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. Part 2 of the cluster labeling algorithm, where vertical inconsistencies in cluster labeling
are fixed.
183
Supplemental Information References
P. B. Balbuena and Y. Wang, Lithium-Ion Batteries: Solid-Electrolyte Interphase. London: World
[1]
Scientific Publishing Company, 2004.
[2]
A. Andersson, "Surface Phenomena in Li-lon Batteries," Uppsala University, 2001.
[3]
X. Zhang, R. Kostecki, T. J. Richardson, J. K. Pugh, and J. Ross, "Electrochemical and Infrared
Studies of the Reduction of Organic Carbonates," Journal of The Electrochemical Society, vol. 148, no. 12,
p. A1341-A1345, Dec. 2001.
[4]
R. A. Huggins, Advanced Batteries: Materials Science Aspects, 1st ed. Stanford: Springer, 2008.
T. F. Fuller, M. Doyle, and J. Newman, "Simulation and Optimization of the Dual Lithium Ion
[5]
Insertion Cell," Journal of The Electrochemical Society, vol. 141, no. 1, pp. 1-10, Jan. 1994.
L. 0. Valoen and J. N. Reimers, "Transport Properties of LiPF[sub 6]-Based Li-lon Battery
[6]
Electrolytes," Journal of The Electrochemical Society, vol. 152, no. 5, p. A882-A891, May. 2005.
F. Ehrburger-Dolle, S. Misono, and J. Lahaye, "Characterization of the aggregate void structure
[7]
of carbon blacks by thermoporometry," Journal of Colloid and Interface Science, vol. 135, no. 2, pp. 468485, Mar. 1990.
[8]
J.-B. Donnet, R. C. Bansal, and M.-J. Wang, Eds., Carbon Black: Science and Technology, 2nd ed.
New York: CRC Press, 1993.
E. K. Sichel, Ed., Carbon Black-Polymer Composites: The Physics of Electrically Conducting
[9]
Composites. New York: Marcel Dekker Inc, 1982.
[10]
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.
[11]
P. B. Balbuena and Y. Wang, Lithium-Ion Batteries: Solid-Electrolyte Interphase. London: World
Scientific Publishing Company, 2004.
S. S. Zhang, "A review on electrolyte additives for lithium-ion batteries," Journal of Power
[12]
Sources, vol. 162, no. 2, pp. 1379-1394, Nov. 2006.
D. Aurbach et al., "Design of electrolyte solutions for Li and Li-ion batteries: a review,"
[13]
Electrochimica Acta, vol. 50, no. 2-3, pp. 247-254, Nov. 2004.
[14]
K. Xu, "Nonaqueous Liquid Electrolytes for Lithium-Based Rechargeable Batteries," ChemInform,
vol. 35, no. 50, p. no-no, Dec. 2004.
184
[15]
B. Mandelbrot, Les objetsfractals :forme, hasard et dimension. Paris: Flammarion, 1975.
[16]
T. Vicsek, Fractal Growth Phenomena, 2nd ed. Singapore: World Scientific, 1992.
[17]
D. A. Weitz and M. Oliveria, "Fractal Structures Formed by Kinetic Aggregation of Aqueous Gold
Colloids," Physical Review Letters, vol. 52, no. 16, p. 1433, Apr. 1984.
[18]
J. Liu, W. Y. Shih, M. Sarikaya, and
I. A. Aksay, "Fractal colloidal aggregates with finite
interparticle interactions: Energy dependence of the fractal dimension," Physical Review A, vol. 41, no.
6, p. 3206, Mar. 1990.
[19]
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.
[20]
R. Jullien, "Aggregation phenomena and fractal aggregates," Contemporary Physics, vol. 28, no.
5, p. 477, 1987.
[21]
J. N.
Israelachvili, Intermolecular and Surface Forces, Third Edition, 3rd ed. Oxford: Academic
Press, 2010.
[22]
W.-H. Shih, W. Y. Shih, S.-l. Kim, J. Liu, and
I. A. Aksay, "Scaling behavior of the elastic properties
of colloidal gels," Physical Review A, vol. 42, no. 8, p. 4772, Oct. 1990.
[23]
N. Roussel, "A Theoretical Frame to Study Stability of Fresh Concrete," Materials and Structures,
vol. 39, no. 1, pp. 81-91, Mar. 2006.
[24]
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.
[25]
Y. B. He, J. S. Laskowski, and B. Klein, "Particle movement in non-Newtonian slurries: the effect
of yield stress on dense medium separation," Chemical Engineering Science, vol. 56, no. 9, pp. 2991-
2998, May. 2001.
[26]
G. Ovarlez, S. Rodts, X. Chateau, and P. Coussot, "Phenomenology and physical origin of shear
localization and shear banding in complex fluids," RheologicaActa, vol. 48, no. 8, pp. 831-844, Jan. 2009.
[27]
P. D. Olmsted, "Perspectives on shear banding in complex fluids," Rheologica Acta, vol. 47, no.
3, pp. 283-300, Mar. 2008.