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Design and characterization of flow batteries for large-scale energy storage

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Design and characterization of flow batteries for large-scale energy storage

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DESIGN AND CHARACTERIZATION OF FLOW BATTERIES FOR LARGE-SCALE
ENERGY STORAGE

by
Advaith Murali

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATERIALS SCIENCE)

December 2022

Copyright 2022 Advaith Murali

ii

Acknowledgements

I would like to thank Professor Narayan for his guidance, mentorship and steadfast
optimism that proved to be a shining beacon to strive towards during this research journey. It has
been a tremendous honor and privilege to be considered a student of a person who has been a
pioneer in the field of electrochemistry and energy storage for over 30 years. When I joined his
lab in 2015 as a young researcher who was losing his way due to bad experiences with prior
advisors, he provided a warm welcome and a gentle but firm guiding hand that helped me
rediscover my passion for research. The creative freedom and strong fundamental approach he
provided are the foundation upon which this thesis was possible. I am eternally grateful to him,
and can only hope to follow in his footsteps as I begin my professional journey.
Dr. Surya Prakash, Dr. Aniszfeld and the Loker Hydrocarbon Research Institute gave me
opportunities and room to grow, while constantly helping me learn about both the scientific and
business side of energy storage technologies. The support and infrastructure they provided, along
with constant guidance and advice have been a fundamental part of this journey. They have my
utmost gratitude and thanks. I would like to extend my thanks to my committee members, Dr. Nutt,
Dr. Ravichandran and Dr. Shing, whose questions and comments have helped me refine my work
and ask the right questions to truly understand not just what I was working on, but also why.
This research is not possible without the hard work and dedication of my project mates –
Dr. Bo Yang, Dr. Lena Hoober-Burkhardt, Dr. Sankarganesh Krishnamoorthy, Dr. Archith
Nirmalchandar, Dr. Vinayak Krishnamoorthy and Sairaj Patil. Their knowledge and contribution
allowed me to focus on my work with passion and helped fill in the gaps where I was lacking. I
would also like to thank all past and present members of Dr.Narayan’s lab, for being a well-knit
iii

group of people who were ever ready with help and advice, and whose varied perspectives
encouraged me to think outside the box and develop creative solutions to research problems.
Much of this research was funded by ARPA-E, who supported our research in aqueous all-
organic system and guided our scale-up efforts to conduct tests at ITN Energy Systems in
Colorado. Our continued efforts in this field are currently funded by Pacific Northwestern National
Labs, allowing us to focus on deciphering the secrets of molecular design towards stable and
durable organic molecules. I would also like to extend my gratitude to California Energy
Commission and University of California San Diego who identified the potential of our iron-
organic flow battery system and have provided us with an opportunity to scale-up and test the
system on their microgrid facilities.
None of this would be possible without the stable support of my family and friends, who
never gave up their support in this long and arduous journey of mine. In a world that pushes their
children to rapidly become earning members of society, my parents gave me the freedom and
encouragement to pursue my research without expectations and worry, for which I thank them
from the bottom of my heart. My sister and brother-in-law who were always there for me, who
encouraged me every time I questioned my path, and were ready to help no matter what I needed,
you have my utmost thanks and respect. All of them have been a safety net I never had to question,
without whom I may not have gotten as far as I have today.
Finally, my wife, who has been both a rock that has supported me when I faltered, and
pushed me to succeed every step of the way, I can only hope I can be there for you as you have
been there for me – a partner, a friend, a cheerleader, and a guide. To the final member of my
iv

family - my dog - who has shown me how to enjoy the little things and how to love unconditionally,
I promise all the love (and treats) I can provide.

v

Table of Contents
Acknowledgements ....................................................................................................................... ii
List of Tables ............................................................................................................................... vii
List of Figures ............................................................................................................................... ix
Abstract ....................................................................................................................................... xvi
1. Introduction ........................................................................................................................... 1
1.1. The Vagaries of Renewable Energy ................................................................................ 1
1.2. Stationary Energy Storage Technologies ......................................................................... 4
1.3. Redox Flow Batteries ....................................................................................................... 7
1.4. Characterizing the Performance of RFBs ........................................................................ 9
1.5. Factors Affecting Levelized Cost of Energy Storage .................................................... 13
1.6. Focus of the Research Study .......................................................................................... 15
1.7. Publications and Patents Resulting from the Research Study ....................................... 16
2. All-Organic Aqueous redox flow batteries ........................................................................ 18
2.1. Inception of All-Organic Aqueous Flow Batteries ........................................................ 18
2.2. Synthesis Challenges and Michael Reaction, lead up to DHDMBS ............................. 18
2.3. Analysis of Capacity Fade in Asymmetric DHDMBS - AQDS Cell ............................ 22
2.4. Determining the Rate of Protodesulfonation ................................................................. 25
2.5. Membranes to Lower Crossover Rate............................................................................ 29
2.6. Symmetric Cells with Mixed Electrolyte ....................................................................... 31
2.7. Mix-and-Split Cycling Protocol ..................................................................................... 36
2.8. Switch Cycling Protocol ................................................................................................ 37
2.9. Concentration Gradient of DHDMBS Across the Cell .................................................. 38
2.10. Long-term Cycling Performance and Protodesulfonation ............................................. 40
2.11. Scale-up and 1 kW testing ............................................................................................. 41
2.12. Learnings from the All-Organic Redox Flow Studies ................................................... 42
3. Iron-Organic Redox Flow Batteries ................................................................................... 45
3.1. Use of Iron in Redox Flow Batteries ............................................................................. 45
3.2. Introduction of the Iron-Organic Aqueous Flow Battery .............................................. 46
3.3. Performance and Characterization of Iron-Organic Flow Battery ................................. 47
3.4. Semi-Symmetric Protocols ............................................................................................ 51
vi

3.5. Cost Analysis of Iron Sulfate/Anthraquinone Disulfonic Acid (AQDS) Battery. ......... 54
4. Design and Characterization of Electrodes ....................................................................... 60
4.1. History of Electrode and Flow-Field Studies in Redox Flow Batteries......................... 60
4.2. Electrode Modifications and Microstructure of Felt Electrodes .................................... 63
4.3. Impedance Spectroscopy for Characterizing Electrode Structure and Performance ..... 65
4.4. Determining Surface Area ............................................................................................. 66
4.5. Determining Kinetic Parameters and Diffusion Layer Thickness ................................. 69
4.6. Flow Dependence and Mass Transfer Limitations ........................................................ 74
4.7. Limitations of the Proposed Method of Measuring  Based on Rmt/Rct ...................... 79
4.8. A modified Analytical Model to Predict Current .......................................................... 80
4.9. Experimental Determination of Value of  .................................................................... 97
4.10. Impedance Based Approach to Determining Average Path Length .............................. 99
4.11. Determining the Kinetic Parameters using an RDE .................................................... 104
4.12. Verifying Porous Electrode Analysis by Experiment. ................................................. 106
5. Materials and Methods ..................................................................................................... 110
5.1 Organic Solutions......................................................................................................... 110
5.2. Iron Sulfate Solutions for Iron-Organic Flow Cells .................................................... 111
5.3. Membranes ................................................................................................................... 111
5.4. Flow Cell Set-ups ......................................................................................................... 111
5.5. Characterization Methods ............................................................................................ 112
5.6. NMR Characterization for Quality Control and Crossover Measurements ................. 114
6. Conclusions......................................................................................................................... 115
6.1. Future Work in All Organic Aqueous Redox Flow Batteries ...................................... 116
6.2. Novel Challenges in Iron-Organic Aqueous Redox Flow Batteries ............................ 116
6.3. Future Work in Electrode Design and Optimization ................................................... 119
References .................................................................................................................................. 120

vii

List of Tables

Table 1. Time taken for visible precipitation from protodesulfonation at various
temperatures……………………………………………………………………………….. 26
Table 2. Water content and apparent diffusion coefficients of the different membranes
used………………………………………………………………………………………... 31
Table 3. Initial conditions for simulation of Capacity Evolution…………………………. 35
Table 4. System Specifications used for calculating LCOS for the Iron-AQDS battery…. 58
Table 5. Fixed Energy Specific Costs used for determining LCOS for iron sulfate-AQDS
battery……………………………………………………………………………………... 58
Table 6. Energy Specific Costs and LCOS for projected costs of AQDS for cross-over
resistant operation of symmetric iron sulfate-AQDS battery………………………………. 58
Table 7. Comparing System costs of iron sulfate-AQDS battery and VRFB………………. 59
Table 8. Electrochemically active surface area determined by EIS and the maximum
operable flow rate for various loading on the graphite electrode. All the electrodes in were
prepared with 0.1:1 ratio of Nafion:MWCNT……………………………………………... 69
Table 9. Calculated effective diffusion layer thicknesses, limiting currents and
experimentally obtained limiting currents at varying flow rates…………………………… 77
Table 10. Effective diffusion layer thicknesses and limiting currents for three different
flow fields at a constant flow rate of 0.4 LPM. The ratios of experimental to predicted
limiting current values help determine the effectiveness of the electrode – flow field
configuration………………………………………………………………………………. 79
viii

Table 11. Comparing δ = DRH/2 measured from pressure drop and path length from
transition frequency……………………………………………………………………….. 103
Table 12. Ohmic resistances and thickness comparisons of various electrode combinations
tested for the iron-AQDS system………………………………………………………… 118

ix

List of Figures
Figure 1. Annual change in renewable energy production relative to the previous year,
measured in terawatt-hours. This is the sum of energy from hydropower, solar, wind,
geothermal, wave and tidal, and bioenergy [2]…………………………………………….. 1
Figure 2. Variability in Solar and Wind energy production in the USA [3]………………. 2
Figure 3. Projected energy storage demand in transportation, stationary and pumped-hydro
storage hydropower (PSH) [4]……………………………………………………………... 3
Figure 4 Energy storage technologies and potential applications based on power
requirements [6]…………………………………………………………………………… 5
Figure 5. Global Deployment of Redox Flow Batteries [4]………………………………... 6
Figure 6. Representative image of a typical RFB system………………………………….. 8
Figure 7. Break-down of performance metrics for RFBs [26]……………………………... 10
Figure 8. Typical Polarization Characteristics of Redox Flow Batteries…………………... 11
Figure 9. Schematic representation of the components of a flow cell……………………… 13
Figure 10. Redox reactions of BQDS and AQDS, final Michael product of BQDS and the
subsequent loss in coulombic efficiency over the transformative period………………….. 20
Figure 11. Normalized capacity of flow cell (active area 25 cm
2
) cycled at 100 mA/cm
2
at
23
o
C. Positive electrolyte at the start of cycling was 1 M DHDMBS in 2 M sulfuric acid,
negative electrolyte was 1M AQDS in 1 M sulfuric acid………………………………….. 22
Figure 12. Linear sweep voltammograms at the rotating disk electrode of the positive and
negative electrolyte at 1500 rpm and 50 mV s-1. Samples taken at various cycle numbers
are indicated on the curves………………………………………………………………… 23
x

Figure 13. Concentration of DHDMBS in the positive and negative electrolyte as a
function of time during cycling determined through RDE analysis……………………….. 24
Figure 14. Proposed mechanism of protodesulfonation of DHDMBS in an acidic media…. 25
Figure 15. Capacity as a function of the cycling at 100 mA/cm2 with various membranes
̶ Nafion 117, F1850 and E750…………………………………………………………….. 30
Figure 16. Comparison of capacity fade in a single symmetric cell with three different
cycling protocols. The poor coulombic efficiency of the switch protocol system is owing
to biased cut-off voltages during the cycling program set-up. This was rectified in future
cells………………………………………………………………………………………... 37
Figure 17. Schematic representation of the polarity switch protocol. Cycle 2, after polarity
switch, allows the net crossover to be in the opposite direction to that of cycle 1, essentially
neutralizing the overall crossover every 2 cycles………………………………………….. 38
Figure 18. Simulated concentration changes on both sides of a symmetric cell for the
regular continuous cycling, mix and split (every 4 cycles), and polarity switching
protocols…………………………………………………………………………………... 40
Figure 19. Normalized charge and discharge capacities of a symmetric cell with 0.55 M
DHDMBS/AQDS solution with no added sulfuric acid, E750 membrane and lead
switching protocol…………………………………………………………………………. 41
Figure 20. a) A picture of the scaled-up 1 kW/2 kWh testing system designed and operated
by ITN energy systems, Colorado; b) Long-term performance studies of 1 kW/2 kWh
system over 400 cycles…………………………………………………………………….. 42
xi

Figure 21. Performance and characterization of MMS. The lack of crossover, and lack of
chemical transformations do not aid in explaining the reduction in capacity in the initial
cycling……………………………………………………………………………………... 43
Figure 22. Cell reactions during discharge and charge of the iron-AQDS flow battery……. 47
Figure 23. a) Result of cycling of asymmetric iron-AQDS cell. Note that dramatic capacity
loss within the first 5 cycles as expected; b) Long term cycling of symmetric iron-AQDS
cell. Steady capacity over 500+ cycles with high coulombic efficiency; c) Charge-
Discharge curves over 100 cycles show no degradation or loss in capacity in a symmetric
cell. Both cells were cycled at 100 mA/cm
2
………………………………………………... 48
Figure 24. Performance of Iron/AQDS symmetric cells. Electrolyte composition - 1 M
iron sulfate, 0.5 M AQDS in 2 M sulfuric acid; (a) Cell voltage as a function of current
density at 100% state of charge ; (b) measured values of power density and IR corrected
values; (c) effect of flow rate on cell voltage during charge and discharge; (d) effect of
flow rate on cell impedance; (e) comparison of impedance of carbon paper electrode
coated with MWCNT and graphite felt electrode coated with MWCNT…………………... 50
Figure 25. Schematic representation of a) Semi-Symmetric based on the symmetric system
and b) Reversed Semi-Symmetric based on the asymmetric system. Both behave distinctly
differently than the configurations they were based off, indicating at a possible iron-AQDS
interaction…………………………………………………………………………………. 51
Figure 26. Performance of Iron/AQDS semi-symmetric cells. Electrolyte composition - 1
M iron sulfate, 0.5 M AQDS in 2 M sulfuric acid, 25 cm
2
graphite felt electrodes, forced
flow at 1 L/min; (a) Charge-discharge curves during regular cycling at 100 mA/cm
2
with
a theoretical capacity of 2.4 Ah; (b) Capacity evolution over 100 cycles with 100%

xii

coulombic efficiency; (c) Current density- cell voltage curves, and IR corrected current
density-cell voltage curves and the open circuit voltage (OCV) during this test; (d) Power
density curve showing peak performance of 194 mW/cm
2
…………………………………

52
Figure 27. UV-Vis spectra using a thin film of solution formed between two quartz slides,
with 2 M sulfuric acid as reference………………………………………………………… 54
Figure 28. Three most general classification of types of flow-fields used with porous
carbon electrodes [79]. Parallel has been established as the least effective flow-field for
utilizing the entire area of the electrode, while the interdigitated is preferentially combined
with paper electrodes, and the flow through is combined with felt electrodes ensure more
complete use of the area of the electrode…………………………………………………... 61
Figure 29. The drop-casting method for preparing MWCNT carbon electrodes. This
method was used to prepare both paper and felt electrodes………………………………… 64
Figure 30. Varying solution ratios of Nafion:MWCNT by weight: a) Pristine fibers with
no surface modifications; b) 0:1; c) 0.05:1; d) 0.1:1; e) 0.2:1; MWCNT content is 10% of
the electrode mass…………………………………………………………………………. 65
Figure 31. Typical Electrochemical Impedance Spectrum of a system a) with redox active
species; b) without redox active species. Points reflect data at various frequencies………... 66
Figure 32. Imaginary component of impedance as a function of frequency in 1 M sulfuric
acid flowing across both electrodes………………………………………………………... 68
Figure 33. Schematic for representing the Nernst diffusion layer thickness at an electrode-
electrolyte interface. The concentration gradient C*-Cs determines the rate of diffusion
through the layer…………………………………………………………………………... 70
xiii

Figure 34. Effect of flow rate on EIS spectra for a symmetric flow system with redox
active material. The mass transfer resistance decreases significantly with increasing flow
rate, as a direct consequence of a reduction in diffusion layer thickness. It must be noted
that Rct remains unchanged despite significant changes in Rmt…………………………….. 76
Figure 35. a) Three types of flow fields used in this test. The columnar flow field
represents the lowest pressure drop system, while the forced flow represents the highest;
b) The impact of flow field on EIS clearly depicts the improvement in mass transport
properties between the three flow fields. The forced flow field, which exhibits the highest
pressure drop, has potentially the lowest diffusion layer thickness. This could be a
consequence of better flow distribution through the porous electrode, and a limitation on
bypass flow that tends to occur in the other systems……………………………………….. 78
Figure 36. A schematic showing the difference between the uniform concentration
assumed for Eq.23 vs typical concentration gradients in the electrode with material
actively being consumed…………………………………………………………………... 80
Figure 37. Schematic representation of a plug flow reactor of height Y, an inlet
concentration of Cx.b, in which a plug of height dx and uniform concentration Cx. A current
ix is drawn from the plug and it moves forward with a concentration of C x+dx, which is
lower than Cx………………………………………………………………………………. 82
Figure 38. Effect of boundary layer thickness (a), Volumentric flow rate (b) and kinetic
rate constant (c) on the current as a function of overpotential as determined by the model
in equation 58. This is for a porous electrode of 5000 cm
2
assumed surface area and unless
mentioned, Fv = 1 cm
3
/s, ko = 1e-5 cm/s, δ = 0.01 cm……………………………………... 96
xiv

Figure 39. A plot showing the linear relationship between pressure drop and volumetric
flow rate. A graphite felt electrode combined compressed by 30% was used with an
interdigitated flow field at room temperature of 298 K…………………………………….. 98
Figure 40. Highlighting the differences in velocity profile between conventional flow and
slug flow. Conventional flow shows a parabolic boundary layer, while slug flow profile
has a uniform velocity except at the tube walls…………………………………………….. 100
Figure 41. COMSOL model for flow through a simulated structure with fibers 5 µm thick,
200 µm long and separated by an equal distance of 75 µm. The fibers on each plane are
parallel to each other, with successive planes being at 90, 45 and 180 degrees with the z-
axis to simulate non-uniform fiber orientation…………………………………………….. 101
Figure 42. EIS of a graphite felt electrode with a forced flow-field at two different flow
rates. Both transition into mass transport regions at the same frequency of 0.2712 Hz, as
shown. The electrolyte is a uniform equi-molar mixture of 0.01 M Fe(II) and Fe(III) in 1
M Sulfuric Acid……………………………………………………………………………. 102
Figure 43. a) RDE at 1200 RPM on Graphitic Carbon electrode; b) Plot of overpotential
vs log10(I/(1-I/ILim)), used to determine ko and α. The solution was an equimolar mixture
of 0.01 M Fe(II) and Fe(III) in 1M Sulfuric Acid…………………………………………... 105
Figure 44. Comparing relationship between simulated and experimental current as a
function of overpotential for a felt electrode with a) Forced flow field at two different flow
rates; b) IDFF at 1.67 cm
3
/s………………………………………………………………... 107
Figure 45. Comparing simulated and experimental current as a function of overpotential
for a) 3-Stack toray paper with IDFF; b) 3-Stack toray paper with forced flow-field; c)
Simulations of 3-Stack paper with IDFF vs forced flow-field; d) CNT-decorated felt with

xv

forced flow-field with maximum area used vs actual area used obtained by comparing with
experimental measurements. All experimental and simulated measurements made at a
flow rate of 1.67 cm
3
/s……………………………………………………………………...

108

xvi

Abstract

Energy Storage has been a topic of growing interest over the past several decades as a key
technology in our goal to overcome our dependence on fossil fuels. Large scale energy storage
methods have been sought out in order to support the grid and provide a sustainable method to
maximize our utilization of renewable energy sources such as wind and solar energy. Redox Flow
Batteries (RFBs) are a relatively new but encouraging solution to this problem, with the ability to
store large amounts of energy with minimal degradation, and the ability to independently support
the power and energy needs. The research in this thesis focuses on the various aspects of aqueous
RFBs and highlight the challenges and innovations that make this a popular and widely pursued
research for energy storage. We have synthesized and studied multiple organic molecules, their
electrochemical behavior and degradation pathways in order to identify pathways to design robust
and scalable contenders. We also identified membranes that aid in reducing crossover and provide
alternative operational protocols that help extend the lifetime of RFBs. This work has resulted in
the first all-organic aqueous RFB to be tested at a 1kWh scale and showed that these types of RFBs
are capable of meeting the demands of the industry. We also demonstrated a ready-to-scale iron-
organic flow battery that has shown extraordinary durability, capable of operating for over 20
years, while simultaneously meeting the cost goals laid out by the U.S Department of Energy.
Aside from the active materials, the electrode plays a key role in achieving high power
densities which influences the costs and the size of the RFB. Here, we study the problems involved
in designing efficient electrodes and have explored the effect of heat treatment and surface
modification to boost battery performance. We have developed an analytical model to predict the
behavior of an electrode and an innovative impedance-based approach to extract structural
xvii

parameters of porous electrodes. The model has been verified using experimental data and
demonstrating the versatility and potential towards designing electrodes capable of operating at
high power densities, and establishing operating protocols for optimizing performance. The
ultimate goal of this thesis is to provide the reader a fundamental understanding of the problems
and potential solutions and show how RFBs are a prime candidate to help usher the world into a
more sustainable and environmentally friendly future with energy storage.

1. Introduction
1.1. The Vagaries of Renewable Energy
The 8
th
of May, 2022 was a record breaking day for renewable energy as California, the
5
th
largest economy in the world, was completely sustained by green energy [1]. Although this
does not imply a consistent and sustainable self-sufficiency, it does highlight the possibility that
renewable energy sources could be a viable method for energy production without carbon
emissions. Global renewable energy production has seen a steady rise over the last decade. With
an increase over 800 TWh in 2020 alone, the unprecedented investment in green energy has eased
the dependence on fossil fuels, and provided a path forward to wean away from conventional
sources of energy.

Figure 1. Annual change in renewable energy production relative to the previous year, measured in terawatt-hours.
This is the sum of energy from hydropower, solar, wind, geothermal, wave and tidal, and bioenergy [2].
2

The primary factor in the inability to realize the full potential of sources such as wind and
solar has been the inconsistency in the generation patterns (Figure 2). This variable nature requires
careful integration into the power systems’ design and operation in order to prevent large-scale
failure and potential damage to system components. Traditional power sources produce power in
the form of alternating current, which can support the very narrow ranges of voltage and frequency
required to support the power grid. Typically, renewable energy sources produce direct current
which need inverters to convert the AC to DC current before they can be connected to the grid, as
required by federal regulations [3]. The energy generated from these sources also do not align with
daily peak demands, and therefore require other sources to balance their usage.

Figure 2. Variability in Solar and Wind energy production in the USA [3].
To temper the inconsistency of energy produced by renewable sources, there has been a
rising demand to improve the ability to store the produced energy to use during peak hours. As
shown in Figure 3, the global energy storage market is expected to increase by a factor of 5 within
the coming decade. Mobile energy storage, primarily in the transportation sector in the form of
EVs have gained a stronger foothold and grown into the largest single demand for energy storage.
3

Combined with a rapid decrease in battery storage costs, and an increased investment in various
renewable generation has led to a surge in both commercial and demonstration-type deployments.
Stationary energy storage has now been identified as a tremendous opportunity to bridge the gap
between renewable energy production and grid reliability. The ability to siphon a portion of the
produced energy from wind and solar power to store for later use will go a long way towards
improving the resilience of the grid and aid with demand management.

Figure 3. Projected energy storage demand in transportation, stationary and pumped-hydro storage hydropower (PSH)
[4].
The rapid growth in the deployment of renewable electricity generation systems demands
the deployment of large-scale energy storage systems to deal with the fluctuations in supply.
Energy time-shift and “firming” applications involving daily charge and discharge from 4 to 12
hours, demand substantially higher durability and cycle life than offered by most conventional
4

batteries. The anticipated “mega” scale of deployment of such energy storage systems demands a
paramount level of safety, almost unlimited reserves of critical materials, and avoidance of
negative impacts on the environment [5].
1.2. Stationary Energy Storage Technologies

Typical stationary storage requirements are classified into 3 major categories, based on the
power requirements (Figure 4). In the bulk power management category, Pumped Hydro and
Compressed Air Energy Storage (CAES) are the only currently available technologies that are
capable of providing power in the GW scale. Both systems are considered mature technologies
and have been commercially deployed around the world. CAES requires either large natural
caverns or containers to hold the compressed air (at over 1000 psi), while pumped hydro power
requires substantial amounts of land and water sources and appropriate geography to be viable.
Hence, they involve considerable long-range development timelines, few opportunities to reduce
costs, the scope for expansion is very limited, and is location-specific.
5

Figure 4 Energy storage technologies and potential applications based on power requirements [6].
The more widespread applications of energy storage systems operate in the 1 kW to 10
MW scale, depending on behind the meter (residential and small scale commercial) or front of the
meter (grid support) applications. Well-known chemistries such as lead-acid and nickel-cadmium
have historically found a lot of usage in these areas, but are being phased out due to the toxicity of
the materials involved, and lower life expectancy before needing to be recycled or replaced.
Among the newer technologies, lithium based energy storage has been the subject of much
study and with the costs of lithium-ion batteries dropping by as much as 80% over the past decade.
With the growing popularity and acceptance of electric vehicles, the lithium-ion battery is
commonly proposed as a viable solution for stationary energy storage applications. Despite the
widespread accessibility and use of lithium-ion batteries, these batteries have severe limitations
6

that prevent it from being considered as the front-runner for large-scale deployment for stationary
storage. Primarily, the high temperature sensitivity and dangers of thermal runaway presented by
the active materials make them hazardous, and a significant portion of the system costs go towards
mitigating and planning for safety [7]. Lithium is also of low earth abundance in the earth’s crust.
Other components such as cobalt and nickel are also mined and recently have come under scrutiny
for human rights abuses [8]. There is also a significant negative environmental impact arising from
the expensive recycling of the many hazardous materials involved in the construction of the
batteries. While the high energy and power density make it ideal for portable and short-term energy
storage applications, lithium-ion batteries are still in its infancy with respect to large-scale energy
storage due to the high upfront costs and potential safety and environmental hazards.

Figure 5. Global Deployment of Redox Flow Batteries [4].
The emergence of Redox Flow Batteries (RFBs) has been driven primarily by their ability
to be operated on a mega-scale and the ease with which they can be modified to meet specific
requirements of power and energy independently. There has been increasing interest over the past
7

decade (Figure 4) with deployments of RFBs totaling over 700 MWh globally. Specifically, RFBs
based on aqueous chemistry have the potential to meet the demanding economic, environmental
and technical requirements for large-scale energy storage [9].
1.3. Redox Flow Batteries
A typical redox flow battery (Figure 5) consists of two major components – a cell that
determines the power output, and reservoirs that hold the dissolved redox active material that store
the energy. The cell has two porous electrodes separated by a proton (or cation) exchange
membrane (PEM). The redox active material is pumped from the reservoir through the cell where
oxidation occurs on the positive electrode during charge while reduction occurs on the negative
electrode. The reverse process occurs during discharge. Once the battery is charged, the energy
can be stored in the tanks and used when needed. The amount of energy stored is determined purely
by the moles of redox active material in solution and can be increased or decreased by modifying
the volume of the solution in the tanks. Similarly, the power output can be independently modified
by adjusting the size and number of cells in the power-producing element called the cell stack.
Aqueous RFBs can be operated in acidic [10,11], basic [12,13] or neutral media [14], with
the redox active material defining the operating pH of the solutions. Solutions of redox active
metal ions such as vanadium, iron and chromium have been studied for at least a couple of decades
[15–18] and have been the subject of many review articles [9,19,20]. Inorganic electrolytes result
in low efficiencies owing to hydrogen evolution and poor reaction kinetics with respect to
deposition and re-dissolution of the ions. Organic redox materials are relatively inexpensive in
general, but must avoid undesired chemical reactions either due to transformations within the
molecule or by reaction with the solvent. In general, it is necessary for the redox couples to have
8

fast kinetics of charge-transfer reaction, while being chemically stable to repeated
charge/discharge cycling, and have a long shelf life.
The ability to separate the components that produce power and store the energy offers not
only ease of scalability but also intrinsic safety. The charged electrolyte being restricted to separate
tanks outside the power-producing element (cell stack) precludes a runaway hazard situation, an
advantage not often emphasized. Fire hazards are reduced by using water as a solvent. Further, the
soluble redox couples avert degradation induced by phase changes commonly experienced during
charge and discharge of solid active materials. However, “hybrid” RFBs that entail metal
deposition at the negative electrode (typically elemental iron or zinc), cannot offer all the foregoing
advantages.

Figure 6. Schematic of a typical RFB system.
Among the mature aqueous RFBs are the all-vanadium and zinc-bromine systems that have
been studied for over 25 years [21–23]. At a large scale the installed cost of these systems is
projected to be in the range of $300- $500/kWh, while their projected lifetimes are as long as 20
9

years. Despite these long lifetimes the large-scale commercialization of vanadium and zinc-
bromine systems has been limited mainly by the high-cost of the redox materials and system
components, and the hazards of handling relatively toxic active materials [19]. Yet from a
commercial standpoint these systems may be considered as a springboard for designing and
deploying next generation energy storage systems. Thus, besides being durable and safe, the next
generation systems must use active materials that are low-cost, abundantly-available, and
environmentally-benign.
Electrical energy storage in RFBs could be a major enabler for the large-scale deployment
of renewable energy systems. This type of battery presents a scalable solution for a variety of
applications encompassing micro-grids, remote distributed applications, and grid-level load
management [20,24,25].
1.4. Characterizing the Performance of RFBs
The performance of any battery system is defined by 4 primary criteria – energy density,
power density, energy efficiency and durability (Figure 7). While the components of the cell
ultimately decide the performance of the battery, there are multiple parameters that influence the
selection of these components, such as cell voltage, solubility of redox species, viscosity of the
electrolyte, redox kinetics, overpotentials at the electrodes, chemical durability, etc. All these
factors may not be independently controllable or optimizable and may even influence each other.
Therefore, two system level metrics are used to define the performance of a redox flow battery,
which are the combined effects of the other properties - the energy efficiency and the power
density.
10

Figure 7. Break-down of performance metrics for RFBs [26].
Energy efficiency is governed by the energy losses caused by rate processes occurring
during storage and delivery of energy. These include the energy losses due to the ohmic resistance
of the electrode and electrolyte, mass transport limitations, and energy barriers to charge-transfer.
While this is only a measure of cell-level efficiency, a global or system-level energy efficiency
accounts for the energy consumption for pumping, thermal management and power conversion,
and system controls. Energy losses also arise from Coulombic inefficiency resulting from
migration of species across the PEM, or chemical degradation, or transformations of the active
material. Crossover of redox active materials from one side of the cell to the other through the
membrane affects the Coulombic efficiency but is a recoverable loss as the redox material can be
returned to its original form by rebalancing techniques. Chemical transformations can also occur
11

in the cell during cycling, in some cases only affecting the cell potential, but sometimes undergoing
degradation into inactive materials. Such transformations result in irrecoverable material loss.
Not only does this situation lead to poor energy efficiency, but losses in voltage and reduced
concentration that can adversely affect power density.
Figure 8. Typical Polarization Characteristics of Redox Flow Batteries.
Fast redox process with a standard heterogeneous electron transfer rate constant of 1x10
-5

cm s
-1
or higher are desirable to allow high efficiencies to be attained. We find that poor kinetics
is dependent on the molecular structure. For example, when intramolecular hydrogen bonding of
the quinone group with a sulfonic acid or hydroxyl group in the ortho- position is possible, the
charge-transfer process is hindered. The inefficiencies are often dominated by overpotential from
mass transport and electrolyte resistance (Figure 8). Under these conditions, the molecular
properties of solubility, diffusion coefficient, viscosity, and the degree of ionic dissociation
become intertwined in determining the voltage losses and the power density. Inorganic redox
electrolytes tend to be less viscous, of higher concentration, have higher diffusion coefficients, and
exhibit greater degree of ion dissociation than their organic counterparts.
12

With organic molecules, the properties of the oxidized form relative to that of the reduced
form are often quite different and this could affect how the power density varies with the state-of-
charge. For example, in the case of anthraquinonedisulfonic acid (AQDS), the solution of the
reduced form is considerably more viscous compared to the oxidized form because of hydrogen
bonding and the formation of stacked dimers. This increased viscosity and intermolecular
interaction leads to reduced utilization of the capacity and lower power density [27]. Further, when
using solutions of high concentration, it is important to ensure that solubility limits are not
exceeded during charge or discharge because of the reduced solubility of the transformed species.
Solubility can be enhanced by operating at elevated temperatures, but this comes with the concern
of accelerating undesirable side reactions. Thus, improvements to durability would also
beneficially impact power density by permitting higher temperatures of operation.
An important approach towards improving energy efficiency and power density of redox
flow battery stacks is by the rational design of flow fields and electrode structures (Figure 9) [28].
This approach is broadly applicable to RFBs and forms a core aspect of the presented study. The
primary source of ohmic resistance is the membrane separating the two electrode chambers (Figure
6). During charging, protons are released from the positive side and move to the negative electrode
to facilitate reduction, and this process reverses during discharge. This proton transport occurs
through a proton exchange membrane. Nafion
®
212 is a proton exchange membrane that combines
a high value of proton conductivity and chemical stability. Other potentially lower cost membranes
suitable for this purpose include those based on hydrocarbon polymers such as sulfonated
polyetheretherketone [29], cross-linked polystyrenesulfonic acid [30], and sulfonated
polyethersulfone [31]. It is important to note that while the Nafion membranes offer the lowest
ohmic resistance, but they also have high water content which facilitates movement of small
13

positively charged molecules to the negative side, leading to a reduced value of Coulombic
efficiency.

Figure 9. Schematic representation of the components of a flow cell.
Redox couples that offer a high cell voltage have the advantage of producing high power
densities at a proportionately lower cell current density. Considering that organic molecules are
susceptible to degradation by oxidation at high positive electrode potentials, attaining the cell
voltages as high as those seen in vanadium flow batteries is a challenge. However, redox couples
operating at a low cell voltage will also be viable if they can offer the required power density at
high energy efficiency and minimal overpotential. With such a view, the gamut of redox molecules
is quite broad.
1.5. Factors Affecting Levelized Cost of Energy Storage
The levelized cost of energy storage (LCOS) is the metric used to rate the economic
competitiveness of energy storage systems. LCOS is calculated by simply dividing the sum of the
capital and operating costs of the system by the total energy stored and delivered over the lifetime
of the system. To achieve market competitiveness, the LCOS target for large-scale energy storage
14

systems suggested by the US Department of Energy (DoE) is 2.5 cents/kWh [32]. To satisfy this
LCOS target, a system costing $200/kWh must store 8000 kWh over its lifetime. Assuming one
charge/discharge cycle per day, such an energy storage system must last at least for 22 years. To
achieve such an LCOS target, the system should be based on inexpensive and abundant materials
that are available without geopolitical constraints, while also being sustainable and eco-friendly.
The cost of active materials is one of the principal economic drivers for RFB systems
operating for longer than 3 hours. The active materials cost can be 25-50% of the system cost
depending on the power density of stack. At the active materials cost of $50/kWh, for 5 hours of
charge/discharge at a cell power density of 1 kW/m
2
, the system cost is estimated to be $200/kWh.
Such a system when operated for 20 years with a capacity degradation rate of no more than 2.5
x10
-3
% /day will meet the U.S. Department of Energy target for the levelized cost of energy
storage (LCOS) for utility scale systems of 5 cents/kWh [33]. Thus, the battery industry is seeking
cost-effective alternatives to common battery materials such as lead, zinc, lithium, vanadium,
chromium, etc.
The RFB cell stack is also a significant contributor to the overall system cost. A significant
cost driver is whether the redox electrolyte solutions are acidic or alkaline. Acidic solutions
necessitate carbon-based corrosion-resistant materials for the current collectors and electrodes.
Titanium plates may also be used as in the case of the negative electrode of the all-iron RFB. Other
parts of the cell can be serviced by inexpensive polypropylene. Alkaline media permit stainless
steel components to be used in the flow fields and connector plates, although nickel would be
preferred for long-term stability. Electrode structures continue to be made of carbon felt or carbon
fiber paper although nickel foam could be an option for alkaline media. Recent advances in iron-
15

based substrates for alkaline electrolyzers can be adapted for RFBs [34]. Where oxidative stability
of the membrane is not an issue, expensive perfluorinated membranes may be replaced with
hydrocarbon membranes. Sulfonated PEEK and sulfonated PES are the most common and cost-
effective alternatives. Today’s alkaline RFBs most commonly use Nafion as the alkali metal ion
transporter. Next generation alkaline systems can benefit from alkaline ion exchange membranes
that can transport anions and hydroxide. These membranes have an aromatic backbone, polymers
based on biphenyl and terphenyl groups and those with polynorbornene backbones developed for
alkaline fuel cells. The latter membranes are likely to be less expensive than their fluorinated
counterparts [35–37]. These new membranes can also serve as anion transporters for chloride,
bromide, and sulfate.
1.6. Focus of the Research Study
The research encompassing this dissertation focuses on addressing the principal measures of
battery performance for achieving a sustainable battery-based energy storage solution using the
principle of Redox Flow Batteries. The research focuses on :
(1) Properties of organic redox materials and their selection. We studied capacity fade in
aqueous redox flow batteries and determined the chemical pathways by which the systems
can degrade. We also identified membranes and alternate cell configurations to mitigate
the effects of crossover.
(2) Design, performance evaluation, and economic assessment of the operation of a novel
iron-based organic flow battery that addresses the durability and sustainability
requirements for large-scale energy storage.
16

(3) Analysis of the factors affecting the performance of porous electrodes and flow field
elements in the flow battery stack. We have developed a steady-state one-dimensional
model for describing the current-voltage characteristics and mass transport in porous
electrodes. The predictions of the model have been verified by comparing with
experimental data on laboratory cells. The model leads to identification of a figure of merit
that can be used for designing electrode structures and optimizing electrode performance.
1.7. Publications and Patents Resulting from the Research Study
• V. Krishnamurti, B. Yang, A. Murali, S. Patil, G. K. S. Prakash, S. R. Narayan, Aqueous
Organic Flow Batteries for Sustainable Energy Storage, Curr. Opin. Electrochem., Accepted
for Publication (2022)
• B. Yang, A. Murali, A. Nirmalchandar, B. Jayathilake, G. K. S. Prakash, S. R. Narayan, A
durable, inexpensive and scalable redox flow battery based on iron sulfate and anthraquinone
disulfonic acid, J. Electrochem. Soc., J. Electrochem Soc., 167, 060520 (2020)
• S. R. Narayan, A. Nirmalchandar, A. Murali, B. Yang, L. Hoober-Burkhardt, S.
Krishnamoorthy and G. K. S. Prakash, Next-generation aqueous flow battery chemistries,
Curr. Opin. Electrochem., 18, (2019)
• Murali, A. Nirmalchandara, S. Krishnamoorthya, L. Hoober- Burkhardta, B. Yang, G.
Soloveichikb, G. K. S. Prakash and S. R. Narayanan, Understanding and mitigating capacity
fade in aqueous organic redox flow batteries, J. Electrochem. Soc., 165, A1193 (2018).
• L. Hoober-Burkhardt, S. Krishnamoorty, B. Yang, A. Murali, A. Nirmalchandar, G. K. S.
Prakash, and S. R. Narayanan, A new Michael-reaction-resistant benzoquinone for aqueous
organic redox flow batteries, J. Electrochem. Soc., 164, A600 (2017)
17

• B. Yang, L. Hoober-Burkhardt, S. Krishnamoorthy, A. Murali, G. K. S. Prakash, and S. R.
Narayanan, High-performance aqueous organic flow battery with quinone-based redox
couples at both electrodes, J. Electrochem. Soc., 163, 7 (2016)
• US10,833,345B2 – New Materials for High-Performing Aqueous Redox Flow Batteries
(Issued Nov 2020)
• US20190115594A1 - Stable Positive Side Material for All-Organic Redox Flow Batteries
(Issued April 2019)
• US-16/980,549– Crossover Resistant Materials for Aqueous Organic Redox Flow Batteries
• US-16/973,922 –Inexpensive and Efficient Organic Redox Flow Battery Configurations for
Large-Scale Energy Storage

18

2. All-Organic Aqueous redox flow batteries
2.1. Inception of All-Organic Aqueous Flow Batteries
In the year 2014, a new type of RFB based on aqueous solutions of organic redox couples
was introduced by the researchers at the University of Southern California under the acronym
ORBAT [10]. In this type of RFB, water-soluble organic redox couples constitute the positive and
negative electrolyte solutions. The USC researchers demonstrated the potential of this type of
redox flow battery to operate at high power densities and efficiency using variations of sulfonated
anthraquinone and benzoquinone [38,39]. The ability to synthesize organic redox couples with a
variety of molecular structures and substituents presented a new opportunity for tuning the
molecular properties required of these redox couples. We and other researchers were able to
demonstrate that the electrode potentials, solubility and chemical stability could be improved by
judicious modification of molecular structure [13,39,40]. As a result, a large number of redox
active organic molecules have become the subject of research reports and patents [14,41–46]. Also,
several modifications of the ORBAT arrangement using inorganic materials in combination with
organic redox couples have also become the subject of recent investigations [12,47]. Thus, the use
of water-soluble organic redox couples has opened a new pathway to a sustainable electrical energy
storage system with the potential to be inexpensive and environmentally-friendly.
2.2. Synthesis Challenges and Michael Reaction, lead up to DHDMBS
We first reported the properties of an “all-quinone” organic redox flow battery in 2014 in
which the positive electrode was supplied with a solution of 4,5-dihydroxybenzene-1,3-disulfonic
acid (BQDS), while the negative electrode used a solution of either anthraquinone-2-sulfonic acid
(AQS) or anthraquinone-2,6-disulfonic acid (AQDS) [10]. The system could be charged and
19

discharged repeatedly with a round-trip energy efficiency of 70% at 100 mA/cm
2
and 100%
Coulombic efficiency for 100 cycles, and achieved a power density of 100 mW/cm
2
, when
operating at high concentrations of reactants [38].
In the early stages of cycling BQDS, it was found that undesired chemical transformations
of BQDS occur in addition to the necessary redox reactions. While AQDS is stable and does not
undergo such chemical transformations, BQDS undergoes the Michael reaction with water. In this
reaction, BQDS transforms through sequential steps of water addition and electrochemical
oxidation to eventually form 1,2,4,6-tetrahydroxybenzene-3,5-disulfonic acid – a fully substituted
benzoquinone (Figure 10). Although we may start with BQDS, it is the fully-substituted 1,2,4,6-
tetrahydroxybenzene-3,5-disulfonic acid that undergoes charge and discharge during subsequent
cycling of the cell.
This transformation is quite rapid and comprehensive. But, since it is a two-step reaction
that occurs when BQDS is in the charged state, it requires 2 equivalents of AQDS to undergo the
reactions, and one more equivalent of AQDS in order to continue cycling. Thus, these reactions
result in poor Coulombic efficiency in the first cycle and the requirement of excess AQDS to
complete the subsequent additions of the hydroxyl group (Figure 10).

20

Figure 10. Redox reactions of BQDS and AQDS, final Michael product of BQDS and the subsequent loss in coulombic
efficiency over the transformative period.
Another disadvantage of this reaction is that the substituted product of the Michael has a
lower potential than the starting material. Experimentally, the equilibrium potential was found to
decrease by 100 mV for each step of water addition, thus resulting in a net decrease of 200 mV.
Incomplete utilization of AQDS on the negative side reduced the maximum current density
attainable during subsequent charging.
In 2017, we presented for the first time the synthesis, characterization and properties of
3,6-dihydroxy-2,4-dimethylbenzenesulfonic acid (DHDMBS) as a new positive side electrolyte
material for aqueous organic redox flow batteries [39]. We demonstrated that DHDMBS overcame
the major issue of the Michael reaction with water faced with previously reported positive
electrolyte materials based on substituted benzoquinones such as BQDS. We showed that
DHDMBS could be synthesized relatively inexpensively and that no products of the Michael
reaction were detected upon charge and discharge in a redox flow battery. Specifically, a flow
21

battery with DHDMBS and anthraquinone-2,7-disulfonic acid was shown to cycle continuously at
100 mA/cm
2
, with the ability to sustain 500 mA/cm
2
current density without noticeable short-term
capacity fade for at least 25 cycles. Thus, DHDMBS presented the prospect of a viable positive
side material in an aqueous all-organic aqueous redox flow battery operating under acidic
conditions. However, there was a slow decrease in the capacity of the flow cell over hundreds of
cycles attributable to the crossover of DHDMBS from the positive side to the negative side of the
cell. Thus, our subsequent efforts focused on understanding the long-term effects of cycling and
demonstrating approaches to mitigate crossover with DHDMBS.
We have explored specifically various approaches to mitigate crossover including the use
of low-permeability membranes, a new symmetric cell configuration using mixed electrolytes, and
operating protocols that involve polarity-switching. We have also uncovered the mechanism of
slow chemical modification that leads to a gradual capacity decrease under strongly acidic
conditions during long-term cycling.
All the DHDMBS needed for the experiments was synthesized in-house by methods
described in detail in chapter 5, Section 5.1 [39]. These solutions contained greater than 95% of
DHDMBS and the remaining material was the starting material 2,6-dimethylhydroquinone.
Further, the solutions were either diluted with water or water was evaporated under reduced
pressure to obtain the required concentrations. When needed, the water was completely evaporated
to yield solid DHDMBS.
22

2.3. Analysis of Capacity Fade in Asymmetric DHDMBS - AQDS Cell
When a flow cell with DHDMBS as the positive electrolyte and AQDS as the negative
electrolyte was cycled continuously at 100 mA/cm
2
we observed a gradual fade rate of about 0.27%
per cycle in a continuous cycling test that spanned 15 days (Figure 11).

Figure 11. Normalized capacity of flow cell (active area 25 cm
2
) cycled at 100 mA/cm
2
at 23
o
C. Positive electrolyte
at the start of cycling was 1 M DHDMBS in 2 M sulfuric acid, negative electrolyte was 1M AQDS in 1 M sulfuric
acid.
With 100 ml of solution in each of the reservoirs, the cell had an initial capacity of 5.53
Ah. The cell was charged to a cut off voltage of 1.0 V and discharged down to 0.0 V. In every
cycle, we ensured that we extracted all the capacity that could be had at the current density of 100
mA cm
-2
. Such conditions of cycling were chosen to be relevant to the practical operation for redox
flow batteries. We found that over the duration of 325 cycles the capacity decayed to 0.53 Ah. The
decay in capacity previously observed with other positive electrolytes was attributed to the rapid
transformation of materials via the Michael reaction. However, in the present study with
DHDMBS we did not detect any products of the Michael reaction by
1
H-NMR even after 325
cycles of charge and discharge [39]. While these cycling tests confirmed the relative robustness of
23

DHDMBS with respect to the Michael reaction with water, we were led to investigate other reasons
for the decrease in capacity with cycling. Samples of the positive and negative electrolyte were
withdrawn periodically at various points in the 325 cycles. When these samples were analyzed by
linear sweep voltammetry at a glassy carbon rotating disk electrode (Figure 12) we found a steady
decrease in concentration of DHDMBS in the positive electrolyte, and a slow enrichment of the
negative solution with DHDMBS.

Figure 12. Linear sweep voltammograms at the rotating disk electrode of the positive and negative electrolyte at 1500
rpm and 50 mV s
-1
. Samples taken at various cycle numbers are indicated on the curves.
24

We did not detect any change of the concentration of AQDS on the negative side, nor was
any AQDS detected in the positive electrolyte even after 325 cycles. However, the concentration
of DHDMBS decreased in the positive electrolyte and increased in the negative electrolyte.
The concentration of DHDMBS in the positive electrolyte fell below 0.4 M, less than half
the starting value of 0.8 M. However, the concentration of DHDMBS on the negative side was
less than 0.4 M. If there was crossover one would have expected that the loss on the positive side
would be accompanied by an equal amount of positive electrolyte material gained on the negative
side. Thus, the sum of the moles of DHDMBS did not add up to the total moles of DHDMBS that
are started with (Figure 13). This apparent inconsistency was resolved when the NMR analysis of
the solutions was carried out.

Figure 13. Concentration of DHDMBS in the positive and negative electrolyte as a function of time during cycling
determined through RDE analysis.
We confirmed the crossover of DHDMBS from the positive to the negative side by
1
H-
NMR (Section 5.6), but did not observe any crossover of AQDS from the negative to the positive
Concentration on positive side
Concentration on negative side
Loss in net concentration
25

side. However, in addition to crossover, a small change in the chemical signature of DHDMBS
was also observed. Albeit small, this change was persistent and appeared to be increasing slowly
in intensity with cycling. This chemical transformation was attributed to loss of the sulfonic group
from DHDMBS. This desulfonated product is relatively insoluble in aqueous media and when
produced in excess of 10% -15% could separate from the electrolyte solutions. Such a reaction
would be termed “protodesulfonation”. In essence, this was the reversal of the sulfonation process
used in the synthesis of DHDMBS. In Figure 14 we depict the reaction sequence for this process
of proto-desulfonation of DHDMBS.

Figure 14. Proposed mechanism of protodesulfonation of DHDMBS in an acidic media.
2.4. Determining the Rate of Protodesulfonation
We were able to confirm that the protodesulfonation reaction also occurred ex-situ even in
the absence of the charge/discharge cycling process. The rate of protodesulfonation increased with
the acid concentration (Table 1). Thus, the process of protodesulfonation, albeit slow at room
26

temperature, increases in rate upon raising the temperature to 60
o
C. Also, in 4 M sulfuric acid,
insoluble de-sulfonated material was rapidly formed. While higher acidity was desirable for
improved electrolytic conductivity, the resulting protodesulfonation was undesirable. Thus, we
found that sulfonated molecules that are robust to the Michael reaction could become susceptible
to degradation by the protodesulfonation mechanism at higher temperature and higher acid
concentration.
Table 1. Time taken for visible precipitation from protodesulfonation at various temperatures.
Concentration of sulfuric
acid (M) along with 1M
DHDMBS
Time for visual observation of protodesulfonation at
various temperature values
Room
temperature
40 °C 50 °C 60 °C
1 - - - 12 hours
2 - 17 days 10 days 12 hours
3 - 7 days 5 days 12 hours
4 21 days 2 days 12 hours 12 hours

We noted in discussing the results of Figure 13 that the concentration of the positive
electrolyte starting at 0.8 M decreases with extended cycling to a value lower than 0.4 M that is
less than half the starting value. Also, the concentration of the negative side remained at less than
0.4 M. Although the concentrations deviate from the expected value of 0.4 M by a small amount,
the evolution of concentration with cycling indicated that an additional process beyond crossover
27

contributed to the reduction of concentration with time. Such a process could now be attributed to
the low level of protodesulfonation that we had detected from NMR studies. To verify this
explanation, we set out to analyze the concentration of DHDMBS with time from the long-term
cycling experiments to determine the rate constant for protodesulfonation.
Based on the scheme shown in Figure 16, we can describe the kinetics of
protodesulfonation to be a second order process with the protonation step as the rate determining
step [48]. Thus, the rate law would be,
Rate of proto-desulfonation = kPDS CDHDMBS CH+ - (24)
Where kPDS is the second order rate constant for the protodesulfonation process and
CDHDMBS and CH+ are the concentration values of DHDMBS and protons in solution. Since we did
not observe any crossover of AQDS, the following analysis of the concentration data will focus
only on the crossover and protodesulfonation of DHDMBS.
Let C+ represent the total concentration of DHDMDS (in both the oxidized and reduced
forms) at any time on the positive side of the cell. Similarly, let C- be the total concentration of
DHDMBS on the negative side of the cell at any time. The change in concentration of DHDMBS
on either side of the cell is then the sum of the changes caused by diffusion through the ion-
exchange membrane and the protodesulfonation process. Incorporating the rate of
protodesulfonation from Eq. 24, the concentration changes of DHDMBS on the positive and
negative sides of the cell are given by Eqs. 25 and 26.
dC+/dt = -(Dapp A/V) d

C+/dx

– (kPDS/V) C+ CH+ - (25)
dC- /dt =-(Dapp A/V) d

C-/dx

– (kPDS/V) C- CH+ - (26)
28

Where Dapp is the apparent diffusion coefficient, and x is the thickness of the membrane. A
is the active area of the electrode and membrane and V is the volume of solution in the reservoir.
We may assume no difference in the concentration of solution in the reservoir and the surface of
the membrane given that the flow rates of circulation of the solutions are high compared to
transport rates by diffusion across the membrane. We have also defined (kPDS/V) as k’PDS .
Adding Eqs. 25 and 26, and incorporating d

C+/dx = – d

C-/dx, we obtain for any time t,
dC+/dt + dC-/dt = - k’PDS CH+ (C++C-) - (27)
Thus, a plot of the sum of the rates of change of concentration of DHDMBS on the positive
and negative sides plotted against the sum of the concentration is expected to be linear for a given
background concentration of protons. Results derived from Figure 15 as per Eq.27 allow us to
determine the pseudo first-order rate constant, kPDS CH+, at a concentration of 1M sulfuric acid to
be 2 x10
-6
s
-1
.
The diffusion coefficient for DHDMBS was calculated from either equation 25 or 26 by
substituting the value for kPDS and using the results from Figure 15. The average diffusion
coefficient for DHDMBS through the membrane was thus calculated to be 3 E-6 cm
2
s
-1
. We also
determined the value of diffusion coefficient in liquid sulfuric acid electrolyte by linear sweep
voltammetric oxidation of DHDMBS at the rotating disk electrode. From the slope of the Ilim vs.

1/2
(Levich Plot), we determined the diffusion coefficient to be 5E-6 cm
2
s
-1
. We find that the
apparent diffusion coefficient of DHDMBS through the Nafion membrane is significantly lower
than that in free sulfuric acid electrolyte. Since we expect DHDMBS to diffuse through the aqueous
phase of the Nafion membrane, we concluded that the water content of the membrane would
29

influence the diffusion coefficient. The water content of Nafion 117 being about 40 weight % of
the membrane we could justify that the apparent diffusion coefficient of DHDMBS in Nafion to
be 2/3
rd
of the value in the free electrolyte. This value of diffusion coefficient suggested that the
DHDMBS was largely in the unionized form in the presence of 1M sulfuric acid. Thus, in addition
to solubility in the aqueous phase, we could also expect molecular size and degree of ionization to
dictate the rate of crossover. We found that AQDS did not crossover unlike DHDMBS, a difference
attributable to the significant differences in degree of ionization (as suggested by conductivity
measurements) and molecular size.
2.5. Membranes to Lower Crossover Rate
With the goal of reducing the rate of crossover, we investigated the properties of
membranes with different levels of water content. Specifically, we compared the cycling
performance of cells with Nafion 117 (175 microns), Fumatech F1850 (50 microns) and Fumatech
E750 (50 microns). The Fumatech F1850 consisted of a polyperfluoroethylene sulfonic acid with
an equivalent weight of 1850 g/mole of protons, as opposed to Nafion 117 with similar
fluoropolymer but with an equivalent weight of 1100 g/mole of protons. The E750 membrane was
cast from sulfonated polyphenyletheretherketone. The capacity fade was significantly lower with
F1850 and E750 membranes despite their lower thickness compared to Nafion 117 (Figure 15).
30

Figure 15. Capacity as a function of the cycling at 100 mA/cm
2
with various membranes ̶ Nafion 117, F1850 and
E750.
Analysis of the change of concentration of the solutions as a function of time, similar to
that performed with Nafion 117 yielded apparent diffusion coefficients for DHDMBS through
F1850 and E750 membranes (Table 2). The apparent diffusion coefficients for DHDMBS through
each of the membranes was found to decrease with the equilibrium water content of the
membranes. Therefore, the F1850 and E750 membrane were found to be more desirable over
Nafion 117 from the standpoint of achieving a lower crossover rate. Due to their lower thickness,
the F1850 and E750 membranes were comparable to Nafion 117 in ohmic resistance.

31

Table 2. Water content and apparent diffusion coefficients of the different membranes used.
Membrane
Thickness,
(µm)
Water
Content,
(wt %)
Dapp, Apparent
Diffusion Coefficient
(cm
2
s
-1
)
Normalized Diffusion
Coefficient for
thickness
(Dapp*thickness in µm)
Nafion 117 175 40% 3.12E-06 5.46E-04
Fumatech
F1850
50 17% 1.66E-06 8.3E-05
Fumatech
E750
50 <10% 1.63E-07 8.15E-06

So far, we have identified two major mechanisms of capacity fade, namely crossover and
proto-desulfonation. Both these processes can be significantly slowed down by using an
appropriate type of membrane and by reducing the acid concentration. However, we were desirous
of completely suppressing both these mechanisms of capacity loss. Thus, our focus shifted to
testing cells with mixed electrolytes on both the positive and negative sides of the cells that we
called symmetric cells that we discuss next.
2.6. Symmetric Cells with Mixed Electrolyte
In this type of cell, we use the same electrolyte mixture (consisting of DHDMBS and
AQDS) on the positive and negative sides of the cell. We term this configuration a ‘symmetric
cell’. Since the concentration of the reactants is the same on both sides of the cell, we expected to
avoid crossover and consequently not experience a fast capacity fade.
32

The results of cycling experiments did indeed prove that symmetric cells had a significantly
slower capacity fade rate compared to the asymmetric cells. While the asymmetric cell had a
capacity fade rate of 0.23% per hour, the symmetric cell was 0.078% per hour. Although one would
not expect the symmetric cell to have any crossover, we found that some crossover still occurred.
This crossover is because the concentration of the oxidized form of DHDMBS on the positive side
increases and decreases during charge and discharge while the concentration of this oxidized form
is always zero on the negative side during the entire cycle of charge and discharge. Thus, the ratio
of the discharge to charge capacity proved to be 99% in any particular cycle. While we can attribute
the discharge to charge capacity ratio of less than 100% to the higher crossover rate of the oxidized
form in every cycle, the small yet finite capacity loss from the protodesulfonation process that we
had also observed in the asymmetric cell is also expected to occur in the symmetric cell. To verify
that the observed capacity fade rate was indeed consistent with the diffusion process and the
protodesulfonation rate, we carried out a numerical simulation of the concentration changes with
time during the cycling of the symmetric cell. An analytical solution for the concentration of
DHDMBS vs. time for multiple cycles of charge and discharge with decreasing capacity was not
straightforward and thus a numerical approach was adopted.
The numerical simulation used the initial experimental conditions of concentration,
volume, discharge and charge current densities and electrode area. The apparent diffusion
coefficient values in the simulation were those that were determined experimentally from the
asymmetric cell with Nafion membrane. The simulation involved calculation of the concentration
in finite time steps for the entire charge and discharge cycle repeated for about 200 cycles. The
concentration changes were obtained from a mass balance calculation that accounted for the fluxes
from crossover of the oxidized and reduced form of DHDMBS from one side of the cell to the
33

other, the reduction by AQDS of the oxidized form of the DHDMBS that crosses over to the
negative side during charging, and the loss of DHDMBS by the protodesulfonation process
(similar to that in the asymmetric cell). We did not include any crossover flux for AQDS because
we had not observed experimentally the crossover of AQDS. We estimated the decrease in
concentration of DHDMBS over multiple cycles and then inferred the capacity fade rate. The time
step used in this simulation was 120 s, selected to be much greater than the time needed for the
active material to diffuse completely across the membrane, ( x)
2
/2Dapp). The equations used in the
simulation of the change of concentration are included below:
ΔCox+/Δt = -Dox*A*(ΔCox)/(Δx*V) - kpds*Cox+/V - (28)
ΔCred+/Δt = -kpds *(Cred+)/V + Dred*A*ΔCred /(Δx*V) - (29)
ΔCred-/Δt = -Dred*A*(ΔCred)/(Δx*V) - kpds*(Cred-)/V + Dox*A*ΔCred /(Δx*V) - (30)
Where,
Cox+ Concentration of the oxidized form of DHDMBS on the positive side
Cred+ is concentration of the reduced form of DHDMBS on the positive side
Cred- is concentration of the reduced form of DHDMBS on the negative side
ΔCred is the difference in concentration of the reduced form of DHDMBS between both sides of
the cell
ΔCox is the difference in concentration of the reduced form of DHDMBS between both sides of the
cell
34

Dox and Dred are diffusion coefficients of the oxidized and reduced forms of DHDMBS,
respectively.
kpds is the rate of protodesulfonation
A is the area of the membrane across which cross-over occurs
Δx is the thickness of the membrane
V is the volume of the reservoir
We found that by using the rate constant for protodesulfonation and the diffusion
coefficient values determined from the experimental studies on the asymmetric cell we could
reproduce the concentration fade rate quite satisfactorily. The initial conditions assumed for the
simulation are given in Table 3. The experimentally determined fade rate was 0.078%/ hour while
that from the simulation was 0.12%/hour. The discharge to charge capacity ratio was estimated
from the simulations to be 85% and was consistent with the experimentally determined charge
capacity ratio of 84%. These agreements suggested that the cycling behavior of the asymmetric
cell could be used to predict the characteristics of the symmetric cell. Some of the differences
between the simulations and the experimental cycling data could arise from the slow changes that
occur in the cell such as the swelling of the membrane during the cycling that could lead to change
of the value of the apparent diffusion coefficient. Such effects were not included in the simulations.

35

Table 3. Initial conditions for simulation of Capacity Evolution

To verify that the rate constant for protodesulfonation determined by the analysis of cycling
data was indeed realistic we conducted separate ex situ kinetic experiments. We measured the rate
of protodesulfonation by monitoring the concentration of DHDMBS with time by NMR and RDE
voltammetry. Since protodesulfonation is a slow process at room temperature, we accelerated the
protodesulfonation process by raising the temperature to 60
o
C. We did not expect to change the
mechanism of protodesulfonation between 25
o
C and 60
o
C. Specifically, our starting solution was
1.2 M in both DHDMBS and sulfuric acid. The resulting solution was stirred at 60 °C on an oil
bath. Samples of this solution were filtered through a syringe filter before analysis.100 𝜇 L of the
sample was mixed with 4 mg of imidazole and diluted with 500 𝜇 L of D2O for
1
H NMR studies.
Imidazole was used as an internal standard for obtaining the concentration of DHDMBS. Using an
activation energy of 29 kcal/mole [49] we determined the pseudo-first order rate constant for
protodesulfonation at 25
o
C to be 1.77 x 10
-6
s
-1
.
Parameter Value Units
Dred 2.40E-06 cm
2
/s
Dox 5.27E-06 cm
2
/s
Cred+ = Cred- 5.00E-04 mole/cm
3

Volume 1.00E+02 ml
Δx 1.78E-02 cm
Current 2.50E+00 A
Area 2.50E+01 cm
2
/s
Kpds 3.64E-06 s
-1

36

This value of rate constant determined from the ex situ kinetic studies was in reasonably
close to the value of 3.68 x 10
-6
s
-1
predicted by the analysis of capacity fade during cycling, a
totally independent experiment. The general agreement between the measured values from two
independent experiments serve to validate our hypothesis that the main cause of permanent
capacity fade with DHDMBS was protodesulfonation. In addition, the simulation studies that used
the experimentally determined values of diffusion coefficients helped verify the experimentally-
observed coulombic efficiency loss resulting from crossover.
The simulation results indicated that the concentration of DHDMBS was higher on the
negative side of the symmetric cell at the end of discharge. With additional rest time between the
cells these concentrations differences would equilibrate. However, depending on how fast we
choose to do the cycling and the amount of rest time allowed between cycles, the transiently higher
capacity of the negative side would have a significant effect on the observed capacity and
coulombic efficiency even in a symmetric cell.
2.7. Mix-and-Split Cycling Protocol
An approach to annul the concentration differences between the positive and negative side
in a symmetric cell is by mixing the solutions and re-distributing the solutions between the two
reservoirs at the end of discharge. We call this the “mix-and-split” approach. This method has been
used for capacity re-balancing in other redox flow batteries [50]. In this approach, the
concentration gradient due to crossover is allowed to build up, and capacity fade is allowed to
occur for a certain length of time before the mix-and-split step is implemented. After the mix- and-
split step, the capacity again rises as the concentration values are restored. We demonstrated this
approach to capacity recovery through experiments. The first mix-and-split step was introduced
37

after 150 cycles. The first cycle following the mix-and-split indeed showed a spike in charge
capacity back to the starting values. Repeating this process of mix-and-split periodically allowed
us to regain the capacity loss due to crossover in the symmetric cell (Figure 16).

Figure 16. Comparison of capacity fade in a single symmetric cell with three different cycling protocols. The poor
coulombic efficiency of the switch protocol system is owing to biased cut-off voltages during the cycling program
set-up. This was rectified in future cells.
2.8. Switch Cycling Protocol
While the mix-and-split approach restored the cell to its original configuration, the cell
continued to show a steady capacity fade in subsequent cycles resulting from resumption of
crossover and also protodesulfonation in the subsequent cycles. An expedient protocol to take
advantage of the higher capacity of DHDMBS on the negative side due to crossover was to switch
the polarity of the cell and make the negative side as the positive side, at the end of every charge-
discharge cycle (Figure 17). This allowed the excess DHDMBS (on the formerly negative side) to
cross back into the formerly positive side. Such polarity switching is possible only with the mixed
cell (symmetric) configuration.
38

Figure 17. Schematic representation of the polarity switch protocol. Cycle 2, after polarity switch, allows the net
crossover to be in the opposite direction to that of cycle 1, essentially neutralizing the overall crossover every 2 cycles.
In Figure 16 we compare the experimental results of capacity evolution resulting from all
three cycling protocols (continuous cycling, periodic mix-and-split with continuous cycling, and
continuous cycling with polarity switching in every cycle). The capacity fade rate of 0.06% per
cycle from the polarity switching approach was significantly lower than that observed under the
mix-and-split cycling protocol (0.44% per cycle) or the continuous cycling of symmetric cell
(0.47% per cycle). Thus, under the conditions of polarity switching, the observed net fade was
primarily due to protodesulfonation.
2.9. Concentration Gradient of DHDMBS Across the Cell
The progressive reduction in capacity during continuous cycling in the symmetric cell was
rationalized by a larger diffusion coefficient for the oxidized form of DHDMBS compared to the
reduced form that resulted in the net crossover of charged form of DHDMBS to the negative side.
During the first few cycles, the capacity loss is accompanied by the establishment of a
concentration gradient of DHDMBS across the cell, following which the capacity stabilized. After
such an equilibration process, the subsequent capacity fade was only due to protodesulfonation.
In the case of the polarity switching experiment, the concentration gradient was reset in every
cycle. Thus, switching allowed the excess material that has crossed over to cross back to the first
39

reservoir and thus return the cell to its original capacity. The concentration gradient of DHDMBS
across the cell is the major contributor for rates of crossover over the life cycle of the symmetric
cell. While in the regular cycling configuration of the symmetric cell a large gap in concentration
between the positive side and negative side is maintained throughout the cycle life, polarity
switching and the “Mix-and-Split” are re-balancing techniques that restrict the growth of the
difference in concentration between the positive and negative sides.
A simulation of these concentration changes arising from the three cycling protocols for
the symmetric cell (Figure 18) was able to verify the trends in the experimental results. Using the
same parameters as used in the previous simulation of the asymmetric cell, we find that regular
continuous cycling resulted in the highest concentration gradient for DHDMBS across the cell.
This concentration difference was maintained throughout the cycling regime. The mix-and-split
approach had a smaller gradient, but one that oscillated across a mean value because of the periodic
mix-and-split operation. The lowest concentration gradient of DHDMBS across the cell was
observed during the polarity-switching method since the gradient is forcibly reset at the end of
every cycle.
40

Figure 18. Simulated concentration changes on both sides of a symmetric cell for the regular continuous cycling, mix
and split (every 4 cycles), and polarity switching protocols.
2.10. Long-term Cycling Performance and Protodesulfonation
Using the knowledge and insight gained from the experimental studies and simulations, a
symmetric cell was set-up. We used an E750 membrane to reduce crossover and the polarity
switching protocol to reverse the capacity imbalance. To minimize the effect of
protodesulfonation, we avoided adding sulfuric acid to the electrolyte; we did not experience any
significant reduction in electrolytic conductivity despite not having any sulfuric acid. The
electrolyte was a mixture of 0.55 M DHDMBS/AQDS (with no added sulfuric acid) was cycled at
100 mA/cm
2
for over 4 months and over 1800 cycles. This cell showed a discharge capacity fade
rate under 0.04% per cycle (Figure 19). This fade rate was attributed entirely to the
protodesulfonation process. This fade rate was also consistent with our estimates of
protodesulfonation rate. We were thus able to isolate the degradation processes from the decrease
in capacity due to crossover losses.
41

Figure 19. Normalized charge and discharge capacities of a symmetric cell with 0.55 M DHDMBS/AQDS solution
with no added sulfuric acid, E750 membrane and lead switching protocol.
The relatively steady value of charge capacity suggested a self-discharge process
associated with the proto-desulfonated form of the positive side material. The protodesulfonated
material is known to undergo electrochemical oxidation and accept charge. The resulting
molecules being un-ionized, could have a high diffusion coefficient and can crossover to the
negative side through the hydrophobic regions of the membrane. Once on the negative side, these
oxidized molecules could discharge the AQDS, thus reducing the discharge capacity of the cell.
When the polarities are switched for the next cycle, this process repeats in the opposite direction,
rebalancing the concentrations of the desulfonated material. In the meanwhile, protodesulfonation
continues to degrade the active materials producing more of the desulfonated material. As a result,
a steady charging capacity and a steadily falling discharge capacity were observed.
2.11. Scale-up and 1 kW testing
Based on the chemical and operational information gained at USC, our collaborators – ITN
Energy System, Colorado – were able to run a series of tests in cells of large area of 150 cm
2
,
42

under various load conditions. The purpose of these studies was to determine the practical
applicability of the ORBAT systems for commercial applications. As a result of this collaboration,
ITN was able to set-up and operate a 1kW/2kWh system on their premises (Figure 20). This
consisted of a 15 cell, 400 cm
2
stack, and tanks that stored over 4000 Ah of energy. AQDS in its
acid form was procured from Riverside Specialty Chemicals, while DHDMBS was synthesized by
HBC Chem based on USC’s protocols. This demonstration was the first and only time that an all-
organic aqueous system was scaled-up and tested at this level.

Figure 20. a) A picture of the scaled-up 1kW/2kWh testing system designed and operated by ITN energy systems,
Colorado; b) Long-term performance studies of 1kW/2kWh system over 400 cycles.
2.12. Learnings from the All-Organic Redox Flow Studies
While crossover effects can be mitigated by the symmetric cell configuration and polarity-
switching protocols, the degradation due to proto-desulfonation, albeit slow, is damaging to the
overall performance. Thus, the focus of our research in the future will be on molecules with larger
size than DHDMBS that do not crossover and are also resistant to protodesulfonation.
In this process, we have identified and tested several molecules that have shown promise for long
term study and eventual scale-up. One molecule of particular promise belongs to the family of
43

DHDMBS, and is the mono-methylated version, 1,4-dihydroxy-6-methylbenzoquinone-3-sulfonic
acid (MMS). MMS was able to show stable cycling without undergoing any transformations or
degradation. MMS also has a much lower crossover rate than DHDMBS. The stark differences in
properties, while being extremely similar in structure to DHDMBS is a fascinating line of enquiry
and is still being investigated. However, the electrochemical performance of this material when
cycled draws attention other problems that are possible in the organic flow battery systems (Figure
21).

Figure 21. Performance and characterization of MMS. The lack of crossover, and lack of chemical transformations do
not aid in explaining the reduction in capacity in the initial cycling.
This anomaly in performance was also identified in another potential candidate that we
termed PHQDS, which has the same structure as MMS, but has a phenyl sulfonic acid group in
place of the methyl. Both MMS and PHQDS appeared to suffer from poor reduction kinetics,
which result in a low discharge capacity. As a result, most of the material is retained in the charged
form, and therefore, subsequent cycles show a reduced, but steady capacity. The reasons behind
44

this poor kinetics have not been fully understood, but we hypothesize that on the positive side of
the cell, the polarization of the electrode surface in acidic conditions could cause a drop in proton
concentration due to bisulfate absorption, thereby interfering with the reduction of the
hydroquinones. It is also important to note that both MMS and PHQDS possess a higher potential
than DHDMBS, and are more asymmetric in their structure.
Identifying electrode structures and possible functionalization that could positively impact the
reduction kinetics of these molecules forms part of the future work in this field. Therefore, it is not
only necessary to have chemically robust active materials, but it is imperative that the
overpotentials for the redox reactions at the electrode are also addressed in an effective manner.

45

3. Iron-Organic Redox Flow Batteries
3.1. Use of Iron in Redox Flow Batteries
While the issues with all-organic systems are being tackled with, we were curious to
explore the possibility of testing the robustness of one of the most commonly used, and cheaply
available materials on the planet – iron. Iron is a particularly attractive battery material because of
its abundance, low cost and environmental friendliness [5], Globally, over 1600 million metric
tons of iron (steel) are produced every year [51]. While we recognize that alkaline nickel-iron and
iron-air batteries are a promising approach for taking advantage of iron [52–54], there have been
also been many previous reports in the literature attempting to use iron-based compounds as the
positive electrolyte in redox flow batteries. In these examples, the iron was deployed as the
ferrocyanide/ferricyanide couple [55,56], ferrocene/ferrocenium couple [40,47], or as iron-
phenanthroline complexes [57]. Although these examples use iron-based materials, the specific
compositions used entail significantly higher cost and also present the challenge of long-term
chemical stability and durability [58,59].
The aqueous “all-iron” flow battery uses only iron (II) chloride that is relatively
inexpensive [11,60]. One of the major challenges for the continuous operation of such an all-iron
system is the parasitic evolution of hydrogen at the negative electrode [53,60]. Additional sub-
systems and reactors are required to capture and recombine the hydrogen and preserve the acidity
of the solutions. The kinetics of iron deposition is also relatively slow, necessitating operation at
low current densities. These characteristics of the all-iron flow battery system lead to higher
systems costs despite the low materials cost. Iron-Chromium redox flow batteries use iron (II)
chloride at the positive electrode [61]. However, this battery is also faced with a challenge of
hydrogen evolution at the chromium electrode [62–64]. More recently, Tucker et al proposed a
46

low-cost single-use portable battery based on iron (III) salts and metallic iron as an inexpensive
power source for developing countries emphasizing the non-toxicity and inexpensive nature of
iron-based battery materials [65]. However, the large-scale exploitation of iron as an active
material in redox flow batteries has hitherto been a challenge, despite the economic and
environmental advantages.
3.2. Introduction of the Iron-Organic Aqueous Flow Battery
The iron-organic redox flow battery we propose, overcomes many of the limitations of the
iron batteries described above. This flow battery uses aqueous solutions of iron (II)/iron (III)
sulfate at the positive electrode and a water-soluble organic redox couple,
anthraquinone/dihydroanthraquinone disulfonic acid (AQDS/AQDSH2) at the negative electrode.
Steel mills generate enormous amounts of iron sulfate as the waste product of scale removal, and
hence iron sulfate is available for as low as $0.10 /kg [66]. We and several others have studied the
use of AQDS in flow batteries [10,13,27,38,67]. Our research has shown that AQDS is robust and
efficient for repeatedly storing and delivering charge [38,39,68]. In addition, the large-scale
manufacturing cost of AQDS is projected to be as low as $1/kg [69,70]. Therefore, we can expect
the iron sulfate /AQDS system to be a particularly promising as a low-cost solution for large-scale
energy storage. The reversible electrochemistry of the iron-AQDS system is presented in Figure
22. This system has a reversible cell voltage of 0.62 V.
47

Figure 22. Cell reactions during discharge and charge of the iron-AQDS flow battery.
3.3. Performance and Characterization of Iron-Organic Flow Battery
In a conventional redox flow battery configuration, each type of redox couple is circulated
past the appropriate electrode (positive or negative). This type of arrangement is referred to often
as the “asymmetric cell” configuration. In such a configuration, the redox materials can crossover
from one electrode to the other through the proton exchange membrane resulting in capacity fade
[68,71–73], as we have observed and studied in the RFBs cycled with 3,6-dihydroxy-2,4-
dimethylbenzenesulfonic acid (DHDMBS). Since the proton exchange membrane is permeable to
cations, iron (II) and iron (III) crossover from the positive side of the cell to the negative side. As
observed previously, we found that AQDS did not permeate the Nafion® 212 membrane consistent
with previous observations in an aqueous all-organic redox flow battery [39,68]. We attributed this
inability of AQDS to crossover to its relatively large molecular size and being anionic in solution.
However, the crossover of iron ions does lead to a capacity loss and renders the asymmetric cell
configuration unsuitable for long-term operation (Figure 23 a).
Since we have experienced the consequences of crossover in our previous studies with
DHDMBS, we were quick to mitigate this problem by using the symmetric configuration (Figure
Discharge
Charge
2Fe
3+
+
OH
OH
SO
3
H HO
3
S
O
O
SO
3
H HO
3
S
2Fe
2+
+ 2H
+

+
O
O
SO
3
H HO
3
S
2Fe
2+
+ 2H
+

+
2Fe
3+
+
OH
OH
SO
3
H HO
3
S
(3)
(4)
48

23 b). The mixed electrolyte configuration has also the benefit of maintaining similar osmotic
pressures on both sides of the cell thus avoiding irreversible water transport across the cell.
Although additional material is needed to constitute the solutions in the reservoirs, this requirement
is less of a concern when the active materials are as inexpensive as iron sulfate and AQDS.
However, one negative aspect of the mixed electrolyte system is the increased viscosity of the
solutions because both the redox couples are present in the same solution at high concentrations.

Figure 23. a) Result of cycling of asymmetric iron-AQDS cell. Note that dramatic capacity loss within the first 5
cycles as expected; b) Long term cycling of symmetric iron-AQDS cell. Steady capacity over 500+ cycles with high
coulombic efficiency; c) Charge-Discharge curves over 100 cycles show no degradation or loss in capacity in a
symmetric cell. Both cells were cycled at 100 mA/cm
2
.
When cycled at 200 mA/cm
2
the capacity of the asymmetric cell showed a steady capacity
decay as expected (Figure 23a). However, the capacity of the symmetric cell did not show any
noticeable change in capacity even after 500 cycles (Figure 23b). In all these charge/discharge
studies, we started with equal amounts of active material on both sides of the cell, and discharged
and charged it to full capacity. The high level of stability in capacity values is indicative of the
inherent durability of the redox couple system.
One of the best indicators of chemical stability is the evolution in the shape of the
charge/discharge curves. We find that even after repeated cycling, the charge/discharge curves did
not exhibit any anomalous features such as the appearance of new plateaus (Figure 23c). These
49

results suggested that AQDS in a mixed electrolyte environment is stable to oxidation by iron (III).
The results confirmed that iron (II) and iron (III) that crossed over undergo reversible
electrochemical reactions with AQDS and AQDSH2 during the cycling. Further, we found that the
rate of crossover of iron (II) and iron (III) was rapid enough under the conditions of the test that
the mix-and-split protocol was not even necessary, and the Coulombic efficiency was 99.63%
averaged over the 500 cycles (Figure 23b).
To characterize the electrical performance of the iron/AQDS symmetric cell, we measured
the current-voltage curves. The electrodes in these cells consisted of graphite felts coated with
multi-wall carbon nanotubes (MWCNTs). Using the “forced flow” configuration for electrolyte
movement through the felt electrodes, we could achieve current densities as high as 840 mA/cm
2

at 100% state-of-charge (Figure 24 a). The impedance measurements on this cell confirmed that
the overall impedance is largely determined by the ohmic resistance of the cell. The ohmic
resistance contribution arises largely from the electrolyte resistance across the thick porous felt
electrodes.
To highlight the role of losses resulting from ohmic resistance, we have plotted the current-
voltage curves after correcting the cell voltage for the ohmic overpotential (Figure 24 a). The cell
voltage is indicated as the “IR corrected cell voltage”. The curves after IR-correction indicate that
by reduction of the ohmic resistance, power densities as high as 400 mW/cm
2
can be achieved with
the iron sulfate/AQDS (Figure 24 b) and the voltage efficiency of the cell at this power density
can be projected to be as high as 93%.
50

Figure 24. Performance of Iron/AQDS symmetric cells. Electrolyte composition - 1 M iron sulfate, 0.5 M AQDS in
2 M sulfuric acid; (a) Cell voltage as a function of current density at 100% state of charge ; (b) measured values of
power density and IR corrected values; (c) effect of flow rate on cell voltage during charge and discharge; (d) effect
of flow rate on cell impedance; (e) comparison of impedance of carbon paper electrode coated with MWCNT and
graphite felt electrode coated with MWCNT.
When the flow rate was 0.27 L/min, the impedance measurements indicate that in addition
to the ohmic resistance (as measured at the high-frequency limit), the mass transport impedance
arising from a finite diffusion layer at the surface of electrode (as measured at the low frequency
limit) dominates the voltage losses in the cell (Figure 24 d); at a flow rate of 1 L/min the mass
transport impedance is less than a third of that at 0.27 L/min. Consequently, the cell voltage and
capacity exhibit strong sensitivity to the flow rate (Figure 24 c).
The use of a thin electrode such as Toray paper with an overall electrode thickness of 1/5th
of the felt resulted in a 50% reduction in ohmic resistance (Figure 24 e). However, the Toray paper
electrode will have to be modified to provide the necessary surface area (and roughness) and the
flow rate needed for supporting the current densities realized with the graphite felt electrodes. By
51

combining a thin carbon paper structure coated with MWCNT (Section 6.2) and using an
interdigitated flow field can reduce the ohmic losses and achieve even higher power density than
with the graphite felt.
3.4. Semi-Symmetric Protocols
Our work reported in Chapters 2 and 3 up to this point have demonstrated the inability of
AQDS to crossover through the proton exchange membrane. Given that in this system AQDS is
the primary material cost driver, it was hypothesized that a system that is symmetric only from the
iron’s perspective should behave identical to the symmetric cell described above. This new
configuration was termed the ‘semi-symmetric’ protocol and produced some interesting results
(Figure 25 a). The reverse configuration of this system, with AQDS on both sides and iron only
on the positive side, was also tested (Figure 25 b) and is expected to behave identical to the
asymmetric cell since the iron is present only on one side.

Figure 25. Schematic representation of a) Semi-Symmetric based on the symmetric system and b) Reversed Semi-
Symmetric based on the asymmetric system. Both behave distinctly differently than the configurations they were
based off, indicating at a possible iron-AQDS interaction.
52

The charge-discharge curves showed reversible behavior and at least 80% utilization of the
active materials (Figure 26 a). We observed coulombic efficiencies over 99.97% across 100 cycles
with a very low capacity fade of 0.024% per cycle (Figure 26 b).
To characterize the electrical performance of the iron/AQDS semi-symmetric cell, we
measured the current-voltage curves. The electrodes in these cells consisted of graphite felts coated
with MWCNT, prepared as described before. Using the “forced flow” configuration for electrolyte
movement through the felt electrodes, we could achieve current densities as high as 1160 mA/cm
2

at 100% state-of-charge (Figure 26 c).

Figure 26. Performance of Iron/AQDS semi-symmetric cells. Electrolyte composition - 1 M iron sulfate, 0.5 M AQDS
in 2 M sulfuric acid, 25 cm
2
graphite felt electrodes, forced flow at 1 L/min; (a) Charge-discharge curves during
regular cycling at 100 mA/cm
2
with a theoretical capacity of 2.4 Ah; (b) Capacity evolution over 100 cycles with
100% coulombic efficiency; (c) Current density- cell voltage curves, and IR corrected current density-cell voltage
curves and the open circuit voltage (OCV) during this test; (d) Power density curve showing peak performance of 194
mW/cm
2
.
53

To highlight the role of losses resulting from the ohmic resistance, we have also plotted the
current-voltage curves after correcting the cell voltage for the ohmic overpotential loss (Figure 26
c). This corrected cell voltage is indicated as the “IR-corrected voltage”. The difference between
the IR-corrected voltage and the open circuit voltage points to the low mass transfer resistance in
this cell. The observed peak power density of 194 mW/cm
2
is comparable to the baseline
performance of vanadium RFBs that use graphite felts [74].
The data presented above indicate that the symmetric and semi-symmetric cells provide
identical conditions for the crossover of iron species, the capacity fade rates are significantly
different. Similarly, the asymmetric and reversed semi-symmetric cells should have behaved in a
similar fashion, but have surprisingly different capacity fade rates. This observation opens up the
possibility of interaction between the Fe and AQDS ions in solution. The fact that the cell voltage
does not change between all three cell configurations points to an interaction weak enough to not
interfere with the redox potentials, but strong enough to slow down the cross over rates.
To determine if there was any interaction between iron and AQDS, we conducted UV-Vis
measurements with 1 cm cuvettes, using 0.01M solutions of Fe(III), AQDS and Fe(III)-AQDS
mixtures. The solvent was 2 M Sulfuric acid, to replicate the conditions used in the cell. We
observed that the absorption produced by the mixed solution was a numerical sum of the individual
absorption of Fe(III) and AQDS samples. Therefore, we premised that the interactions between
iron and AQDS occur only at the higher concentrations used in the cell. At operational
concentrations of 1 M Fe(III) and 0.5 M AQDS, the absorbance was very large and saturated the
sensors. A simple fix for this problem was to reduce the path length by making a thin-liquid film
of the solutions, held between quartz slides. This modification allowed us to observe the behavior
54

of higher concentration solutions by drastically reducing the path traveled by the light. The result
(Figure 27) showed that the mixed solution had a different absorbance than the sum of the
individual samples, indicating interaction between the ions in solution. The exact nature of this
interaction requires further study, but the complexation of the anthraquinone family of molecules
with iron has been extensively studied in biological systems [75–77] and provide clues to further
understand the complexation with AQDS in the iron-AQDS RFBs.

Figure 27. UV-Vis spectra using a thin film of solution formed between two quartz slides, with 2 M sulfuric acid as
reference.
3.5. Cost Analysis of Iron Sulfate/Anthraquinone Disulfonic Acid (AQDS) Battery.

As mentioned earlier, despite the relatively low operating potentials of the Iron-AQDS
system, the low cost and abundance of the active materials make it a prime candidate for large-
scale applications. To see the tangible benefits and practical viability of this system, we calculated
the Levelized Cost of Storage (LCOS) using guidelines provided by ARPA-E [33].
55

[1]
The individual terms utilized in this calculation are explained as follows:
• Input cost of charging the active material at a fixed Round Trip Efficiency (RTE) at a fixed
cost (Pc). The cost is compounded at a rate ‘r’ per year ‘t’ for all the cycles accomplished
within ‘t’. This cost adds up every year for “T” years.

• The cost of maintenance and repair (O&M) per year t adds up over the total life of the
system T.

• The cost of energy components ‘CE’ such as active materials and tank increases with lower
discharge efficiency ‘nD’ since more material and larger tanks are needed. The power
component ‘Cp’ varies with discharge duration ‘d’. Both are only initial investments and
do not incur annual costs and therefore are free from the discount rate per se.

• The total cost of the system calculated thus far covers the operational parameters. But the
investment undergoes usage and is subject to a discount rate which is accounted for here.
𝐿𝐶𝑂𝑆 = [(
1
𝜂 𝑅𝑇𝐸 − 1) 𝑃𝑐 ∑
𝑛𝑐 (𝑡 )
(1 + 𝑟 )
𝑡 + ∑
𝑂 &𝑀 (𝑡 )
(1 + 𝑟 )
𝑡 + (
𝐶𝐸
𝜂 𝐷 +
𝐶𝑃
𝑑 )
𝑇 𝑡 =1

𝑇 𝑡 =1
] ∗ [∑
𝑛𝑐 (𝑡 )
(1 + 𝑟 )
𝑡 𝑇 𝑡 =1
]
−1

[(
1
𝜂 𝑅𝑇𝐸 − 1) 𝑃 𝑐 ∑
𝑛 𝑐 (𝑡 )
(1 + 𝑟 )
𝑡 𝑇 𝑡 =1
]
[ ∑
𝑂 &𝑀 (𝑡 )
(1 + 𝑟 )
𝑡 𝑇 𝑡 =1
]
[(
𝐶 𝐸 𝜂 𝐷 +
𝐶 𝑃 𝑑 )]
56

The system, as a whole, is subjected to ‘nc(t)’ cycles per year over a lifetime of T years
and these costs add up. But higher usage also means a better return on investment and
therefore this is a term that averages the total expenses over the entire lifetime of the
system.

The calculation provides a value for LCOS in $/(kWh-cycle) which is essentially the cost
of discharging 1 kWh of energy from an energy storage system, normalized over the operational
costs, and charging costs over a predetermined time period t, during which the system is discharged
n times. This means that the more number of times we cycle the system, the lower the LCOS, since
the cost of the energy and power components is a one-time investment, but has been utilized
multiple times to extract value. This factor implies that a more durable system capable of being
cycled several hundred times without degradation would have a lower LCOS, and a higher long-
term profitability.
We first have to calculate the cost of energy components of the system, which are the active
materials to determine the fixed energy costs.
The Faraday constant is the charge of one mole of electrons is approximately equal to 26.8
Ah. So, for a two-electron system like AQDS 53.6 Ah of charge can be stored per mole of the
compound and for a one-electron system like FeSO4 26.8 Ah of charge can be stored per mole of
the compound.
For AQDS
[∑
𝑛 𝑐 (𝑡 )
(1 + 𝑟 )
𝑡 𝑇 𝑡 =1
]
−1

57

1 mol of AQDS yields 33.23 Wh of energy in a FeSO4/AQDS system (53.6 Ah * Cell Voltage
(0.62 V)). Therefore, for 1 kWh we need 30.09 moles of AQDS which is 11.08 kg of AQDS
(Molecular Weight of AQDS = 368.33 g/mol)
For FeSO4
1 mol of FeSO4 yields 16.61 Wh of energy in a FeSO4/AQDS system (26.8 Ah * Cell Voltage
(0.62 V)). Therefore, for 1 kWh we need 60.20 moles of FeSO4 which is 16.73 kg of FeSO4
(Molecular Weight of FeSO4.7H2O = 278.01 g/mol)
If we assume the cost of AQDS as $1 /kg and the cost of FeSO4 as $0.1 /kg based on available
information,[1–3] the $/kWh value for an asymmetric FeSO4/AQDS will be:
= Cost of AQDS for 1 kWh + Cost of Iron Sulfate for 1 kWh.
= (Cost of AQDS/kg*Amount of AQDS required for 1 kWh) + (Cost of FeSO4/kg*Amount of
FeSO4 required for 1 kWh)
= (1*11.08) + (0.1*16.73)
= $12.75
The $/kWh for a FeSO4/AQDS symmetric cell will be (Symmetric cell requires twice the amount
of material when compared to an asymmetric cell) = $25.50
For a system designed for daily use it is only practical to consider a maximum use of a
single complete discharge per day. When used on an almost daily basis, we can assume it will be
discharged 360 times a year, leaving a few days for cleaning and/or maintenance protocols. For
such a system, the primary drivers of upfront costs are the active materials. By having a durable
redox couple, the large number of daily cycles anticipated in a year will off-set the cost of energy
58

components. Table 4 and Table 5 show the specifications used to model such a daily use system.
The resulting LCOS for an Iron-AQDS system calculated using equation 1 is shown in Table 6.
Table 4. System Specifications used for calculating LCOS for the Iron-AQDS battery.
System Specifications
Cell Voltage 0.62 V
AC Round Trip Efficiency 0.75 %
Discharge Efficiency 0.80 %
Input electricity price 0.025 $/kWh
Discount Rate 0.1 %
Total Lifetime 20 years
Maintenance Cost /year 0.1 $/kWh
Power Specific Cost 250 $/kW
Daily Storage 10 Hours
Daily Cycles per year 360 #cycles

Table 5. Fixed Energy Specific Costs used for determining LCOS for iron sulfate-AQDS battery.
Fixed Energy Specific Costs
FeSO4 Bulk 0.1 $/kg
AQDS Bulk 3 $/kg
Acid (98%) Bulk 0.2 $/Kg

Table 6. Energy Specific Costs and LCOS for projected costs of AQDS for cross-over resistant operation of symmetric
iron sulfate-AQDS battery.
Discharge
Efficiency
Cost of
FeSO4
Cost of
AQDS
CapEx LCOS
% $/kg $/kg $/kWh $/kWh-cycle
80 0.1 3 54 0.048

A similar calculation for commercial Vanadium flow batteries is shown below in Table 7.
We can see that despite the lower operating voltage of the Iron-AQDS battery, the lower cost of
the active material significantly diminishes the system costs. Additionally, the Iron-AQDS system
does not suffer from hydrogen evolution, solubility issues nor does it need rebalancing over time
59

due to crossover. Therefore, from a fiscal and operational perspective, the proposed Iron-AQDS
battery system is a more sustainable and beneficial energy storage solution.
Table 7. Comparing System costs of iron sulfate-AQDS battery and VRFB.
Battery
System
Theoretical
Voltage
Materials Cost at
Theoretical
Voltage*
Assumed Power
Associated
Costs
System Cost
VRFB 1.26 V $164/kWh
#
$250/kW $656/kWh @ 1.1 V
Fe-AQDS 0.62 V $54/kWh $500/kW
$519/kWh @ 0.3 V
$390/kWh @ 0.5 V
*cost of storage tanks not included
# Lowest cost of Vanadium Pentoxide @ $15/kg

60

4. Design and Characterization of Electrodes
4.1. History of Electrode and Flow-Field Studies in Redox Flow Batteries
Given that flow batteries are well-suited for large-scale energy storage, the performance
and cost of the stack and system are key factors in commercialization. Maximizing power densities
by reducing ohmic and mass transport polarization is an important strategy for reducing capital
and operational costs [28]. A fundamental requirement for achieving high power density at high
voltage efficiency is maximizing the utilization of the active material flowing through the
electrodes. The relationship between flow field design and electrode performance was first
highlighted by Zawodzinski, et.al [78], and followed by various other groups [28,79,80]. The effect
of controlled distribution of electrolyte paved the way for multiple researchers to propose specific
flow field structures optimized for particular electrode structures, such as graphitized carbon paper
or felt. However, a generalized approach to achieving an effective electrode and flow field
combination is not readily available in the literature.
Flow fields are classified based on how the liquid flows relative to the electrode (Figure
28). In parallel, columnar and serpentine flow fields, the liquid flows through channels over the
surface of the electrode either in linear or patterned routes. Interdigitated flow fields (IDFF) and
its derivatives the liquid flows into closed channels that force the liquid to penetrate the electrode
and exit from an adjacent channel that leads to the outlet. The IDFF exhibits a high pressure drop
for liquid flow and is often used with thin, porous electrodes. The flow through (or forced) flow
field works best with thick and highly porous electrodes. The lack of defined channels forces the
liquid to rise along the entire thickness of the electrode to the exit.
61

Figure 28. Three most general classification of types of flow-fields used with porous carbon electrodes [79]. Parallel
has been established as the least effective flow-field for utilizing the entire area of the electrode, while the
interdigitated is preferentially combined with paper electrodes, and the flow through is combined with felt electrodes
ensure more complete use of the area of the electrode.
There have been several attempts to understand the behavior of fluid flow and consumption
through the porous electrode. Using direct imaging methods such as in-situ fluorescence
microscopy [81], X-ray [82] tomography and radiography [83] researchers have tried to obtain a
picture of the pathways and track the consumption of active material through a flow cell. They
were able to study the influence of the pore size of the studied electrode on the consumption of
active material, and the impact of wetting and compression on the cell performance. Unfortunately,
the applicability of these methods is limited by the fact that no two porous electrodes are identical.
Therefore, any results obtained from scanning the micro-structure and imaging the fluid
distribution has limited predictive value to obtain an ideal structure suited for an RFB. While the
conclusions would point towards certain features or improvements, any new type of electrode
would need to undergo the same detailed study before the electrode effectiveness is analyzed.
On the other hand, there have been attempts made to predict the relationship of current to
the potential applied for various porous structures either using complex numerical methods such
62

as a 3D Lattice-Boltzmann model [84], or even an impedance-based approach [85] to separate the
resistance contributions from various processes occurring in the porous structures. The first
approach requires an intimate knowledge of the structure of the electrode, as evidenced by the
need for imaging to understand the size and distribution of pores. The second approach provides
an model to explain the observed impedance in terms of the various processes, but does not provide
a predictive connection to the performance characteristics of porous electrodes. While both cases
provide insights into how a chosen electrode performs, the methods do not offer the ability to
predict the design for a high-performance electrode.
In the following sections, we explore how to improve the inherent performance of an RFB
by modifying the electrode, and developing an impedance based approach to provide design
parameters for building high performance RFBs. Initially, we prepare and characterize the
performance of carbon felt electrodes with surface modification to enhance surface area and boost
power densities. Such modifiers included acid treatment of the felts and coating with carbon
nanotubes. The effect of dispersant content used in the coating of the carbon nanotubes were
analyzed using scanning electron microscopy (SEM) images. The surface area of these electrodes
was determined using electrochemical impedance spectroscopy. The electrode with the maximum
surface area was then selected.
The effects of flow rate and flow fields on the mass transport properties of each of these
electrodes was also studied and a simple method to determine the effective diffusion layer
thickness was also obtained. We also developed an analytical model to predict the relationship
between current as a function of applied overpotential. The model also allowed us to vary the
structural parameters of porous electrodes to study the influence of surface area, inter-fiber
distances and diffusion layer thickness on the RFB performance for a known redox couple. As a
63

result, we are able to identify the critical variables affecting electrode design to minimize losses
and maximize material utilization.
4.2. Electrode Modifications and Microstructure of Felt Electrodes
Carbon-based electrodes for flow batteries are most commonly prepared by pyrolyzing
polyacrylamide (PAN) or cellulose-based Rayon fibers. Carbon fiber felt electrodes that are 3-5
mm thick are prepared directly from the carbonization of the precursor felts. Chopped PAN fibers
are cast into thin layers and graphitized to form thin porous paper-type electrodes that are 120-400
µm thick. The carbon felt and paper electrodes are available from commercial sources such as
SGL, Fuellcell Store, SpectraCarb, etc. The felt form of the electrodes, 3 mm thick, have been
primarily used in this study. Although highly porous (>90%) and having high surface area, these
graphite felts are also hydrophobic and non-wetting in an aqueous environment. Therefore,
chemical modifications such as nitrogen doping, acid treatments, [86–89] or thermal modifications
by heating in air at 300
o
C-400
o
C [90,91] have been recommended to make these surfaces more
suitable for improving the rate of redox reactions. These modifications result in lowering
overpotentials and improve charge-transfer kinetics, and increase energy efficiency. This increase
in activity of the electrode was attributed to enrichment of the oxygen content on the surface
[89,91,92], despite this not being verified. Mench et.al, have demonstrated that an enhanced
microstructure provided significant improvement in cell performance and lowered overpotentials
for redox reactions [93]. Their characterization studies were able to associate the increase in
performance to an increase in surface area, rather than chemical functionalization of the electrode
surface. It is also possible that the enriched oxygen content lowers the activation barrier for the
charge transfer process in the redox reactions.
64

Carbon nanotubes (CNTs) have been extensively used as surface modifiers to increase
surface area of electrodes [86,94,95]. In fuel cell applications in particular, the increased resistance
caused by the use of binders and adhesive polymers have driven electrochemists to push towards
growing nanotubes directly on the surface of the electrodes [96–98]. In our flow systems, the
attritional forces caused by the liquid constantly flowing across the electrode require the use of a
polymeric glue to hold the carbon additives in place. Since there are not too many conducting
polymers to choose from, Nafion was selected to act as both the glue and the dispersant. The drop-
casting method used to prepare the composite electrodes is depicted in Figure 29. This method is
simple and provides a uniform coating of multi-walled carbon nanotubes (MWCNT) through the
electrode. The electrodes produced by this method have reproducible surface areas. The dilution
of 1 mL isopropanol per mg of carbon nanotubes is used to ensure a well-dispersed ink.

Figure 29. The drop-casting method for preparing MWCNT carbon electrodes. This method was used to prepare both
paper and felt electrodes.
The role of Nafion as a dispersant is quite important since MWCNTs are hydrophobic and
tend to agglomerate when introduced into a solution. Although a high Nafion content would assure
effective dispersion of the MWCNT, Nafion being a poor electrical conductor, increasing the
Nafion content of the dispersant could potentially also add to the ohmic resistance of the electrodes.
65

The effect of Nafion content on loading 10% MWCNT by weight on a graphite electrode is shown
in the electron microscope graphs in figure 30. The size of the MWCNT aggregates significantly
reduced going from 0.05:1 to 0.1:1 ratios, but the trend did not continue to the 0.2:1 sample (Figure
30 a to 30 e). Therefore, the 0.1:1 Nafion:MWCNT ratio was selected for preparing the electrodes
in this project.

Figure 30.Varying solution ratios of Nafion:MWCNT by weight: a) Pristine fibers with no surface modifications; b)
0:1; c) 0.05:1; d) 0.1:1; e) 0.2:1; MWCNT content is 10% of the electrode mass.
4.3. Impedance Spectroscopy for Characterizing Electrode Structure and Performance
Electrochemical Impedance Spectroscopy (EIS) is non-destructive experimental technique
able to characterize the electrical response of an electrochemical system, and allowing the
separation and quantification of the effect of several processes that contribute to the system’s
energy losses. An impedance spectrum is obtained by the application of a sinusoidal AC excitation
signal of 2–10 mV (Vmax sin( t)) over a range of frequencies and measuring the magnitude and
phase shift of the sinusoidal current response (Imax sin( t + )). The magnitude of the impedance
(Zmag) is calculated from the ratio of the voltage and current amplitude (Vmax/Imax). The capacitive
66

and resistive elements of the system can be then calculated from the magnitude of the in-phase(
Zreal =Zmag cos( )) and out-of-phase (Zimag= Zmag sin( ))impedance response over the range of
frequencies (  values) of interest.
Typical impedance spectrum for the system with and without redox active components are
shown in Figure 31. By constructing an equivalent circuit based on the processes that occur in the
system containing the redox couple, it is possible to isolate the value of the charge transfer and
mass transfer resistances. These resistances are measured in-situ and are sensitive to the accessible
surface area, kinetic parameters of the redox reaction, and mass transport coefficients and flow
characteristics in a redox flow cell.

Figure 31. Typical Electrochemical Impedance Spectrum of a system a) with redox active species; b) without redox
active species. Points reflect data at various frequencies.
4.4. Determining Surface Area
Impedance spectroscopy can be used to measure the electrode surface area accessible by
electrolyte. In this respect it differs from the BET method that uses a gas that can access a greater
fraction of the electrode area (such as nanopores) that may not participate in the electrochemical
process. This distinction is an important one since in a porous electrode with varying pore sizes,
67

some regions may be inaccessible to the electrolyte owing to the tiny pore sizes and the high
pressure needed to penetrate these pores. As a result, for a given flow rate, the surface area
measured electrochemically through impedance spectroscopy would be the most relevant value
for our analysis of redox reactions occurring at the interface of the electrode and the solution.
The equivalent circuit given in Figure 31 b represents the interface with just indifferent
electrolyte and no active redox couple. In this case, the capacitance arises purely from the
accumulation of charge at the double layer at the interface of the electrode and electrolyte solution.
The ability to store charge at this interface is given by a specific capacitance with units of
Farad/cm
2
. By knowing the specific capacitance for the electrode, we can determine the surface
area using the following the relationships in Eqs. 1-3.
Zimag = -1/ ω Cdl [1]
Slope of Zimag vs 1/ω = -1/Cdl [2]
Cdl/Specific Capacitance = Surface Area [3]
Where, Zimag is the imaginary component (out of phase component) of the measured
impedance, ω is the frequency and Cdl is the double layer capacitance. The imaginary component
of the impedance determined from impedance spectroscopy measurements is plotted against the
1/  to yield the capacitance from the slope of the curve (Eq. 1, Figure 32).
68

Figure 32. Imaginary component of impedance as a function of frequency in 1 M sulfuric acid flowing across both
electrodes.
For example, in Figure 32, using the specific capacitance value of 20 µfarad/cm
2
for a flat
graphite surface, the surface area for the electrodes is determined to be 66,694 cm
2
[94].
Using the above-described method, we determined the surface area gained by decorating
the graphite felts with carbon nanotubes. This measurement allowed us to determine how the
surface area evolved with the loading level of the nanotubes. By testing electrodes prepared by the
method shown in figure 32 with increasing nanotube content, we could determine the composition
at which the pores became inaccessible and the surface area enhancement ceased (Table 8).

69

Table 8. Electrochemically active surface area determined by EIS and the maximum operable flow rate for various
loading on the graphite electrode. All the electrodes in were prepared with 0.1:1 ratio of Nafion:MWCNT.
Electrode
Modification
Surface Area
(cm
2
)
Max flow rate
(LPM)
Plain 3049 1
5% CNT 16949 1
10% CNT 66694 1
20% CNT 126903 0.7
30% CNT 125945 0.5

The measurements showed a steady increase in surface area until about 20% of carbon
nanotubes, although the flow rate began to diminish at this point. Since adequate flow rate was
also important to the performance of the RFBs (as shown in later section), 10% CNT was appeared
to be the optimum composition. This is also the reason why 10% loading was chosen as the
standard for the electrode performance shown in Figure 33. Despite their high surface area values,
the electrodes with higher loading produced a high pressure drop and were therefore considered
non-optimal. This method of determining surface areas was applied to various electrodes and
configurations used in the research.
4.5. Determining Kinetic Parameters and Diffusion Layer Thickness
Mass transport to the surface of the electrode occurs through a boundary layer formed at
the surface of the electrode called the diffusion layer [99]. Within this layer diffusion and migration
are the only means of mass transport. This layer is termed the Nernst Diffusion Layer. Within this
layer there exists a concentration gradient that governs the flux of electroactive material for the
electrochemical reaction. Under steady-state conditions, the concentration gradient in the diffusion
70

layer is linear. The electroactive materials are transported to the outer edge of the diffusion layer
by forced convection. Thus, the rate of forced convection (flow) not only maintains the supply of
materials to the diffusion layer but also determines the diffusion layer thickness. The diffusion
layer thickness together with the concentration and diffusion coefficient determines the mass
transport resistance. Figure 33 shows a schematic representation of the Nernst diffusion layer and
the variables that will be used to define it.

Figure 33. Schematic for representing the Nernst diffusion layer thickness at an electrode-electrolyte interface. The
concentration gradient C*-Cs determines the rate of diffusion through the layer.
The steady-state mass transfer rate per unit area across the diffusion layer of thickness, δ,
is given in terms of the steady-state current, I, according to Fick’s First Law of Diffusion.
I/nFA = D(C*-Cs)/δ [4]
The maximum current, termed the limiting current, ILim , occurs when Cs = 0
ILim = nFADC*/δ [5]
71

Dividing Eq. 4 by Eq. 5 allows us to simplify the relationship between the currents and
concentrations as
1 – I/ILim = Cs/C* [6]
The change in electrode potential resulting from a change of concentration of the reactants
for a reaction that has fast charge-transfer kinetics is given by the Nernst Equation (Eq.7). By
substituting for Cs/C* based on Eq. 6, we may write the Nernst equation as,
E = E
o
+ (RT/nF)ln(Cs/C*) [7]
E = E
o
+ (RT/nF)ln(1 – I/ILim) [8]
At each electrode, using Eq 7, potential, Ec for the cathode and Ea for the anode, can be
determined using the concentrations of the oxidized (Cc,o;Ca,o) and reduced species (Cc,r;Ca,r) at
each electrode. Similarly,Eq4 can be represented in terms of the concentrations of oxidized and
reduced species at each electrode
Ec = Ec
o
+ (RT/nF)ln(Cc,o/Cc,r) [9]
Ea = Ea
o
+ (RT/nF)ln(Ca,o/Ca,r) [10]
Fick’s Law used in Eq4 also allows us to define the current as a function of the
concentration gradients, using C
*
o,c and C
*
r,c as the bulk concentrations of the oxidized and reduced
species respectively.
I = nFAD(C
∗
o,c − Co,c )/δ [11]
I = nFAD(Cr ,c − C∗r ,c )/δ [12]
72

Re-arranging equations 11 and 12, we obtain the relationship between current and surface
concentration at the cathode (equation 13) and can write a similar relation for the anode (equation
14).
Co,c = C
∗
o,c − I/nFA(D/δ) ; Cr,c = I/nFA(D/δ) + C
∗
r,c [13]
Co,c = I/nFA(D/δ) + C∗o,c ; Cr ,a = C∗r ,c − I/nFA(D/δ) [14]
The change in concentration resulting from changes at the anode and cathode is given by
dCo,c = − dI/nFA(D/δ) [15 a]
dCr,c = dI/nFA(D/δ) [15 b]
dCo,c = − dI/nFA(D/δ) [15 c]
dCr,a = − dI/nFA(D/δ) [15 d]
Equations 9 and 10 can be rewritten as:
dEc = (RT/nF){(1/Co,c)dCo,c − (1/Cr,c)dCr,c} [16 a]
dEa = (RT/nF){(1/Co,a)dCo,a − (1/Cr,a)dCr,a} [16 b]
We can relate the electrode potential difference between the anode and cathode to the
maximum current for a given concentration of oxidized and reduced species at the anode and
cathode by using expressions 15 and 16 to get,
𝒅 (𝑬𝒄 − 𝑬𝒂 )/𝒅𝑰 = −
𝑹𝑻
𝒏 𝟐 𝑭 𝟐 𝑨 (
𝑫 𝜹 )
(
𝟏 𝑪𝒐 𝒄 +
𝟏 𝑪𝒓 𝒄 +
𝟏 𝑪𝒐 𝒂 +
𝟏 𝑪𝒓 𝒂 ) [10] [17]
73

In a symmetric system, concentrations are identical on both sides. Therefore, the mass
transfer resistance, Rmt, at 50% state of charge is given by
𝑹 𝒎𝒕 =
𝑹𝑻
𝒏 𝟐 𝑭 𝟐 𝑨 (
𝑫 𝜹 )
(
𝟒 𝑪 ) [18]
For a reversible electrochemical system, the linearized form of the Butler-Volmer Equation
may be applied and the polarization resistance for charge transfer can be expressed by the
following current-potential relationship:
ΔI = ioA(nF/RT) ΔE (linearized form of Butler-Volmer Equation) [19]
The charge-transfer resistance, Rct, of an electrochemical reaction is given in terms of the
rate constant and exchange current density io.
Rct = ΔE/ΔI = (RT/nFAio) [20]
io = nFkoC*, where ko is the heterogeneous rate constant at the equilibrium potential.
Substituting this in the above expression for charge transfer resistance, and accounting for the
presence of two electrodes, we obtain the equation for Rct and subsequently the expression for the
kinetics of the redox reaction.
Rct = 2RT/(n
2
F
2
AkoC*) , ko = 2RT/(n
2
F
2
ARctC*) cm/s [21]
Dividing the mass transfer resistance Rmt, with the charge transfer resistance (Eqs. 18 and
21), we can derive an expression for the diffusion layer thickness based on the parameters obtained
form an EIS spectrum. It is important to note here that the area available for charge-transfer is also
74

the area available for mass transport, because without mass appearing at the surface of the
electrode, no charge-transfer can be sustained.
𝑅 𝑚𝑡 /𝑅 𝑐𝑡 =4𝛿𝑘 𝑜 /𝐷 [22]
𝛿 = (Rmt/Rct)*(D/4ko) [23]
For a planar electrode, this value of δ represents a single value of diffusion layer thickness
for the electrode. In a porous distributed network, the liquid velocities, and concentration gradients
will vary over the entire volume of the electrodes. Therefore, the number obtained through this
method would represent an “effective” diffusion layer thickness across the entire volume of the
electrode. For example, a δ value that equals 1 mm, or 1/3
rd
the thickness of the electrode, points
to extremely poor utilization of the electrode and indicates that the liquid is most probably flowing
around the electrode, as a by-pass flow, rather than through it.
The methodology described here provides us with a calculated measure of the effectiveness
of an electrode-electrolyte combination. This value of  can be used to optimize operational
variables such as flow rate and flow field dimensions, both of which influence distribution of the
redox material throughout the electrode.
4.6. Flow Dependence and Mass Transfer Limitations
The effect of the combination of the flow field and electrode type on the flow battery
performance has been discussed in detail through the years by various other researchers
[28,78,93,100,101]. Although these studies help identify factors that influence the performance of
cells, there remains no definitive method to predict the performance of an unknown electrode-flow
field combination without the deployment of a complete cell system. With the help of EIS and the
75

diffusion layer thickness method outlined in the previous section, we expect to quantify the
properties of the system and predict performance in the presence of a redox couple.
To assert the usefulness of the method derived above in distinguishing between the charge
transport and mass transport properties, we decided to study the impact of flowrate for a fixed
electrode-flow field configuration. We expect the kinetics of charge transport, that give rise to the
charge transfer resistance, Rct, must remain unchanged with flowrate, while the mass transport
resistance, Rmt, should ideally reduce with increase in flow rate. To demonstrate this, a well-known
redox couple with fast electrode kinetics, Fe(II)/(III) was used for this study. To ensure the
symmetry of the cell, a 0.1 M solution of a mixture of Fe(II) and Fe(III) in 1 M sulfuric acid was
prepared and circulated through both sides of the flow cell. The cell had an in-house fabricated
interdigitated flow field coupled with a 10% MWCNT modified graphite felt electrode prepared
(based on the procedure in section 4.2). The EIS for this system (Figure 34), clearly shows us that
Rct (as seen in the semicircular arc at high frequencies) is unchanged in all three values of flow
rate, while Rmt sees dramatic reductions with increasing flow rate.
76

Figure 34. Effect of flow rate on EIS spectra for a symmetric flow system with redox active material. The mass transfer
resistance decreases significantly with increasing flow rate, as a direct consequence of a reduction in diffusion layer
thickness. It must be noted that R ct remains unchanged despite significant changes in R mt.
Using known values for diffusion coefficients for the Fe(II)/Fe(III) system from literature
[102], and the kinetic rate constant obtained from EIS measurements, ko = 1.064 x10
-5
cm/s, the
effective diffusion layer thickness at various flowrates was calculated (Table 9). The effective
diffusion layer thickness was used to calculate the limiting currents. The calculated values of the
limiting current were then compared with the experimentally determined values of limiting current
at each flow rate. At high flow rates, the higher current densities also meant increased
overpotentials and the limiting currents fell short of the calculated values. Therefore, for future
experiments, a flow rate of 0.4 LPM was selected.

77

Table 9. Calculated effective diffusion layer thicknesses, limiting currents and experimentally obtained limiting
currents at varying flow rates.
Flow Rate
(LPM)
Rmt
(ohm)
Rct
(ohm)
δeff
(cm)
I
LimPr

(A)
I
LimExp

(A)
0.3 0.015 0.01 0.233 8.28 8.91
0.4 0.011 0.009 0.202 9.55 10.35
0.5 0.01 0.009 0.137 14.07 11.03
0.6 0.01 0.009 0.121 15.86 11.55
0.7 0.009 0.009 0.104 18.43 12.55
0.8 0.009 0.009 0.102 18.94 12.61

Once the method was established as being reliable, we moved on to test the effectiveness
of flow-fields at distribution of electrolyte through the electrode. Although several configurations
are available in literature [79,80,103], three of the most common flow fields – columnar,
interdigitated (IDFF) and forced (or pass through) – were selected for this study. It is important to
note here that the IDFF and forced flow fields were made in house by modifying the columnar
flow field. As a result, this study helped identify trends in the effectiveness of flow fields in
combination with a MWCNT coated felt electrode, and the best performing flow fields were later
purchased for future organic redox flow battery experiments. A general schematic of the different
flow fields used are shown in Figure 35 a and the EIS spectra of each of these flow fields is shown
in Figure 35 b. The large difference in ohmic resistance between the forced flow field and the other
78

two is due to a higher contact resistance between the electrode and the flow field. These design
compromises were later eliminated as shown in future discussion of organic redox flow batteries.

Figure 35. a) Three types of flow fields used in this test. The columnar flow field represents the lowest pressure drop
system, while the forced flow represents the highest; b) The impact of flow field on EIS clearly depicts the
improvement in mass transport properties between the three flow fields. The forced flow field, which exhibits the
highest pressure drop, has potentially the lowest diffusion layer thickness. This could be a consequence of better flow
distribution through the porous electrode, and a limitation on bypass flow that tends to occur in the other systems.
The ratios of the experimental and predicted limiting currents (Table 10) can be used to
describe how effectively the electrode has been utilized by the electrolyte. A ratio of 0.79
79

demonstrates that all the active material is consumed within 79% of the electrode structure, while
a ratio >1 exhibits a poorly utilized electrolyte that retains a large part of its concentration when it
passes through the electrode and a larger electrode or more residence time is required. Therefore,
we can conclude that the forced flow configuration works best for the 10% MWCNT felt. This
configuration was used for all the organic redox flow cells that were conducted in future.
Table 10. Effective diffusion layer thicknesses and limiting currents for three different flow fields at a constant flow
rate of 0.4 LPM. The ratios of experimental to predicted limiting current values help determine the effectiveness of
the electrode – flow field configuration.
Flow Field
δeff
(cm)
ILimPr
(A)
ILimExp
(A)
I
LimExp
/I
LimPr

Columnar 0.441 4.38 5.14 1.17
Interdigitated 0.202 9.55 10.35 1.08
Forced 0.116 16.63 13.15 0.79

4.7. Limitations of the Proposed Method of Measuring  Based on Rmt/Rct
This model shows greater congruence with experimental data at lower flow rates and lower
currents, while the discrepancies grow larger at higher values. Though this can be interpreted as
poor utilization of the available surface area, the true cause stems from assumptions made
regarding the concentration gradients in the bulk of the electrode. To be precise, as shown in figure
36, we had extended the Nernst diffusion layer model to be applicable at all parts of the electrode,
where a steady bulk concentration C* allows for a development of a uniform diffusion layer. In
reality, the consumption of the active species as it flows through the electrode causes a drop in C*
80

(Figure 36), allowing for a large variation in diffusion layer thicknesses. This leads to regions of
the electrode seeing little to no active material, which manifests as poor area utilization.

Figure 36. A schematic showing the difference between the uniform concentration assumed for Eq.23 vs typical
concentration gradients in the electrode with material actively being consumed.
The model also fails to provide a method to identify parameters to design an electrode, and
can only be used as a comparative tool to determine the effectiveness of a given structure-flow
field combination. We are still unable to adequately explain why the interdigitated flow field is
less effective than the forced flow when using the felt electrode, and what kind of electrode will
be more useful in the place of the felt.
4.8. A modified Analytical Model to Predict Current
The current that can be drawn from each point of the electrode is directly proportional to
the concentration of active material at that location. Therefore, if we are able to understand the
behavior of concentration as it is being consumed within the electrode, we would have a better
understanding of the distribution of the liquid through the electrode. Since the distribution of the
81

liquid is a direct consequence of the internal structure of the electrode, we should be able to use
this method of analysis to interpret the effect of the electrode structure.
Limiting current is the maximum current that can be sustained for a given set of operating
conditions at a specific electrode for a particular electrochemical reaction. As we have defined it
before in equation 5, this condition is met when the surface concentration is zero and all the
material is consumed. In the prior model, we made an assumption that the concentration of bulk
solution is a constant to achieve a steady limiting current.
IL = n F A D (Cb)/  [5]
In a flow-through cell consumption occurs throughout the electrode. The current flowing
through the cell can be estimated from the inlet and outlet concentrations and volumetric flow rate
(Fv).
I/nF = Fv*(Cb – Coutlet) [24 a]
This equation is simply the result of the mass balance requirement. When the outlet
concentration is zero, the current reaches a maximum value for the electrode:
Imax = nF Fv Cb [24 b]
At every point in the electrode, the bulk concentration and interfacial concentration will
vary depending on the local current. This follows principles similar to a plug flow reactor (Figure
37). We can consider an element of uniform concentration and volume dV moving through a
column, and at each point on the column a portion of the active material is consumed. Therefore,
every subsequent point downstream sees a lower concentration of active material than the previous
82

position, leading to an exponential decay. In the case of the RFB, the amount of material consumed
is determined by the local current density ix Acm
-2
.

Figure 37. Schematic representation of a plug flow reactor of height Y, an inlet concentration of C x.b, in which a plug
of height dx and uniform concentration C x. A current i x is drawn from the plug and it moves forward with a
concentration of C x+dx, which is lower than C x.
If I is the total current gathered from various parts of the electrode and the bulk
concentration that supports the mass transport across the diffusion layer reduces down the flow
path because of consumption. We represent the variation in bulk concentration by the variable Cx,b.
The analysis is one-dimensional in that it considers only changes along the length of the electrode
for a plug of uniform concentration along the width.
The local current density ix A cm
-2
is given by:
ix /nF = D (Cx,b –Cx,s)/  [25]
Where Cx,s is the local surface concentration at each point. Thus, the limiting current for
the cell is the integrated sum of various local current values along the length of the electrode. The
diffusion layer thickness is the same for all values along x. Under limiting current conditions at
every point on the electrode, the surface concentration becomes zero,
83

ix,L /nF = D(Cx,b –0)/  [26]
The concentration of Cx,b is infinitesimally different from Cx+dx,b because of the
consumption due to the current.
Cx,b.Fv = Cx+dx,b Fv + ix,L A dx/nF [27]
Note: A is the electrode area per unit length of the electrode (units of cm
2
/cm =cm).
From Eq. 27, for a differential change in position along the length of the electrode, the
change in concentration is given by
dCx,b = -ix,L A dx/nF. Fv [28]
From Eq.26, taking the differential on both sides of the equation,
dix,L/nF = (D/ )dCx,b [29]
Equations 28 and 29 may be used to determine how the local currents and the
concentrations vary for the surface condition of zero concentration.
Current Analysis:
Substituting for dCx,b from Eq. 28 into Eq.29,
dix,L/nF = -(D/ ) ix,L Adx/(nF Fv )
or dix,L/ix,L = -(D/ )A dx/Fv [30]
Integrating over the distance x,
Ln ix,L = - (D/ )A x/ Fv + integration constant [31]
84

When x=0, i0,L = nF D(Cb)/ .
Therefore, constant = Ln (nF D(Cb)/ )
Eq.31 then may be re-written as:
Ln (ix,L /(nF D(Cb)/ ) = - (D/ )A x/ Fv [32 a]
Note that left and right quantities are unit less. In Eq. 32a we have an expression for the
limiting current density at each point on the electrode. Rearranging this, we have an exponential
decay of the local currents along the flow path, which is analogous to the plug-flow reactor.
ix,L = (nF D(Cb)/ ) exp( -(D/ )A x/ Fv) [32 b]
The total limiting current is the sum of all limiting currents. To determine the total current
resulting from these local currents, we can integrate the current density over the entire electrode.
Multiplying both sides of Eq. 32b by A dx
ix,L A dx = [(nF D(Cb)/ ) exp( -(D/ )A x/ Fv)] Adx
Integrating we calculate max limiting current.
I= ix,L A x
I = -A(nF D(Cb)/ ) [exp(-(D/ )A x/ Fv)]/(D/ )A /Fv)+ integration constant [33]
Simplifying Eq.33,
I = ix,L Ax = -(nF (Cb) Fv) exp(-(D/ )A x/ Fv) + integration constant [34]
Applying the definite integral limits for the height of the electrode Y,
85

Iy =iY,L A[Y]-0 = -(nF (Cb) Fv) {exp(-(D/ )A Y / Fv) +1} [35]
Therefore, Equation 35 becomes:
Iy,L = iY,L AY = [nF(Cb)Fv] [1- exp(-(D/ )AY/ Fv)] [36]
Eq.36 yields the total current for the electrode that satisfies the surface limiting current
condition. However, the outlet concentration does not have to be zero, because the condition of
zero concentration is only applied to the surface. Therefore, as the electrode becomes longer or the
flow rate becomes smaller, the Iy will tend to the Imax. The variation of concentration in the bulk
of the solution is obtained by analysis similar to that of the current.
Concentration analysis:
From Eq.28,
dCx,b = -ix,L A dx/nF. Fv [28]
From Eq.29,
ix,L/nF = (D/ )Cx,b [29]
Substituting for ix,L in Eq.28 from Eq. 29,
dCx,b = -(D/ )Cx,b A dx/ Fv
Upon integration over the entire length of the electrode, we have
Ln Cx,b =-(D/ ) A x/ Fv + integration constant [37]
Evaluating the integration constant,
At x=0, Ln Cb = 0+ integration constant
86

Ln Cx,b/Cb = -D/  Ax/Fv
Cx,b = Cb exp[- (D/ )Ax/Fv ] [38]
The exponential term represents the mass transport characteristics of the cell, and
determine how much of active material is available for reaction at a given instance of time. When
this term is greater than -5, then Cx,b will tend to zero, implying that all the active material is
consumed in a single pass. Otherwise,
CY,b = Cb exp[- (D/ )AY/Fv ] [39]
Equation 39 can be used to either determine the outlet concentration for a given cell, or can
provide a design goal to build an electrode that performs to desired expectations. Suppose we want
to realize the maximum current regardless of the size of the electrode or flow rate, we can set the
outlet concentration to <0.01Cb, and this we would need to satisfy the condition:
(D/ )AY/Fv >> 5, for CY,b <<0.01Cb
Thus, we can establish that the dimensional parameter (D/ )AY/Fv can now serve as a
figure of merit for the electrode performance. By decreasing the flow rate and increasing the mass
transport coefficient or by increasing the area available for reaction, the utilization of the
concentration can be maximized.
In practice, we may not know the concentration at the outlet. However, we may be able to
measure the currents under mass transport limited conditions at various potentials.
Iy,L = iY,L AY = [nF(Cb)Fv] [1- exp(-(D/ )AY/ Fv)] [36]
(1/AY)* Ln[nFCbFv)/(nFCbFv-Iy,L)] = (D/ )/Fv [40]
87

So a plot of the left side for various measured values of Iy vs 1/Fv taken at the same
potential when local mass transport limit is achieved should yield a straight line with slope of D/ .
Thus, by knowing A, the area per unit length of the electrode, we can determine D/ .
Much of the analysis above focuses on predicting the limiting current. It is unlikely that a
practical RFB would be operated close to the limiting current. Therefore, it would be necessary
for us to derive the current at any potential of the cell and determine the mass transport and charge-
transfer limitations at any particular flow rate and surface area. This analysis for fast (reversible)
and slow (irreversible) charge-transfer is provided in the following sections.
Case 1. Derivation of the variation of electrode potential with total current and predicting the
limiting Current from the observed current for the case of a reversible reaction
Under “non-limiting” current conditions the electrode, the surface concentration is non-
zero, and equation 25 must be used without invoking the limits of surface concentration
ix,I /nF = D(Cx,b –Cx,s)/  [26]
This can be rewritten as
ix,I /nF = D Cx,b(1 –mI)/ , where mI = Cx,s/Cx,b [41]
By using the subscript ix,I , we distinguish the non-limiting current condition from the limiting
current ix,L. For a reversible reaction, the potential at this point is given by,
Ex,I= Eeq + (RT/nF) Ln(mI)
88

Since all the surface is equipotential and only the current changes, and in the absence of
resistive losses, we must have the same Cx,s/Cx,b value, although the actual values of Cx,s and Cx,b
will vary from point to point.
Ex,I= Eeq + (RT/nF) Ln(mI)
mI= exp( Ex,I-Eeq)nF/RT
The value of mI varies with total observed current, but not with the position on the electrode.
Cx,b.Fv = Cx+dx,b Fv + ix,I A dx/nF [42]
From Eq. 42, for a differential change in position along the length of the electrode, the change in
concentration is given by
dCx,b = -ix,I A dx/nF. Fv [43]
dix,I/nF = (D/ ) dCx,b (1-mI) [44]
Current Analysis for non-limiting values
Substituting for dCx,b from Eq. 43 into Eq.44,
dix,I/nF = -(D/ ) ix,I A(1-mI)dx/(nF Fv )
or dix,I/ix,I = -(D/ )A(1-mI) dx/Fv [45]
Integrating over the distance x,
Ln ix,I = - (D/ )A (1-mI) x/ Fv + integration constant [46]
When x=0, i0,I = nF D Cb(1-mI)/ .
89

Therefore, the integration constant = Ln (nF DCb (1-mI)/ )
Eq.46 then may be re-written as:
Ln (ix,I /(nF D Cb(1-mI) / ) = - (D/ )A (1-mI) x/ Fv [47]
Note that left and right quantities are unit less.
In Eq. 47 we have an expression for the non-limiting current density at each point on the
electrode for a given value of mI. Rearranging Eq.47 we have an exponential decay of the local
currents along the flow path for any value of mI,
ix,I = (nF DCb(1-mI)/ ) exp( -(D/ )A (1-mI) x/ Fv) [48]
The non-limiting currents decay exponentially from inlet to outlet. In order to verifyEq48,
if we set x=0, the current i0,I = (nF D(Cb)(1-mI)/ ). When -(D/ )A(1-mI) x/ Fv is large, then ix,I
will go to zero. This is the expected result.
Let us calculate the total current resulting from these local non-limiting currents. For this
we will integrate the current density over the electrode.
Multiplying both sides of Eq. 48 by Adx
ix,I A dx = (nF DCb(1-mI)/ ) exp( -(D/ )A (1-mI) x/ Fv) Adx
Integrating we calculate max limiting current.
I = -A(nF D(Cb)(1-mI)/ ) [exp(-(D/ )A(1-mI)x/ Fv)]/(D/ )A(1-mI) /Fv)+ integration constant
[49]
Simplifying this,
90

I = ix,I Ax = -(nF (Cb) Fv) exp(-(D/ )A (1-mI)x/ Fv) + integration constant [50]
Applying the definite integral limits for the length Y,
Iy =iY,I A[Y]-0 = -(nF (Cb) Fv) {exp(-(D/ )A Y(1-mI) / Fv) +1} [51]
Therfore, Equation 50 becomes:
Iy,I = iY,I AY = [nF(Cb)Fv] [1- exp(-(D/ )AY(1-mI)/ Fv)] [52]
Iy,I represents the observed current under “non-limiting” conditions, to distinguish from Iy,L
for limiting current conditions. Therefore, Eq.52 yields the total current I for the electrode that
satisfies the surface potential condition of mI. However, the outlet concentration will be decided
by the local currents at the outlet, because the condition of potential is only applied to the surface.
Therefore, as the electrode becomes longer or the flow rate becomes smaller, the Iy,I will tend to
Imax.
The variation of concentration in the bulk of the solution is obtained by analysis similar to
that of the current. The potential varies with the mI value as shown in Eq.52, and we know that,
mI= exp( EI-Eeq)nF/RT
Iy,I = iY,I AY = [nF(Cb)Fv] [1- exp(-(D/ )AY(1-exp( EI-Eeq)nF/RT)/ Fv)]
Let us define EI-Eeq = - E
Iy,I = iY,I AY = [nF(Cb)Fv] [1- exp(-(D/ )AY(1-exp(- E)nF/RT)/ Fv)] [53]
At limiting current mI =0 and thus - E is a large negative number, and we can obtain
equation 36 which was derived for the limiting condition:
91

Iy,L = iY,L AY = [nF(Cb)Fv] [1- exp(-(D/ )AY/ Fv)] [36]
Thus equations[53] and [36] relate the observed currents to the potential before the limiting
current is reached. Also for a given flow condition, we can calculate the limiting current.
Now let us relate Iy,I with Iy,L
Rearranging [53]
(Iy,I/nFCbFv)= 1- exp(-(D/ )AY(1-exp(- E)nF/RT)/ Fv)]
Ln[1-(Iy,I/nFCbFv)] = -(D/ )AY(1-exp(- E)nF/RT)/ Fv)
{Ln[1-(Iy,I/nFCbFv)]}/ (1-exp(- E)nF/RT) = - (D/ )AY/Fv = Z
We have already established the relationship between IY,L and the figure of merit,
Iy,L = [nF(Cb)Fv] [1- exp Z]; Z =- (D/ )AY/Fv
In terms of Iy,I,
Iy,L = nFCbFv(1-exp[{Ln[1-(Iy,I/nFCbFv)]}/([1-exp(- E)]nF/RT)]) [54]
Case 2. Derivation of the variation of electrode potential with total current for the case of a slow
electrochemical reaction.
The current at anywhere in the electrode can be related to the mass transport gradient at the
surface. For an irreversible process, where the charge-transfer process is slow, the surface
concentration is determined by the amount of current that flows at any potential and is given by
the Butler-Volmer equation that includes the effect of charge-transfer kinetics and mass transport.
ix,I = io,x,I (Cx,s/Cx,b) exp (- nF(EI-Eeq)/RT) [55]
92

Here, io,x,I is the exchange current density given by nFkoCx,b where ko is the standard rate constant.
Therefore,
ix,I = nFkoCx,s exp (- nF(EI-Eeq)/RT)
dix,I = nFkodCx,s exp (- nF(EI-Eeq)/RT) at a constant potential EI.
Always,
ix,I /nF = D(Cx,b –Cx,s)/ 
dix,I/nF = (D/ ){dCx,b - dCx,s}
Based on mass balance requirements,
Cx,b.Fv = Cx+dx,b Fv + ix,I A dx/nF [56]
Note: A is the electrode area per unit length of the electrode (units of cm
2
/cm =cm).
From Eq. 56, for a differential change in position along the length of the electrode, the change in
concentration is given by
dCx,b = -ix,I A dx/nF. Fv [57]
From above,
dCx,s= dix,I /nFko exp (- nF(EI-Eeq)/RT) = dix,I/Z
where Z = nFko exp (- nF(EI-Eeq)/RT)
Substituting for dCx,b and dCx,s from above,
dix,I = nF(D/ ){-ix,I A dx/(nF. Fv)- dix,I/Z}
93

dix,I(1+ nF(D/ )/Z) = (D/ )(-ix,I A dx/Fv)
or dix,I = -(D/ ){ix,I A dx/(Fv)} /(1+ nF(D/ )/Z)
dix,I/ ix,I=-(D/ ){A dx/(Fv)} /(1+ nF(D/ )/Z)
Integrating over d ix,I and dx
dix,I/ ix,I=- (D/ ){A dx/(Fv)} /(1+ nF(D/ )/Z)
Ln(ix,I) =-(D/ ){A x/(Fv)} /(1+ nF(D/ )/Z) +integration constant.
Evaluation of the integration constant:
At x=o, Lnix,I = Ln io,I
io,I = Z Co,s or Co,s = io,I/Z
io,I = nF(D/ )(Co,b-Co,s) = nF(D/ )(Cb-Co,s)
Substituting we have,
io,I = nF(D/ )(Cb-Co,s) = nF(D/ )(Cb- io,I/Z)
io,I = nF(D/ )Cb /(1+ nF(D/ )/Z)
ln io,I = Ln nF(D/ )Cb /(1+ nF(D/ )/Z) = integration constant.
Therefore,
Ln(ix,I) = -(D/ ){A x/(Fv)} /(1+ nF(D/ )/Z) + Ln[nF(D/ )Cb /(1+ nF(D/ )/Z)].
Ln[(ix,I)/ [nF(D/ )Cb /(1+ nF(D/ )/Z)]} = - (D/ ){A x/(Fv)} /(1+ nF(D/ )/Z)
94

ix,I = {[nF(D/ )Cb /(1+nF(D/ )/Z)]} exp-(D/ ){A x/(Fv)}/(1+ nF(D/ )/Z)
Multiplying by A.dx and Integration over the definite internal Y < x <0
ix,I A.dx = A. {[nF(D/ )Cb /(1+nF(D/ )/Z)]} exp-(D/ ){A x/(Fv)}/(1+ nF(D/ )/Z) dx
Iy = A{[nF(D/ )Cb /(1+nF(D/ )/Z)]} exp-(D/ ){A Y/(Fv)}/(1+ nF(D/ )/Z) /{-(D/ ){A/(Fv)}/(1+
nF(D/ )/Z}
Simplifying:
IY = nF Cb Fv {1-[exp-(D/ ){A Y/(Fv)}/(1+ nF(D/ )/Z)] } [58]
Z = nFko exp (- nF(EI-Eeq)/RT)
For the case where both active species are present in equal concentrations, such as the
mixed electrolyte that we use in the characterization experiments, Z can be modified to account
for the presence of the oxidative and reductive species present.
Z = nFko [exp (- nF(Eox-Eeq)/RT) – exp ( nF(Ered-Eeq)/RT)]
Rearranging:
(1/AY) Ln (nF Cb Fv/( nF Cb Fv –Iy) = (D/ )/(Fv)}/(1+ nF(D/ )/Z)
Therefore, the experimental data of IY, Cb, Fv, A, Y and ko can be used for various values
of potential and current to determine (D/ ). With increasing value of ko or EI becoming more
negative, the Z term will becomes large and can become <<<1. This is the same equation we have
for the mass transport limited case, Eq 36.
IY = nF Cb Fv {1-[exp-(D/ ){A Y/(Fv)}
95

Therefore, using equation 58, given the overpotential and observed current at any point in
the test, we can determine the limiting current for that condition. We do not need to reach the
limiting current values as this may be vitiated by other reactions taking over.
When we calculate the limiting current from the Rmt value determined from impedance at
open circuit using Rmt = RT/(nFAILim), we calculate the maximum current that can be sustained
at a planar electrode of equivalent area supplied with uniform concentration equal to the inlet
concentration and a boundary layer thickness determined by the flow conditions and the fibrous
structure of the electrode. In practice at any flow rate through a porous electrode the bulk
concentration cannot be maintained unless operated at an impractically high flow rate, or if the
electrode is very short and has a low surface area. For any custom flow-field design, the focus
should be on limiting the development of a concentration gradient by the optimal placement of
inlets and outlets. The functionality of the design can be tested using this model, and the
characteristics of the electrode can be determined from EIS measurements.
The sensitivity of the model to boundary layer thickness, flow rate and kinetic rate constant
are shown below (Figure 38). The smaller the boundary layer, the faster the material can diffuse
to the surface, resulting in higher currents. For a given cell configuration, a higher flow rate results
in a higher limiting current since more active material is available per second. On the other hand
the rate constant influences the slope of the curve, and for a given flow rate and cell configuration,
a higher rate constant leads to a rapid increase in current with additional overpotential. Both of
these holds true as seen in figure 38. In figure 38 b the flow rate increases the rate of availability
of active material, allowing a larger current to be drawn. It also results in a lower mass transport
resistance, as seen in EIS curves comparing flow rates (Figure 34). In the case of rate constants,
for a given flow rate, the limiting current does not change. The kinetic constant has a greater impact
96

at lower overpotentials, indicating the amount of resistance to charge transfer reduces with the
increasing current, as seen in figure 38 c.

Figure 38. Effect of boundary layer thickness (a), Volumentric flow rate (b) and kinetic rate constant (c) on the current
as a function of overpotential as determined by the model in equation 58. This is for a porous electrode of 5000 cm
2

assumed surface area and unless mentioned, F v = 1 cm
3
/s, k o = 1e
-5
cm/s, δ = 0.01 cm.
The behavior follows the same pattern as a conventional RDE, and therefore the expected
behavior of the current-overpotential curves as a function of the variables are known. The diffusion
coefficient, surface area, and boundary layer thickness influence the magnitude of the limiting
currents, while the kinetic parameters such as rate constant and the transfer coefficient, , influence
the slope of the curve. The advantage of the model is that it allows us to generate the equivalent
of RDE curves for any electrode of unknown structure, and if the boundary layer thickness δ and
surface area can be determined through other means, provides a method to simulate the current-
potential response and allows comparison with experimental results. We have discussed how the
97

surface area can be measured directly by the EIS method. In the following we discuss the
experimental determination of the boundary layer thickness, .
4.9. Experimental Determination of Value of 
The operation of RFB is very similar to a well-studied reactor design in chemical
engineering known as a packed-bed column or a plug-flow reactor. The operational similarities
have been established by Langlouis and Coeuret [104–106], for a porous nickel electrode with
known pore sizes. The packed fibrous electrode, however, cannot be described as a collection of
particles like a packed column, nor like a porous electrode of known pore sizes. Hence, we resort
to characterizing the flow through the porous electrode using the Hagen-Poiseuille equation 55,
for a flow through a pipe that can be modified to suit our purposes.
[55]
If we can measure the pressure drop experimentally as a function of the flow rate we should
be able to use the Hagen-Poiseuille equation to determine the average channel width presented in
the flow-through electrode. The primary difference between an open tube and rectangular tube
with packed material, is the cross-section available for the flow of liquid. In the case of an RFB
electrode, the porosity is known and the cross-sectional area of the electrode under compression is
also easily determined. As a result, the mean velocity of the liquid is determined by:
𝑢 𝑚 =
𝐹 𝑣 𝑎𝑏 ∗ 𝘀
98

Where um is the mean velocity, Fv is the net volumetric flow rate, a and b are the dimensions
of the face of the electrode perpendicular to the flow of liquid and ε is the porosity of the electrode.
This changes Eq.55 into:
𝛥𝑃 =
32 .𝐿 .µ .𝑢 𝑚 𝜀 .𝐷 𝑅𝐻
2
[59]
Where DRH is the Real Hydraulic Diameter, and is a representation of the average path
width over the total length L of the electrode. By using this approach, we do not make any
assumptions based on fiber width, length or positions and go purely based on known and
experimentally observable quantities. Therefore, this can be used to define the average channel
width of any porous structure, independent of the internal variations and relative fiber orientations.
The validity of this equation can be easily proven by observing the linear relationship between
pressure drop and volumetric flow rate (Figure 39).

Figure 39. A plot showing the linear relationship between pressure drop and volumetric flow rate. A graphite felt
electrode combined compressed by 30% was used with an interdigitated flow field at room temperature of 298 K.
y = 382914x
R² = 0.9975
0
1
2
3
4
5
6
7
8
0 0.000005 0.00001 0.000015 0.00002
Pressure Drop (psi)
Vol. flow rate (m
3
/s)
99

The slope of the plot allows us to determine the width of the path traversed by the fluid
using equation 56, which in the case pictured above is DRH = 78µm. Similarly, the pressure drop
across different electrodes can be measured, and the corresponding hydraulic diameters
determined (Table 11). This approach simplifies the parameter needed to describe the internal
structure of an electrode that affects the boundary layer thickness. The hydraulic diameter
calculated in this manner for a porous electrode must match with the path length for mass transport
from the impedance measurements, discussed below.
4.10. Impedance Based Approach to Determining Average Path Length
As discussed earlier, the impedance response shows a clear dependence on the flow rate
with the semicircular arc at low frequencies corresponding to the mass transport process. We
expect the frequency at which mass transport control of the impedance appears to be governed by
the thickness of the boundary layer for mass transport. As observed in figure 34 and figure 35 (b),
the mass transport effects are easily distinguished at the lower frequencies of EIS. Specifically,
Figure 34 highlights that although the shape and magnitude of the mass transfer impedance varies
with flow rate, for a given electrode-flow field combination, the frequency at which the mass
transport effects impact the impedance remains unchanged. The use of a specific frequency from
impedance to determine the diffusion coefficient, using equation 60, through a film of known
thickness has been established in prior works [107–109].
[60]
Where t = 1/f, for frequency f, diffusion coefficient, D and the distance traversed, d by
the ion in time t. The specific frequency at which the charge transfer limited region transitions to
100

the mass transport limited region is known as the transition frequency. In the RFB set-up, it is
expected that the path length remains independent of the flow rate. This conclusion is based on the
analysis that the fluid in the porous electrode does not develop a conventional parabolic boundary
layer, but manifests itself as a slug flow, where there is no significant velocity gradient between
the fibers.
Slug flow commonly refers to a phenomenon where the liquid segment moves as a single
unit, rather than a sheared stream influenced by viscous forces. Slug flow is also represented by a
distinct lack of a boundary layer, indicating that all the liquid within the slug moves at a single
velocity (Figure 40).

Figure 40. Highlighting the differences in velocity profile between conventional flow and slug flow. Conventional
flow shows a parabolic boundary layer, while slug flow profile has a uniform velocity except at the tube walls.
Within a structure of randomly oriented fibers, such as a porous fibrous electrode, the flow
velocity distribution is determined by the interaction with the random placement of fibers within
the porous electrode. The liquid flowing around a fiber, does not have the time to develop a distinct
flow profile before being forced to interact with another fiber in its path. As a result, the liquid
travels through the electrode at a uniform velocity.
To verify this, we have simulated using the application COMSOL, the flow through a body
of randomly oriented fibrous field. Early COMSOL studies support this hypothesis (Figure 41).
101

We can see that even though the collection of fibers shown here is not truly randomized, the
velocity within the bulk of the electrode deviates from a parabolic form and tends towards a more
uniform velocity distribution, with gradients at the edges of the electrode. It can be expected that
in a larger simulation with highly randomized fibers, this behavior would extend to encompass
most of the electrode. However, the simulation of a limited porous body has been sufficient to
support the expectation of convection as slug flow through a porous structure of randomly oriented
fibers. Consequently, the characteristic distance for the ion to move by diffusion is equal to the
average distance between the fibers. The COMSOL simulations were performed by Sairaj Patil.

Figure 41. COMSOL model for flow through a simulated structure with fibers 5 um thick, 200 um long and separated
by an equal distance of 75 um. The fibers on each plane are parallel to each other, with successive planes being at 90,
45 and 180 degrees with the z-axis to simulate non-uniform fiber orientation.
The independence of this transition frequency to the flow rate indicates that the mass
transport regime is dictated by the characteristic distance between the fibers rather than the flow
rate. To study this further, we set-up a cell with a felt electrode in combination with a forced flow
field and measured the EIS at different flow rates. A mixed electrolyte of an equimolar mixture
0.01 M Fe(II) and Fe(III) in 1 M Sulfuric acid was used to prevent the effects of crossover and to
reduce the differences between the two electrodes. The goal was to identify the transition
frequency from charge transfer control to the onset of mass transfer control at various flow rates.
102

Figure 42. EIS of a graphite felt electrode with a forced flow-field at two different flow rates. Both transition into
mass transport regions at the same frequency of 0.2712 Hz, as shown. The electrolyte is a uniform equi-molar mixture
of 0.01 M Fe(II) and Fe(III) in 1 M Sulfuric Acid.
At two different flow rates, the point of transition was found to be the same at 0.2712 Hz
(Figure 42). This could be indicative of the time taken for an ion to traverse from the convective
stream to the walls of the fibers. Given that we know the diffusion coefficient of Fe(II) and Fe(III)
in 1 M sulfuric acid, we are able to determine the path length using Equation 57, which was found
to be 0.0035 cm, which, coincidentally is half the DRH measured from the pressure drop calculation
for the same electrode-flow field combination in figure 39. Just like how the DRH remains constant
with flow rate, the transition frequency also remains unchanged with flow rate, lending credence
to the approach that we can use EIS to determine the characteristic length in the porous electrode
that determines the mass transport properties. To verify this, we measured the pressure drop and
transition frequency for a multitude of electrode flow field combinations, using felt, paper and
CNT-coated felts to verify the agreement between these two methods (Table 11).
103

Table 11. Comparing δ = D RH/2 measured from pressure drop and path length from transition frequency.
Electrode
Flow
Field
Transition
Frequency
(Hz)
δ EIS
(cm)
δ ΔP
(cm)
Variation
(%)
Felt Forced 0.2712 0.0035 0.0038 7.89
Felt IDFF 0.2154 0.0039 0.0041 4.88
Paper Forced 0.0943 0.0059 0.0060 1.67
Paper IDFF 0.1359 0.0049 0.0051 3.92
CNT-Felt Forced 0.6309 0.0024 0.0025 4.00

It is known that the IDFF flow field works better with thinner electrodes like the Toray
paper, while the forced flow is better used with thicker materials like the felt. The value of the
average diffusion layer thickness obtained from this method provides proof to the experimental
observations. It also shows that the CNT-decorated felt is much better at utilizing active material,
and therefore would be able to handle much higher concentrations of active material than any of
the other electrodes.
Thus, we can conclude that EIS can be used to effectively determine the average distance
that an ion must traverse within the electrode under mass transport limited conditions. The lower
pathlength in the case of paper electrodes used with IDFF indicates that this flow-field allows for
better utilization of the electrode than when used with a forced flow-field. The sensitivity also
allows us to determine the best flow-field for each type of electrode, allowing further optimization
in the design of the RFB.
The consistency between the hydraulic diameter, the path length for mass transport from
EIS measurements suggest that these values correspond to the effective boundary layer thickness
δ in our model to predict the relationship between overpotential and current. By using this value
of  we can simulate the overpotential and current response in an RFB.
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4.11. Determining the Kinetic Parameters using an RDE
The surface properties of the electrode have a definitive influence on the rate of the
reaction. An inactive surface, such as a glassy carbon electrode, will have a much lower rate
constant for charge transfer compared to a graphitic electrode that has reactive surface groups.
Therefore, it is imperative to measure the rate of the reaction on a surface that is similar to the
electrodes used in the RFB. To determine the rate constant ko, a 0.01 M mixture of Fe(II) and
Fe(III) was prepared in 1 M sulfuric acid. This mixture is the same as that used in the RFB
experiments as well. The linear region of the RDE response (Figure 43 a) between overpotentials
of 100 mV - 200 mV region where charge-transfer controls the overpotential. This part of the
voltammetry curve was therefore used to determine the kinetic rate constant. A plot of
overpotential against log10(I/(1-I/ILim)) should provide a straight line as seen in figure 43 b. The
ratio of the slope to the intercept is the log10 io, where io is the standard exchange current as used
in Equation 21:
io = nFkoAC
Where A is the area of the RDE electrode, and C is the concentration of the active material.
This number is a constant for the reaction on this surface, independent of area and concentration.
Thus the rate constant ko was calculated from the standard exchange current to be
ko = 2.225 E-5 cm s
-1

The other kinetic parameter here is α, the transfer coefficient. This represents the fraction
of the overpotential that is used to lower the activation energy barrier for the charge-transfer
105

reaction to take place. The value was found to be α=0.17, determined from the slope of the same
plot as:
α = RT/(nF*slope) [61]

Figure 43. a) RDE at 1200 RPM on Graphitic Carbon electrode; b) Plot of overpotential vs log 10(I/(1-I/I Lim)), used to
determine k o and α. The solution was an equimolar mixture of 0.01 M Fe(II) and Fe(III) in 1M Sulfuric Acid.
106

4.12. Verifying Porous Electrode Analysis by Experiment.
To make use of the porous electrode model, we experimentally measured the steady state
current produced by applying incremental overpotenials and compared it to the results predicted
by the model. We used the known diffusion coefficient of the active. The electrode properties such
as surface area and diffusion layer thickness can be obtained from EIS through the methods
mentioned earlier in this chapter. Similarly, the kinetic parameters  and ko was obtained from and
RDE measurements on a graphitic electrode. With these parameters obtained from experiment we
can use equation 58 to predict the behavior of the RFB cell with a 1 M mixture of Fe(II)/Fe(III)
redox couple in 1 M sulfuric acid.
IY = nF Cb Fv {1-[exp-(D/ ){A Y/(Fv)}/(1+ nF(D/ )/Z)] } [58]
Z = nFko [exp (- nF(EI-Eeq)/RT) – exp ( nF(EI-Eeq)/RT)]
Figure 44 shows a current at various overpotentials as predicted by the model, compared
to experimental data for 2 different flow fields, using the same felt electrode compressed by an
identical 30%. The agreement between model prediction and experiment is good up to
overpotential values of 0.3 V. The primary difference between the two configurations arises from
the difference in electrolyte distribution through the electrode, and hence utilization, brought about
by the flow field. We can see that at higher overpotentials (>0.3 V), the experiment produces lower
values from that predicted by the model. This is a result of the development of a concentration loss
across the length of the electrode brought about by the complete consumption of active material
upstream as discussed earlier (Figure 36). Due to the lack of significant concentration near the exit,
there are areas of dead-zones in the electrode, and the measured currents drop. The model does not
account for this condition as it assumes that the entire length of the electrode is utilized. At the
107

lower overpotentials (<0.3 V), a finite value of bulk concentration is maintained through the entire
area of the electrode and thus the predicted currents are in agreement with experiment.

Figure 44. Comparing relationship between simulated and experimental current as a function of overpotential for a
felt electrode with a) Forced flow field at two different flow rates; b) IDFF at 1.67 cm
3
/s.
By analyzing the difference between the measured and predicted currents, we can
determine the deficiencies in the design and operation of the RFB. We can also identify the regions
where the RFB performs with minimal losses and thereby choose the operational parameters. In
this case, the forced flow field performs closer to the predicted values since it produces a more
even distribution of electrolyte through the porous structure. The IDFF is optimized to work with
thinner electrodes such as stacks of Toray paper. Therefore, it is expected that the IDFF would
work better than the forced flow-field for paper electrodes (Figure 45 a & b). The model can also
be used to compare the effectiveness of a particular flow field with an electrode (Figure 45 c), and
we can determine the impact of δ found in Table 4 on the performance of the cell.
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Figure 45. Comparing simulated and experimental current as a function of overpotential for a) 3-Stack toray paper
with IDFF; b) 3-Stack toray paper with forced flow-field; c) Simulations of 3-Stack paper with IDFF vs forced flow-
field; d) CNT-decorated felt with forced flow-field with maximum area used vs actual area used obtained by
comparing with experimental measurements. All experimental and simulated measurements made at a flow rate of
1.67 cm
3
/s.
For specially functionalized electrodes, such as a felt electrode decorated with CNTs, the
capacitive area is exceptionally high. Practically, it is not possible for the entire surface of the
electrode to be utilized by the active material. For example, a felt electrode loaded with 10% CNT
by weight has a total area of over 300,000 cm
2
. A lot of this area could be inaccessible due to
narrow passages. Figure 18 d shows the comparison of using the maximum area versus the
experimental value, which uses only ~35000 cm
2
, which is roughly 10% of the available electrode.
This indicates that almost all the active material is consumed within the first 10% of the electrode,
meaning that most of the electrode behaves as a dead-zone. This conclusion allows us to either
increase the concentration of the active material, or in cases where the concentration is limited, we
can build a cell with a much smaller electrode to be more efficient and reduce pressure losses. The
109

predictive value of the model for a desired current, flow rate, and inlet concentration, is to calculate
the required area and path length (e.g., distance between the fibers) for an optimal electrode design.

110

5. Materials and Methods
5.1 Organic Solutions
Solutions of anthraquinone-2,7-disulfonic acid (AQDS) were used as the electrolyte for the
negative side of the flow cell. AQDS was obtained in the sodium form (Riverside Specialty
Chemicals, NJ) that was then dissolved and passed through an ion-exchange column to produce a
solution in the acid form. The resulting solutions were concentrated using a rotary vacuum
evaporator to yield the required concentration in the range of 1 to 2 M.
All the DHDMBS needed for the experiments was synthesized in-house by methods
described in detail in our earlier publication that introduced this compound for use in redox flow
batteries. Briefly, 2,6-dimethylhydroquinone (0.125 mmol, TCI) was added to a stirred solution
of concentrated sulfuric acid (0.375 mmol, EMD Chemicals Inc.), yielding a dark brown solution
that turned into a cake. After 24 hours, the reaction mixture was cooled and diluted with ice-cold
DI water (50 mL) to yield a solution. It was important keep the solution ice-cold during the dilution
of the sulfuric acid or else protodesulfonation, the reverse of the sulfonation reaction, ensued. To
the ice-cold solution, solid barium carbonate (0.25 mmol or 2 equivalents, Sigma-Aldrich) was
added in small quantities with vigorous stirring to neutralize the excess sulfuric acid. About 100
mL of ice-cold DI water was added to the solution during the course of the neutralization process
to facilitate better stirring. Barium sulfate was precipitated as the neutralization proceeded. The
solution was decanted and then centrifuged to remove the barium sulfate by-product, and this
yielded a solution of DHDMBS in the acid form directly. NMR analysis of this solution verified
the concentration of DHDMBS and its purity. These solutions contained greater than 95% of
DHDMBS and the remaining material was the starting material 2,6-dimthylhydroquinone.
Further, the solutions were either diluted with water or water was evaporated under reduced
111

pressure to obtain the required concentrations. When needed, the water was completely evaporated
to yield solid DHDMBS.
5.2. Iron Sulfate Solutions for Iron-Organic Flow Cells
Ferrous sulfate heptahydrate (J.T. Baker, > 99%), anthraquinone-2,7-disulfonic acid
(Riverside Specialty, 99.9%), sulfuric acid (VWR, ACS grade) and deionized water of 18 MOhm
cm was used in preparing the active material solutions for all the experiments.
5.3. Membranes
Proton-exchange membranes of various types were used in the study. These included
Nafion 117 (Equivalent Weight 1100, Dupont), F1850 (perfluorinated membrane, Fumatech) and
E750 (sulfonated PEEK membrane, Fumatech). The Nafion 117 membranes were conditioned by
boiling in 1 M sulfuric acid and then in deionized (DI) water to ensure complete hydration and
maximum proton conductivity, while the F1850 and E750 membranes were used as received as
per the recommendations of the manufacturer.
5.4. Flow Cell Set-ups
For the flow cell experiments, we adapted fuel cell test hardware with an electrode active
area of 25 cm
2
, fabricated with densified graphite flow field plates (EFC-25-01-DM, Electrochem
Inc.). We used interdigitated and flow-through flow fields and graphite felt electrodes (3 mm thick,
PAN Graphite Felt, Graphite Store). Specifically, our asymmetric cell experiments used the
interdigitated flow field. For the symmetric cells, we used the flow-through flow field. The
graphite felt electrodes were immersed in concentrated sulfuric acid for three hours to increase
their wettability. Following the sulfuric acid treatment, the felts were washed repeatedly with DI
water to remove the excess acid before the electrodes were used in the cell. We used centrifugal
112

pumps (March Pump Model #: BC-2CP-MD 12 VOLT DC) to circulate the reactant solutions at
flow rates in the range of 0.1-0.3 liter min
-1
. For flow rates of 1 L/min a gear pump (Eclipse pump
E02KLVF-X, Baldor Motor CDP3310, SCR DC control BC140) was used. All flow-cell
experiments were carried out at 23
o
C with the acid form of the redox couples dissolved in 1 M or
2 M sulfuric acid except where mentioned otherwise. Two glass containers served as reservoirs
for the solutions of the redox couples. The volumes of the solutions were typically 100 mL. A flow
of Argon was maintained at all times above these solutions to avoid reaction of the reduced form
of the redox couples with air (oxygen). We found that the exclusion of air was critical to
maintaining stable cell capacity during cycling.
For the electrode characterization studies, a symmetric system with an equimolar mixture
of Fe(II)/Fe(III) in 1 M sulfuric acid was used. In order to ensure that bulk concentration in the
reservoir was maintained, the solution was looped through both sides of the cell before returning
to a single tank. As a result, the amount of Fe(II) oxidized on one side to Fe(III) was compensated
by an equivalent amount of Fe(III) being reduced to Fe(II) on the other side. This ensured that the
bulk solution in the reservoir always had the same concentration of Fe(II) and Fe(III) at all times.
5.5. Characterization Methods
The electrochemical kinetic parameters and diffusion coefficients were determined by
conducting experiments in a three-electrode glass cell using a rotating glassy-carbon disk working
electrode, a platinum wire counter electrode, and a mercury/mercurous sulfate (MSE) reference
electrode (E
o
= +0.65 V). DHDMBS was dissolved in 1 M sulfuric acid to a concentration of 1
mM. The solution was de-aerated and maintained under a blanket of argon gas throughout all the
electrochemical experiments. Linear-sweep voltammetry measurements were conducted at a scan
113

rate of 5 or 50 mV s
-1
(Versastat 300 potentiostat) at rotation rates in the range of 500 rpm to 3000
rpm using a Pine Instruments Rotator. Cyclic voltammetry measurements were performed on a
static glassy carbon electrode at a scan rate of 50 mV s
-1
over a potential range of -1.0 to 0.8 V vs
MSE.
The current-voltage characteristics of the flow cells were measured at 100% state of charge
under galvanostatic conditions. Charge/discharge cycling studies were carried out using a battery
cycler (Maccor 4200 with 15 Ampere current capability). Charge and discharge were conducted
at a constant current of 2.5 A (100 mA cm
-2
) using voltage cut-off of 1.0 V during charge and
0.001 V during discharge, unless specified otherwise.
Electrochemical Impedance Spectroscopy (EIS) measurements were carried out over the
frequency range of 100 mHz to 10 kHz with a sinusoidal excitation of amplitude ± 5 mV peak-to-
peak (Parstat 2273 potentiostat). Solutions were circulated across both electrodes at a steady flow
rate with a steady blanket of Argon gas bubbling through the reservoir to de-aerate in order to
avoid oxygen reduction.
The composition of the products of cycling and concentration of various constituents was
also analyzed using
1
H NMR (400 MHz with D2O),
13
C-NMR and electron-spray-ionization high-
resolution mass spectrometry (ESI-HRMS).
1
H and
13
C NMR spectra were recorded on Varian
500 MHz or 400 MHz NMR spectrometers.
1
H NMR chemical shifts were determined relative to
the signal of a residual protonated solvent, D2O (δ 4.79).
13
C NMR chemical shifts were
determined relative to the
13
C signal of solvent, DMSO-d6 (δ 39.52). We also used imidazole as
an internal standard for measuring concentration, wherever applicable. NMR samples for the
crossover analysis were typically prepared by diluting 150 microliters of electrolyte with 350
114

microliters of deuterated water (D2O) and
1
H NMR spectra were obtained on Varian 500 MHz
NMR instruments with 128 scans.
5.6. NMR Characterization for Quality Control and Crossover Measurements
The composition of the products of cycling and concentration of various constituents was also
analyzed using
1
H NMR (400 MHz with D2O),
13
C-NMR and electron-spray-ionization high-
resolution mass spectrometry (ESI-HRMS).
1
H and
13
C NMR spectra were recorded on Varian
500 MHz or 400 MHz NMR spectrometers.
1
H NMR chemical shifts were determined relative to
the signal of a residual protonated solvent, D2O (δ 4.79).
13
C NMR chemical shifts were
determined relative to the
13
C signal of solvent, DMSO-d6 (δ 39.52). We also used imidazole as
an internal standard for measuring concentration, wherever applicable. NMR samples for the
crossover analysis were typically prepared by diluting 150 microliters of electrolyte with 350
microliters of deuterated water (D2O) and
1
H NMR spectra were obtained on Varian 500 MHz
NMR instruments with 128 scans.

115

6. Conclusions
With the rising demand for green energy technology, the rapid adoption of electric vehicles,
and the increasing global access to technology, sustainable energy storage systems are needed at
very large scale for bridging the global transition to using renewable energy resources. Redox
flow batteries (RFBs) hold the prospect of becoming these energy storage systems. The focus of
this thesis has been to advance this method of energy storage, and address the key techno-
economic challenges for the commercialization of RFBs.
Our work on aqueous all-organic flow batteries has led the way to synthesize and investigate
materials for the positive side of the flow battery, in addition to developing insight into the various
chemical degradation pathways and capacity fade mechanisms. The scaled-up test of DHDMBS
as positive side molecule was proof that organic molecules could be a viable redox materials for a
commercial product capable to meeting the varied load demands. The low-cost and easy to scale
iron sulfate-organic system is capable of meeting the U.S. Department of Energy’s LCOS goals
of < $0.05/kWh-cycle even in its current form. Exhibiting extreme durability and being based on
abundantly available and inexpensive redox active materials, it is an example of an RFB that has
commercial value even despite its low operating cell voltage.
The analytical model, coupled with EIS measurements described in this thesis provide us with
tools to intimately study the relationship between electrodes and flow fields and deduce design
parameters for the optimized electrode structure for a flow battery. Furthermore, for a given redox
couple and electrode, we can determine the ideal concentration and flow rate required to achieve
performance targets. Such a tool will be invaluable when considering the limitations that arise
from scaling up from lab scale to match real world applications.
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6.1. Future Work in All Organic Aqueous Redox Flow Batteries
Much of the effort in the last six years of research has served well to understand the
technical requirements and challenges with various new types of RFBs. The inherent advantages
and the interesting challenges of the water-soluble organic redox couples have been unveiled.
These efforts indicate that a safe, affordable, sustainable, and robust long-duration energy storage
system is quite promising with next generation RFBs. However, the future rests on addressing the
specific molecular designs that will simultaneously satisfy the primary techno-economic drivers
of cost, durability, efficiency and power density. Computational screening methods such as DFT
and molecular dynamics have been increasingly used in rational molecular design, particularly to
raise solubility, suppress reactivity and increase cell voltage [110,111]. These modeling efforts
could be extended to examining the propensity of specific undesirable transformations such as the
Michael reaction, dimer formation and proto-desulfonation, prior to synthesis and testing.
A simple rotating disk electrode assembly can provide a small-scale testing environment
to determine reaction kinetics and mass transport properties of newly synthesized molecules. These
tests can be conducted on modified surfaces, just by swapping out the working electrode used to
conduct the test. By using this method to screen molecules for their oxidation and reduction
kinetics, a lot of time and resources can be saved in the synthesis process, since only a few mg of
active material is required here. In comparison, 100 mL of 1 M solution of a low molecular weight
quinone requires over 20 g of active material to be synthesized.
6.2. Novel Challenges in Iron-Organic Aqueous Redox Flow Batteries
The most important features of the iron sulfate/AQDS system are the durability and low
cost of materials. We have found no measurable change in the capacity of these cells over 500
117

cycles in the symmetric configuration. Although the thermodynamic cell voltage of 0.62V is not
as high as that for the vanadium system, or even the other iron-based systems, we can project a
material cost of $25/kWh for a symmetric cell using iron sulfate and AQDS couple. This value of
materials cost is significantly lower than that of the state-of-art vanadium systems at $180-
200/kWh,[112,113] The impedance studies presented here suggest that with the iron sulfate/AQDS
system and appropriate modifications to the electrodes and flow fields, the ohmic losses can be
reduced so as to increase the power density. These performance characteristics render the iron
sulfate/AQDS system a unique and attractive candidate for meeting the LCOS target for large-
scale energy storage systems.
Since the primary limitation for the iron-AQDS system comes from the poor solubility of
iron sulfate, both in sulfuric acid and in the presence of AQDS, this could be a technical issue to
investigate to improve the performance and reduce the size of the battery system. Other iron salts
such as iron chloride and iron methanesulfonate have higher solubilities and could be options to
boost the current densities of the cell. Since the iron salts will continue exist as aquo-complexes in
solution, we do not expect major changes in cell potential with these salts. On the other hand,
various iron complexes with ligands such as phenanthroline, glycine, xylitol, etc have been studied
in non-aqueous and near-neutral pH that show another pathway towards improving both potential
and solubility of the active species [57,114].
During performance studies conducted with iron-organic redox flow batteries, the ohmic
polarization were found to originate from the cell construction. Traditionally, thinner electrode
such as stacks of Toray paper have lower resistances than thicker felt electrodes, but suffer from a
lack of active surface area, preventing higher current densities. Modifying these thinner electrodes
118

with multi-walled carbon nanotubes (MWCNT) resulted in surface areas similar to that of felts,
but were found to have significantly higher mass transport resistances. This could arise from the
fact that being denser, the carbon papers tend to have their pores blocked when loaded with the
large amounts of MWCNT required for operating at high current densities. On the other hand, it
was possible to prepare felt electrodes with low ohmic resistances similar to those of carbon paper
electrodes (Table 12).
Table 12. Ohmic resistances and thickness comparisons of various electrode combinations tested for the iron-AQDS
system.

Electrode Modification
Ohmic
Resistance
(mohm)
Thickness
(mm)
Cell 1 Graphite Felt
Nafion:MWCNT
(0.1:1)
27 3
Cell 2
Toray Paper
090 + 120
Heat Treated @
400
o
C for 6 hrs
16 0.65
Cell 3 4xA0550
Nafion:MWCNT
(0.1:1)
8 0.68
Cell 4 Graphite Felt
Nafion:MWCNT
(0.05:1)
9 3

Cell 3 and Cell 4 highlight the effects that surface modification can have on ohmic
resistances. These observations opens up the possibility of designing thicker electrodes with
large open flow channels allow to have low electrical resistance.
119

6.3. Future Work in Electrode Design and Optimization
The analytical model is a highly-flexible tool that can be used with any electrochemical
system that used a porous electrode and where the kinetics of the active material are known.
Therefore, it is possible that the concepts can be extended to any battery system. The combination
of bulk concentration and flow rate in an RFB can be interpreted as total number of moles of active
material present in the porous electrode, and the rest of the model can be used in its current form.
This will help characterize different electrodes to minimize mass transport losses and optimize
operational parameters.
With further progress in the COMSOL model, we will have a much deeper insight into the
fluid behavior within porous structures, and determine the limits of the slug flow assumption. This
can be used to study the effect of fiber thickness, surface modifications and viscosity. Future
possible iterations of the model could be used to study the effect of different flow field designs,
the resulting flow patterns and how the thickness of the electrode influences the extent of
utilization and fluid distribution.

120

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Abstract (if available)

Abstract Energy Storage has been a topic of growing interest over the past several decades as a key technology in our goal to overcome our dependence on fossil fuels. Large scale energy storage methods have been sought out in order to support the grid and provide a sustainable method to maximize our utilization of renewable energy sources such as wind and solar energy. Redox Flow Batteries (RFBs) are a relatively new but encouraging solution to this problem, with the ability to store large amounts of energy with minimal degradation, and the ability to independently support the power and energy needs. The research in this thesis focuses on the various aspects of aqueous RFBs and highlight the challenges and innovations that make this a popular and widely pursued research for energy storage. We have synthesized and studied multiple organic molecules, their electrochemical behavior and degradation pathways in order to identify pathways to design robust and scalable contenders. We also identified membranes that aid in reducing crossover and provide alternative operational protocols that help extend the lifetime of RFBs. This work has resulted in the first all-organic aqueous RFB to be tested at a 1kWh scale and showed that these types of RFBs are capable of meeting the demands of the industry. We also demonstrated a ready-to-scale iron-organic flow battery that has shown extraordinary durability, capable of operating for over 20 years, while simultaneously meeting the cost goals laid out by the U.S Department of Energy.
Aside from the active materials, the electrode plays a key role in achieving high power densities which influences the costs and the size of the RFB. Here, we study the problems involved in designing efficient electrodes and have explored the effect of heat treatment and surface modification to boost battery performance. We have developed an analytical model to predict the behavior of an electrode and an innovative impedance-based approach to extract structural parameters of porous electrodes. The model has been verified using experimental data and demonstrating the versatility and potential towards designing electrodes capable of operating at high power densities, and establishing operating protocols for optimizing performance. The ultimate goal of this thesis is to provide the reader a fundamental understanding of the problems and potential solutions and show how RFBs are a prime candidate to help usher the world into a more sustainable and environmentally friendly future with energy storage.

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Asset Metadata

Creator Murali, Advaith (author)

Core Title Design and characterization of flow batteries for large-scale energy storage

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Degree Conferral Date 2022-12

Publication Date 08/23/2024

Defense Date 08/23/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag anthraquinone,Batteries,electrochemistry,electrode,energy storage,grid scale,hydroquinone,impedance,iron sulfate,OAI-PMH Harvest,porous electrode,quinone,redox flow battery,slug flow

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nutt, Steve (committee chair), Narayan, Sri (committee member), Ravichandran, Jayakanth (committee member)

Creator Email amurali@usc.edu,m.advaith@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111379779

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Source 20220825-usctheses-batch-975 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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