer Model B produced by Inversion Machines Ltd., where it is mixed at a 40 RPM rotation speed for 1 hour. The motion of a Schatz mixer is well suited to the thorough mixing of powders that differ significantly in density and size, as the powders are mixed while continuously suspended in air. Alternatives, such as V-blenders, rely on gravity to settle powders and light, low density components preferentially segregate upwards. The second step combines the mixed, dry powders with the liquid electrolyte under an argon atmosphere. A quantity of electrolyte is transferred into the scintillation vial with an Eppendorf pipet. The powders are then dispersed within the electrolyte with a rotor-stator homogenizer (PRO Scientific Bio-Gen PRO200). The shearing action of the homogenizer promotes the dispersion of localized carbon black agglomerates. In the final step, the vial is sealed once more and immersed in an ultra-sonic bath for one hour. A Cole-Parmer Model 8890 ultra-sonic bath promotes gelation by mobilizing particles to their lower energy configurations. The electrode is complete and ready for testing after sonication. Electronic conductivity measurements on the prepared gels are made in a two-probe parallel plate geometry, described previously in section 2.2.2. SEM images of the SSE samples are measured in Quantomix QX-102 capsules in the same manner described in section 2.2.2. The only difference in the SEM protocol is the use of a lower 10 kV acceleration voltage, rather than 15 kV, in order to simultaneously image the LCO and carbon black phases. Rheological measurements were performed on a Malvern Kinexus Pro rheometer under an argon environment. Measurement protocol were consistent with those described in section 2.2.2, with the following exceptions. With LCO particles having diameters between 1 and 10 microns, the sandblasted plates used in the carbon black studies were found to be on insufficient roughness to 84 prevent wall slip. More aggressive P220 and P120 grit sandpaper having average particle sizes of 68 microns and 125 microns, respectively, were attached to a 20 mm diameter parallel plate geometry with Krazy Glue; the choice of sandpaper grit will accompany the description of the specific results. Measurements were made at a 1 mm gap. An additional departure is the elimination of a sample pre-shear. Unlike the carbon black gels, application of a pre-shear to the SSE slurries does not reset the microstructure. Instead, it permanently alters the rheological properties, lowering the viscosity and decreasing the magnitudes of the viscoelastic moduli. A more detailed discussion is provided as background material in section S.9 As the rheological measurements are intended to characterize the as-prepared samples, pre-shearing is an undesirable procedure. The penalty for excluding a pre-shear is the introduction of experimental variability produced by the unquantified shear imparted upon the slurries as they are loaded into the rheometer. X-ray microtomography affords a three dimensional view of the slurry microstructure. Tomography experiments were conducted at the Swiss Light Source's TOMCAT beamline, located at the Paul Scherrer Institut. Sample slurries were prepared at MIT by the standard protocol described previously. The slurries were injected into and sealed within a 0.8 mm inner diameter polypropylene sample holder shown in Figure 3.1. The slurry was loaded into a 5 mL luer-lock syringe and coupled to a polypropylene tube (McMaster-Carr part number 6934A43). After partially filling the tube, the open end was sealed with a heat crimp. UV-cure adhesive (Loctite 3494) was applied to the crimped end as a secondary seal. A polypropylene luer lock cap (McMaster-Carr part number 51525K371) sealed the other end. Again, a bead of UV-cure adhesive formed a secondary seal. The hermeticity of the sample holder was tested by loading a sample holder with acetone and measuring its mass loss over 48 hours. Mass loss was undetectable within the 0.1 mg limit of the analytical balance. 85 Measure Here Figure 3.1. The fluid sample holder, designed to image a 0.8 mm diameter cylindrical slurry sample at the TOMCAT beamline at the Swiss Light Source. A polypropylene dispensing tip is modified to seal a fluid sample within the tube tip (pink). The sample holder is shown here, mounted on magnetic sample mount that is compatible with the robotic arm system at the TOMCAT facility. The sample holders were flown to the beamline and subjected to a 1 hour treatment in an ultrasonic bath, 24 hours prior to measurement. Tomographic scans were performed with a 21.9 keV beam, passed through a double crystal multilayer monochromator. After transmission through the sample, a 20X objective placed in front of the 2048 by 2048 pixel CCD detector provided a 370 nm image resolution. Each scan consisted of 1401 absorption contrast micrographs taken over a 180 degree sample rotation. Each exposure was 400 ms. Software at the facility was used to reconstruct the raw scans into a 3-dimensional tomogram, which were saved as 32 bit gray-scale horizontal sections. The total imaged volume for each sample was 750 um x 750 um x 750 um. Marone and colleagues at the TOMCAT facility have published more details on the instrument [3]. The tomography experiments face two challenges. One is that the organic electrolyte and the carbon black do not present a detectable x-ray absorption contrast. It is therefore only possible to image the lithium storage compounds, while the carbon-based phases appear identical. The carbon black gel structure cannot be imaged with this method, without modification. The second challenge is 86 cobalt's strong x-ray absorption. For a sample thickness of 800 um, a solid loading of 40 volume percent LCO approaches the lower limit of transmitted signal, given the light intensity provided at the TOMCAT facility. At the same time, the dissipation of absorbed light as heat causes the organic electrolyte to decompose into gaseous form. The movement caused by bubble formation during the measurement prohibits reconstruction of the tomogram. The first challenge of imaging the carbon black phase may possibly be overcome by incorporating heavy elements onto the carbon black surface. The second may be overcome by imaging lithium compounds that do not contain strongly absorbing elements such as cobalt. Measurements performed on lithium titanate produced clear results without the gas formation problem encountered with lithium cobalt oxide. Otherwise, a higher flux light source or a thinner sample can address the issue of adequate transmitted light. The problem of heating may be addressed in future experiments with in-situ sample cooling with a jet of liquid nitrogen. The grayscale data gathered from the tomography experiments are post-processed in Mathematica in two steps. The first is to binarize the data to isolate the pixels representing the LCO phase from those representing the carbon phases. In order to set the threshold level at which the pixels are binned into either phase, a histogram is constructed based upon the entire measured volume of 750 um, cubed. A key assumption in setting the threshold level is that the volume fraction of LCO phase in the measured area matches the target volume fraction of the sample slurry. If the sample is synthesized as 30 volume percent LCO, the imaged area is also assumed to be 30 volume percent LCO. Using this assumption, a threshold value is set for each measurement in which the binarized results yield the appropriate count of LCO voxels. This method allows for local variations in LCO content above and below the average value - it only constrains the total volume average to a given value. The second step is the identification of agglomerate clusters, along with the assignment of a unique integer to each cluster. A pre-binarized dataset is run through a custom algorithm, which 87 identifies nearest neighbor voxels (corner neighbors excluded) as belonging to a common cluster. Each cluster is given an integer identifier so that analysis may be performed on the degree of agglomeration in a given sample. Computational limits, particularly in memory usage, restricts the labeling algorithm to volumes of 700 voxels, cubed (equivalent to 260 um, cubed, for 370 nm resolution tomograms). A more memory-efficient algorithm or more memory resources may surmount this limit. Details of the algorithm are available in section S.10. 3.3 Resufts Microscopic structure studies are combined with macroscopic measurements to demonstrate the stable, electronically integrated dispersion of lithium cobalt oxide in a DLCA carbon black gel. X-ray microtomography and electron microscopy directly image the microstructure of the SSE, demonstrating that the LCO is stably dispersed within a gel matrix. Rheological and electronic conductivity measurements show that bonding between the LCO and carbon black allows for the transmission of shear forces and electrons between the two solid phases. 100 10 -o 1 0 ... (A Viscous Modulus 0.1 'Elastic Modulus 0.01 0.001 0 200 800 600 400 Time Since Sessation of Shear (s) 1000 1200 88 Figure 3.2. The time-dependent viscoelastic response of 30 vol% LCO in 70 vol% of pure SSDE electrolyte. The LCO suspension behaves as a liquid, with a viscous modulus that greatly exceeds the elastic modulus, in magnitude. The decay of the viscous modulus is attributed to the sedimentation of the LCO particles. Jet-milled LCO particles are, by themselves, gravitationally unstable in SSDE electrolyte. A 30 volume percent LCO suspension in SSDE is sheared at 100 1/s to ensure that the LCO particles are in suspension. The shear is stopped and a constant stress amplitude oscillation at 1 Hz is immediately initiated. Figure 3.2 plots the measured viscoelastic response, as a function of time. The viscous modulus exceeds the elastic modulus by an order of magnitude; this behavior is characteristic of a liquid. The viscous modulus is time-dependent, with a decay of roughly 2 orders of magnitude over the course of 20 minutes. Initially, the shear oscillation generates viscous losses from both the electrolyte viscosity and the hydrodynamic dissipation of the LCO particles in suspension. As the LCO particles settle out of suspension, the latter contribution drops out and the viscous modulus decreases in magnitude. LCO is gravitationally unstable by itself in electrolyte, but the presence of a yield stress fluid, such as a carbon black gel, can stabilize the particles. Section O.X provides a review of background literature regarding this stabilization technique. Calculations derived from this work predict that a yield stress of 0.02 Pa is sufficient to stabilize 10 um LCO particles. Figure 3.3 plots the viscoelastic moduli of a 7 weight percent Shawinigan black-EC:DMC gel, along with a sample of 30 volume percent LCO in a 7 weight percent Shawinigan black-EC:DMC gel. A stress amplitude sweep oscillation experiment identifies the elastic modulus, viscoelastic phase angle, yield stress, and limit of linearity for both samples. These parameters are summarized in Table 3.3. 89 The yield stress of the LCO-filled gel, defined as the stress at which the viscous modulus exceeds the elastic modulus, is 650 Pa - over 4 orders of magnitude larger than predictions require for stabilization of the LCO phase against sedimentation. There are two orders of magnitude in stress of which the response of the LCO-filled gel is non-linear prior to this yield stress, reflecting a gradual breakdown of the solid structure. Taking the stress limit of linearity (10 Pa) as a more conservative metric of yielding still exceeds the stability criterion of 0.02Pa by four orders of magnitude. 1000000 ALCO + Shawinigan Elastic Modulus w LC0 + SShawnngaSng Elastic Modulus 0 .1000 000 > ~LCO + Shawinigan Shawinigan Viscous Modulus Viscous Modulus 10 0.01 0.1 1 10 100 1000 10000 Stress Amplitude (Pa) Figure 3.3. The viscoelastic response of two samples: a 7 wt% Shawinigan Black-EC:DMC gel and 30 vol% LCO in a 7 wt% Shawinigan Black-EC:DMC gel. Both samples are solid-like, with a elastic modulus greater than the viscous modulus in the linear viscoelastic regime. Both samples have yield stresses above 100 Pa, while the yield stress criterion for the stability of a 10 um LCO particle is 0.02 Pa. Table 3.3 (below) summarizes the quantitative metrics extracted from the curves. 30 vol% LCO in a 7 wt% Shawinigan black7 wt% Shawinigan blackEC:DMC gel EC:DMC gel 60,000 Pa 15,000 Pa Elastic Modulus 100 30 Phase Angle 650 Pa 200 Pa Yield Stress 10 Pa 4 Pa Limit of Linearity (stress) 0.019% 0.028% Limit of Linearity (strain) Table 3.3. A summary of mechanical properties derived from the viscoelastic response of two gel samples to a stress amplitude sweep in a 1 Hz mechanical oscillation. A carbon black gel and a LCO-filled 90 carbon black gel are compared. The LCO-filled gel demonstrates a mechanical reinforcement of the elastic modulus, with the value increasing from 15,000 Pa to 60,000 Pa. On the other hand, the LCOfilled gel experiences the loss of linearity at a lower strain than the carbon black-only gel. The LCO-filled gel's yield stress of 650 Pa provides a stabilizing matrix to prevent LCO sedimentation. Comparison of the mechanical properties of a 7 wt% Shawinigan gel with and without LCO shows that the presence of LCO increases the elastic modulus of the gel from 15,000 Pa to 60,000 Pa. The yield stress increases from 200 Pa to 650 Pa with the addition of LCO. The elastic modulus of the LCO-filled gel decays by 2 orders of magnitude, relative to its linear response value, before yielding; the carbon black-only gel yields more abruptly. The strain limit of linearity is smaller for the LCO-filled gel than the carbon black-only gel, meaning that the structure of the gel begins to break down at lower applied strains with LCO. LCO stability against gravitational forces is demonstrated with x-ray microtomography in Figure 3.4. A sample of 30 volume percent LCO in a 7 weight percent Shawinigan black-SSDE matrix was agitated in an ultrasonic bath for one hour and allowed to rest for 24 hours prior to a tomographic scan. After binarizing the dataset, each horizontal slice, of 370nm height resolution, has its LCO content measured over a 520 um by 520 um area. The profile in Figure 3.4 plots the vertically resolved LCO content. Sample horizontal slices are shown at three different heights, as insets. The LCO phase (white) is homogenously distributed at all three heights within the carbon black-SSDE matrix (black). 91 0 100 200 300 E C400 a) 500 600 700 10 20 30 40 5b Local LCO Volume Fraction (%) 520 urn Figure 3.4. X-ray microtomography results of 30 vol% LCO in a 7 wt% Shawinigan - SSDE gel, showing the stabilization of LCO against sedimentation. The 3D reconstructions of the tomography data are binarized to identify the LCO phase (white) against the background carbon black and electrolyte phases (black). The local LCO concentration, as measured 24 hours after ultra-sonic aggitation, is plotted along the vertical direction to show that the LCO content does not collapse due to sedimentation. Three sample horizontal slices at different depths are presented showing a homogenous distribution across 520 um. The voxel resolution is 370 nm in each dimension. As the high LCO content in the previous 30 vol% sample obscures a clear view of individual clusters in a 3-dimensional representation, a 10 vol% sample is shown in Figure 3.5. In this 10 vol% 92 sample, the carbon black gel phase is 2 wt% Ketjenblack in SSDE - a formulation having very similar mechanical and electronic properties as a 7 wt% Shawinigan black sample. The 740 nm resolution tomography reconstruction is binarized to isolate the LCO phase from the carbon black gel. An algorithm then identifies individual clusters as nearest neighbor collections of LCO voxels, and assigns each cluster a unique color. A sparser LCO phase reveals details on presence of multi-scale clusters within the carbon black gel matrix. In this 260 um by 260 um by 74 um field of view, the jet-milled LCO particles (average particle size of 3 um) show a mild agglomeration into small clusters. A cumulative histogram of Figure 3.5's agglomerates is plotted in Figure 3.6. Figure 3.6 incorporates analyses a larger, 260 um, cubed, dataset. Agglomerate sizes span 6 orders of magnitude, from a lum cube to a 100 um cube. The volume of a 3 um diameter LCO particle is labeled for reference. Normalizing the cluster volumes by this average LCO particle volume leads to a d(0.1), d(0.5), and d(0.9) value of 2.5, 31, and 6200 particles, respectively. The presence of clusters smaller than the volume of a single LCO particle is accounted for by LCO particles with diameters on the bottom end of the LCO particle size distribution (see Table 3.1). 93 Figure 3.5. A 260um x 260um x 74 um (350 x 350 x 100 voxel) x-ray tomogram of 10 vol% LCO in a 2 wt% Ketjenblack-SSDE matrix. Each cubic voxel measures 740 nm on each side. Only the LCO phase is visible in this reconstruction - the carbon black and electrolyte phase are binned into the black voxels. Coloring is determined by a cluster labeling algorithm. Each color identifies a unique cluster of nearestneighbor connected voxels. Mild agglomeration is present, but the LCO is generally well dispersed in three dimensions. 94 100 0 90 8 80 LL A 40 E - 060 50 Average Single Particle Volume 20 -J30 0 E E 10 0 1 10 10,000 1,000 100 3 Agglomerate Volume (urn 100,000 1,000,000 ) 0 Figure 3.6. An agglomerate size distribution based upon the tomography dataset used in Figure 3.5. The presence of agglomerates below the average particle size is attributed to particles at the smaller end of the LCO particle size distribution. 80% of the LCO phase is composed of agglomerates between 2.5 and 6200 particles in size. SEM images of LCO-filled gels are presented in Figure 3.7 and 3.8. Using WETSEM capsules from Quantomix, the LCO-filled gels are imaged in their wet state. Figure 3.7 is a sample of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel matrix. The LCO particles are well distributed across the imaged area. A higher resolution scan on the same sample (Figure 3.8) simultaneously images the LCO and carbon black phases. The bright white region in the top-left corner is a metallic current collector on the sample capsule. Clustered carbon black agglomerates are seen in the focal plane. Looking beyond the focal plane, larger carbon black floc formations are seen occupying the space between LCO particles. 95 Figure 3.7. A SEM image of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel, taken in its fluid state in a Quantomix WETSEM capsule. The micrograph shows a well dispersed LCO phase (white) in a Shawinigan black-EC:DMC electrolyte matrix (black). 96 of clustered Figure 3.8. The same sample imaged in Figure 3.7, at higher magnification. The presence DLCA flocs are visible as part of the carbon black gel. The Shawinigan black aggregates are below 500 nm in size, the structures visible on the scale of multiple microns are therefore agglomerates. There is no obvious adsorption of carbon black onto the LCO particles visible in this image. As seen in Figure 3.9, the carbon black matrix largely dictates the conductivity of the 30 vol% LCO electrodes. The LCO particles have a measured conductivity of 0.00062 S/cm. Electronic conductivities are DC values measured in a parallel plate, two-electrode geometry. The addition of 30 vol% LCO to the carbon black gel generally reduces the electronic conductivity by one order of magnitude for a given gel composition. An electrode of 30 vol% LCO in a 8 wt% Shawinigan black-SSDE gel obtains a conductivity of 3.3 mS/cm, a factor of 2 lower than the bulk ionic conductivity of the electrolyte. 1E-1 E ~~" I E-2 1E-2 ShawihiganOny__ a 1 1E-3 01 E-4 0 - Shwnia- __n "1 E-5 M 1 E-6 0 2 4 6 8 10 Weight Percent Shawinigan Black in Electrolyte (%) Figure 3.9. The reduction in electronic conductivity upon loading 30 vol% LCO into a carbon black gel. The X-axis plots the Shawinigan black content in the carbon black-electrolyte gel phase. The carbon black gel conductivity largely defines the LCO-filled gel conductivity. 97 In Figure 3.9, the carbon black gel largely determines the conductivity of the SSE. In order to investigate the role of the dispersed LCO phase in aiding electron conduction, LCO samples are chemically delithiated to 3 different degrees, Li. 0CoO 2 (0% delithiated), LiO. 98CoO 2 (2% delithiated), and Lio.84CoO 2 (16% delithiated). The three LCO samples have measured electronic conductivities of 0.00062 S/cm, 0.054 S/cm, and 1.4 S/cm, respectively. These three LCO samples are mixed with into a 7wt% Shawinigan black-SSDE gel at four different LCO volume fractions and their electronic conductivities are measured (Figure 3.10). Increasing LCO loadings, regardless of the LCO bulk conductivity, leads to monotonically decreasing conductivities. This holds true even for the most highly delithiated LCO, where the LCO phase has a conductivity (1.4 S/cm) that is 2 orders of magnitude higher than the carbon black matrix in which it is dispersed (0.013 S/cm). For a given LCO volume fraction, increasing the LCO phase conductivity does increase the overall electrode conductivity. A data series is also included for 16% delithiated LCO in a 2 wt% Ketjenblack-SSDE gel. 2 wt% Ketjenblack gels have similar electronic and viscoelastic properties as a 7 wt% Shawinigan black gel (see Chapter 2). The data in Figure 3.10 demonstrates that the two carbon black gels also behave as similar electronic hosts to the LCO phase. 1.4 S/cm LCO + 7 wt% Shawinigan Black in Electrolyte - 0.016 .1 -i-n 0.012 - Electrolyte - - E 0.01 0 0 0.008 - - - -9 0.006 .0.054 Black in Electrolyte 10 5 . SicmLCO& +wt% Shawinigan Black in Electrolyte 0.002 - 0100062 S/cni LCO + 7 wt% Shawinigan Va 0.004 U) 25 20 15 Volume Percent LCO (%) 30 35 98 Figure 3.10. The effect of LCO volume fraction is shown for 4 samples. Three samples explore the role of the LCO electronic conductivity on the overall slurry conductivity by incorporating partially delithiated LCO particles, with bulk electronic conductivities spanning over 3 orders of magnitudes, into a 7 wt% Shawinigan black - SSDE gel. Increasing the LCO particle conductivity leads to an increase in the electrode conductivity. The fourth sample compares the electrode conductivity across two different carbon black gel matrices, 7 wt% Shawinigan black and 2 wt% Ketjenblack in SSDE. It demonstrates that the electrical behavior of the slurry is not unique to one grade of carbon black. In each of the four series, increasing LCO content leads to monotonically decreasing conductivities Figure 3.11 identifies one possible origin of the monotonic decrease in electronic conductivity of the electrodes with increasing LCO loadings. An increased volume fraction of LCO increases the total surface area of LCO phase present in a given volume of electrode. Another method of increasing the total surface area of LCO is to decrease the LCO particle size and thereby increase the specific surface area of the LCO phase. As-received Seimi LCO and its jet-milled version, having 5-fold different specific surface areas of 0.43 m 2 /g and 2.02 m 2/g, respectively, are dispersed in a 7 wt% Shawinigan black gel. At any given volume fraction of LCO, the jet-milled LCO samples will have a 5-fold larger total surface area of LCO. The jet-milled samples consistently demonstrate lower electronic conductivities. 99 - 0.018 0.016 E O 0.014 Specific Surface Area = 043 m2/g - 0.012 0.01 C 0 0.008 .0 0.006 C a. 0.004 0 0.002 0 5 Specific Surface Area = 2.02 m 2Ig 4 25 15 Volume Percent LCO (%) 35 2 Figure 3.11. High specific surface area, jet-milled LCO particles (2.02 m /g) consistently demonstrate lower electronic conductivities, for a given LCO volume fraction, than a low specific surface area, nonjet-milled (0.43 m 2/g) equivalent when dispersed in a 7 wt% Shawinigan black-SSDE gel. As in Figure 3.10, increasing volume fractions of LCO lead to a monotonically decreasing overall conductivity for both LCO samples. Results on the microscopic structure and macroscopic properties of the LCO-filled carbon black gels that constitute the electrodes of a SSFC have been presented. The following section discusses how these observations relate to one another, and consistently support a microstructure of weakly agglomerated LCO particles stably arrested in a carbon black gel matrix, with carbon black-LCO van der Waals bonding providing a mechanical and electronic coupling between the two solid phases. 3.4 Discussion Results presented in the previous section highlight several important features of semi-solid electrodes composed of LCO, carbon black, and an alkyl carbonate electrolyte. LCO particles, which are 100 non-colloidal and gravitationally unstable in the electrolyte (Figure 3.2), are stabilized by the carbon black gel (Figure 3.4). The LCO phase is well dispersed in the carbon black gel matrix, distributing the electrochemical reaction evenly through the electrode (Figure 3.5). Mechanical and electrical measurements point to a bonding of the carbon black and LCO, allowing for charge to transfer effectively between the conductive gel phase and the storage compound (Figures 3.3 and 3.10). These observations also support a simplification of the three component fluid composite as a two component system; LCO particles are suspended as a distributed solid phase within a coarse-grained carbon blackelectrolyte gel matrix. The jet-milled LCO particles are gravitationally unstable, given its large density mismatch with the electrolyte. With the relevant material properties for this system, summarized in Table 3.4, a Stokes settling velocity of 2 um/s is expected from Equation 2.2. Value Property 5.0 g/mL LCO Density Electrolyte Density 1.3 g/mL LCO Particle Radius 1.5 um Electrolyte Viscosity 0.01 Pa*s Table 3.4. Material parameters to calculate the Stokes settling velocity (2 um/s) of jet-milled LCO in electrolyte. Further particle size reduction of the LCO to retard sedimentation is restricted for two reasons. The carbon black aggregates should fit within the interstices of the LCO particles to avoid volume exclusion effects. Given that the grades of carbon black studied here have aggregates that are a few hundred nanometers in breadth, the LCO particles should be larger than 1 micron. Colloidal LCO particles will agglomerate readily and result in inefficient packing densities, as seen in the carbon black system. The lithium compounds should therefore be large and non-colloidal. 101 This prediction of instability is confirmed in Figure 3.2. Here, the viscous modulus of the LCOelectrolyte suspension decreases in time as the LCO sediments out of suspension. As the LCO settles, the particles no longer contribute to the viscous dissipation of energy via their hydrodynamic drag and the strain oscillation is concentrated in the liquid electrolyte. The time scale of this sedimentation, as seen by the decay of the viscous modulus over roughly ten minutes, is in good agreement with the calculated Stokes settling rate. With a measurement gap of 1 mm, the LCO should sediment out over 500 seconds. The carbon black gel must play a dual role by supporting the storage compound against sedimentation, in addition to assisting electronic conduction. The yield stress behavior of the carbon black gel, observed in Chapter 2, allows it to fill this second role. Many diverse applications of particle suspensions, ranging from cosmetics to concrete, rely upon the ability to indefinitely suspend a particle in a yield stress fluid. There exists a body of theoretical and experimental work which outlines the conditions required to achieve stability [4][5][6]. More detail on this approach to stabilization can be found in section S.8 Conservatively assuming a particle size of 10 um to represent the upper tail of the particle size distribution, Equation 3.1 predicts that a supporting fluid with a yield stress of 0.02 Pa will effectively suspend the LCO phase. Measurements of the yield stress of a 30 volume percent LCO electrode, in a 7 weight percent Shawinigan black gel matrix (Figure 3.3) demonstrates that the measured yield stress of 650 Pa is many orders of magnitude in excess of the stability criterion. The SSE is a microscopically heterogeneous composite and the LCO particles are supported locally by the carbon black gel. Even if the yield stress of the unfilled carbon black gel is used to determine stability, the measured yield stress of that material, at 200 Pa, still exceeds the criterion by orders of magnitude. 102 Tyield - d(p, - pf)gk 18 Equation 3.1. The yield stress criterion presented by Roussel [4]. The minimum yield stress to stabilize a particle of diameter, d, with a density of ps, in a fluid of density pf is given by Tyield. The scaling constant k deals with how the shear rate imposed by a falling particle is related to its velocity and diameter - its exact value is debatable, but is demonstrated to be very near 1. The predicted of stability is confirmed by a vertically resolved LCO concentration profile in Figure 3.4. The tomogram of a slurry with the same composition as measured in Figure 3.3 is binarized according to methods described earlier. Taken 24 hours after re-dispersion in an ultra-sonic bath, the data shows LCO concentrations very near the as-prepared value of 30 volume percent over a depth of 750 microns. At 30 volume percent, the LCO content is half of the glass transition loading limit. The particles have ample free volume and driving force to sediment, were it not for the stabilization provided by the carbon black gel. Insets of binarized horizontal sections (LCO appears white) at three different height levels show the absence of vertical differentiation in the LCO microstructure. X-ray microtomography also affords a view into the spatial distribution of the LCO phase. Figure 3.5 shows a 3-dimensional tomographic reconstruction of a 10 vol% LCO sample, sitting in a 2 wt% Ketjenblack gel. A cluster identification algorithm was applied to the binarized data and nearestneighbor connected voxels are color coded into common clusters. A 10 volume percent sample was used to provide greater separation between LCO clusters for clarity of cluster identification. Visual inspection shows a good volume coverage with the LCO phase, which is organized into a range of cluster sizes. While a few clusters spanning tens of microns are visible, the greatest numbers of clusters are much smaller. 103 Quantitative sorting of the clusters by size in a cumulative histogram (Figure 3.6) yields a better view of the degree of agglomeration present between the LCO particles. The occupied volume of a single LCO particle, calculated from its mean particle diameter, is 14 cubic microns. Based upon this unit of measure, the d(0.1), d(0.5), and d(0.9) values of the size distribution of agglomerates are 2.5, 31, and 6200 particles, respectively. The average agglomerate size is equivalent to a cubic packing of particles measuring roughly 3 particles on a side. This mild agglomeration lends to the well dispersed microstructure seen in Figure 3.5. Scanning electron microscopy reveals the coexistence of a DLCA carbon gel with the LCO phase in Figure 3.8. The same cluster-cluster DLCA microstructure observed in Chapter 2 is present in the complete electrodes. The focal plane shows three agglomerates on the micron scale, while a few submicron aggregates can also be seen. Below the focal plane, carbon black agglomerates occupy the space around LCO particles. Imaging a larger field of view (Figure 3.7) shows a spatial distribution of LCO in line with images produced by tomography measurements. The tomograms show a well dispersed LCO phase agglomerating mildly in the SSE slurry. The SEM images show that the carbon black continues to form DLCA clusters in the presence of LCO, which is expected as the presence of LCO is not expected to alter the DLVO colloidal interactions of the carbon black agglomerates; the salt concentration is unaffected and the pairwise van der Waals interactions are likewise unchanged. The results are consistent with a hypothesis that the largest effect of the LCO phase on the gelation of carbon black is the geometric obstruction presented by the LCO phase. Not only is the LCO stably dispersed in a carbon black-electrolyte gel, it is also electronically integrated with that gel. The bulk electronic conductivity is a relevant metric in that it quantifies the ability to transport charge over macroscopic distances across the SSE. On the other hand, this property 104 neglects the final stage of charge transport; charge must transfer between the conductive gel network and the lithium storage compound in order to reach the redox reaction sites. A mechanical coupling between the LCO particles and the carbon black gel is demonstrated by the increase in the elastic modulus of the gel upon addition of LCO. The elastic modulus in the linear viscoelastic regime (LVER) increase from 15,000 Pa to 60,000 Pa for the unloaded and LCO-loaded samples, respectively (Figure 3.3). Researchers, particularly in the field of food science, have studied the effect of fillers on the viscoelastic response of gels [7][8][9110]. Along the vein of the reinforcement of composites with solid inclusions studied by van der Poel and developed by Smith [11], they find that the strengthening of a gel by a solid filler requires the mechanical coupling of the two phases so that shear forces can be transmitted from the gel to the filler. The dependence of the overall SSE electronic conductivity on the bulk conductivity of the LCO phase is evidence of the electronic coupling between the gel and LCO. An infinite resistance interface between the LCO particles and gel phase (no coupling) would lead to a slurry conductivity that is independent of the LCO conductivity. As the resistance of this interface decreases, the LCO conductivity plays an increasing role in the composite. In Figure 3.10, three different LCO samples, each at a different degree of delithiation, are incorporated into slurries at four loadings. The composition of the Shawinigan black gel is fixed at 7 wt/o. Delithiation increases the bulk conductivity of the LCO particles, and these three samples have measured conductivities of 0.00062 S/cm, 0.054 S/cm, and 1.4 S/cm. For all four volume fractions of LCO investigated, increasing the LCO conductivity increases the overall slurry conductivity, demonstrating that the observed mechanical coupling of LCO and gel is also accompanied by an electronic coupling. The origin of this coupling is likely due to van der Waals interactions between the LCO and carbon black. Cho and colleagues calculated the expected interaction energies of battery materials in 105 solvent; among these is the interaction of graphite and LCO [12]. While the alkyl carbonates used in this study were not present in the study, carbon black and LCO show attractive van der Waals interactions in every similar solvent system studied. As discussed in Chapter 2, any repulsive electrostatic interaction would be screened by the 1 M ion concentration in the electrolyte. While the coupling between LCO particles and carbon black gel is a favorable interaction for facile electrochemical kinetics, Figure 3.10 indicates another, negative interaction between the gel matrix and filler. Regardless of the conductivity of the LCO phase, increasing the volume fraction of LCO present in the gel monotonically decreases the SSE electronic conductivity. In its most conductive form, the LCO (1.4 S/cm) is roughly two orders of magnitude more conductive than a 7 weight percent Shawinigan black gel (0.013 S/cm), yet its addition to the gel lowers the overall electrode conductivity by roughly a factor of 2. As high energy densities require a high loading of storage compound, this effect introduces a conductivity penalty for increasing the energy density. There are two probable origins of this conductivity decrease, the depletion of carbon black from the gel network by adsorption onto the LCO particles and the geometric frustration of the carbon black network by the impenetrable LCO particles. While the former cannot be definitely ruled out, the geometric interpretation is the more likely the source of this loss of conductivity. Figure 3.11 isolates the contribution of the LCO surface area by comparing the conductivities of SSE across four LCO loadings, using two differently sized LCO samples. Jet-milled particles have a specific surface area of 2.02 m 2 /g and unmodified particles have a specific surface area of 0.43 m 2/g. At every measured volume fraction of LCO, the higher specific surface area (smaller particle) sample exhibits a lower electronic conductivity. While there is a significant surface area effect, re-plotting the same conductivity data against a new variable, the LCO surface area present per unit volume of electrode slurry, shows that the 106 conductivity reduction is not purely dependent upon the LCO surface area as might be expected from carbon adsorption (Figure 3.12). If the conductivity reduction were due entirely to surface area effects, the conductivities measured from the two differently sized samples should fall onto a common curve. Instead, the two curves are unique - for example, a conductivity of roughly 4 mS/cm may be achieved by the low and high specific surface area LCO samples at two distinct slurry-specific surface areas of 0.014 E2 - 2 below 1 m 2/mL and above 2 m /mL, respectively. - Powder SA0.43 mg0.012 002 4 -- --- 0.01 -- --Powder SSA= 2.02 m2 g S0.008 0 0.006-9 0.004 - 0.002 -0 0 3 2 1 LCO Surface Area Per Unit Slurry Volume (m2/mL) 4 Figure 3.12. Results from Figure 3.11 are plotted against the amount of LCO surface area present per unit of slurry volume. For a purely surface area dependent effect, the two different powder samples should fall onto a common master curve, with the conductivity of the slurry only dependent on the amount of LCO particle surface area present in a given volume of slurry. The two, differently sized LCO powders fall on two, unique curves. If carbon black adsorption is dependent on the LCO surface curvature, and therefore particle size dependent, then the phenomenon may account for the two different curves seen in Figure 3.12. The simpler, and more likely scenario is that the decrease in conductivity is due to the obstruction of the gel network by the occluded volume of the LCO particles. As shown in the tomograms (Figure 3.4), the 107 well dispersed LCO phase constrains the carbon black gel to occupy the remaining interstitial space. Wall exclusion effects, where an carbon black aggregate cannot occupy space within half an aggregate diameter of a solid boundary, further limits the available volume for the gel. This wall exclusion effect will scale with the surface area of the LCO phase present. The number density of LCO particles present will also affect the geometric frustration of the DLCA gel. As seen schematically in Figure 3.13, given a fixed volume fraction of LCO present, smaller particles present a larger number of obstacles to gel formation, altering the gel structure. As discussed in Chapter 2, the gel structure determines its electronic conductivity and therefore the conductivity depression will be surface area and particle size dependent. o o a sun M 0 Figure 3.13. Schematic illustration of three different particles sizes at the same area coverage of 25%. Smaller particles constrain the interstitial gel to smaller dimensions, thereby affecting the gel structure and structure dependent electronic conductivity. The results presented in this chapter inform several considerations in engineering semi-solid electrodes. As the LCO particles are immobilized by the surrounding carbon black gel network, care must be taken to properly disperse the LCO during synthesis. The easiest point to achieve a good dispersion is prior to the addition of the liquid electrolyte, while the carbon black and LCO are dry powders. The carbon black will gel upon addition of the electrolyte and the yield stress behavior of the gel, along with its high viscosity, complicates efforts to disperse the LCO phases in slurry form. Particle 108 segregation during flow (see Chapter 4) should also be minimized, as segregated microstructures will not spontaneously homogenize. A homogenous dispersion of LCO phase is desirable for two reasons. The first is that a local saturation of LCO will exclude carbon black and electrolyte, and depress the local electronic and ionic conductivity. This conductivity depression is compounded by an increase in the local reaction rate. Under a fixed macroscopic reaction rate, a higher concentration of LCO particles will increase the electrochemical reaction rate in the region. A larger required flux of electrons and ions needed to feed the local reaction, traveling over a region of depressed conductivity, results in a greater dissipation of energy as Ohmic losses. While the interpretation of the depressed conductivity with higher specific surface area LCO could benefit from further study, the measured effect is unambiguous; smaller particles result in lower electronic conductivities of the slurry. The approach of increasing particle sizes may increase the electronic conductivity, but this strategy runs counter to two kinetic benefits of smaller particles. The first is the interfacial reaction rate. The area specific reaction rate, multiplied by the specific surface area, gives the total reaction rate. The total rate may therefore be increased by using smaller particles with a larger specific surface area, holding other variables of reaction kinetics (overpotential, local reactant concentration, temperature) constant. Another consideration is that smaller particles feature shorter diffusion lengths for mass transport from the particle surface into the bulk. While increasing the particle size benefits the slurry electronic conductivity, this gain should be tuned against the counteracting effects of interfacial reaction rate and solid phase mass transport kinetics. An attractive van der Waals interaction between carbon black and LCO was proposed to yield a mechanical and electronic coupling between the dispersed LCO and the carbon black-electrolyte gel matrix. As other lithium storage compound chemistries or electrolyte solvent systems are explored, the 109 sign of the Hamaker constant may become negative, leading to repulsive van der Waals interactions. The decoupling of the storage compounds from the gel network introduces a large charge transfer resistance which is detrimental to reaction kinetics. If this situation arises, one strategy to mitigate the problem is coating the lithium storage compound with a thin layer of a material which exhibits an attractive interaction with carbon black. At short length scales, the van der Waals interactions of coated particles are dominated by the coating layer [13]. A safe choice for a coating layer is graphite, as the interactions of identical chemistries (coating graphite and carbon black) are always attractive in a dielectric medium [13]. As a final design note, comparison of Figures 3.9, 3.10, and 3.11 shows that the dominant determinant of electronic conductivity in the SSE is the conductivity of the carbon black gel matrix. Tuning the LCO phase conductivity by over three orders of magnitude only increases the overall slurry conductivity by a factor of five. Increasing the gel conductivity two orders of magnitude, by increasing the carbon black content from 3 wt% to 8 wt%, increases the slurry conductivity by two orders of magnitude. The gel matrix properties dominate the slurry properties. Dramatic gains in slurry conductivity require the further engineering of the mixed conductor gel phase. 3.5 Conclusion The filling of a DLCA carbon black gel with weakly agglomerating LCO particles leads to a stable, electrochemically active semi-solid electrode. The stability of non-colloidal LCO particles in the slurry is confirmed through x-ray tomography, in agreement with expectations based upon a theoretical yield stress criterion [4]. Quantitative analysis of tomographic data and electron microscopy show that the LCO phase is well dispersed, with a DLCA carbon gel structure occupying the remaining space. 110 Chapter 2 demonstrated carbon black gels with electronic conductivities of the same order of magnitude as the ionic conductivity of the bulk electrolyte, thereby creating a mixed conductor gel phase. This chapter presents results that reflect a mechanical and electronic coupling of that gel network with the LCO particles. The ability to transport charge across macroscopic distances, and across the gel-LCO interface, explains the origin of the electrochemical functionality of the SSE; a mixed conductor carbon black gel matrix allows the distributed lithium storage compounds to access the ions and electrons required for charging and discharging. Finally, design constraints for the electrodes were discussed in light of observed couplings between the LCO and carbon black-electrolyte gel. The LCO particles and matrix gel may be considered quasi-independent entities, and tuning the performance of each component generally improves the performance of the overall electrode within this framework. There are interactions between the two phases, particularly when the geometric constraints imposed by the filler phase significantly disrupts the formation of a cluster-based gel network. In the following chapter, as prepared SSE are subjected to shear and flow. While the electrode microstructure is arrested under stationary conditions, the imposition of shearing flow leads to significant migration and phase segregation effects which affect the macroscopic properties of the slurry, particularly the electronic conductivity. As a SSFC relies upon a flowing electrode, these effects will be studied in detail. 111 Chapter 3 References J. Molenda, A. Stoklosa, and T. Bak, "Modification in the electronic structure of cobalt bronze 11] LixCoO2 and the resulting electrochemical properties," Solid State lonics, vol. 36, no. 1-2, pp. 53-58, Oct. 1989. [2] A. R. Wizansky, P. E. Rauch, and F. J. Disalvo, "Powerful oxidizing agents for the oxidative deintercalation of lithium from transition-metal oxides," Journal of Solid State Chemistry, vol. 81, no. 2, pp. 203-207, Aug. 1989. [3] F. Marone et al., "X-ray Tomographic Microscopy at TOMCAT," Journal of Physics: Conference Series, vol. 186, p. 012042, Sep. 2009. [4] N. Roussel, "A Theoretical Frame to Study Stability of Fresh Concrete," Materials and Structures, vol. 39, no. 1, pp. 81-91, Mar. 2006. Y. B. He, J. S. Laskowski, and B. Klein, "Particle movement in non-Newtonian slurries: the effect [5] of yield stress on dense medium separation," Chemical Engineering Science, vol. 56, no. 9, pp. 29912998, May. 2001. [6] L. Jossic and A. Magnin, "Drag and stability of objects in a yield stress fluid," AIChE Journal, vol. 47, no. 12, pp. 2666-2672, Dec. 2001. [7] T. van Vliet, "Rheological properties of filled gels. Influence of filler matrix interaction," Colloid & Polymer Science, vol. 266, no. 6, pp. 518-524, Jun. 1988. [8] J. Chen and E. Dickinson, "Effect of surface character of filler particles on rheology of heat-set whey protein emulsion gels," Colloids and Surfaces B: Biointerfaces, vol. 12, no. 3-6, pp. 373-381, Jan. 1999. R. Richardson, G. Robinson, S. Ross-Murphy, and S. Todd, "Mechanical spectroscopy of filled [9] gelatin gels," Polymer Bulletin, vol. 4, no. 9, 1981. [10] S. Nie and C. Basaran, "A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds," International Journal of Solids and Structures, vol. 42, no. 14, pp. 4179-4191, Jul. 2005. [11] J. Smith, "Simplification of van der Poel's Formula for the Shear Modulus of a Particulate Composite," Journal of Research of the National Bureau of Standards A, vol. 79, no. 2, pp. 419-423, Nov. 1974. [12] Y. K. Cho, R. Wartena, S. M. Tobias, and Y.-M. Chiang, "Self-Assembling Colloidal-Scale Devices: Selecting and Using Short-Range Surface Forces Between Conductive Solids," Advanced Functional Materials, vol. 17, no. 3, pp. 379-389, Feb. 2007. 112 [13] J. N. Israelachvili, Intermolecular and Surface Forces, Third Edition, 3rd ed. Oxford: Academic Press, 2010. 113 Chapter 4 Flow-induced Segregation in Semi-solid Electrodes Abstract This chapter concludes the four part study of semi-solid electrodes for use in novel SSFC devices by considering the effect of flow on electrode microstructures. Flow through 1.6 mm diameter tubes, replicating the laboratory-scale reaction cell, leads to two forms of particle segregation. Particle depletion at the fluid-wall interface, known also as wall slip, and particle segregation by size in the bulk both lead to increases in the electron transfer resistance in a SSFC device. In-situ electronic conductivity experiments under flow and electron microscopy are used to correlate the observed structure-property relationship in flowed electrodes. Electrochemical cycling of semi-solid cathodes confirms that the detrimental effects of segregation on electronic conductivity translate to increased polarization and reduced charge capacity in a SSFC. Electronic conductivities above 1 mS/cm are demonstrated for twenty flows through a 10 cm cell by addressing the wall slip and particle size segregation with roughened surfaces and in-situ ultra-sonic disruption, respectively. 4.1 Introduction This chapter explores the effects of flow on the microstructure and electrochemical performance of semi-solid electrodes. Chapters 2 and 3 developed an understanding of the structureproperty relationship of as-prepared electrodes. These complex fluids must undergo shearing flow in a working SSFC device, and this shear introduces driving forces for particle segregation. The migration 114 and segregation of particles in tube and channel flow is a studied phenomenon, and existing literature provides a basis for understanding the microscopic origins of segregation [1][2][3][4]. Two types of segregation are observed to increase the electronic resistance in a reaction cell. The first is a particle depletion effect at the electrode-current collector interface. The depletion of carbon black from this interface increases the charge transfer resistance from the current collector into to the electrode bulk. The second effect is the segregation of carbon black to the walls and into isolated inclusions within the bulk. The associated depletion of carbon black from the rest of the electrode decreases the macroscopic conductivity of the slurry, transverse to flow. The consequence of flow-induced segregation is the diminished charge rate capabilities of the battery. Chapter 1 has demonstrated that electron transport is a majority contributor to the overall electrochemical impedance for electrodes with electronic conductivities close to 1 mS/cm. The electronic limitations lead to an increased Ohmic loss at a given current density, which reduces the round-trip efficiency of the energy storage device. Those Ohmic losses also translate to a potential drop and limit the maximum charge and discharge rate for the battery, given a set voltage window for electrochemical stability. Electrochemical test on flowed electrodes confirms that the reduction in electronic conductivity lead to diminished electrochemical performance. Understanding the source of increased electron transfer resistances, caused by flow, leads to experimental solutions. Roughened wall surfaces and ultra-sonic disruption are shown here to enable the continued flow of a semi-solid electrode, while maintaining an electronic conductivity of 1.84 mS/cm after 20 flows through a 10 cm channel. Microstructures observed with electron microscopy are correlated with electronic conductivity measurements to attribute the high retained conductivity to a suppression of segregation. The conclusions of Chapter 2 and 3 aid the link of flow-induced 115 heterogeneity with observed electronic conductivities. This chapter concludes the microstructural study of the semi-solid electrodes presented in Chapter 1. 4.2 Methods This section presents the methods used to demonstrate the segregation of LCO and carbon black of caused by shearing flow. Material selection and slurry preparation will be followed by modeling approaches that predict flow profiles of the electrodes in tube flow. Given the diversity of shear rates and shear rate gradients predicted in tube flow of a complex fluid, the impact of flow on microstructure is studied under tube flow conditions, rather than in the rheometer. Methods to measure the evolution of electronic conductivity, transverse and parallel to flow, are discussed. Correlation of segregated microstructures with electronic properties is accomplished with scanning electron micrographs of frozen, cleaved surfaces. The same laboratory SSFC used in Chapter 1 for electrochemical tests return here to confirm that the observed changes in electronic conductivity lead to expected changes in charging and discharging behavior. 4.2.1 Materials Samples consist of three components, lithium cobalt oxide, carbon black, and electrolyte. The lithium cobalt oxide is produced by the AGC Seimi Chemical Company, Ltd. The received LCO is jetmilled with a grinding air pressure of 60 PSI and classified at 15,000 RPM to produce a smaller particle size distribution. This chapter uses a different batch of LCO than Chapter 3, with a specific surface area of 2.50 m 2/g, compared the previous batch's value of 2.02 m 2/g. Chevron Shawinigan black (Chevron Corporation) is exclusively used here as the carbon black additive. All electrodes are of a common 116 composition, 30 vol% LCO in a 7 wt% Shawinigan black-electrolyte gel. Semi-solid electrodes are synthesized in the same manner outlined in Chapter 3. Two electrolytes are synthesized for use in this chapter. An electrolyte composed of 1.0 M UPF 6 in a 1:1 volume blend of ethylene carbonate (EC) and dimethyl carbonate (DMC) is synthesized from materials purchased from the Sigma Aldrich Corporation, and is referred to as an EC:DMC electrolyte in this work. EC:DMC mixes a low melting point alkyl carbonate (DMC, m.p. = 2-40C) with a high melting point specie (EC, m.p. = 34-37*C). To aid sample freezing for electron microscopy, the DMC component is removed from the second electrolyte; the second electrolyte is 1.0 M UPF6 in ethylene carbonate, and is referred to as a an EC electrolyte. With the presence of salt, the freezing point is depressed. Figure 4.1 shows the viscoelastic response of 30 vol% LCO in a 7 wt% Shawinigan black-electrolyte gel, as a function of temperature. The gel solidifies over a 5'C range centered on 25*C, allowing the gels to be handled as solids with moderate cooling from room temperature. 1E+8 Elastic Modulus 1 E+7 a. Viscous Modulus 1E+6 1E+5 0 1E+4 90 1E+3 1 E+2 1E+1 1 E+0 10 15 20 25 30 35 40 Temperature (*C) Figure 4.1. The viscoelastic response of 30 vol% LCO in a 7 wt% Shawinigan black-EC gel, as a function of temperature. The temperature is stepped up in 1*C increments from 10*C to 40"C while a 1 Hz stress 117 controlled oscillation of 100 Pa is applied, after a 1 minute temperature equilibration. The transition from solid to liquid reflects a melting point centered about 25"C. 4.2.2 Experimental The shear stress-shear rate viscometry curve is measured in a Malvern Kinexus Pro rheometer outfitted with a 20 mm diameter parallel plate geometry. P220 grit sandpaper is attached to the plate surfaces with Krazy Glue to mitigate wall slip effects across a 1 mm measurement gap. The rheometer is operated in a rate-controlled mode, with a 3 minute equilibration time at each shear rate. A solvent trap allows for extended measurements at 25*C. As discussed in section S.9, no pre-shear is applied. A Herschel-Bulkley (H-B) behavior is fit to the measured viscometry curve for 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC. The first ramp of shear rates, upwards from 0.1 1/s to 500 1/s, is excluded as transient behavior. Section S.9 discusses how this first ramp results in the irreversible restructuring of the gel. A power law relationship is fit to all data between shear rates of 0.5 1/s and 500 1/s. Data below 0.5 1/s is fit with a constant stress plateau. Three H-B fluid parameters, the yield stress, power law prefactor, and power law exponent, are inputted into a flow model outlined by Fordham [5]. Given a flow rate, pipe radius, and the H-B fluid parameters, Fordham's method solves for the pressure gradient by a numerical root finding method. The radial profiles can then be solved for analytically. Electronic conductivity measurements are made in a custom flow-conductivity cell, shown schematically in Figure 4.2. This cell enables the in-situ measurement of conductivities of slurries during, and in between, flow. The geometry mimics a 1.6 mm diameter pipe and measures the ability to transfer current transverse to the flow direction, as required in a SSFC reaction cell. A polytetrafluoroethylene (PTFE) body hosts two, alloy 316 stainless steel electrodes. A 1.6 mm diameter channel runs through the body. As the slurry flows through this channel, it makes contact with the 118 stainless steel electrodes via flat surfaces measuring 11.6 mm by 1.7 mm. The electrode plates are spaced 1.7 mm apart. The cell factor of 1.3 1/cm is measured with a 15 mS/cm conductivity from Oakton Instruments. Barbed, polyvinylidene fluoride (PVDF) connectors couple the cell to 1.6 mm inner diameter tubing at both ends. Slurries are loaded into the system by syringe, and the flow is driven by a digitally controlled peristaltic pump in the same manner described in Chapter 1. Masterflex ChemDurance and Gore Chem-Sure tubing, with inner diameters of 1.6 mm, are run through the pump head and connected to the conductivity cell on either end with barbed connectors, forming a closed loop. Stainless Steel Electrodes PTFE Shell Figure 4.2. Two schematic views of the flow-conductivity cell, across and along the flow axis. A PTFE shell features a 1.6 mm diameter pipe, coupled to 1.6 mm inner diameter tubing running through a peristaltic pump. Stainless steel electrodes, spaced 1.7 mm apart, make contact to the flowing slurry with a flat, rectangular surface measuring 11.6 mm by 1.7 mm. The stainless steel electrodes are prepared in two surface finishes, smooth and roughened. The smooth electrodes are polished progressively down to a 1 um grit polishing paper. The rough electrodes have their surface hammered into a P120 grit sand paper. Surface height profiles obtained by confocal microscopy (Keyence Corp. Model VK-9710) are shown in Figures 4.3a and 4.3b. Line profiles, taken along the dotted lines, are inset to the figures and provide a clearer view of the vertical features present in each finish. The imaged area of 280 um by 200um shows typical height features on 119 the order of 0.1 um and 10 um for the smooth and rough surfaces, respectively. Table 4.1 lists the two normalized surface areas, defined as the true surface area divided by the projected surface area. Figures 4.3a (left) and 4.3b (right). Height profiles of the two, stainless steel flow-conductivity electrodes. The colored area maps are accompanied by a line profile (inset at bottom) taken across the dotted line. The total height variation across the line profile is labeled. The area maps are 200 um by 280 um. The smooth plates show surface features on the order of 0.1 um. The rough plates show surface features on the order of 10 um. Surface Finish Smooth Rough Normalized Surface Area 1.03 2.35 Table 4.1. The normalized surface areas of the two surface finishes. The normalized surface area is defined as the true surface area divided by the projected surface area. Electronic conductivity measurements in the flow-conductivity cell are performed with a Solartron 1455 potentiostat. DC electronic conductivities are monitored with a constant 50 mV bias across the two stainless steel electrodes. Trials of bias voltages up to 100 mV confirm that 50 mV is 120 within the linear response of the electrode, for a 1.7 mm gap. The current response, /, and measured cell factor, C, are used to calculate the DC conductivity. CI V Equation 4.1. The DC conductivity is calculated with the cell factor, C, applied voltage, V, and current response, I. Extended flow experiments of linear displacements up to 200 cm are conducted in a repeating, four step procedure outlined in Figure 4.4. The electrode is pumped for 0.2 mL at a time, equivalent to an area-averaged linear displacement of 10 cm in a 1.6 mm diameter pipe. The linear velocity, flow rate, and pump interval relationships are tabulated in Table 4.2. The slurry is pumped and allowed to rest for 5 minutes while a conductivity value is read. The pump head rotation is reversed and the slurry is pumped in the reverse direction. This process continues for 20 intervals, totaling a linear displacement of 200 cm. The pump head and conductivity cell are separated by 300 cm of tubing to ensure that the slurry that flows through the conductivity cell does not interact directly with the peristaltic pump head. When ultra-sonic vibrations or a heat bath is applied to the sample, the conductivity cell and 200 cm of tubing on either end are immersed. Results from the velocity profile calculations show that fluid near the axis of the pipe flow at twice the average linear velocity, the core of the slurry is therefore considered to travel up to 20 cm for an area averaged displacement of 10cm. Both the 50'C heat bath and ultra-sonic bath use No. 19 vacuum pump oil as the medium to minimize any interactions of the cell with water. A Cole Parmer Model 8890 bath sonicator delivering 70 W at 42 kHz is used to apply ultrasonic disruption. 121 [Pump Pm PupIPM (r)) 50 C Temperature Control Ultra-Sonic Disruption Figure 4.4. Schematic illustration of the 4 steps repeated in a flow-conductivity experiment. A slug of slurry is pumped back and forth through the conductivity cell under the control of the peristaltic pump. This back-and-forth method prevents the peristaltic pump from applying unknown shears onto the slurry being measured. Area Averaged Linear Velocity 0.28 cm/s 2.8 cm/s 10 cm/s Flow Rate in 1.6 mm Diameter Pipe 0.33 mL/min 3.3 mL/min 11.9 mL/min Pump Interval For an Area Averaged 10 cm Displacement 36 s 3.6 s 1s Table 4.2. The relationship between various flow parameters used in the flow-conductivity measurement. Figure 4.5. Photograph of a flow-conductivity cell immersed in an ultra-sonic bath. Electronic conductivity measurements parallel to flow are destructive, and are made on a sample after completing transverse conductivity measurements on 200 cm of linear displacement. The 122 tubing is cut to lengths between 10 mm and 20 mm and flat-ended, 1.6 mm diameter stainless steel rods are contacted to the slurry from the two open tube ends (Figure 4.6). A parallel plate, two electrode, DC conductivity measurement is made across the length of the tube. The applied DC voltage, current response, and cell factor (calculated from the geometry), is used to calculate the conductivity. The length of each cut section is individually measured and a unique cell factor is calculated based on the geometric separation of the two stainless steel electrodes. Stainless Steel Electrodes Chem-Durance Polymeric Tube Figure 4.6. Schematic representation of the electronic conductivity measurements, made parallel to the flow axis. A section of tubing containing flowed slurry is cut after completion of the transverse conductivity measurements. Two, 1.6mm diameter stainless steel rods are contacted to the slurry to measure a DC conductivity. The mid-planes of the flowed electrodes are imaged with scanning electron microscopy. After completion of the transverse and parallel conductivity experiments, slurry samples are frozen by immersion in boiling 1,1,1,2-tetrafluoroethane (b.p. = -26*C). Sections of tubing, roughly 5 mm in length, are cut. The frozen cores are extruded from the tubing and cleaved along their diameter with a surgical blade. The half-cylinder is placed on a temperature-controlled Peltier stage with the mid-plane facing upwards. Measurements are made in a FEI/Philips XL30 FEG ESEM microscope at a temperature of -10'C. All scans are made with a 5 kV accelerating voltage and spot size of 4, at a working distance of 123 10 mm. Backscattered electron images are presented to highlight the distribution of LCO and carbon black phases. SEM Flow Imaged Surface Figure 4.7. A schematic representation of the tube mid-plane imaged under a scanning electron microscope. A section of tubing is frozen and the solid slurry core is extruded and cleaved along its diameter. The mid-plane is imaged in frozen form, while held at -10'C by a Peltier stage. Electrochemical tests on flowed electrodes are made in the same test apparatus described in the Methods section of Chapter 1. Alloy 316 stainless steel current collectors are used to study the wallslip phenomenon while gold-sputtered stainless steel current collectors are used to study effects of bulk segregation. Smooth and rough surface finishes are accomplished in the same way outlined above for the flow-conductivity cell. The two finishes correspond to the same surface feature sizes found in the flow-conductivity cells. In the study of the effects of current collector surface finish on electrochemical performance, the semi-solid electrode is directly injected into the flow channel in order to eliminate the effect of bulk segregation. The rate of injection is roughly 2 mL/min. In the study of the effect of extended flow on electrochemical performance, the semi-solid electrode is flowed through 100 cm of 1/16" tubing at 1 mL/min, under the control of a peristaltic pump, before entering the reaction cell. A control experiment injects the electrode directly into the reaction cell at 1 mL/min. 124 4.3 Results A SSFC architecture requires the flow of semi-solid electrodes through a reaction cell. A typical laboratory cell consists of a 1.6 mm diameter tubular channel, through which slurries demonstrating a Herschel-Bulkley behavior are flowed. The flow profiles of 30 vol% LCO in a 7 wt% Shawinigan blackEC:DMC gel are calculated under various flow rates, to model expected flow patterns in a reaction cell. Low rates of flow experienced in the stoichiometric regime, where a slurry may travel through a 10 cm channel in one hour, result in plug flow behavior. High flow rates in the intermittent operational regime, where the same channel might be cleared in seconds, apply shears across the entire sample. The flow behavior of slurries is expected to depend, not only on the shear rates applied, but also on the shear rate gradients and bounding geometries. Measurements on the effect of shearing flow are therefore made in a geometry mimicking the conditions of a laboratory flow cell. Results show conductivity values transverse to flow dropping over an order of magnitude after 200 cm of linear displacement. The conductivity along the flow axis increase at the same time, leading to a near-1000fold anisotropy in conductivity. SEM micrographs of frozen slurries reveal that tube flow leads to segregation of LCO and carbon black, which explains the origins of anisotropic conductivities. In-situ ultra-sonic disruption is demonstrated to mitigate this segregation and maintain electronic conductivities above 1 mS/cm. Semi-solid electrodes of LCO and carbon black in electrolyte have a yield stress and shear thinning behavior. More specifically, their shear stress-shear rate relationship may be approximated by a Herschel-Bulkley model where the stress exhibits a power law dependence on shear rate. Figure 4.8 plots the measured viscometry data alongside a Herschel-Bulkley fit, in red. The yield stress, ro, is 1 Pa, 125 the power law exponent, n, is 0.803, and the power law prefactor, A, is 2.33. A power law exponent less than one indicates a shear thinning behavior. 80 3 ...... 1000 y = 2.3285xO. 100 10 CO 0.1 0.1 1 10 Shear Rate (1/s) 100 1000 Figure 4.8. The Herschel-Bulkley fit to the stress-shear relationship of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel. As the shear rate approaches zero, a stress plateau appears at 1 Pa, indicating a 1 Pa yield stress. Shear rates of 1 1/s and above roughly follow a power law relationship with a exponent less than 1, indicating a shear thinning behavior. The yield stress and two power law fitting parameters are inputs to calculate the shear and velocity profiles in tube flow. Analytical expressions for the shear and velocity distribution are available for Herschel-Bulkley fluids flowing through the common geometries of tubes, rectangular channels, and annular tubes [5]. The three Herschel-Bulkley fluid parameters defined above allow for the computation of the radial flow profiles seen in Figures 4.9a and 4.9b. Here, the model fluid of 30 vol% LCO in a 7wt% Shawinigan black-EC:DMC gel flows through a 1.6mm diameter tube at 5 different flow rates. As the absolute flow velocities vary across orders of magnitude, they are normalized by the area-averaged velocity to convey the shape of the radial velocity profile. The same approach normalizes the absolute shear rate with its maximum value occurring at the tube wall (r = 0.008 m). The different flow rates are reported in electrochemical c-rate metrics, used to describe the charge rate under stoichiometric conditions. In 126 terms of flow rates, the c-rate is the inverse time (measured in inverse hours) required to traverse one length of the reaction channel. Conversion to a linear flow velocity requires a c-rate and a channel length. The c-rates of 0.1C, 1C, 10C, 100C, and 1000C convert to average linear velocities of 0.00028 cm/s, 0.0028 cm/s, 0.028 cm/s, 0.28 cm/s and 2.8 cm/s, respectively for a 10 cm long channel. Low flow rates in the stoichiometric flow operational regime, where the slurry travels the reaction cell over the course of roughly an hour (c-rate = 1C), lead to plug flow behavior. High flow rates in the intermittent regime, where the slurry is cleared from the cell in seconds (equivalent c-rate = 1000C), lead to profiles resembling the Poiseuille flow of a Newtonian fluid. In the former instance, the yield stress of the electrode creates an un-sheared region in the center of the tube. In the latter, all of the material in the tube is sheared. Normalized Shear Rate Normalized Flow Velocity MM .C1.0 \ 0. 0.5. 1100 0.4 10C 0.2 0O 1C 20.10 -0.0005 0.0005 Radial Position (m) 0.0005 0.0005 Radial Position (m) Figure 4.9a (left) and 4.9b (right). Figure 4.9a plots the radial dependence of flow velocity for five different flow rates of a semi-solid electrode (H-B behavior shown in Figure 4.8) in a 10 cm long section of 1.6mm diameter tube. The flow velocity is reported as a normalized value -the absolute velocity divided by the area-averaged value. The shear rates in Figure 4.9b are also normalized, the absolute value is divided by the maximum value present at the tube wall (+/- 0.0008 m radial position). The five flow rates are reported in electrochemical c-rates. The values of 0.1C, 1C, 10C, 100C, and 1000C convert 127 to linear velocities of 0.00028 cm/s, 0.0028 cm/s, 0.028 cm/s, 0.28 cm/s and 2.8 cm/s, respectively for flow across a 10 cm long channel. Based on extensions of computations performed in Figures 4.9a and 4.9b, shear conditions are shown for a variety of flow parameters in Figures 4.10a and 4.10b. The normalized yield radius is defined as the fractional radius, up to which the material is un-sheared and flows as a plug. The different curves in Figure 4.10a represent different possible reaction channel lengths, while the x-axis plots the flow rate in the metric of electrochemical c-rates. For example, at an x-axis value of 0.1C, the five curves correspond to flowing across a 10 cm, 30 cm, 50 cm, 70 cm, and 90 cm reaction channel in ten hours. This calculates to five different linear flow rates of 0.00028 cm/s, 0.00083 cm/s, 0.0014 cm/s, 0.0019 cm/s, and 0.0025 cm/s, respectively. The faster flow rates have smaller yield radii as more material in the tube experiences shear. The five curves of Figure 4.10b use the same c-rate metric to plot the maximum shear rates experienced in the electrode for different flow conditions. Here, faster flow leads to higher shear rates. OM 1.C I 0.8 0. a) 0.6& > (D 0.4 N z 10cm 30cm 50cm 1000 90cm c V N 70CMrIn o 90cm 0.1 1 100 70CM 10 50cmI 0.1- 1c 0.1 1 a) S0. 10 100 C-Rate (1/hr) 1000 'R C. 730cm 10 100 C-Rate (1/hr) 1000 Figures 4.10a (left) and 4.l0b (right). Figure 4.10a conveys calculated results on the plug flow nature of the electrode, under various flow rates. The normalized yield radius indicates the extent of the unsheared plug. As the c-rate (and flow rate) increases, the plug shrinks in radial extent and an increasing amount of the slurry is subject to shear. Different curves correspond to various reaction channel 128 lengths. A fixed c-rate, such as 1C, will correspond to different linear velocities for different length channels. Figure 4.10b plots the maximum absolute shear rate experienced at the tube walls. Rheological testing of particle suspensions and gels often requires roughened surfaces to mitigate wall slip effects [1]. To test for the effect of wall slip on electronic properties, an electrode of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel is flowed through a 1.6mm tube, between two stainless steel electrodes. The electrodes are produced in two variants, polished and roughened, having surface feature heights on the order of 0.1 um and 10 um, respectively. Confocal microscopy surface profiles of the two variants are presented in this chapter's Methods section. The slurry is flowed through a length of tubing, at an average linear velocity of 0.8 cm/s, as noted in Table 4.3 before its static electronic conductivity is measured transverse to the flow direction. The reported conductivities are calculated from the measured cell factor and total DC resistances. They do not reflect the bulk conductivity of the slurry, as other sources of electron transfer resistance, such as interfacial charge transfer resistances, are also included. The roughened electrodes read conductivities of 0.8 and 1.0 mS/cm, very close to the value of 1.1 mS/cm measured in a parallel-plate well geometry (Chapter 3). The smooth electrodes measure lower apparent conductivities of 0.03 and 0.05 mS/cm in the two trials. Plate Type Smooth Roughened Distance Flowed at 0.8 cm/s 46 cm 46 cm 56 cm 69 cm Electronic Conductivity (mS/cm) 0.05 0.03 1.0 0.8 Table 4.3. The electronic conductivities measured across a semi-solid electrode, transverse to flow, with smooth and roughened electrodes. Measurements were made by flowing the electrode across smooth electrodes (surface roughness on the order or 0.1 um) and roughened electrodes (surface roughness on the order of 10 um). The roughened electrodes demonstrate measured conductivities that are over an order of magnitude higher than their smooth equivalents. 129 A roughened current collector surface is tested against a smooth surface to investigate how the observed electronic interfacial resistance affects the electrochemical behavior in a SSFC. Figures 4.11a and 4.11b plot the voltage profiles of a C/20 charge and discharge of a semi-solid cathode of composition 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel. The roughened alloy 316 stainless steel current collectors demonstrate the expected lower polarization on both charge and discharge reactions. The lower polarization also allows for larger charge capacity utilization in the roughened current collector cell. The roughened current collector has a C/20 discharge capacity of 121 mAh/g, versus 92 mAh/g for the smooth surface finish. The high polarization seen in the charge and discharge curves are quantified in Figure 4.12. The C/20 current was interrupted at 10% state of charge increments during charge and discharge. The 1 ms response in voltage was used to calculate the effective DC impedance of the cell, via a simple Ohmic relation of R=AV/Al. Rough current collectors decrease the total cell impedance from 150-2000 down to 50-1000. These values are the total cell impedance, including sources such as the bulk ionic impedance, bulk electronic impedance, interfacial reaction impedance, and the current collector-electrode interfacial impedance. 4.5 4.5 - Rough SS316 4.0 4.0 Rough SS316 > .03.5 03.5 * >Smooth SS316-- 2.50 Smooth SS316 3.0 3.0 10 20 Time (hr) 30 40 2. 20 40 60 80 100 120 Specific Charge Capacity (mAh/g) 140 130 Figure 4.11a (left) and 4.11b (right). Galvanostatic charge and discharge of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel. The electrode capacity is 18.5 mAh, and the 0.925 mA current corresponds to a C/20 rate. The current is interrupted for is every 2 hours to monitor the DC cell impedance. Figure 4.11a plots the voltage profile, as a function of elapsed time, while Figure 4.11b plots the same data against the specific LCO charge capacity. The smooth current collector exhibits a higher polarization and lower capacity utilization, consistent with a higher interface impedance. 250 2 200 0120- - -_ ----- N Smooth SS316 / Charge OSmooth SS316 / Discharge --- N Rough SS316 / Charge E Rough SS316 / Discharge CU E 00 50 0 o 07 0 0 0 State of Charge Figure 4.12. Calculated DC cell impedances from the measured voltage drops during the current interrupts seen in Figure 4.11. The total cell impedance is significantly lower for rough current collectors, by a factor of 2-3. This is a sum of all of the series impedances, therefore the difference in interfacial impedance is even more pronounced. The same roughened electrodes studied above are used to measure the evolution of the slurry electronic conductivity with progressive displacement under tube flow, driven by a peristaltic pump. Electrodes of 30 vol% LCO in a 7 wt% Shawinigan black-EC gel, are subjected to four different flowing conditions. The experiments are run at 50*C, in an oil bath to ensure fluidity of the EC electrolyte. Asprepared slurries are loaded into the conductivity cell and flowed back and forth, for 10 cm linear 131 displacements at a time. Measurements on the slurry conductivity are taken at rest, between pumping to simulate an intermittent flow operation of a SSFC. The electronic conductivities of three samples decrease by one order of magnitude, or more. Electrodes flowed at area-averaged linear velocities of 0.28 cm/s, 2.8 cm/s, and 10. cm/s have conductivity values that decrease to 0.021 mS/cm, 0.0033 ms/cm, and 0.0036 mS/cm, respectively, after a cumulative displacement of 200 cm (20 pumping intervals). The fourth flow condition applies constant, ultra-sonic disruption to a slurry flowed at 0.28 cm/s by immersing the tubing and conductivity cell in a bath sonicator. Its electronic conductivity remains nearly constant over 200 cm of displacement, finishing with a conductivity of 1.51 mS/cm. At the end of the experiment, the conductivity value at rest is measured with the ultra-sonic disruption turned off; the conductivity increases to 1.84 mS/cm. In some samples, the conductivity oscillates up and down - this is attributed to the periodic, back and forth pumping of the slurries and the development of heterogeneities along the length of tubing. 100.28 cm/s With Sonication CI) AjA > 6- .g 2.8 cm/s 0.1 0 .1 0.28 cm/s 0.01 0 W 0.001 . 10 Cm/s 07%0 0 0 0 0 PO0 I0 p '0 0 '90 0 Total Linear Distance Under Flow (cm) Figure 4.13. The evolution of electronic conductivity, transverse to flow, under four intermittent flow conditions. An electrode of 30 vol% LCO in a 7 wt% Shawinigan black-EC electrolyte matrix is 132 intermittently flowed for an area-averaged increment of 10 cm. After each flow increment, the electronic conductivity is measured at rest for 5 minutes and reported here. Three flow rates of 0.28 cm/s, 2.8 cm/s and 10 cm/s lead to decreases of conductivity to values of 0.021 mS/cm, 0.0033 mS/cm, and 0.0036 mS/cm, respectively, after a total displacement of 200 cm. Applying constant ultra-sonic disruption to a flow rate of 0.28 cm/s maintains a near constant electronic conductivity, with a final value of 1.51 mS/cm after 200 cm of displacement. The electronic conductivity, parallel to the axis of flow, is measured after completion of transverse conductivity measurements. Sections of tubing are cut, and the conductivity along the tube axis are measured by a two-probe, parallel plate geometry. The anisotropy ratio, defined as the electronic conductivity parallel to flow divided by that transverse to flow, is 800:1 without ultra-sonic disruption. The more moderate anisotropy of 2:1, with ultra-sonic disruption, is attributed to a lower parallel conductivity and a higher transverse conductivity. Sample 0.28 cm/s Flow, Electronic Conductivity Transverse to Flow 0.021 mS/cm Electronic Conductivity Parallel to Flow 16.8 mS/cm Anisotropy Ratio 1.84 mS/cm 3.6 mS/cm 2:1 800: 1 No Ultra-sonic Disruption 0.28 cm/s Flow, With Ultra-sonic Disruption Table 4.4. The decrease in transverse electronic conductivity seen in Figure 4.13 is accompanied by an increase in the conductivity parallel to flow, and the development of anisotropic conductivities. Ultrasonic disruption maintains a higher transverse conductivity, and lowers the parallel conductivity, both acting to lower the anisotropy ratio. Figures 4.14a-4.14d are backscattered electron images of four samples, all 30 vol% LCO in a 7 wt% Shawinigan black-EC electrolyte gel. Higher magnification images of each sample are presented in Figures 4.15a-4.15d. The LCO phase appears as white, the carbon black appears as gray, and voids 133 appear as black. In Figures 4.14b-4.14d, the locations of the tube walls are marked by superposed lines; varying degrees of axial tilt are present in the imaged samples. The as-prepared slurry (Figure 4.14a and 4.15a) shows a homogenous mixing of carbon black and LCO across millimeter length scales. The high magnification image shows a good mixing of solid phases. The same slurry, flowed in a 1.6mm diameter tube for 200 cm at 2.8 cm/s, shows two modes of segregation (Figures 4.14b and 4.15b). Carbon black segregates to the tube walls, forming a 20 um layer of dense carbon black. In another form of segregation, the carbon black in nearer to the tube axis forms carbon black inclusions. As seen in Figure 4.15b, these inclusions deplete the surrounding areas of carbon black. A lower flow rate of 0.28 cm/s, seen in Figures 4.14c and 4.15c, lead to segregation as well, but with less defined structure. Carbon black segregates to the walls, but does not form a sharp, uniform layer as seen in 2.8 cm/s flow. Inclusions of carbon black also deplete surrounding areas of conductive additive, but these inclusions do not develop into compact spherical structures. Figures 4.14d and 4.15d show that ultra-sonic disruption, during flow at 0.28 cm/s, mitigates both forms of segregation. Layers of carbon black do not develop on the tube walls and the formation of carbon black inclusions is much reduced in the bulk. The high resolution image taken in the bulk (Figure 4.15d) shows a good mixing of LCO and carbon black phases. 134 Figures 4.14a-4.14d. Figure 4.14a is a backscattered electron micrograph of an as-prepared slurry of 30 vol% LCO in a 7 wt% Shawinigan black-EC gel. Figures 4.14b, 4.14c, and 4.14d are the same slurry flowed 200 cm through 1.6mm tubing at 2.8 cm/s, 0.28 cm/s, and 0.28 cm/s with ultra-sonic disruption. Each micrograph is the tube mid-plane; the flow axis runs vertically and the two vertical lines indicate the locations of the tube walls. Different degrees of axial tilt present in the measured samples results in the midplane appearing narrower than 1.6 mm in some instances. The LCO phase appears as white, the carbon black appears as gray, and voids appear as black. 135 Figures 4.15a-4.15d. Higher magnification images of Figures 4.14a-4.14d. Figure 4.15a is a backscattered electron micrograph of an as-prepared slurry of 30 vol% LCO in a 7 wt% Shawinigan blackEC gel. Figures 4.15b, 4.15c, and 4.15d are the same slurry flowed 200 cm through 1.6mm tubing at 2.8 cm/s, 0.28 cm/s, and 0.28 cm/s with ultra-sonic disruption. The LCO phase appears as white, the carbon black appears as gray, and voids appear as black. The results of Figure 4.13 and the associated SEM images in Figures 4.14b and 4.14c show that flow induced segregation is detrimental to the electronic conductivity of semi-solid electrodes. The electrochemical ramifications are tested by comparing the performance of two semi-solid electrodes in a laboratory SSFC. The control experiment directly injects the electrode into the reaction cell, minimizing the amount of applied shear. Another cell, where the electrode is flowed at 1 mL/min through 100 cm of tubing, demonstrates how the accessible charge capacity is reduced from 96 mAh/g down to 10 mAh/g under a galvanostatic C/10 cycling experiment. The electrode undergoing 100 cm of tube flow exhibits a higher DC cell impedance, as seen in Figure 4.17, but the absolute values of 70-900 are well below the impedances measured in a smooth current collector cell (Figure 4.12). 136 4.5 4.5 Injection via 100cm of Tube Flow Direct Syringe Injection (control) 4.0 4.0 0)3.5 C.M3.5 .2 Injectior via 100cm 0 > of Tube Flow 3.0 2.5 I1 0 10 Time (hr) 5 15 Injection 80 100 0 205 20 (control) Direct Syringe 40 20 60 0 120 140 Specific Charge Capacity (mAh/g) in a 7 wt% Figure 4.16a (left) and 4.16b (right). Galvanostatic charge and discharge of 30 vol% LCO Shawinigan black-EC:DMC gel. The electrode capacity is 18.5 mAh, and the 1.85 mA current corresponds to a C/10 rate. The current is interrupted for is every 1 hour to monitor the DC cell impedance. Figure data 4.11a plots the voltage profile, as a function of elapsed time, while Figure 4.11b plots the same of 1/16" against the specific LCO charge capacity. Flowing the semi-solid electrode through 100 cm tubing at 1 mL/min, prior to the reaction cell reduces the C/10 discharge capacity from 96 mAh/g down to 10 mAh/g. - m Direct Loading / Charge a 100cm Tube Loading / Charge o 100cm Tube Loading / Discharge 3Direct Loading / Discharge 100 9Q o 80 0 70 60 6 50 40 30 C: - CL E 0) 20 10 o 0 17Z V7ilt qOe 0 2;? 0 State of Charge 6> 0~ 0 137 Figure 4.17. Calculated DC cell impedances from the measured voltage drops during the current interrupts seen in Figure 4.16. The total cell impedance is higher for the electrode flowed through 100 cm of tubing, yet the increase in impedance is well below that seen in smooth current collectors (Figure 4.12). 4.4 Discussion Shearing flows present in the operation of a SSFC device lead to irreversible changes in electrode microstructure that negatively impact the electrode's electronic conductivity and electrochemical performance. There are two modes of shear induced segregation, present in tube or channel flow, that are shown to increase the electrochemical impedance in a device. Particle depletion near walls, also known as wall slip, creates an insulating lubrication layer that presents a high resistance junction for charge transfer from the current collector into the semi-solid electrode. Gradients in shear rate drive a second form of segregation, where large particle preferentially migrate to regions of low shear rate near the tube axis. The segregation creates regions depleted of carbon black, where low electronic conductivities isolate the LCO from the current collectors. Experimental evidence of wall slip and shear gradient segregation are presented, along with methods of mitigation. Both forms of segregation are shown to be detrimental to the transfer of electrons across the semi-solid electrode. Use of roughened wall surfaces, a traditional technique in suspension rheology, enables the low impedance transfer of charge across the current collectorelectrode interface. Ultra-sonic disruption screens the driving force for shear gradient segregation and results in an electrode with a more homogenous microstructure and higher electronic conductivity. 138 The flow of a complex fluid in the near-tubular channels of a laboratory SSFC device gives rise to non-uniform shear and velocity profiles. Calculated flow patterns in a 1.6 mm diameter tube are presented in Figures 4.9a, 4.9b, 4.10a, and 4.10b. These profiles are based on a H-B fluid model fit (Figure 4.8) to a prototype electrode composed of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel. Calculation show that even the slowest flow rates, a C/10 stoichiometric charge rate in a 10 cm tube translating to an average linear velocity of 2.8 um/s, result in a normalized yield radius of 0.82. At this flow rate, 33% of the material undergoes shear. Increasing the flow rate ten-fold, to a IC stoichiometric charge rate, shears 66% of the material. Flow rates associated with intermittent flow, on the order of 1000C, result in the shearing of all material in the tube. According to the shear rate profile in Figure 4.9b, all of the material under shear is also subject to a shear rate gradient, and therefore to driving forces for particle size segregation. The spatial distribution of driving forces for segregation is particular to the flow geometry. As results measured under the controlled shear environment of a rheometer will not necessarily translate to behavior in a device, all experimental studies were conducted in tube flow apparatus to replicate the conditions present in laboratory electrochemical reaction cell. Flow of a particulate suspension past a solid boundary can drive the local depletion of particles to create a low viscosity, lubricating layer [1][6]. This phenomenon is well studied in the field of suspension rheology and wall slip may either be removed by use of roughened tool surfaces, or by compensated in the data analysis phase [7]. Wall slip may actually be a favorable phenomenon when transporting high viscosity fluids, as it reduces the pumping energy requirements. While this is also the case for a SSFC device, the depletion of carbon black from the current collector wall presents a negative consequence for charge transfer. Calculated electronic conductivities of identical slurries, flowed across smooth and rough stainless steel electrodes, are given in Table 4.3. The surface feature heights of 0.1 um on the smooth 139 electrodes are smaller than the average carbon black aggregate size. Those on the roughened electrodes, at 10 um, are larger than both the carbon black aggregates and LCO particles. The difference in apparent conductivity is attributed to a high charge transfer resistance from the stainless steel electrode into the slurry. As shown schematically in Figure 4.18, these apparent conductivities incorporate the complete resistance to transfer charge into the slurry (Ri), across the slurry (R), and back out of the slurry (Rj). For smooth and rough electrodes, the resistance within the slurry should not differ significantly as they are identical composition slurries are pumped at the same flow rate over similar distances. The large variation in calculated conductivity may therefore be attributed to a high interfacial charge transfer resistance that develops with smooth surfaces. By assuming that the slurry in the channel has a conductivity of 1.1 mS/cm, measured for an asprepared sample from Chapter 3, the interfacial, area-specific resistance can be isolated. The true surface area of the electrodes, measured with confocal microscopy is used to account for the fact that the roughened electrodes have a greater surface area. This analysis calculates area-specific interfacial resistances of 2500 Q0cm 2 and 4200 Q-cm 2 for the two measurements made with smooth surfaces. The 2 . rough surfaces have values, nearly 2 orders of magnitude lower, of 27 O-cm 2 and 100 0-cm Wall slip is known to originate microscopically with particle depletion. This depletion of carbon black from the current collector surface will lead to an insulating boundary. The presence of a high resistance boundary is demonstrated. The expected mitigation of this particle depletion with roughened surfaces successfully reduces the area specific interfacial resistance by nearly two orders of magnitude. 140 @0 0 0 - O cv (n w * Ri U, V * Rs Ri Figure 4.18. A schematic illustration of the three series charge transfer resistances present in the flow conductivity cell. Charge must enter and exit the slurry across two interfaces, Ri, as well as the traverse the slurry itself, R,. =C/(Ri +Rs +R) Equation 4.2. The effective conductivity measured in a flow conductivity cell with cell factor, C, includes two interfacial charge transfer resistances, Ri, and the resistance across the slurry, Rs. Plate Type Smooth Apparent Electronic Conductivity Cell Factor 0.05 mS/cm Projected SS316 Electrode Area Assumed Bulk Slurry Conductivity Actual SS316 Electrode Area Calculated interfacial Area-Specific Resistance 0.03 Rough 1.0 mS/cm mS/cm 1.3 1/cm 0.20 cm2 1.1 mS/cm 0.46 cm 2 0.20 cm 2 2500 (l-cm 2 4200 O-cm 2 0.8 mS/cm 27 0-cm 2 100 (-cm 2 Table 4.5. Summary of parameters and results for the calculation of the stainless steel-slurry interfacial area-specific resistance. The roughened plates have area-specific resistances lower by nearly two orders of magnitude. This difference is attributed to the suppression of a particle-depleted wall slip layer. 141 A similar experiment is repeated in a flow cell to demonstrate that the observed interfacial electronic resistance affects the electrochemical impedance. The same formulation cathode electrode is injected into two reaction cells, with smooth and rough stainless steel current collectors. The electrodes are charged and discharged at a C/20 rate (Figure 4.11a and 4.11b) with intermittent current interrupts to monitor the cell impedance. The qualitative observation of higher polarizations arising from a higher impedance in the smooth current collector are confirmed by the quantitative values shown in Figure 4.12. Use of roughened stainless steel electrodes lower the cell impedance and lend to higher rate capability and higher efficiency batteries. While roughened surfaces can mitigate particle depletion at the slurry-wall interface, there are additional segregation phenomena taking place in the bulk of the flowing electrode. As seen in the 3 lowest curves in Figure 4.13, continued flow leads to decreasing electronic conductivities. The same composition of 30 vol% LCO in a 7 wt% Shawinigan black-EC gel is flowed in 10 cm displacement intervals at three different flow rates. The slurry is pumped back and forth through the flowconductivity cell, outfitted with roughened stainless steel electrodes. This alternating pumping leads to the sawtooth behavior seen in some curves. With bulk values of ionic conductivity in the electrolyte between 5 and 10 mS/cm, the electronic conductivities should aim for similar values, as not to be a rate limiting mechanism in the electrochemical cell. Flow rates of 0.28 cm/s, 2.8 cm/s, and 10 cm/s all fall within the intermittent flow regime of SSFC operation, as they correspond to a complete refilling of a 10 cm channel in 36 s, 3.6 s, and 1 s, respectively. Unfortunately, continuous, stoichiometric flow rates in the range of 0.0028 cm/s cannot be achieved with current pumping mechanisms. The highest retained electronic conductivity after 200 cm of total displacement, corresponding to 20 re-fillings of a 10 cm reaction cell, is achieved with the 142 lowest flow rate of 0.28 cm/s. Even then, the measured value of 0.021 S/cm is two orders of magnitude lower than the ionic conductivity and will hinder reaction kinetics. Many studies, motivated by fields as diverse as solid rocket propellant processing and food science, have produced quantitative experimental evidence of particle size segregation of polydisperse suspensions in tube and channel flow [8][9][4][10][11][12][13]. The basic physical interpretation of the segregation phenomenon is as follows. All particles tend to migrate towards regions of lower shear rate in the presence of a shear rate gradient. Collisions of particles between shear planes impart a force component normal to the shear planes. The frequency of collisions scales with the absolute shear rate. When a shear gradient is present, there exists an imbalance in collision frequencies on either side of a shear plane. A net force is imparted on a particle, leading to a drift along the shear rate gradient. A key factor to particle size segregation, outlined by Leighton and Acrivos, is a migration flux which is a function of the particle size, squared [8]. Larger particles therefore migrate more quickly under a shear rate gradient, saturating the regions of low shear. Small particles are excluded to regions of high shear. The semi-solid electrodes feature solid components of very different size and density; it is likely that the carbon black and LCO phases segregate under the shear profiles calculated earlier. Flow induced drops in electronic conductivity are accompanied by clear microstructural segregation, as seen by electron microscopy (Figures 4.14a-d, Figure 4.15ad). Figures 4.14a and 4.15a are backscattered electron images of an as-prepared slurry. LCO (white) and carbon black (gray) are well mixed in a filled gel structure described in Chapter 3. Flow at 2.8 cm/s leads to a final electronic conductivity of 0.005 mS/cm. The electron micrographs (Figures 4.14b and 4.15b) show clear segregation of LCO and carbon black in two manners. In the first, the carbon black migrates to the walls of the tube, which are marked by the dotted vertical lines. This carbon rich layer develops a sharp, linear interface with the bulk of the slurry and exhibits a near-complete exclusion of LCO particles. The 143 second form of segregation is the accumulation of carbon black into inclusions of 10 - 50 um in diameter. These carbon black inclusions preferentially occupy the center for the tube. The saturation of carbon black along the tube wall and in inclusions deprives the remaining slurry of carbon black, resulting in the macroscopic drop in electronic conductivity. The LCO phase surrounding the carbon black inclusion in Figure 4.15b lacks the interstitial carbon black phase found dispersed in Figure 4.15a. Chapter 3 concluded that the primary electron transfer medium in a semisolid electrode is the carbon black gel. The overall depletion of this gel, with selective saturation in a narrow, 20 um layer along the wall and in isolated inclusions, leaves the bulk largely insulating in nature. As a point of reference, the final electronic conductivity of 0.005 mS/cm corresponds to an as-prepared, homogeneous sample of 30 vol% LCO in a 2 wt% Shawinigan black-SSDE gel (Figure 3.9). Flowing at a slower rate of 0.28 cm/s lowers the magnitude of the shear rate gradients and leads to a less strongly segregated microstructure seen in Figures 4.14c and 4.15c. Carbon black still segregates to the tube walls and into inclusions near the central tube axis. The interface between walllayer and bulk is less defined for this slower flow rate, as are the bulk inclusions. The higher magnification SEM micrograph shows that the inclusions are not developed into compact spheres. Lower flow rates and smaller magnitude shear rate gradients lead to a less segregated microstructure and a higher retained electronic conductivity of 0.021 mS/cm. Coupling this lower flow rate with constant ultra-sonic disruption further mitigates particle segregation and leads to a retained electronic conductivity of 1.84 mS/cm after 200 cm of linear displacement. The ultra-sonic energy is expected to create and cavitate micro-bubbles throughout the flowed sample. These shocks may screen out the more moderate driving force for particle migration. Another interpretation of the approach is that it increases the effective temperature of the slurry system. The higher temperature stabilizes the higher entropy state of a mixed microstructure, relative 144 to the more ordered, segregated arrangement. Figures 4.14d shows mild segregation. A layer of carbon black does not form along the tube walls and bulk inclusions are muted. At higher magnification, carbon black and LCO are well mixed, retaining the microstructure of LCO dispersed in a carbon black gel host. Constant ultrasonic disruption, along with a lower driving force for migration from a slower flow rate, mitigates phase segregation and maintains a high electronic conductivity of 1.84 mS/cm. The observed drop in electronic conductivity of semi-solid electrodes upon extended flow is shown to lower the electrode's charge storage capacity. In Figure 4.16a and 4.16b two identical semisolid cathodes are charged and discharged galvanostatically at a C/10 rate in a flow cell, at rest. One cell had its electrode directly syringe injected, keeping the tube flow displacement under 10cm. The other cell had its electrode flowed through 100cm of tubing prior to the reaction cell. The difference in storage capacity can be explained by the segregated microstructure seen in Figures 4.14b and 4.14c. There is a small amount of LCO near the walls that remains accessible to electrons, but the bulk of the lithium storage compound is electrically isolated. The calculated cell impedance values show that the cell impedance does not dramatically increase after segregation, as a degree of storage capacity near the walls is readily accessible to charge. Segregation manifests itself in a significantly reduced charge capacity. The discussion of this section translates to device design considerations. The large interfacial charge transfer resistance that arises from a wall-slip lubrication layer is detrimental to a SSFC reaction cell. The solution here is relatively simple, roughened current collector surfaces with height features on the order of 10 um are sufficient to provide a low resistance interface. On the other hand, wall slip can be desirable in other sections of a SSFC device, outside of the reaction cell. Wall slip lubricates the ordinary transport of the semi-solid electrode and concentrates shear on a narrow fluid layer along the wall. This reduces the energy cost of flow and preserves the electrode bulk from shear and migration 145 effects when it is not in the reaction cell. A smooth tubing material with repulsive colloidal interactions with the carbon black and LCO particles will promote wall slip. Particle segregation can be mitigated with ultra-sonic disruption. Lower flow rates are also expected to reduce segregation. Lower flow rates reduce the amount of material under shear and also lower the magnitude of the shear rate gradient. While the lowest, continuous stoichiometric flow rates cannot be accessed experimentally at the moment, further study may reveal that ultra-sonic disruption is unnecessary for true stoichiometric flow. If not, ultra-sonic energy may be dispensed in a targeted manner during flow in the reaction cell. Tailoring the electrode composition to combat segregation is possible, but impractical given the multiple electrochemical and rheological constraints already present on each component. Device features such as the pumping rate, channel geometry, and possible ultrasonic disruption are demonstrated as viable methods for maintaining electronic conductivity under flow. 4.5 Conclusion Two forms of flow-induced particle segregation were shown here to increase the resistance to electron transfer in a simulated SSFC reaction cell. Particle depletion along smooth walls creates a high resistance lubrication layer at the current collector-slurry interface. The local depletion of carbon black leads to calculated area-specific resistances of 2500 and 4200 0-cm 2. Tube flow also results in particle segregation within the slurry bulk, decreasing the transverse electronic conductivity. A semi-solid electrode with an as-prepared conductivity of 1.1 mS/cm experiences a drop of over two orders of magnitude under high flow rates, down to 0.0036 mS/cm. These electronic conductivity measurements were correlated to decreased charge rate and charge storage capabilities in laboratory SSFC devices. 146 While both effects increase Ohmic losses and decrease the rate capabilities of a device, results are demonstrated that suppress both forms of segregation. Roughened surfaces, a common rheological solution to wall slip, address the particle depletion effect. Application of ultra-sonic vibrational energy screens the driving force for particle migration along shear rate gradient, and maintains a largely homogeneous electrode microstructure. With the combined tactics, the semi-solid electrode maintains a conductivity of 1.84 mS/cm after 20 passes through a 10 cm reaction channel. Flow of a complex fluid electrode in a SSFC device presents engineering challenges, as the microstructure of as-prepare slurries are subject to segregation. Given the many electrochemical and rheological constraints already in place for a semi-solid electrode, it may be simpler to build resistance to segregation into the device, rather than the material. Ultra-sonic disruption requires energy, and the minimum requirements have not been explored here. A more spatially targeted application of ultrasonic energy, limiting its application to coincide with flow, and reducing the flow rate are all strategies for minimizing the energy requirements. 147 Chapter 4 References H. A. Barnes, "A review of the slip (wall depletion) of polymer solutions, emulsions and particle [1] suspensions in viscometers: its cause, character, and cure," Journal of Non-Newtonian Fluid Mechanics, vol. 56, no. 3, pp. 221-251, Mar. 1995. [2] D. Leighton and A. Acrivos, "The Shear-Induced Migration of Particles in Concentrated Suspensions," Journal of Fluid Mechanics, vol. 181, pp. 415-439, 1987. D. M. Husband, L. A. Mondy, E. Ganani, and A. L. Graham, "Direct measurements of shear[3] induced particle migration in suspensions of bimodal spheres," Rheologica Acta, vol. 33, no. 3, pp. 185- 192, 1994. [4] D. Semwogerere and E. R. Weeks, "Shear-induced particle migration in binary colloidal suspensions," Physics of Fluids, vol. 20, no.4, p. 043306, 2008. E. J. Fordham, S. H. Bittleston, and M. A. Tehrani, "Viscoplastic flow in centered annuli, pipes, [5] and slots," Industrial & Engineering Chemistry Research, vol. 30, no. 3, pp. 517-524, Mar. 1991. [6] P. J. A. Hartman Kok, S. G. Kazarian, C. J. Lawrence, and B. J. Briscoe, "Near-wall particle depletion in a flowing colloidal suspension," Journal of Rheology, vol. 46, no. 2, p. 481, 2002. [7] A. Yoshimura, "Wall Slip Corrections for Couette and Parallel Disk Viscometers," Journal of Rheology, vol. 32, no. 1, p. 53, 1988. [8] D. Leighton and A. Acrivos, "The Shear-Induced Migration of Particles in Concentrated Suspensions," Journal of Fluid Mechanics, vol. 181, pp. 415-439, 1987. A. Shauly, A. Wachs, and A. Nir, "Shear-induced particle migration in a polydisperse [9] concentrated suspension," Journal of Rheology, vol. 42, no. 6, p. 1329, 1998. [10] J. F. Morris, "A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow," Rheologica Acta, vol. 48, no. 8, pp. 909-923, Mar. 2009. [11] D. M. Husband, L. A. Mondy, E. Ganani, and A. L. Graham, "Direct measurements of shear- induced particle migration in suspensions of bimodal spheres," RheologicaActa, vol. 33, no. 3, pp. 185- 192, 1994. [12] M. K. Lyon and L. G. Leal, "An Experimental Study of the Motion of Concentrated Suspensions in Two-Dimensional Channel Flow. Part 2. Bidisperse Systems," Journal of Fluid Mechanics, vol. 363, pp. 57- 77, 1998. 148 [13] J. E. Butler, P. D. Majors, and R. T. Bonnecaze, "Observations of shear-induced particle migration for oscillatory flow of a suspension within a tube," Physics of Fluids, vol. 11, no. 10, p. 2865, 1999. 149 Chapter 5 Conclusion and Future Work 5.1 Conclusion The previous 4 chapters have presented results and discussion on the links between semi-solid electrode microstructure and electrochemical performance; key conclusions are summarized here, with reference to the figures and discussions in the main chapters. As introduced in Chapter 1, there are four electrochemical performance metrics that are the focus of microstructure engineering, energy density, power density, roundtrip efficiency, and cycle life. These metrics are addressed below. 5.1.1 Energy Density Maximizing the energy density translates to maximizing the volume fraction of lithium storage compound present in the semi-solid electrode. The results of Chapter 3, particularly the tomographic images in Figures 3.4 and 3.5 and the SEM image in Figure 4.14a, demonstrate that micron-scale LCO particles act as a solid suspension in a carbon black gel matrix. Based on this finding, lessons from particle suspension rheology can inform routes to maximizing the loading of lithium compounds. Monodisperse spheres stay fluid in suspension up to a glass jamming transition at 58 vol%, while a bimodal distribution of spheres can stay fluid up to 75 vol% [1]. Potentiostatic charge and discharge esults on semi-solid LCO cathodes of 40 vol% loading were presented (Figure 1.7b), demonstrating that near-theoretical charge capacity utilization is attainable with the proper amount of conductive carbon black. The challenges of increasing the LCO loading further are two-fold. First, the viscosity increases with increasing LCO loading (Figures 1.10a and 1.10b). As the loading approaches a glass transition, the 150 viscosity is expected to diverge upwards [1][2]. Furthermore, Figure 3.10 shows that increasing amounts of LCO decrease the overall electronic conductivity of the electrode for a fixed gel matrix composition. Increasing the LCO loading requires increasing the carbon black loading to maintain an acceptable electronic conductivity, compounding the viscosity increase. One design criterion to achieving high loadings of lithium compounds is to separate the length scales of the lithium storage compound and the carbon additive so that the carbon additive can occupy the interstitial volume of the larger lithium storage compounds, thus minimizing volume exclusion effects between the two phases. 5.1.2 Power Density and Electrochemical Efficiency Power density and electrochemical efficiency are grouped together, as they both relate to minimizing the electrochemical impedance of a semi-solid electrode. Contributions to electrochemical impedance are discussed in section S.2. Microstructural considerations can affect the ion mass transport, electron transport, interfacial reaction rate, and solid phase mass transport. Lithium compounds suspended in DLCA gels formed by carbon black dispersed in electrolyte (Chapter 2 and 3) are well suited for facile ion transport. The large electrolyte volume fraction and highly interconnected pathways present in an open, gel matrix allow for the low impedance movement of lithium ions in solution. Figure 1.9 confirms that the contribution to the cell impedance from ion mass transport remains low despite increases in carbon black content in a semi-solid electrode. The interfacial reaction and solid phase mass transport contributions to cell impedance can be lowered by using smaller LCO particles. Smaller particles have a higher specific surface area, lending to a higher aggregated interfacial reaction rate. The radial diffusion distance from the particle surface to core is also shortened, reducing solid phase mass transport limitations. Decreasing particle size also decreases the electronic conductivity of electrodes, lending to an increase in electrochemical impedance which runs counter to the aforementioned effects. Figure 3.11 plots how a smaller particle size LCO 151 sample consistently demonstrates a lower electronic conductivity across multiple volume fractions. A hypothesis is presented in the discussion section of Chapter 3 that attributes this conductivity depression on the geometric frustration of the carbon black gel network. Returning to Figure 1.9, it is clear that the largest reductions in cell impedance come from increases in the electronic conductivity of the electrode. Figures 3.9 and 3.10 show that the electronic conductivities of both the LCO particles and carbon black gel affect the overall electrode properties, with the latter having a more pronounced effect. The largest gains in electronic conductivity should be achievable with engineering of the gel. The simplest approach is to increase the loading of carbon black, and the electrochemical performance improvements of this approach are seen in the reduced cell impedance (Figure 1.9) and increased charge capacity utilization (Figure 1.8). The discussion in Chapter 2 posits that the electronic conductivity is limited by the inter-aggregate tunneling junctions in a carbon black gel. Minimizing the number of series junctions with larger or higher aspect ratio additives is another potential approach to increasing the gel conductivity; this tact is discussed in the future work section below. Carbon coating the LCO particles, or other lithium storage compounds, is a way to increase the effective electronic conductivity of the storage particles. This is also discussed further as future work. Interfacial charge transfer resistances between the metallic current collector and semi-solid electrode can also lead to increased electrochemical impedances. Particle depletion at the current collector-electrode interface cause by flow lead to high electron charge transfer resistances as seen in Table 4.5. This wall slip effect is observed as a significant contributor to the electrochemical cell impedance in a SSFC in Figure 4.12. Using roughened current collector surfaces is shown to mitigate wall slip and reduce the electrochemical impedance in a flow cell. 5.1.3 Device Efficiency 152 Aside from electrochemical sources of inefficiency, pumping losses are the main concern for device efficiency. The flow geometry, flow rate and viscosity of the semi-solid electrode determine the hydrodynamic losses from SSFC operation. Semi-solid electrodes were shown to function under both continuous flow (Figure 1.6) and stationary conditions (Figures 1.7a and 1.7b). It is advisable to flow the semi-solid electrode through reaction channels with length scales of under 1 mm to minimize charge transport impedance contributions. Flowed very slowly in a stoichiometric or intermittent manner, the calculated pumping losses are below 1%, making these operating modes preferable to rapid recirculation. Slow flow also mitigates particle segregation in the electrode, as discussed below. Further reductions in pumping losses can come from engineering low viscosity electrodes and promoting wall slip for flow outside of the reaction cell. Engineering low viscosity electrodes is a difficult endeavor, as high energy density and low impedance electrodes require a high loading of lithium storage compound and carbon black, both of which contribute to the electrode's viscosity. High aspect ratio conductive fillers such as carbon nanotubes may allow for high conductivity gels of low viscosity; this possibility is discussed further below as future work. Wall slip inside the reaction cell is undesirable for its contribution to electron transport impedances. Outside of the reaction cell, using smooth, inert surfaces such as PTFE can promote wall slip and lower the pressure head required to flow the viscous semi-solid electrodes. 5.1.4 Cycle Life Microstructure evolution by particle sedimentation and flow-induced particle segregation can be detrimental to a semi-solid electrode's cycle life. The large density mismatch between electrolyte and lithium storage compound, and the non-colloidal size of the latter, leads to an instability against settling (Figure 3.2). The yield stress of the carbon black gel matrix is able to stabilize the LCO against 153 sedimentation (Figure 3.4) so long as the gel's yield stress exceeds the stability criterion presented in Equation 3.1. Segregation of the carbon black and LCO phases, driven by the shear rate gradients present in tube flow, is demonstrated by electron microscopy in Figures 4.14a-d and 4.15a-d. The effect of this segregation is to decrease the electronic conductivity of the semi-solid electrodes by over an order of magnitude, depending upon the rate of flow and accumulated displacement (Figure 4.13). The segregation decreases the accessible charge capacity under electrochemical cycling as LCO particles are electronically isolated from the current collector (Figures 4.16a and 4.16b). A combination of slower flow and ultra-sonic disruption is shown to mitigate the segregation effect (Figure 4.14d) and preserve high electronic conductivities under large accumulated flow displacements (Figure 4.13). Chapter 5.2 Future Work Promising avenues for additional work have presented themselves over the course of this work, but limitations on the scope of this thesis have left them unexplored. These ideas are summarized here as future work. Three areas that are of particular interest are low dimensionality conductive additives, surface coating of lithium storage compounds, and passive mixing of flowing electrodes. 5.2.1 Carbon Nanotubes as Conductive Additives Chapter 2 discussed how the inter-aggregate tunneling junctions determine the macroscopic electronic conductivity of the carbon gel network. Decreasing the number of series junctions that must be surmounted can increase the conductivity of a gel without the associated increase in yield stress seen in Chapter 2. One way to achieve this is to increase the size of the carbon filler. Yet the filler must simultaneously remain colloidal in nature to undergo rapid agglomeration to form spanning gels. These 154 two limitations can be circumvented by using lower dimensionality carbon additives such as carbon nanotubes or graphene sheets. A sample of MWCNT manufactured by Nanostructured & Amorphous Material, Inc. demonstrates the appeal of low dimensionality additives. Exploratory experiments with multi-walled carbon nanotubes (MWCNT), a few microns in length, have shown that they form high conductivity gels with lower yield stresses than carbon blacks (Figure 5.2). Not only do the MWCNT achieve higher absolute values of electronic conductivity, they do so at yield stresses and viscosities that are at least an order of magnitude lower than the equivalent carbon black gels. Figure 5.1. An SEM image of the NanoAmor MWCNT, provided by the manufacturer [3]. The difficulty in homogeneously dispersing MWCNT in a semi-solid electrode presents a challenge to their use. While a microscopically heterogeneous dispersion of MWCNT can effectively transport charge across macroscopic distances, a semi-solid electrode requires the local delivery of electrons to the LCO particles. As seen in Figure 5.3, the MWCNT have a strong affinity towards agglomeration and form dense nests. Figure 5.4 shows how these agglomerates then lead to a poor distribution of the conductive additive. 155 Research into processing methods to obtain a better dispersion of MWCNT could produce higher conductivity, lower viscosity electrodes. Another approach is to mix MWCNT with carbon black. The MWCNT can provide high conductivity pathways to transport charge across large distances, while a well dispersed carbon black phase can deliver charge locally to the redox reaction sites. Chevron TIMCAL C45 100 - 10 0.1 * NanoAmor MWCNT ~ 1E-5 IE-6 b Ketjunblack EC-600JD - a A Shawingan 1E-3 IE-4 Conductivity (S/cm) 1E-2 1E-1 ioooo low1000 ~100 - 10 1E-5 1E-6 1E-4 1E-3 1E-2 1E-1 Conducvity (S/cm) -44 10000 - 1000 - 100. - 5 -- - - 0 10 1E-6 1E-5 1E-4 1E-3 Conducdvity (S/cm) 1E-2 1E-1 156 Figure 5.2a-c. The correlation of yield stress, elastic modulus, and shear viscosity with electronic conductivity. The data of Figure 2.10a-c is expanded with the addition of MWCNT. The MWCNT form high conductivity gels that of lower yield stress, elastic modulus, and viscosity than the three grades of carbon black. Figure 5.3. A secondary electron SEM image of a semi-solid electrode of 30 vol% LCO in a 5 wt% NanoAmor MWCNT-EC electrolyte gel. The semi-solid electrode is frozen for imaging. The MWCNT are seen agglomerating into dense nests. 157 Figure 5.4. The same sample as Figure 5.3, imaged at a lower magnification with a backscattered electron detector. The LCO particles appear as white and the MWCNT as gray. The agglomeration of the MWCNT into nests creates a heterogeneous microstructure with patches of electronically isolated LCO. 5.2.2 Conductive Surface Coatings on Lithium Compounds Another topic for future work is the application of surface coatings on lithium storage compounds to improve the electronic conductivity of semi-solid electrodes. In particular, carbon coating of lithium compounds is an attractive avenue towards a low impedance electrode. Figure 3.10 demonstrated how increasing the bulk electronic conductivity of LCO led to higher overall electrode conductivities. A thin, conductive, carbon coating on the LCO particles could further improve the transport of electronic charge across the particles. The carbon coating would have an additional benefit in coupling the LCO particles into the carbon black gel network. As chemically identical species, in this case graphite, always feel attractive van der Waals forces in the presence of an intermediate dielectric 158 medium, the carbon coating would facilitate the transfer of charge from the gel network into the LCO particles [4]. This approach would be particularly important for other lithium chemistries where the carbon black has a repulsive van der waals interaction with the uncoated material. A high performance coating should be engineered to have a high graphitic content for a high electronic conductivity. At the same time, the coating must remain thin and porous in order for lithium ions to rapidly diffuse across the coating. The processing conditions of Ketjenblack may provide lessons for an effective coating as Ketjenblack pairs a high graphitic content with a large degree of meso and micro-porosity. 5.2.3 Static In-line Mixers A third area for additional research is in methods for mitigating shear-induced segregation. As seen in Chapter 4, the shear gradients present in tube flow drive the segregation of particles by size. This segregation was shown to lower the electronic conductivity of the semi-solid electrodes and reduce the accessible charge storage capacity under electrochemical cycling (Figures 4.13, 4.16a, and 4.16b). Ultra-sonic disruption during flow was shown to mitigate the segregation (Figure 4.14d) and maintain high electronic conductivities. The practical difficulties of implementing an active disruption mechanism, and the associated parasitic power consumption, make ultra-sonic disruption unattractive as a form of segregation-control. Other fields, particularly polymer processing, have developed passive methods of mixing high viscosity fluids during tube flow. Two such commercial mixers are shown in Figures 5.5a and 5.5b. The incorporation of these static mixers into the SSFC device may provide a much simpler method of maintaining homogeneity in semi-solid electrodes under flow. The static mixers move material radially inwards and outwards, thus preventing material from experiencing a shear rate gradient for prolonged amounts of time. While this area of research might be considered device engineering, rather than 159 materials engineering, it does have the potential to greatly prolong the cycle life of semi-solid electrodes under flow. Figures 5.5a (left) and 5.5b (right). Two examples of static mixing geometries commercially available to mitigate flow-induced segregation in fluids processing. Courtesy of StatMixCo-USA [5]. 160 Chapter 5 References [1] H. A. Barnes, J. F. Hutton, and K. Walters, An Introduction to Rheology. Elsevier Science, 1993. [2] R. G. Larson, The Structure and Rheology of Complex Fluids. Oxford University Press, USA, 1998. [3] "NanoAmor Conductive Additive MWCNT Product Data Page.". [4] J. N. Israelachvili, Intermolecular and Surface Forces, Third Edition, 3rd ed. Oxford: Academic Press, 2010. [5] "StatMixCo USA website." http://www.statmixco-usa.com. 161 Supplemental Information S.1 Solid Electrolyte Interphase (SEI) Solid electrolyte interphase (SEI) is a layer that may form on any solid surface in an electrode, such as the lithium compound, conductive additive, or current collector, as a result of electrolyte decomposition. SEI may occur on the cathode or anode of an electrochemical couple, but the phenomenon is typically of more concern on the anode in a lithium-ion battery. Reduction of the electrolyte at the anode typically leads to solid deposits of lithium salts (LiF, Li 2 CO 3 , and others) as well as polymeric material 11][2]. SEI products are typically porous, allowing for the passage of ions, but are electronic insulators. The formation of SEI consumes not only the electrolyte solvent, but electrochemically active lithium species as well, leading to irreversible loss of capacity in a battery. Commercial lithium-ion electrolytes typically include additives to create stable, self-terminating SEI layers to avoid continued capacity fade beyond the first formation cycles. SEI forms from the thermodynamic instability of the organic electrolyte at anode potentials. The solid phase surface characteristics may kinetically accelerate or impede the formation of SEL. Graphite, a common anode material, is observed to form an SEI around 0.7V vs lithium metal. Gold is shown to reduce common alkyl carbonate solvents at much higher potentials of 1-1.4V vs lithium [3]. In a semi-solid electrode, the electrical contacts are formed by inter-particle bonds are broken and reformed during flow. Coating of lithium compounds, conductive additive, or current collector with a insulating film is detrimental to the cell impedance. S.2 Contributions to the Cell Impedance A very simple interpretation of electrochemical impedance sources is presented here, more complete discussions may be found in literature [4][5]. There are 4, main contributions to cell 162 impedance, ion transport in the electrolyte, electron transport through the solid network, solid-phase mass transport of the intercalated specie, and the interfacial reaction. Ion transport in the electrolyte phase is characterized primarily by the ionic conductivity (S/cm). Alkyl carbonate lithium-ion electrolytes typically have values of 0.005-0.01 S/cm. The ionic conductivity is affected by the local lithium concentration, with a maximum occurring in the 1M-2M concentration range [6]. The overall impedance contribution of ion transport is affected by the volume percentage of electrolyte phase, the tortuosity of the electrolyte phase, local conductivities, and the length scale of transport. Electronic conductivity in the solid phase is fairly analogous to ionic conductivities, except the local electronic conductivity is practically independent of the local electron concentration. On the other hand, the local electronic conductivity is much more sensitive to the local microstructure. The overall impedance contribution due to electron transport may be broken down to a series of resistances. The contribution of conduction from the load, through conductive leads, and across the metallic current collector is typically negligible. Electrons must then transfer across the current collector-electrode interface, a process that can be quite resistive as seen in discussions on lubrication layers in Chapter 4. Once in the electrode, the electrons must travel across the network of conductive particles to reach the redox reaction sites, located at the interface of lithium storage compounds and the electrolyte. The bulk conductivity of semi-solid electrodes studied in this work vary widely from 0.00001 S/cm up to 0.01 S/cm. The interfacial reaction rate is perhaps the most complex of the contributions to impedance. The area-specific reaction rate is a often expressed with Butler-Volmer functional dependence on the local over-potential (applied potential minus the equilibrium potential), temperature, and the local concentration of electrochemically active specie (ie lithium) in the electrolyte and solid phases. The area-specifc rate multiplied by the specific surface area yields the absolute rate, or inversely the impedance, of the interfacial reaction. Finally, the electrochemically active specie (ie lithium) must 163 diffuse in and out of the lithium storage compound. The mass transport is characterized by the lithium diffusivity. A) B) C) D) Electrolyte Phase Mass Transport Solid Phase Electron Transport Interface Reaction Solid Phase Mass Transport Li+ e- Lid Li+ Electrolyte Phase Figure Solid Phase 5.1. A schematic of the basic contributions to cell impedance. S.3 Carbon Black Background Information Carbon blacks are a class of material produced from the partial combustion or thermal decomposition of a hydrocarbon feedstock. While a vast diversity of specific properties exist for the numerous grades of carbon black available, they are typically sub-micron in size and have fractal structures composed of roughly spherical particles, of mixed graphitic and amorphous carbon content, fused into aggregates. A transmission electron microscope (TEM) image of a typical carbon black aggregate structure, as measured by Ehrburger-Dolle and colleagues, is presented in Figure 2.1a [7]. This fractal aggregate structure sets carbon black apart from other types of conductive additives such as carbon nanotubes, carbon fibers, graphene sheets, or graphite powder. One of the primary classifications for carbon black grades is the manufacturing process. The vast majorities of carbon blacks are manufactured via the furnace process, and are thus named furnace blacks [8]. Oil undergoes partial combustion in a natural gas fed flame to yield a fractal aggregate. Post processing in an oxidizing environment may be employed to remove the non-graphitic carbon content 164 from the carbon black. Another relevant manufacturing process is the acetylene black process. Here, the exothermic thermal decomposition of an acetylene feedstock provides a self sustaining reaction that also produces a fractal aggregate. The very high temperatures of the acetylene black process often lend to higher graphitic content in the product. Other, less relevant processes include the lamp black, channel black, and thermal black processes [8][9]. With the diversity of carbon blacks available, engineers have developed a set of properties with which to characterize a given grade. The major identifying traits are the primary particle size, porosity, graphitic content, aggregate structure, and surface chemistry [8][9]. A roughly spherical primary particle, typically ten to fifty nanometers in diameter, forms the building block of the carbon black structure. The particle primary particle size affects a carbon black's surface to volume ratio, thereby controlling the extent to which surfaces forces dominate over bulk interactions. The preferred method to characterize particle size is high resolution imaging by methods such as transmission electron microscopy (TEM). Microporosity (pores under 2 nm) and mesoporosity (pores between 2nm and 50nm) may be present in the primary particle structure of the carbon black. These pores develop when the carbon black is placed in oxidizing environments where the non-graphitic content of the carbon black is removed. The core of the particle is most abundant in amorphous content and is most susceptible to removal. The presence of micro and mesoporosity reduces the bulk density of carbon blacks, reducing the mass of additive required to obtain a given conductivity. Porosity is identified by comparing adsorption data based on differently sized molecules. Typically, nitrogen BET measurements are compared against results using a larger molecule such as cetyltrimethyl ammonium bromide (CTAB). Whereas nitrogen may infiltrate the microporosity, CTAB cannot. A nitrogen:CTAB adorption ratio 165 greater than 1 points to a porous primary particle. Figures S.2a and S.2b displays high resolution TEM images of a non-porous and porous carbon black, as measured by Taniguchi and his colleagues [10]. Figure S.2a (left) and S.2b (right). Figure S.2a is a TEM image of an acetylene black produced by the Streams Chemical Company. The specific surface area of 109 m 2/g determined by nitrogen adsorption qualifies it as a relatively low porosity carbon black. Figure S.2b is a TEM image of Ketjenblack EC-600JD from Akzo Nobel Polymer Chemicals, LLC. The high specific surface area of 1453 m 2/g attests to a high degree of porosity in the particles, which is observable under the TEM. Both images are borrowed from the work of Taniguchi and colleagues [10]. The relative graphitic content of a carbon black grade affects the intrinsic conductivity of the material. Synthesis conditions and post treatments affect the graphitic versus amorphous carbon content of a carbon black. Studies using x-ray diffraction methods can identify the abundance of graphite in a sample. A key property, and one of the most difficult to quantify, is a carbon black's aggregate structure. The term structure is employed in describing the degree to which primary spherical particles are fused to construct a fractal aggregate. While the primary particles in a carbon black are tens of nanometers in diameter, the aggregates typically have effective diameters of a few hundred nanometers. A high structure carbon black has an aggregate morphology which involves a large number of primary particles 166 (typically 100-300 [9]) arranged in an open and branched geometry. Conversely, a low structure carbon black has fewer, or more densely, clustered particles leading to a denser aggregate. As a high structure carbon black can fill an effective volume with much less solid material, it is preferred as a conductive additive to achieve percolation at a lower loading. Figure 2.1b illustrates how a high structure carbon black may effectively occupy a large occluded volume due to its geometry. The structure of a carbon black may be directly analyzed with high resolution microscopy techniques. Often, a quicker method of di(n-dibutyl) phthalate (DBP) oil absorption is employed. The ability of a carbon black sample to absorb the large molecular weight oil is related to the degree of internal void space present in an agglomerate, and hence serves as a proxy measure for the degree of structure present in a carbon black. Finally, processing conditions impart carbon blacks with a specific surface chemistry. The surface chemistry affects the degree to which a carbon black will disperse within a host matrix such as a polymer melt or electrolyte solvent. The surface chemistry also affects the conductivity of a carbon black composite. Surface groups can create electron trap states. The adsorption of molecules that interact with surface groups can also prevent the approach of neighboring aggregates, thus preventing the transfer of charge across aggregates. Acid/base titration, IR spectroscopy, and x-ray photoelectron spectroscopy are common methods of analyzing a sample's surface chemistry [8][9]. S.4 Liquid-Lithium Ion Electrolyte Background Information The two, basic components of the liquid electrolytes used in this study are a solvent and salt. As most lithium ion chemistries operate at a voltage above 3 volts, non-aqueous solvents are used to avoid the hydrolysis. The desire to enhance ion mass transport within the electrolyte encourages the use of a solvent or solvent blend, with a combination of a low viscosity and large dipole moment for enhanced ion mobility and salt solubility, respectively. Blends of cyclic and linear alky carbonates are most commonly used. In addition to thermal stability, solvents must also be electrochemically stable against 167 reducing conditions at the anode and oxidizing conditions at the cathode. Electrochemical stability is of utmost importance, as the electrolyte solvent often decomposes into a solid, electrically insulating formation on the electrode, termed a solid-electrolyte interphase (SEI) [11]. In the SSE architecture, any charge or mass transport inhibiting SEI on the lithium storage compounds can lead to the blocking of essential reactants for the electrochemical reactions. Additives are often included in the electrolyte to stabilize the solvent against continuous decomposition. Lithium salts are dissolved in the electrolyte at high concentrations, typically at values above 1 molar, to maximize the conductivity of the electrolyte. The anionic counter ion is chosen to maximize the transference number of the electrolyte and to address concerns of electrochemical stability. Extensive literature exists on the detailed consideration for electrolyte design and readers are encouraged to consult the referenced work for a more complete discussion [12][13][14]. The electrochemical constraints placed on the electrolyte do not offer much freedom in engineering the electrolyte for its rheological role as a host liquid in a SSE. S.5 DLCA - Diffusion Limited Cluster Agglomeration 2 The advent of concepts fundamental to fractal geometry by Mandelbrot in 1975 have led to its application in many areas of the physical sciences [15]. One such area is the field of aggregation and growth phenomena. The decades following Mandelbrot's pioneering work saw the development of models for growth phenomenon via laboratory and computational experiments, as well as from a theoretical point of view [16] [17][18][19][20]. The model of diffusion limited cluster aggregation (DLCA) is of particular interest in this study. The acronym DLCA refers to Diffusion Limited Cluster Aggregation in the literature. The presence of carbon black aggregates may cause confusion in terminology, as the term aggregate is used to describe two distinct structures. Therefore the agglomeration of carbon black aggregates into flocs by a diffusion limited cluster mechanism will be renamed Diffusion Limited Cluster Agglomeration in this work. 2 168 The simpler Diffusion Limited Agglomeration (DLA) mechanism is one where Brownian particles diffuse until they collide. Upon collision, their interparticle attractions are strong enough to yield an immediate and thermally irreversible bonding. Repeated collisions grow clusters. As a cluster grows, it develops radial tendrils where new particles add to the cluster's mass. As the particle interactions are perfectly sticky, approaching particles cannot penetrate into the core of the growing clusters without sticking to some portion of the extended tendril. Therefore as the cluster grows, it develops a open, fractal structure. One of the hallmark traits of a fractal structure is a density which decreases with cluster size. (p ~ r(D-d) Equation S.1. The density of a fractal, p, scales as its size, r, raised to a non-positive exponent. D is the object's fractal dimension and d is the Euclidean dimension that the object occupies. DLCA adds an extra mechanism of growth to DLA; super-clusters grow by the sticking of two or more sub-clusters. The cluster-cluster interactions can create large internal voids on the scale of the clusters themselves. As a result, the fractal dimension of the DLCA mechanism in three-dimensional Euclidian space (1.8) is lower than that of the DLA mechanism (2.5) [16]. Lin and colleagues have demonstrated that the DLCA process is a universal mechanism which may be applied to a variety of colloidal systems of diverse chemistries [19]. A close analogue to the DLCA model is the Reaction Limited Cluster Agglomeration (RLCA) model. The two differ in the crucial element of the interparticle potential. DLCA relies on a purely attractive interparticle potential such that diffusing particles collide and then stick with a probability of unity. If a thermally activated energetic barrier exists to the joining of the particles, then the sticking probability is no longer unity. Instead, one may model the probability with a Boltzmann distribution. The physical implication for the aggregation process is that an impinging particle is now able to sample 169 multiple sites before joining the cluster. This leads to an increased probability of a particle finding its way beyond the outer tendrils of a cluster and into the core of a cluster. The result is a denser cluster, and as clusters interact a more compact overall microstructure. As a result the fractal dimension, in three dimensional Euclidian space, of the RLCA model (2.1) is greater than that of the DLCA model (1.8) [19]. For a comprehensive review of concepts of fractal geometry and their applications to growth phenomenon, readers are encouraged to consult a thorough treatment by Vicsek [16]. In applying the DCLA model to solid dispersion, there are two, primary criteria. The first is that the particles must be colloidal such that their motion is dominated by Brownian forces. The second is that the particle-particle interactions must be attractive, thermally irreversible, and lack any energetic barrier that is relevant on the energetic scale of thermal fluctuations [16]. Under the influence of a DLCA mechanism, there are unique structural features that should arise in a strongly attractive colloidal system. Unlike a random distribution of particles, where percolation requires a volume filling of 16%-18%, the attractive interactions in a DLCA system creates an ordered microstructure which achieves a spanning network at a much lower loading. In fact, because the microstructure is fractal, and thus the density of the structure decreases with increasing domain size (Equation S.1), the percolation threshold is set by the length scale of interest. In a cluster growth mechanism, larger space-filling clusters lead to lower percolation thresholds. The cluster-cluster agglomeration will also lead to self similar structures on multiple length scales. These clusters form the building blocks of a microstructure which includes voids on every length scale, from the particle scale up to the domain boundary scale. A particulate gel is formed if the clusters can agglomerate into a spanning structure before gravitational forces cause sedimentation. The properties of this gel will depend on the quality, density, and homogeneity of the inter-aggregate bonds formed in the DLCA process. Those in turn depend upon the interparticle potential, solids loading, and 170 processing conditions, respectively. A DLCA gel should maintain a stable, static structure at rest, although thermal relaxation and gravitational compaction may age the structure of the gel over an extended period of time Understanding of the mechanism of gel formation in the carbon black - electrolyte system allows for the explanation of many unique features of the material. Furthermore it allows us to posit the engineering constraints present in the system and illuminate methods of material optimization. Here we tie together known properties and observed results of the carbon black gels with expectations of the DLCA model. S.6 Derjaguin, Landau, Verwey, and Overbeek (DLVO) Theory of Colloidal Interactions Energy bamier repuon b Secondary rinmrum WmW Primay minimum W 1ga 10 -- Dstance, O(nm) 0 W S Total a W b C 0 / Avand er Waas Utraction I I S Increasing sal, decreasing swdace PoW"n:9 = Figure S.3. A energy diagram depicting the two particle potential predicted by DLVO theory, borrowed from Israelachvili [21]. 171 The basic principle of DLVO theory rests on the combined effect of two, dominant interparticle forces in colloidal systems. For two particles of identical chemistry, the van der Waals interactions are always attractive and lead to particle agglomeration. Conversely for two particles of identical chemistry, the long range electrostatic interactions that arise from charged surfaces are always repulsive. Their relative strengths at various interparticle separations lead to a variety of possibilities in terms of attractive and repulsive forces. van der Waals forces arise when spontaneous fluctuations create a dipole moment on one particle that, in turn, induces a dipole on a nearby particle. In the case of two particles interacting through a common medium, such as a solvent or electrolyte, these interactions are always attractive. In colloidal systems without repulsive, stabilizing forces, van der Waals attractions lead to spontaneous agglomeration. The addition of a salt to a solvent, to create an electrolyte, generally has a minor effect on the van der Waals interaction. One common repulsive force is the electrostatic, charged double layer interaction. Particles that develop a net surface charge in a host medium will also from a diffuse layer of counter-ions that act to restore net charge neutrality. These diffuse layers of counter-ions surrounding neighboring particles will repel one another. The concentration of ions in solution has a dramatic effect on the electrostatic repulsion. A higher concentration of ions is able to more effectively screen long range electrical fields. The effect of the concentration of ions in solution is demonstrated in the lower-right inset of Figure S.3. Curve a is the case where the salt concentration does not screen the electrostatic repulsion; bringing two particles into close proximity requires work be done on the particles. At very small interparticle separations, the van der Waals attraction will ultimately win out as it scales more strongly with the separation distance. In curves b and c, the increasing salt concentration creates a secondary minimum in energy. The long range stabilization is screened slightly such that the van der Waals 172 attraction initially leads to an attractive force. The partial screening then results in a energy barrier to further approach of the particles. This secondary minimum effect is used to create stable colloidal dispersions. Further screening by increased salt concentration eventually reduces electrostatic effects to the point where particles will spontaneously agglomerate under the influence of van der Waals attractive forces. S.7 Shih's Theory on the Scaling of Elastic Properties of Colloidal Gels In Shih's theory, a gel is modeled as a close packed collection of flocs [22]. In the DLCA mechanism, these flocs correspond to the largest clusters obtainable before the cluster-cluster growth mechanism terminates due to sample domain restrictions. The elastic properties within a floc are determined by an elastic backbone of a fractal dimension x, which is modeled as a collection of springs. Larger flocs display weaker elastic moduli. One can understand this conceptually due to the basic relation of decreasing density in a fractal object with increasing size (Equation S.1). The primary effect of solid phase concentration on elastic moduli is to reduce the largest floc size. A higher concentration of solids leads to the more rapid impinging of clusters against neighboring clusters, thus terminating cluster growth at smaller sizes. Based upon this model, a relationship between elastic modulus and solids loading is given as Equation G' -p S.2 for a three dimensional system. 3+X/-D Equation S.2. The power law scaling behavior predicted for the elastic modulus of a collection offractal clusters. The elastic modulus, G', scales as the solid volume fraction, q5, raised to a function of the elastic backbonefractal dimension, x, and the overall gelfractal dimension, D [22]. In order to solve for the fractal dimensions of the gel microstructure, D, and the separate elastic backbone fractal dimension, x, one more equation is required. Shih introduces the idea that the limit of 173 linearity defines the strain at which bonds along the elastic backbone begin to break. Based on the argument that the weakest bond in a floc is independent of floc size, but that the force imposed on a floc is size dependent, Shih develops the following relationship between the limit of linearity, y., and solids loading: Equation S.3. As part of the same analysis involved in Equation S.2, Shih finds that the limit linearity, y, scales with a power law on the solid volume fraction. One can calculate the fractal dimension by fitting the power law exponent of both the elastic modulus and limit of linearity, with respect to the solids volume fraction. Simultaneously solving two equations will yield values for the overall fractal dimension and the elastic backbone dimension. S.8 Stabilization of Particles with a Yield Stress Fluid A brief summary of the theoretical approach outlined by Roussel is presented here [23]. Similar results are obtained by others [24][25]; Roussel's approach is outlined because of its clear and intuitive presentation. The drag force on a spherical particle of diameter, d, moving at a particle velocity, V,, in a fluid of Newtonian viscosity, p, is given by: F = 37rdpV Equation S.4. The drag force acting on a sphere settling in a Newtonian fluid. This particle causes a shearing of the fluid in its surroundings. One may approximate the shear rate imposed on the fluid as the particle diameter divided by the velocity, modified by some scaling constant, k. The value of this constant is regarded with some uncertainty, but is generally found to be near unity by experiment. 174 kV Y= d Equation S.5. The approximate, average shear rate exerted on the surrounding fluid by a moving sphere. Substituting the Newtonian viscosity in Equation S.4 with the viscosity of a general yield stress fluid and imposing a steady state condition where the drag force equals the buoyant force results in the following expression for a spherical particle settling at a constant velocity in a yield stress fluid. The function f(y) refers to the as-yet unspecified dependence of fluid viscosity on the shear rate. The functional form is left general and may be substituted by the relevant behavior of the specific fluid. k d(p, - pr)q 18p= (k V Tyield + f Equation S.6 The steady state condition for a spherical particle moving through a yield stress fluid The final step is to then consider the limit as the settling velocity approaches zero. As f(O)=O in this case, the term on the right also approaches zero and the yield stress criterion is simply: TyjeLd -kd(ps - pf)g 18 Equation S.7. The yield stress criterion for a spherical particle stably suspended in a yield stress fluid matrix. S.9 The Effect of Pre-shear on Semi-solid Electrode Measurements Sample pre-shear is part of most rheological protocol, as it improves measurement reproducibility by eliminating variations in a sample's shear history that arise from loading into the rheometer. It is particularly relevant to gels and suspensions which are sensitive to its shear rate 175 history. In Chapter 2, pre-shear is employed in all carbon black gel measurements. Pre-shear is excluded from the measurement protocol for the electrodes studied in Chapter 3. The intent is to measure the structure and properties of the electrodes, as prepared. Figures S.4 and S.5 show that the imposition of shear on these electrode samples produces significant and irreversible changes in their structure and properties. In Figure S.4, a sample of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel is subjected to shear rate controlled viscometry experiment immediately after loading. P220 grit sandpaper on 20 mm diameter paralle plates mitigates effects of wall slip. A extended stress plateau appears as the shear rate is increased across 2 orders of magnitude, from 1 1/s to 100 1/s. This plateau behavior may be attributed to shear banding effects, though banding has not been directly observed for this system [26][27]. Upon subsequent sweeps through shear rates in the range of 0.1 1/s to 500 1/s, the electrode demonstrates significantly lower viscosities. Examining the low-rate limit shows shear stress plateaus which indicate a decrease in the electrode yield stress from an original value of 260 Pa to 1 Pa after shear. -- 1000 Start 10 0.1 0.1 1 10 Shear Rate (1/s) 100 1000 Figure S.4. Shear rate controlled flow curves of 30 vol% LCO in a 7 wt% Shawinigan black-EC:DMC gel. The initial shearing of the slurry, as the shear rate is increased from 1 to 100 1/s, displays a shear stress 176 plateau, which may be attributed to a shear banding phenomenon. Subsequent shearing of the material shows a significant decrease in viscosity. The yield stress, as taken from the stress plateau at low shear rates, decreases from 260 Pa to 1 Pa. The viscoleastic response of the same composition electrode, before and after pre-shear, exhibits the same decrease in yield stress. The comparison of viscoelastic moduli in Figure S.5 indicates a decrease in the solid-like properties of the electrode after pre-shear. The elastic modulus in the linear viscolastic regime decreases from 60,000 Pa to 2,500 Pa and the yield stress decreases from 400 Pa to 0.6 Pa. The small discrepancies with yield stress values observed from the viscometry data may be attributed to two different methods of quantifying yield stress. Pre-shear is excluded from rheological measurements because of the demonstrated alteration of the measured sample. Its intent is to increase reproducibility in measurements, but the dramatic changes in electrode properties resulting from pre-shear precludes its use. _ ----As-Loaded Elastic Modulus . 100000 10000 o 1000 . V5> 100 S A 10 A Viscous Modulus 10 fPre-Sheared Vscous Modulus. Pre-Sheared Elastic Modulus 0.01 0.1 100 10 1 Stress Amplitude (Pa) 1000 Figure S.5. Stress amplitude sweep oscillation experiment on 30 vol% LCO in a7 wt% Shawinigan blackEC:DMC gel, as loaded and after subjected to a 200 1/s pre-shear. The solid-like structure of the asloaded sample becomes much weaker after a pre-shear. The yield stress decreases by over 2 orders of magnitude and the elastic modulus decreases by over 1 order of magnitude. 177 S.10 Tomographic Cluster Identification Algorithm A custom cluster identification algorithm was developed in Mathematica (Wolfram Research, Inc.) to bin nearest neighbor voxels into uniquely labeled clusters. After binarizing a tomogram to separate the LCO phase from the background gel (see Chapter 3 Methods), the built-in Mathematica function MorphologicalComponents is applied to each horizontal layer in succession. This built-in function accomplishes the task shown in Figure S.6 in 2-dimensions. The process is started with the bottom layer and moves upward, one layer at a time. At each new layer, the cluster numbers are incremented so that duplicate values do not exist with the lower layer. For example, if layer n has clusters numbered 1204 through 34301, layer n+1 begins labeling its clusters at 34302. Once the clusters within a layer n+1 are identified and labeled, each voxel in that layer is compared against voxels directly below it in layer n. If the upper voxel has a value that is greater than the lower voxel, all voxels of that value (ie belonging to the same 2-dimensional cluster) in layer n+1 are relabeled with the voxel value from layer n. Otherwise if the upper voxel has a value that is less than the lower voxel (which may occur as entire 2-dimensional clusters are re-labeled in the aforementioned step), the voxel location and cluster ID value is tagged for review in a subsequent step. After one pass through, from bottom to top, all LCO voxels are now labeled with a cluster number. No voxel that sits directly above another has a cluster number that is greater than its lower neighbor, although the reverse condition exists. In order to remedy this condition without having to scan back and forth across the entire dataset, a second step takes a more targeted approach. In the first pass, all locations and cluster ID values were logged in which the upper voxel had a value lower than its lower neighbor. Here, those discrepancies are fixed by stepping through all of those logged cluster ID values, from lowest to highest. At each cluster ID value (which is a small subset of all of the cluster numbers present), the lower cluster (now labeled in 3dimensions) is re-labeled with the ID integer of the upper cluster. While logically convoluted and expensive in memory requirements, this approach minimizes redundant operations in the algorithm and 178 is a fast method for analyzing data. Another approach to accomplish the same task of cluster identification is a burn algorithm. Compared to the present approach, it is more memory efficient, but requires more computational time due to redundant operations. The actual Mathematica code is pasted below. Figure S.6. A 2-dimensional schematic depicting how nearest neighbor voxels are tagged with an unique integer. Corner neighbors are not considered contiguous. samplename = "A5A"; pathname="/home/bryanho/Desktop/BigDrive/SLSFeb2011/diskl/"<>samplename<>"/rec_16bit" DistributeDefinitions[samplename,pathname]; $ConfiguredKernels ParallelEvaluate[$KernellD] $HistoryLength=0; The following section takes a set of pre-converted binarized tiff images and puts them into a stack after deleting border components. The dimensions of interest cannot exceed the size of the binary dataset created in the previous section. Also be ware of the amount of memory required to hold the 3 dimensional tensor. SetDirectory[pathname] ParallelEvaluate[SetDirectory[pathname]] startx = 351; endx = 1050; starty = 351; endy= 1050; filestart = 351; fileend = 1050; fileprefix = "Binary_"<>samplename<>"_"; DistributeDefinitions[fileprefix,filestartfileend,startx,endx,starty,endy]; 179 largearray=ConstantArray[O,{filee nd-filesta rt+1,endx-startx+1,endy-starty+1}]; SetSharedVa riable[largearray]; Print [TimeUsed[]]; Parallelize[ Do[ filenum=lntegerString[i,10,4]; fullname=fileprefix<>filenum<>".tif"; A1=lmport[fullname]; A2 = ImageTake[A1,{startx,endx},{starty,endy}]; A3= ImageData[Binarize[A2,O],"Bit"]; largearray[[i-filestart+1]]=A3; ,{i,filestart,fileend}]]; Print[TimeUsed[]]; The following section requires that the binarized data set of interest be loaded into memory in the previous section. The 3D connectivity of particles is then established in a tensor called connectivity, where each element is a point in cartesian space corresponding to the voxels of the tomogram. The element has a value which corresponds to a unique particle, which pixels of the same particle sharing a value. A sweep is made layer, by layer. Certain instances of 'snaking' clusters will not be identified as a contiguous unit. The next sections will address that issue. Unprotect[Out]; connectivity = ConstantArray[O,Dimensions[largearray]]; SetSharedVariable[connectivity]; connectivity[[1]]=MorphologicalComponents[largearray[[1]],CornerNeighbors->False]; vertlist={}; TimeUsed[] vertlistvalues=Reap[ vertlist=Reap[ Do[ ClearAll[Out]; upperlayer=lowerlayer+1; if[Mod [lowerlayer,10]==,Print[lowerlayer," / ",Dimensions[connectivity] [[111," // ",TimeUsed[]]]; connectivity[[upperlayer]]=MorphologicalComponents[largearray[[upperlayer]],CornerNeighbors>False]; connectivity[[upperlayer]]+=Max[connectivity[[lowerlayer]] *largearray[[upperlayer]]; sortedlowerclusterindex=Union [Flatten [connectivity[[lowerlayer]]]]; Do[ clusternum=sortedlowerclusterindex[[clusterindex]]; lowerposlist=Position [connectivity[[lowerlayer]],clusternum]; Do[ upperposvalue=Extract[connectivity[[upperlayer]],lowerposlist[[i]]]; lf[upperposvalue>O, lf[upperposvalue>clusternum, 180 connectivity[[upperlayer]]= ReplacePa rt[connectivity[[u ppe rlaye r]], Position [con nectivity[[u pperlaye r]],u pperposvalue]->clustern um]; ,lf[u pperposvalue<clusternum, vertpos={upperlayer,lowerposlist[[i]] [[1]],lowerposist[[i]] [[2]]}; Sow[vertpos,a]; Sow[u pperposva lue,b];Sow[clustern u m,b]; ]]] ,{i,1,Dimensions[lowerposlist] [[1]]}]; ,{clusterindex,2,Dimensions[sortedlowerclusterindex] [[1]]}]; ,{lowerlayer,1,Dimensions[connectivity][[1]]-1}] ,a],b]; vertlist=vertlist[[2,1]]; vertlist=SortBy[vertlist,Extract[connectivity,#]&]; vertlistvalues=Union [vertlistva lues[[2,1]]]; vertlistdumpvalues=Complement[Union[Flatten [connectivity]],vertlistvalues]; ClearAll[largearray,A1,A2,A3,sortedlowerclusterindex,lowerposlist,vertlistvalues,Out]; connectivity >> "tempconnectivity"; vertlist >> "vertlist"; vertlistdumpvalues >> "vertlistdumpvalues"; Inserted Code. Part 1 of the cluster identification algorithm where the layers are individually labeled in 2-dimensions by the MorphologicalComponents Mathernatica function. samplename = "A14A"; pathnarme="/home/bryanho/Desktop/BigDrive/SLSFeb2011/diskl/"<>samplename<>"/rec_16bit" DistributeDefinitions[samplename,pathname]; $ConfiguredKernels ParallelEvaluate[$KernellD] Kernels[] $HistoryLength=0; SetDirectory[pathname] connectivity=<<"tempconnectivity"; The following section creates a grouped list, where coordtable holds groupings of 3D coordinates of likevalued clusters. The separate expression coordtablelegend, holds as elements the value of the cluster at the corresponding positions in coordtable. Establishing this list enables the execution of the following section without resorting to re-searching for the positions of different cluster elements at every iteration. Unprotect[Out]; ClearAll[Out]; Print["Evaluation Started // ",TimeUsed[]; 181 dim=Dimensions[con nectivity]; interval=20; coordtable={}; upper=interval; While[upper<=dim[[1]], Print[upper," // ",TimeUsed[]]; templ=Complement[Flatten[Table[{i,j,k},{i,1,interval},{j,1,dim[[2]]},{k,1,dim[[3]]}],2],Position[connectivit y[[1;;interval]],O]]; Do[ templ[[m]]=Join [templ[[m]],{Extract[connectivity,templ [[mli]]; ,{m,1,Dimensions[temp1][[1]]}]; connectivity=Drop[connectivity,interval]; temp1[[AII,1]]+=upper-intervaI; coordtable=Join[coordtable,templ]; upper+=interval; ClearAll[Out,templ];]; ClearAll[Out,connectivity]; Print["Zeros Deleted // ",TimeUsed[]]; coordtable=GatherBy[coordtable,#[[4]]&]; ClearAll[Out] Print["Elements Gathered // ",TimeUsed[]]; SetDirectory[pathname] vertlistdumpvalues=<<"vertlistdumpvalues"; Dimensions[coordtable] [[1]] delete=Reap[ Do[ If[Mod[i,10000]==O,Print[i]]; If[MemberQ[vertlistdumpvalues,coordtable[[i] ][[1,4]]]==True,Sow[i]]; ,{i,1,Dimensions[coordtable] [[1]]}]; ][[2,1]]; ClearAll[vertlistdumpvalues,Out]; delete=Partition[delete,1]; coordtable=Delete[coordtable,delete]; ClearAll[Out,delete]; Print["vertlistdumpvalues deleted"]; coordtablelegend=Reap[Do[ Sow[coordtabe[[i,1,4]]]; ,{i,1,Dimensions[coordtable][[1]]}] ][[211[[111; ClearAll[Out]; Print["Legend Created // ",TimeUsed[]]; coordtable=Drop[coordtable,None,None,-1]; 182 ClearAll[Out]; Print["4th elements deleted"]; coordtable >> "tempcoordtable"; coordtablelegend >>"tempcoordtablelegend"; Print["Unncessary Data Dropped, Data Exported. Quit Kernel"]; SetDirectory[path name]; coordtable=<<"tempcoordtable"; coordtablelegend=<<"tempcoordtablelegend"; connectivity=<<"tem pconnectivity"; vertlist=<<"vertlist"; Here, the remaining elemetns that are contiguous, yet not similarly labeled, are corrected. TimeUsed[] Unprotect[Out]; ClearAll[Out] dim=Dimensions[vertlist][[1]]; ClearAll[Out]; Print["Starting Loop"]; Do[ If[Mod[i,10000]==O,Print[i," / ",dim," // ",TimeUsed[]]]; uppervalue=connectivity[[vertlist[[i]][[1]],vertlist[[i]][[2]],vertlist[[i]][[3]]]]; lowervalue=connectivity[[vertlist[[i]][[1]]-1,vertlist[[il][[2]],vertlist[[i]][[3]]]]; ClearAll[Out] If[uppervalue<lowervalue, ctableindex=Position [coordtablelegend,lowervalue][[1]]; connectivity=ReplacePart[connectivity,coordtable[[ctableindex]] [[1]]->uppervalue]; I ClearAll[Out]; ,{i,1,dim}] TimeUsed[] ClearAll[coordtable,coordta blelegend,Out,vertlist]; connectivity >> "ConnectivityWithEdges"; connectivity[[100] //Colorize Inserted Code. 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