Ionic Conductivity and Exchange Current Density
of Non-aqueous Lithium Polysulfide Electrolyte
ARCHNES
MASSACHUSETTS INSTITUTE
OF TECHNOLOLGY
By
Menghsuan Sam Pan
JUN 0 8 2015
Submitted to the
Department of Materials Science and Engineering
In Partial Fulfillment of the Requirements for the Degree of
LIBRAR IES
Bachelor of Science
at the
Massachusetts Institute of Technology
May 2015 (Tene '20
C 2010 Menghsuan Sam Pan
All rights reserved
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part
in any medium now known or hereafter created.
redacted
Signature of Author..................................................Signature
Department of Mater alycience and'Engineering
May 1, 2015
C ertified by ..............................................................................
Signature redacted
Yet-Ming CWang
yocera Professor of Ceramics
A Thesis Supervisor
Signature redacted
.
..
Accepted by ...........................................................
Geoffrey S.D. Beach
Associate Professor of Materials Science and Engineering
Chairman, Undergraduate Committee
1
Abstract
Lithium-polysulfide flow batteries, which utilize the high solubility of lithium polysulfide in
non-aqueous electrolytes to enable flowable electrodes, have high theoretical energy density and
low raw materials cost. To achieve greater electrode-level energy density, higher sulfur
concentrations are needed. In a given electrolyte system, sulfur charge storage capacity (e.g.
mAh/g sulfur) decreases dramatically with increasing sulfur concentration at a fixed C-rate,
which corresponds to higher current output in higher concentration system. Understanding the
limiting factors that undercut the rate capacity is crucial to enhancing the performance of high
energy density systems. In particular, we systematically investigate the ionic conductivity and
exchange current density at the electrode surface with lithium polysulfide solutions of varying
concentration and in differing solvents which solvent molecules of different sizes. Ionic
conductivities are measured using a commercially available conductivity probe, while exchange
current densities are measured using both impedance spectroscopy and galvanostatic polarization
using6 glassy carbo
worki
electroes.
The electrolyte solvent is found to dramatically affect the solution ionic conductivity and
exchange current density. In the concentration range of interest (1-8 M [S]), the ionic
conductivity monotonically decreases with increasing sulfur concentration while exchange
current density shows a more complicated response in a given solvent system. Between solvent
systems, we observed a five-fold increase in ionic conductivity, and a more than 15-fold
enhancement in exchange current density. The conductivity and current density results are used
to interpret the rate capability of suspension-based cells using lithium-polysulfide electrolyte and
2
carbon black as the cathode with different solvents. With the improvement in kinetics
parameters, we also observed better rate capability in solvent. We also study non-carbonaceous
electrode materials to understand how the electrode material can affect exchange current density
and thus cell capacity. Indium tin oxide electrode shows lower exchange current density then
glassy carbon electrode in preliminary results.
3
Table of Contents
1. Introduction ............................................................................................
7
2. Theoretical Background ...............................................................................
8
2.1 Lithium -Sulfur B attery ..................................................................................
8
2.2 E lectrical D ouble Layer .................................................................................
9
2.3 Ionic C onductivity ..................................................................................
10
2.4 Butler-Volmer Relationship ...........................................................................
11
3. Materials and Experimental Methods .............................................................
12
3.1 Ionic Conductivity Measurement ...................................................................
12
3.2 Exchange Current Density Measurement .........................................................
13
3.2.1
Glassy Carbon Electrode Activation ............................................................
13
3.2.2
Three-Electrode System .........................................................................
13
3.2.3
Electrochemical Impedance Spectroscopy ..................................................
15
3.2.4
Galvanostatic Polarization ......................................................................
17
4. Results and Discussion ..............................................................................
20
4.1 Ionic C onductivity .....................................................................................
20
4.2 Exchange Current Density ............................................................................
22
4.2.1
Electrochemical Impedance Spectroscopy versus Galvanostatic Polarization ............ 22
4.2.2
Concentration Effect ............................................................................
24
4.2.3
Solvent Effect ....................................................................................
27
4.2.4
Glassy Carbon versus ITO Electrode .........................................................
28
4.3 Cell Capacity 28
4
5. C onclusion ............................................................................................
30
6. A cknow ledgem ents ....................................................................................
31
References .................................................................................................
32
Appendix 1. Electrochemical Impedance Spectroscopy for Varying Concentration in Different
Solvent System ............................................................................................
34
Appendix 2. Solution Resistance in Different Solvent System .....................................
45
Appendix 3. Galvanostatic Polarization for Varying Concentration in Different Solvent
System ....................................................................................................
5
. . 47
List of Figures
Figure 1: Conventional Lithium-Sulfur Battery ........................................................
8
Figure 2: Bulter-Volmer Relationship ...................................................................
11
Figure 3: Three-Electrode System ........................................................................
15
Figure 4: Electrochemical Impedance Spectroscopy ...................................................
15
Figure 5: C ircuit Equivalence .............................................................................
16
Figure 6: Galvanostatic Polarization and Tafel Plot ...................................................
18
Figure 7: Swagelok Cell .................................................................................
19
Figure 8: Ionic Conductivity .............................................................................
22
Figure 9: Exchange Current Density in Tetraglyme ...................................................
23
Figure 10: Area Concentration Versus Sulfur Concentration .........................................
24
Figure 11: Exchange Current Density vs Sulfur Concentration ...................................
26
Figure 12: Exchange Current Density Comparison ..................................................
27
Figure 13: Cell Capacity of Tetraglyme and Diglyme System at C/5 Rate .........................
29
List of Tables
Table 1: Exchange Current Density of Glassy Carbon and ITO electrodes ........................
28
List of Equations
Equation 1: Ionic Conductivity .........................................................................
10
Equation 2: Butler-Volmer Equation .....................................................................
12
Equation 3: Modified Nernst Equation .................................................................
17
Equation 4: Stokes-Einstein Equation .................................................................
22
6
1. Introduction
Grid-scale energy storage has raised interests in recent years as traditional electric grids currently
operate very inefficiently. The fluctuating energy demand is met by varying electricity
generation in real-time, and the intermittency limits the usage of renewable energies such as
wind and solar powers. This requires the facilities to meet peak energy demands wasting large
amount of capital on building and maintaining high capacity facilities as well as managing the
power outputs
[1].
At the same time, the overall electricity demand increases at an extremely fast
rate (predicted to double by mid-century and to triple by the end of the century). The
development of grid storage helps solve these problems by giving the grid the ability to shave the
peak demands and shift the loads. In addition, storage improves the reliability and the stability of
the grid by storing electricity locally. Moreover, grid storage can provide many other services
such as frequency regulation and load following, cold start services, and contingency reserves [2]
However, grid-scale energy storage has not been implemented widely due to the insufficiency of
energy storage technology. Scientists believe widespread grid storage application requires energy
storage system with cost less than $100 kWh-1 [3].
Electrochemical systems such as lithium-sulfur battery and lithium-air battery have been
considered for grid-scale energy storage. Lithium-sulfur battery, in particular, has advantages of
low cost and high theoretical energy density. Sulfur, the positive electrode material, costs as low
as $40 t-1 and has high theoretical capacity of 1675 mAh g-'
[4.
The soluble property of lithium
polysulfide across a wide range of oxidation states (Li2S 3 to Li2S8) in many organic solvents has
inspired scientists to develop dissolved lithium polysulfides to be used as the cathode [58].
7
However, the technology suffers from several challenges including formation of insoluble nonconductive compounds and slow kinetics [91. These challenges reduce the material utilization
making the energy density much lower than the theoretical value especially in high concentration
systems. Here, ionic conductivity and exchange current density of lithium polysulfide electrolyte
are studied to understand the rate capability limitation.
2. Theoretical Background
2.1 Lithium-Sulfur Battery
disdharp.
dhang
(a)
D Ga
tSulfur partde
SPolywner binder
(b)
2S2 2S
S
Discbarge: U2S
-
muS UA
-
Figure 1: Conventional Lithium-Sulfur Battery [91. Conventional Li-S battery consists of lithium
metal anode, an organic electrolyte, and sulfur composite cathode. Operation of battery involves
lithium-sulfur species of many oxidation states with Li 2S 3 to Li 2S8 soluble in organic electrolyte
solvent.
8
The sulfur-based positive electrode was first introduced by Herber and Ulam in 1962 [10, and
Rao developed high-energy-density metal-sulfur batteries in 1966 [1". After that, scientists
focused more on the developing lithium-sulfur batteries primarily. The conventional Li-S
battery, shown in figure 1, operates in a manner very similar to the lithium-ion battery. Reducing
the cathode materials, in this cases sulfur, outputs energy, while lithium ions move through the
electrolyte to maintain charge balance. Unlike a typical Li-ion battery, however, which only uses
one or two oxidation states of the cathode, a Li-S battery involves multiple oxidization states
(Li2Sx
for x form 1 to 8, and to S) [91. Among these oxidation states, Li2S3 to Li2S8 are formed as
species that dissolve in the electrolyte and can directly react chemically with the negative
electrode, creating severe shuttle behavior and self-discharge effect. On the other hand, Li2S and
S, which are insoluble and non-conductive, form passivation layers resulting in low materials
utilization, poor cycleability, and low energy efficiency [12]
In order to resolve these problems, scientists have taken various approaches [9,13] One of these
takes advantage of lithium polysulfide solubility to design flowable electrodes for use in a flow
battery. Flow batteries decouple the two electrodes by storing them in separate tanks away from
reaction site helping to prevent self-discharge, and has inherent scalability since engineers can
design the flow batteries such that the diffusive limit never constraint the performance of the
batteries
t5-8].
The scalability along with high energy density and low cost makes lithium-sulfur
flow battery promising for grid-scale energy storage.
2.2 Electrical Double Layers
9
Electrical double layer (EDL) forms whenever an electrode or particle is immersed into an
electrolyte solution. The surface develops surface charges, and then another equal and opposite
charged layer form in the electrolyte to balance the charge. The formation of EDLs changes the
particle-to-particle interaction because when the double layers overlap, the force can no longer
be modeled by the simple Columbic force 1I. The electrical properties of the EDL affects the
electrochemical measurements as well as the performance of the electrochemical system. The
structure and the capacity of the double layer depend on the electrode materials, solvents,
supporting electrolyte, and the species in the solution
.53.Since electrochemical reactions happen
on the electrode-electrolyte interface, the exact composition and structure of the EDL affects the
rate of these reactions. The EDL determines both the concentration of reactants at the interface
and the rate that these particles move toward the interface [16J
2.3 Ionic Conductivity
Theemcdtv1ty
assocIate wIth the paricLe
UUnder certain driving force. ionic
conductivity, here, describes the ion movements in electrolyte solution. Ionic flux under electric
field driving force takes into account of both the ion mobility (proportional to ionic diffusivity by
the Einstein relation) and concentration
[171.
As a result, ionic conductivity can be expressed with
equation 1.
Equation1: Ionic Conductivity
'ionic OC C
where Uionic is the ionic conductivity, c is the concentration, and p is the ion mobility.
10
2.4 Butler-Volmer Relationship
The Butler-Volmer relation shown in figure 2 describes one of the most fundamental
relationships that governs the charge transfer mechanism of the electrochemical reactions at the
electrode surfaces. The relation shown in Equation 2 is valid when the electrode reaction rate is
dominated by the charge transfer at the electrode-electrolyte interface instead of mass transfer. In
the equation, the exchange current density io describes the intrinsic rate of charge transfer of the
electrochemical system [181. To give an intuition, this value provides information about the
difficulty for desired molecules to reach the reaction site and the reaction rate in Li-S batteries.
'I'1I
Y-interceptmInII,1
"%".
I
Tafel region
nekjp
AV
Figure 2: Butler-Volmer Relationship. The Tafel region represents the regime where chargetransfer limits the electrochemical reactions. Extrapolating the Tafel region to zero potential
gives the exchange current.
According to the Bulter-Volnor equation, the current has an approximately exponential, or semilogarithmic linear, dependence on overpotential when the absolute value of the overpotential is
large. One of the exponential term goes to infinity, while the other goes to zero as absolute value
11
of the overpotential increases. Therefore, the exchange current density can be obtained by
extrapolation of the linear Tafel region to zero overpotential. Essentially, the extrapolation drops
one of the exponential term, and when the overpotential is set to zero, the value of the remaining
exponential becomes one. Moreover, if the absolute values of the currents are ploted, the Tafel
region extrapolations from positive current and negative current sizes intercept at exchange
current density with zero overpotential.
Equation 2: Butler-Volmer Equation
1181
aqFAV
aaFAV
ioe
-e
RT
RT
where i is the current density, io is the exchange current density, aais the cathodic charge
transfer coefficient, acis the anodic charge transfer coefficient, F is the Faraday's constant, R is
the gas constant, T is the temperature and AV is the overpotential.
3. Materials and Experimental Methods
3.1 Ionic Conductivity Measurement
Ionic conductivity governs the rate of ion movement in the electrolyte solutions. In other words,
the term associates with the resistivity of the solution which affects both the kinetics of the
batteries and the energy dissipation if mass transport is rate limiting. The ability for lithium ions
to move across the solution from one electrode to the other limits the rate that electrons are
extracted into the circuit and output energy. In this work, a portable ionic conductivity probe is
used to measure the overall ionic conductivity of the electrolyte solutions.
12
3.2 Exchange Current Density Measurement
Another crucial kinetics parameter of electrochemical systems is the exchange current density,
which measures the charge transfer limitation of the system. Two different methods of measuring
exchange current density, electrical impedance spectroscopy and galvanostatic polarization, are
utilized and compared.
3.2.1
Glassy Carbon Electrode Activation
The glassy carbon electrodes are commercially available but require activation before each
measurement. Glassy carbon electrodes are first polished with alumina of 1 micron, 0.3 micron,
and 0.05 micron average particle sizes in that order. After each polishing stage, the electrodes are
rinsed with distilled water [191. The polished electrodes are then dried in vacuum overnight before
transferring into glove box for exchange current density measurements. Note that the activated
electrodes are used in experiments within 24 hours of activation to ensure the accuracy of the
result. To capture the effect of electrode deactivation exposed in argon and air, exchange current
density measurements are performed versus the number of days after the electrode activations.
Notable differences in exchange current density are only observed if electrodes are exposed to
argon or air for more than a week.
3.2.2
Three-Electrode System
13
Three-electrode measurement, shown in figure 3(a), presents an accurate method to determine
the current and potential difference of a given electrochemical system. Passing current through
an electrode changes the potential measured, so segregating current and potential measurements
allows more accurate measurements. In a three-electrode measurement, an ammeter, in series
with the power supply, measures the current running from the working electrode to the counter
electrode while the voltmeter measures the potential difference between the working electrode
and the reference electrode
[201.
No current runs from the working electrode to the reference
electrode.
Here, the working electrodes are the potential candidate current collectors for lithium-sulfur
batteries, glassy carbon and indium tin oxide (ITO), while the counter electrodes and reference
electrodes are lithium metal. The glassy carbon electrodes are activated using the procedure
describe in earlier section, and the ITO electrodes are prepared via sputter deposition onto
stainless steel rods. The electrolyte solutions consist of various concentrations of lithium
polysufide Li 2 S6 ya1gi-g fr mi
Lu8
oI
Molar (of sulfur) and 0.5 Molar lithium bis-
trifluoromethanesulfonimide (LiTFSI) as solutes, and dioxolane/dimethoxyethane (DOL:DME =
1:1), diethylene glycol dimethyl ether (Diglyme), Triethylene glycol dimethyl ether (Triglyme),
or Tetraethylene glycol dimethyl ether (Tetraglyme) as the solvent. An illustration of the three
electrode system for lithium sulfur electrolyte solution is shown in figure 3(b). In the simplest
term, this three electrode system essentially measures the potential required to activate the
oxidation or reduction reaction of lithium polysulfide at a given rate.
14
V
Working Electrode
(Glassy Carbon)
Counter Electrode
(Lithium Metal)
C
-'
Reference Electrode
(Lithium Metal)
(a)
(b)
Figure 3: Three-Electrode System. (a) Simple diagram representing the system. Ammeter, in
series with the power supply, measures the current between working electrode and counter
electrode, and the voltmeter measures the potential difference between the working electrode and
the reference electrode. (b) In this project, the working electrode are glassy carbon or ITO while
the counter electrode and the reference electrode are lithium metal.
3.2.3
Electrochemical Impedance Spectroscopy
low0
250
!00
200
.0
Ei 150
,.:
100
0.1
1
10
100
1000
104
'
Frquency
25
20
50
10
300
400
500
600 700
Re[Z]
900
800
1000
01
15
I
10
100
Frequency
1000
10,
Figure 4: Electrochemical Impedance Spectroscopy. The real impedance represents the
resistance term of the circuits, while the negative imaginary impedance represents the
capacitance. The magnitude of the real impedance is the amplitude ratio of the voltage input and
the current response, and the angle is determined by the phase lag of the potential and current.
The charge transfer resistance and the exchange current density are calculated from the width of
the arc.
The first method of measuring exchange current density uses electrochemical impedance
spectroscopy (EIS). EIS measurement applies alternating voltage signal and measures the phase
shift between the current signal and the voltage signal to extract the capacitance or inductance
properties. With this idea, for each given frequency of AC signal, the magnitude of impedance
response is the ratio of the voltage amplitude and current amplitude (note the unit is equivalent to
that of resistance), while the angle maps to the phase lag of current with respect to the voltage
input. The measured data is then expressed by complex impedance with real part representing
imaginary part irepesenting inductance, and negative imaginary part
esistance,sv
representing capacitance [21]
Rcharge transfer
Rbulk
C
Figure 5: Circuit Equivalence. The three electrode systems in this work map to this equivalent
circuit. The bulk resistance accounts for the solution resistance and metal resistance. The charge
16
transfer resistance describes the rate that reaction can happen on the current collector surface,
and the capacitance term describes the charge buildup at the electrolyte-collector interface.
In lithium sulfur batteries, the exchange current density directly relates to charge transfer
resistance, which has capacitance characteristic as charges build up at the electrolyte-current
collector interface while batteries are operating. This capacitance characteristic allows the EIS to
effectively separate charge transfer resistance from the bulk resistance by looking at the
imaginary impedance. As a result, the impedance data is fitted to a simple circuit equivalence
shown in figure 5 which has a typical impedance response shown in figure 4 to obtain the charge
transfer resistance. The capacitor acts as a short circuit at high frequencies and acts as an open
circuit at low frequencies due to the capacitor responses to charge buildup, so the high frequency
limit of the equivalent circuit is just the bulk resistance, while the low frequency limit of the
equivalent is the bulk resistance plus the charge-transfer resistance. In the case, the charge
transfer resistance is the width of the arc in the impedance plot. Equation 3 then relates the
charge transfer resistance to exchange current density.
Equation 3: Modified Nernst Equation
[18]
RT
0
nFRcharge-transferA
where io is the exchange current density, R is the gas constant, T is the temperature, n is the
number of charge per ion, F is the Faraday's constant,
Rcharge-transfer
resistance, and A is the active area of the current collector.
3.2.4
Galvanostatic Polarization
17
is the charge transfer
Input Galvanostatic Steps
6
7~4
3.0 mol S/L as Li2S6 in Diglyme
2
U
-
5.00.
B-4,
0
_61-
Sees 10000 15000 20000 25000 30
Ti.(S)
-1.00
0.50
Potential Response
2.6
=Q
0.10
U 0.05
t22A
2.2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Potential vs. Li*/Li (V)
0
5
10
15
20
25
30
Tb. (OM)
(b)
(a)
Figure 6: Galvanostatic Polarization and Tafel Plot. The current step input and potential response
pairs form the Tafel plot on the right. The semi-logarithmic linear regimes of the Tafel are
governed by the charge transfer limitations and Butler-Volmer relation, and their interaction
represents the equilibrium potential and exchange current.
The second method uses galvanostatic polarization along with knowledge on charge transfer
theory. Galvanostatic polarization applies various constant positive and negative current inputs
over a certain period of time to obtain stable potential responses shown in figure 6(a). Tafel plots
are then constructed with these currents' absolute value and potential pairs for a given system.
The Tafel plot plots the current in logarithmic scale on the vertical axis and the potential in linear
scale on the horizontal axis as shown in figure 6(b). The Butler-Volmer relationship is applied to
the semi-logarithmic linear regime of the Tafel plots in which the system limits by the charge
transfer at the interfaces. The interception of the extrapolated linear regimes of positive currents
18
and negative currents gives the equilibrium potential and the exchange current, which is then
normalized to exchange current density with respect to active area of the current collector.
3.3 Battery Capacity Measurement
The kinetics parameters help to understand the fundamental science and limiting factors of
batteries, but they do not provide information about the usability of batteries. Ultimately, society
cares about the capacity and the energy efficiency of the batteries. Therefore, measuring how the
kinetics properties affects the rate capability links this work to the practical aspect of batteries. In
general, the energy efficiency and capacity drops with increasing charge and discharge rate since
more energies are used to overcome the kinetic resistance. By convention, the charge and
discharge rate are expressed in term of C rates, in which 1 C represents complete charged or
discharged over 1 hour while C/5 represents over 5 hours.
3 Electrode
2 Electrode
mac Obctod(b)
sphmar3r
WN tme ffmcreft (e)
+
PtuOOMr
19
Figure 7: Swagelok Cell [221]. The lithium-polysulfide suspensions are used as the cathode
(working electrode) in 2-electrode Swagelok cells which then undergo capacity test to obtain the
materials utilization with a specific charge/discharge rate.
Carbon black powders are mixed into lithium sulfur electrolyte solution to enhance the electrical
conductivity. The resulting suspension is then used as the cathode in a 2-electrode Swagelok cell
shown in figure 7 with lithium metal as the anode and a porous polymer separator between the
electrodes. Then, the cell undergoes constant current input corresponded to a desired C rate and
the voltage responses are measured until the batteries can no long output any energy. This way,
the total runtime corresponds to the capacity and materials utilization while the current-voltage
relation allows the calculation of total energy output.
4. Results and Discussion
4.1 0nic %CAnductiit
In the sulfur concentration range of interest (1-8 Molar), ionic conductivity decreases
monotonically with increasing sulfur concentration in all solvent systems. The result for the ionic
conductivity measurements are shown in figure 8. However, there exists no single simple
function that describe the decreasing trend for all solvent systems. When considering the ionic
conductivity of a single solvent, there are two opposite trends associated with increasing solute
concentration: the amount of ions available in the solution and the mobility of individual ions.
Obviously, the more lithium polysulfide dissolved the more ions available. On the other hand,
20
the mobility decreases with sulfur concentration because of the "crowdedness" rises with
concentration. Since molecules have volume and mass, larger number of surrounding molecules
make it harder to move through them. In the experiments, higher viscosity is also observed for
higher sulfur concentration, which further supports this explanation. Combining the two trends,
the ionic conductivity is expected to increase initially as the increasing ion concentration
dominates the trend and start to drop after peaking as the decaying mobility takes over. This also
fits the observations that the ionic conductivity dropping rate increases in some systems
(DOL:DME and diglyme) but decreases in others (triglyme and tetraglyme).
Comparing the ionic conductivity across different solvent systems at any given sulfur
concentration, the DOL:DME system (5x of tetraglyme system) has the highest ionic
conductivity, then diglyme, triglyme, and finally, tetraglyme. The different ethers have the same
functional group interacting similarly with molecules and ions, and differ only in molecule chain
lengths, so the effect must come from the size differences. The chain length of the solvent
molecules inversely correlates with the ionic conductivity. Again, ionic conductivity takes into
account the concentration of ions available and the mobility of the ions. The concentration of
ions in the solution remains the same since the same sulfur concentrations are discussed.
However, the mobility of the ions changes from one solvent system to another because larger
solvent molecules create larger resistivity for ions movement. In experiment, the longer molecule
systems exhibit higher viscosity clearly ranging from water like texture (DOL:DME) to ketchup
like texture (tetraglyme), and thus lower mobility according to the Stokes-Einstein equation
shown in Equation 4.
21
Equation 4: Stokes-Einstein Equation
D=
=kB T
k
6 ir 77 r
where D is the diffusion constant, y is the mobility, kB is the Boltzmann's constant, T is the
temperature, il is the viscosity, and r is the radius of the particle.
10
E
-9
U::8
E
DOUD
7
6
Diglyme
5
0
Triglyme
3
-2
tetragtyme
0
0
1
2
3
4
5
6
7
8
9
Sulfur Concentration (Molar)
Figure 8: Ionic Conductivity of Various Solvent Systems. Ionic conductivity decreases
monotonically with concentration and solvent molecule size. In any given sulfur concentration,
DOL:DME system has the highest ionic conductivity while tetraglyme has the lowest.
4.2 Exchange Current Density
4.2.1
Electrochemical Impedance Spectroscopy versus Galvanostatic Polarization
22
Exchange Current Density vs Li2S6 S Molar
Concentration in Tetraglyme
0.0600
,
Electrochemical
0.0500
C
o~0.0400
vanosttic
Potarization
0.0300
0.0200
0.0100
0
1
2
3
4
5
6
7
8
9
Sulfur Concentration (Molar)
Figure 9: Exchange Current Density in Tetraglyme. Galvanostatic polarization generates more
precise data but electrochemical impedance measurement is less time consuming.
The results for tetraglyme system two measurement techniques for which the results for
tetraglyme system are shown in figure 9 have different advantages and disadvantages.
Electrochemical impedance spectroscopy (EIS) provides a time conserving and convenient way
to measure exchange current densities. In volatile solvent systems such as DOL:DME system,
galvanostatic polarization is unfeasible with open cells as the experiments require more than
twenty hours, while EIS takes less than twenty minutes. The DOL:DME system experiences
observable evaporation over twenty hours which alters the results of the measurements as
concentration varies over time. However, EIS is subject to larger trial to trial deviation. In this
work, the results for EIS experience up to 2-fold difference even though the chemicals and
experiments are prepared and setup identically. On the other hand, galvanostatic polarization,
23
although takes a long time, shows very little trial to trial deviations. Therefore, in contrast to EIS,
galvanostatic polarization has characteristic of higher precision although it is more time
consuming. For detail EIS and galvanostatic polarization data and analysis, please see Appendix
l and 3.
4.2.2
Concentration Effect
Area Concentration vs Sulfur Concentration
.~.
3
2.5
C44~
2
u 1.5
0
i-
0.5
0)
0
1
2
3
4
6
5
7
8
9
Sulfur Concentration (Molar)
Figure 10: Area Concentration Versus Sulfur Concentration. Area concentration show slightly
slower dependence on sulfur concentration than linear dependence. This dependence on sulfur
concentration is very similar to that of ionic conductivity in diglyme and triglyme systems.
The exchange current densities of different solvent systems show different and complicated
dependences on concentration. Exchange current density corresponds to the charge transfer
limitation, which relates to the reaction rate and the reactant concentration at the electrodeelectrolyte interface. Within the same solvent system, the reaction rate should not change as the
24
reactants and environments remain the same. In dilute solutions, the solute molecules and ions
are well separated such that their movements and electric double layers do not intervene with
each other. Exchange current density then should increase almost linearly with bulk
concentration since area concentration at the interface scales with the bulk concentration as
shown in figure 10 when electrical field drives ions and molecules toward the interface. The
exchange current densities of the diglyme system and triglyme system do show very similar
dependences on concentration as shown in figure 11 (b, c). The molecules and ions in these
solvent systems barely interact with each other because the electric double layers are not thick
enough to overlap with each other in the sulfur concentration interested.
However, the exchange current density of tetraglyme system shown in figure 11(a) exhibits a
more complicated trend than linear with a nearly constant value beyond 3M. In this case, the
dilute solution assumption does not hold. The polar solvent molecules along with other ions in
the solution form the electric double layers, and the double layer thickness increases as the
solvent molecule size increases. This means, in tetraglyme system, the dilute solution assumption
fails at a lower concentration than other solvent systems. At high concentration, the electric
double layers overlap with each other forming intermolecular forces among the double layer
molecules. In order for the electrochemical reaction to occur, the lithium ions and polysulfide
molecules need to break through the double layers to reach the electrode. But the energy required
to break these double layers increases due to the double layers interactions reducing the
exchange current density. As a result, the exchange current density no longer has a linear
dependence on the sulfur concentration. In fact, the exchange current density peaks at some
25
intermediate concentration and starts dropping because the energy required to reach the interface
becomes so high that this energy limits the exchange current density.
Exchange Current Density vs LizS6 S Molar
Concentration in Triglyme
Exchange Current Density vs Li2S6 S Molar
Concentration in Tetraglyme
0.12
0.0600
Z
EIS
0.0400
Vanostatic
0.06
00200
0.04
0.0100
0.02
0.0000
0
1
2
3
4
5
6
Gavmnostatc
Polarbation
0.08
Potartzation
0.0300
0.1
0
7
8
9
0
2
4
Sulfur Concentration (Molar)
10
6
Sulfur Concentration (Molar)
(a)
(b)
Exchange Current Density vs L12S6 S Molar
Concentration in Diglyme
Exchange Current Density vs 112S6 S Molar
Concentration in DOL:DME
03
1.6
E
0.25
1.4
0.2
S
12
015
0.1
0.6
IA
0.4
0.2
0
0
0
1
2
3
4
5
6
Sulfur Concentration (Molar)
7
8
9
0
1
2
3
4
5
6
7
8
9
Sulfur Concentration (Molar)
(d)
(c)
Figure 11: Exchange Current Density vs Sulfur Concentration. Exchange current density in
different solvent system exhibit different dependence on sulfur concentration. There is an almost
linear dependence in triglyme and diglyme systems while there exists a more complicated
dependence in tetraglyme system with a maximum at 5 Molar sulfur concentration.
26
Finally, for DOL:DME system, only EIS measurements can be performed due to the high
volatility of the solvent. The results shown in figure 11(d) experience large amount of errors such
that no conclusion in concentration dependence can be drawn.
Solvent Effect
4.2.3
Sulfur Concentration (Molar)
0
S
1
E
0.100
x
3
4
5
6
7
8
1.000
C
0
2
iglyme
L:D
Trigtyme
E
-5
TEGDME
0.010
Figure 12: Exchange Current Density Comparison. Exchange current density increases as the
solvent molecule chain length gets shorter in solvent molecules of same chemistry. DOL:DME
system, however, shows a lower exchange current density then diglyme system at high sulfur
concentration. From tetraglyme to diglyme system, there exists a fifteen-fold increase in
exchange current density.
Just like ionic conductivity, exchange current density increases as solvent molecule sizes
decreases in tetraglyme, triglyme, and diglyme systems as shown in figure 12. The size of
molecule affects the electrical double layers of the ions and molecules as well as the electrode.
27
The thicker double layers are expected to require more energy to break through. This means the
thicker the double layer, the lower the exchange current density, which agrees with the results.
On the other hand, DOL:DME system has exchange current densities lower than that of diglyme
even though DME molecules are smaller than diglyme molecules. As mention earlier, the
composition and the structure of the double layer depend on not only the size of solvent
molecules but also the chemistry of solvent. It is unclear how the addition of DOL, which has
different functional group than any other solvents used, will affect the double layer. To
understand the exact effect of DOL, additional experiments on DME as solvent or DOL:triglyme
as solvent are required. Nevertheless, the exchange current density is increased by more than 15fold from tetraglyme to diglyme system.
4.2.4
Glassy Carbon versus ITO Electrode
Electrode
5M in Triglyme
Glassy Carbon
0.097 mA/cm2
ITO
0.022 nA/cm2
Table 1: Exchange Current Density of Glassy Carbon and ITO electrodes. Glassy carbon
electrode shows allows a much higher exchange current density than ITO electrode.
The electrode materials can also alters the structure and composition of the electrical double
layer. Here, glassy carbon electrodes and ITO electrodes are used. As shown in table 1, glassy
carbon electrode has a much higher (more than 4 times) exchange current density that that of
ITO electrode.
4.3 Cell Capacity
28
-I
2.4
2.2
-
c'
0
Diglyme, 5M, C/5
Tetraglyme, 5M, C/5
2.01
0
200
400
800
600
Capacity (mAhlg)
Figure 13: Cell Capacity of Tetraglyme and Diglyme System at C/5 Rate. At C/5 rate, diglyme
system has a 5-fold increase from tetraglyme system.
Tetraglyme has been widely used as the electrolyte solvent in Li-S batteries, but the cell capacity
suffers even at a rate of C/5 charge/discharge rate. Cells using tetraglyme as electrolyte solvent
has a capacity of around 150 mAh g-1 S which is far from the theoretical energy density of 1675
mAh g-'. This means the material utility in that particular experiment is less than 10 percent. To
understand how the kinetic parameters affect the rate capability, cell capacity test of the same
rate using diglyme as the electrolyte solvent was performed. The cells have capacities of more
than 700 mAh g-1 S, 5 times more than cells using tetraglyme as shown in figure 13. Although
the material utility is still less than 50 percent, but the promising results proves that enhancing
the kinetics parameters helps the rate capability. Therefore, the changing the electrolyte solvent
does improve the rate capability of Li-S battery.
29
5. Conclusion
In non-aqueous lithium-polysulfide electrolytes, both sulfur concentration and solvent effect the
ionic conductivity and exchange current density dramatically. In the concentrations of interest,
ionic conductivity decreases as concentration increases and increases as glyme solvent molecules
gets smaller due to the mobility changes. Exchange current density, however, shows much more
complicated responses to concentration and solvent. Nevertheless, a 5-fold increase in ionic
conductivity and a 15-fold improve in exchange current density are observed in the solvent
systems we have tried. These enhancements in kinetics parameters resulted in an improved rate
capability in suspension-based batteries. Although the rate capability and materials utilization
have not reached the desired value, and the capacities fall far short of the theoretical value, this
result has shown that improving the ionic conductivity and exchange current density and
changing the solvent do improve the practicality of the Li-S batteries. In term of solvent, the goal
for the future will be searching for solvents that further improves the kinetics parameters and
thus the rate capability.
In addition to solvent, the electrode material also influences the exchange current density. Here,
we have obtain preliminary data comparing glassy carbon electrode and ITO electrode showing
that glassy carbon electrode is a much more favorable electrode. However, the exact mechanism
of how electrode materials affect the exchange current density remain unrevealed. Therefore,
performing more experiments and characterizations on glassy carbon electrodes and ITO
electrodes are necessary to systematically improve the kinetics from the electrode point of view.
30
6. Acknowledgement
This work was supported as part of the Joint Center for Energy Storage Research, an Energy
Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy
Sciences. The author thanks Prof. Yet-Ming Chiang for the technical instructions and materials
science knowledge inputs, and Dr. William Woodford and Mr. Frank Fan for laboratory trainings
and instructions. Also, Mr. Frank Fan deposited the indium tin oxide electrodes and ran the cell
capacity experiments presented in this work, and Prof. Craig Carter provides the Mathematica
code for fitting the electrochemical impedance spectroscopies and linear regimes of the Tafel
plots.
31
References
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Battery Cathodes. Accounts of Chemical Research, 46(5), 1135-1143.
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33
Appendix
Appendix 1. Electrochemical Impedance Spectroscopy for Varying Concentration in Different
Solvent System
1.1 Electrochemical Impedance Spectroscopy Tetraglyme
1.1.1
Electrochemical Impedance Spectroscopy Tetraglyme 1 Molar Sulfur
8000
20000
6000
15000
10000
7000
.- 45000
3000
2000
1500
2000
~10001
0.
0
5000
10000
Re[Z]
15000
01
20000
1
1
100
1000
104
1000
i04
Frequency
6050
40
LOU
C
30
X= Diftow .
-
O.OW
W22
ewj(Obs-s:)
-60127
aina Resimmc
30
Resilae tO
CPE
a 00
8.759
CPECapaiwce(pF)
Chge-Tinder
20
19759
152
10
0.1
1.1.2
1
100
10
Frequency
1000
104
Electrochemical Impedance Spectroscopy Tetraglyme 2.5 Molar Sulfur
10000
4000
7000
5000
2000
3000
1000
2000
1500
0
2000
4000
6000
Re[Z]
8000
0.1
10000
1
10
100
Frequency
40
Daic. -0561
30 .
Sohm Reasitce
-
1204
2*4
-2 70
ChO/gp-TrAer
CPE
10
CPE Cqacacw
0
0.1
eupouW
1
100
10
Frequency
1000
104
34
Reisume
0191
Uf
10
(Om 10539.178
74
1.1.3
Electrochemical Impedance Spectroscopy Tetraglyme 3 Molar Sulfur
10000
4000
7000
-
3000
5000
N
72000
3000
1000
2000
1500
0.
U
2000
4V0
OqAU
W
IuUU0
120u0
100
10
0.1
Re[Z]
1000
104
1000
104
Frequency
40
USU 1 NMDnt..
30
-0.573
ShinRece'anc
~0
Chge-Tranmsd
hr
032
ResiawteiOwI 11468 1,1
CPE exposm
0 84
CPE CapackWe fJAF
10.
0
94
0**
0 .1
1.1.4
9
1
100
10
Frequency
1000
04
Electrochemical Impedance Spectroscopy Tetraglyme 4 Molar Sulfur
4000
10000
3000
7000
.
5000
2000
3000
1000
0
2000
0
2000
4000
6000 8000 10000 12000
Re[Z]
0 'I
100
10
Frequency
1
40
30
Laa.
D.M.ce
Soho= Reiance W.b-s iO6.,
20
-o si
1625 489
-2256
110"4 115
Chve-T
CPE evpqa
0 8'1
10
CPECqucciyo4
10
01
1
100
10
Frequency
1000
104
35
15
1.1.5
Electrochemical Impedance Spectroscopy Tetraglyme 5 Molar Sulfur
10000
-.
7
2500
2000
7000
1500
5000l
1000
500
3000
0
3000 4000 5000 6000 7000 8000 9000
Re[Z]
100
10
Frequency
1
0.1
1000
104
1000
04
25
20
LOg11
Nn
15
S i
Wwbw
10
Cb.w-Tia
CPE
.
Dma
apOOM
K,.iw.ce
0 66
iOb) 184 -64
I049
CPECaptcita.:F
5
0.519
--
.tie - 2455469'
(Obsts29,254
0
0.1
1.1.6
1
10
100
Frequency
1000
10'
Electrochemical Impedance Spectroscopy Tetraglyme 7 Molar Sulfur
4000,
L !000
3000
10000
E 2000
1000
0
6000
8000
10000 12000
Re[Z]
14000
0.1
100
10
Frequency
1
20
1-5
LEft
"Ni Diste
Sow Resuane
-0.48
5249 22'
WutgOhm-i~ 13-435
10
Ch0
-
-
e-Ttansf Rksice (Oh.) 10220 203
CPE expoes
0 8WI
CPE Cipackwe (p
0
**-
01
1
10
100
Frequency
1000
100
36
8 292
1.1.7
Electrochemical Impedance Spectroscopy Tetraglyme 8 Molar Sulfur
300
15000
2000
1000
10000
0
10000
12000
15
1010
14000
Re[Z]
16000
A
18000
0.1
100
10
Frequency
1
LqNuN0Mw.~S~kMCSWAN~eWubwg(Cbws1
F)
I0
-0A79
8775121
33802
CbVe-Tm3urRwesiw
CE caaimme
1000
(Ohm) 9811411
7 5%
00.1
1.1.8
1
100
10
Frequency
1000
104
Electrochemical Impedance Spectroscopy Tetraglyme Calculation
Sulfur Conc.
(Molar)
1
2.5
3
4
5
7
8
Sulfur Conc.
(Molar)
Ionic Cond.
(mS/cm)
2.12
1.626
1.518
1.106
0.769
0.264
0.161
CPE Exponent
Solution Resist.
(Ohm)
823.9
1204.3
1157.0
1625.5
2455.7
5249.2
8775.8
CPE
Capacitance (uF)
Warburg (Ohm
s-1)
-60.1
-29.7
-16.3
-2.3
29.3
13.4
33.8
Exchange
Current (mA/s)
1
2.5
3
4
5
7
8
0.896
0.891
0.884
0.885
0.866
0.887
7.572
8.76
10.77
9.89
10.16
11.06
8.29
7.57
0.00131
0.00245
0.00225
0.00233
0.00360
0.00253
0.00263
Charge-Transfer
Resist (Ohm)
19759
10539
11468
11074
7184
10228
9811
Exchange
Current Density
(mA/cm2 s)
37
0.0185
0.0347
0.0319
0.0330
0.0509
0.0358
0.0373
1.2 Electrochemical Impedance Spectroscopy Diglyme
1.2.1
Electrochemical Impedance Spectroscopy Diglyme 1 Molar Sulfur
1500
2000
1000
S1000
500
500
1000
U
_2000
.)0W
40v0
0.1
Re[Z]
1
10
100
Frequency
1000
104
1000
104
50
40
,30
LoNa,,.O.ct.
-057
Sdalka Rtsigume Ww
,wv(Os-
252 690
46699
Cawv-Tn.dwRnsime.c0i.
0 $92
EVO
CPE
20
CPE CMPciknf(OiF)
10
3811 632
It031
11
01
1.2.2
1
1000
10
100
Frequency
10(
Electro chemical Impedance Spectroscopy Diglyme 2.5 Molar Sulfur
300
1000
250
200
700
150
z 500
100
77
300 1
5o
400
600
Re[Z]
800
1000
01
1
10
100
Frequency
30
25
20
-0431
Saan Reiace Wutbwg(b,-
24' 243
26236
Cbwe-Trnm
CPE apawa
CPE Cqwpmcta
10
5
n
01
Leos Net. DnW.ce.
1
10
100
Frequency
1000
10'
38
Rei..cef iO.
0 380
("Y 12 26
729990
1.2.3
Electrochemical Impedance Spectroscopy Diglyme 3 Molar Sulfur
250
1000,
200
700
S150
10
100
500
1
50.
300
400
500
600 700
Re[Z]
800
9
1000
0.1
1
10
100
1000
1
1000
104
Frequency
25
20
15
29
It'
Cbi.e-TResitmce tO1) 61 44S
CPE CaPOOM 0.85?
CPE Cqpcbwce (3S)
14 932
WarwugfObs s--l31
10
1
0.1
1.2.4
100
10
Frequency
1000
jQ
Electrochemical Impedance Spectroscopy Diglyme 4 Molar Sulfur
150
700
1005
500
50.
400
300
500
600
700
800
3001,
01
1
100
10
Frequency
20
15
LqaM NKuuMce
SobunomReuma
-0.415
-
CPE IPapOR
0 8,7
CPE Cap40ce IJJ
5
010
01
913
1-9,1
.atmgEOlu-l
Cbwge-Tnsa Pnemteoe (Obwn
10
1
100
10
Frequency
1000
104
39
13 M1
4%
796
1.2.5
Electrochemical Impedance Spectroscopy Diglyme 5 Molar Sulfur
120
goo.
100
850
0
750.
*
40.:
*
650.
20
0.
700.
600.
600
700
800
550.
0.1
900
1
10
100
Frequency
PAMZ
*
S
8
1.2.6
L~jQMNwUwm.
-0.607
Som Rsmeme -
A46 144
Wwbwrg(OkIu
19641
Reaii~wc tO)
Chws-Tnrw
CPE Vpa~w
0 866
CPE CAackce (F)
10 136
100
10
Frequency
1000
10
0
4
1
i0~
0
6
O0.1
1000
1000
33 848
104
Electrochemical Impedance Spectroscopy Diglyme 6 Molar Sulfur
120
750.
700
80
650
ST600.
40
550.
2
500.
0
500
450
550
600
Re[Z]
650
700
750
450.
0.1
100
10
Frequency
1
J
10
8
.
I0
6
Lft,,N.DwN... -037O
sA ma..e.ce - 446 3SI
CUre-T
4
fv
CPE ea.em
CPE
L
0.1
1
100
10
Frequency
1000
104
40
CqNCkee
Rtm.w 1Ohi
0 859
(gF) 1 415
*93336
1.2.7
Electrochemical Impedance Spectroscopy Diglyme 8 Molar Sulfur
1500.
60
1450.
40.
1400.
1300.
e
20
1300.
0
1300
1350
1400
1450
1500
1550
01
1
Re[Z]
10
100
Frequency
1000
104
3
Le6,NcnD--c*
-0.371
So~Mo Resiauct - 13142
32884
Wwbg(Ohw,.V1
C~aq-T~~ Res~ce
MP e~9owa 0 940
51"~
CME CwwtM"(IAFI
~
0.1
1.2.8
1
100
10
Frequency
14 9.10
1000
Electrochemical Impedance Spectroscopy Diglyme Calculation
Sulfur Conc.
(Molar)
1
2.5
3
4
5
6
8
Sulfur Conc.
(Molar)
Ionic Cond.
(mS/cm)
6.47
6.02
5.81
5.38
4.89
4.00
2.27
CPE Exponent
Warburg (Ohm
Solution Resist.
s-1)
(Ohm)
46.7
252.7
26.2
247.2
31.2
294.0
18.0
300.9
19.6
546.3
6.8
446.4
32.9
1285.4
Exchange
CPE
Capacitance (uF) Current (mA/s)
Charge-Transfer
Resist (Ohm)
3811.6
730.0
652.5
450.8
338.9
293.3
214.9
Exchange
Current Density
(mA/cm2 s)
1
2.5
3
4
5
6
8
0.892
0.888
0.857
0.877
0.866
0.859
0.96
0.00678
0.03541
0.03961
0.05734
0.07628
0.08813
0.12028
11.03
12.73
14.93
13.88
10.15
13.42
8.16
41
0.0959
0.5010
0.5604
0.8113
1.0791
1.2467
1.7016
1.3 Electrochemical Impedance Spectroscopy DOL:DME
1.3.1
Electrochemical Impedance Spectroscopy DOL:DME 1 Molar Sulfur
e
2000,
1500
800
1000
700
A
400
soo
200
300
0
-
0200
500
1000
1500
Re[ZJ
2000
2500
0
10
1
100
1000
10
1000
i0
Frequency
50
40
Lgoa NaU.M.
wet..g
20I
(O S..r)
2952:
ChwIt-TA ROC2 (ohm)
0.91S
CPE epam
20
a
so
14,260
CVCqee C..e1&)
10
0
0.1
1.3.2
-O 562
Sa.e.ec
- 30
1
10
100
Frequency
1000
104
Electrochemical Impedance Spectroscopy DOL:DME 2.5 Molar Sulfur
1000
2000
800
1500
g-
1000
00700
400
500
200
300
0[-
0
500
500
1000
1500
2000
2500
200
1500.1
1
Re[Z]
10
100
Frequency
50
40
CC 30
5.1., Ressae -
1"9749
I. W,, .g (Os-. -96s'9
20
Cbme-Tzd
CPEpw..i.
10
0.1
1
100
10
Frequency
1000
104
42
a=
0934
(Ohm) 2533 069
1.3.3
Electrochemical Impedance Spectroscopy DOL:DME 4 Molar Sulfur
600
1500
500
1000
400
700
N
500
200
300
100
0o
___200
-
0.1
1500
1000
500
0
1
100
10
Re[ZJ
1000
104
1000
10
Frequency
40
30
i.L.,No
s
-
CP0C48k=MtF)
10
0
0.1
1.3.4
-A81
D.nf
Reie
1
100
10
Frequency
1000
14.719
15696
104
Electrochemical Impedance Spectroscopy DOL:DME 5 Molar Sulfur
1000
*20
1500
800
1000
-600-
S700
400
500
200
300
0
500
1000
1500
Re[Z]
2000
2500
0
1
10
100
Frequency
50
40
-0 o
LAU, N.. n..
saWn Raife.t= 29W14
C- 30
ubwat,(O..s")
10
0
01
-19669
) 224 932
smi.
cawe-T...
CP ECRO. 0-919
cvocap.epe fn 13441
20
1
100
10
Frequency
1000
104
43
1.3.5
Electrochemical Impedance Spectroscopy DOL:DME 6 Molar Sulfur
.
700
60
500
1500
1000
700
400
300
500
200
100
0.\
300
0
1000
500
0.1
1500
10
1
Re[Z
10
1000
10
1000
10
Frequency
40
30 ,e...
.
Se" Ra-te
-53
2~bw(0=s-'
-0 53
227,641
W
cimge-Tvde 3*smce lOtan 1199
CPE so..
0.910
10
0.1
1.3.6
cCp.wm
1
100
10
Frequency
1000
213
"f
17
104
Electrochemical Impedance Spectroscopy DOL:DME 8 Molar Sulfur
1400
12003000
1000
Nsw
2000
1500
160
400
1000
200
01
0
500 1000 1500 2000 2500 3000 3500
Re[Z]
01
1
10
100
Freauencv
40
-0.*551
19
Wab~rt (Ohm s
-23155
c
-e-..Aw
R*40we On) 3398 740
CPE me..
0 911
12600
egecbm..l..
CE
"".N ","
30 ,a
SOMgin..e -
20
10
0
01
1
10
100
1000
10'
Frequency
44
403
1.3.7
Electrochemical Impedance Spectroscopy DOL:DME Calculation
Sulfur Conc.
(Molar)
1
2.5
4
5
6
8
Sulfur Conc.
(Molar)
Ionic Cond.
(mS/cm)
9.29
9.07
8.42
7.08
6.02
3.72
CPE Exponent
Solution Resist.
hm)
181.02
159.75
184.72
209.15
227.64
403.20
CPE
Capacitance (uF)
Warburg (Ohm
s-1)
9.0
-9.9
4.5
-19.7
-5.7
-23.9
Exchange
Current (mA/s)
1
2.5
4
5
6
8
0.918
0.914
0.915
0.919
0.91
0.911
14.26
15.33
15.66
13.44
15.79
12.60
0.01093
0.01021
0.01872
0.01024
0.01616
0.00761
Appendix 2. Solution Resistance in Different Solvent System
1.4 Solution Resistance versus Concentration in Tetraglyme
Solution Resistance vs Li2S6 S Molar
Concentration in Tetraglyme
10000.0
9000.0
E
8000.0
o
7000.0
6000.0
.E
5000.0
4000.0
30o0.0
0
2000.0
9
1000.0
*
-
0.0
0
1
2
4
3
5
6
Sulfur Concentration (Molar)
45
7
8
9
Charge-Transfer
Resist (Ohm)
2365
2533
1381
2525
1599
3399
Exchange
Current Density
(mA/cm2 s)
0.1546
0.1444
0.2649
0.1448
0.2287
0.1076
1.5 Solution Resistance versus Concentration in Triglyme
Solution Resistance vs Li2S6 S Molar
Concentration in Triglyme
3000
2500
20DO
1500
C
o
1000
In
500
0
0
1
3
2
4
5
6
7
8
9
Suffur Concentration (Molar)
1.6 Solution Resistance versus Concentration in Diglyme
Solution Resistance vs Li2S6 S Molar
Concentration in Diglyme
1400.0
0
1200.0
o1000
800.0
600.0
0
0
0
400.0
.0
200.0
0
0.0
0
1
2
3
4
5
6
7
8
9
7
8
9
Sulfur Concentration (Molar)
1.7 Solution Resistance versus Concentration in DOL:DME
Solution Resistance vs Li2S6 S Molar
Concentration in DOL:DME
450.00
400.00
E 350.00
0
300.00
m 250.00
3 200.00
,
0
,
o 150.00
100.00
50.00
0.00
0
1
2
3
4
5
6
Sulfur Concentration (Molar)
46
Appendix 3. Galvanostatic Polarization for Varying Concentration in Different Solvent System
3.1 Galvanostatic Polarization Tetraglyme
1.0 mol S1 L as Li 2S6 in TEGDME
.
1.000
0.500
----9
-
i-
- 0.100
0.050
-i1
t 0.010
Q 0.005
2 .1
2.2
2.3
2.4
Potential vs. Li' I Li VI
2.5
2.6
2.5 mol S1 L as Li 2S6 in TEGDME
1.000
0.500
,-1
9----.
1- ~
-$0.100
9i'
0.050
~1
9,
99
0 0.010
Q 0.005
2.1
2.2
2.3
2.4
2.5
2.6
Potential vs. LiV I Li VI
3.0 mol S1 L as Li 2 S6 in TEGDME
1.000
0.500
0.100
of1
0.050
S..
0.010
Q 0.005
S-i
2.1
2.2
2.4
2.3
Potential vs. Li' ILi IVI
47
2.5
2.6
4.0 mol SI L as Li 2S6 in TEGDME
5 1.000
0.500.
- 0.100
0.050l''
0.010
Q0.005
2.1
2.2
2.3
2.4
Potential vs. L ILi V
2.5
2.6
5.0 mol S1 L as Li 2 S6 in TEGDME
1.000
0.500
-0.100
0.050
0.010
0.005
2.1
2.2
2.3
2.4
2.5
2.6
Potential vs. Li' / Li IVI
7.0 mol S1 L as Li 2S6 in TEGDME
't-
'
,
2.3
2.4
.
0.100
0.050
,
1.000
0.500
0.010
Q0.005
2.1
2.2
Potential vs. Li' / Li IVI
48
2.5
2.6
8.0 mol S1 L as Li 2 S6 in TEGDME
1.000
0.500
I
-
0.100
0.050
- - - -..--
-
I
I
0.010
It
ra 0.005
2.2
2.1
3.1.1
------ I
~I
2.4
2.3
Potential vs. LV ILi IVI
2.6
2.5
Tetraglyme Exchange Current Density from Galvanostatic Polarization
Sulfur Conc. (Molar)
Exchange Current Density (mA/cm2 s)
1
2.5
3
4
5
7
8
0.0228
0.0334
0.0351
0.0355
0.0395
0.0389
0.0376
3.2 Galvanostatic Polarization Triglyme
1.0 mol S1 L as LiAS in Triglymne
5.00
1.00
-0.50
0.10
AA
0.05
2.1
2.2
2.5
2.4
Potential vs. Li' / Li IVI
2.3
49
2.6
2.5 mol S1 L as Li 2 S6 in Triglyme
10.00
5.00
1.00
0.50
0.10
0.05
2.0
2.1
2.3
2.2
Potential vs. Li
2.4
2.6
2.5
Li I VI
4.0 mol S1 L as Li 2S6 in Triglyme
10.00
5.00
1.00
0.50
0.10
0.05
2.0
2.1
2.5
2.4
2.3
2.2
Potential vs. Li' Li ( V
5.0 mol S1 L as Li 2 S6 in Triglyme
10.00
5.00
1.00
0.50
0.10
0.05
2.0
2.4
2.2
Potential vs. Li' Li VI
50
2.6
2.6
6.0 mol S1 L as Li 2 S6 in Triglyme
10.00
5.00
2
1.00
kI
0.50 ('il-I
0.10
0.05
2.0
2.1
2.2
2.3
2.4
2.5
Potential vs. L I Li I VI
2.6
8.0 mol S1 L as Li 2 S6 in Triglyme
5.00
S21.00
.
1 1-1-1
J-4.
11-k
0.50
I
'-.9
0.10
9
Q 0.05
1.8
3.2.1
I
2.0
2.2
2.4
2.6
Potential vs. Lf I Li I V)
2.8
Triglyme Exchange Current Density from Galvanostatic Polarization
Sulfur Conc. (Molar)
Exchange Current Density (mA/cm2 s)
0.0732
2.5
0.0807
4
5
6
8
0.0859
0.0974
0.1015
0.1103
51
3.3 Galvanostatic Polarization Diglyme
2.5 mol S1 L as Li 2 S6 in Diglyme
,4-5.0 0
2
E
1.0 0
4-I
*0.5 0
I I
0.1 0
II
a..
Q 0.c 5
2.2
2.5
2.3
2.4
Potential vs. LiV I Li IVi
2.6
3.0 mol S1 L as Li 2S 6 in Diglyme
5.C 0
1
0
.~ 0.5 0
0.1 0
0.1 5
2.2
2.3
2.4
Potential vs. Li
2.5
2.6
I Li IV
4.0 mol S1 L as Li 2 S6 in Diglyme
5.0
-rE 2.0
1.0
'I I f
0.5
0.2
2.25
2.30
2.35 2.40 2.45 2.50 2.55
Potential vs. Li' I Li I V
52
2.60
2.65
10.0
'
5.0 mol S1 L as Li2 S6 in Diglyme
'/9
5.0
~2.0
1
9
0.5
2.1
41'
99"~
1.0
2.2
2.3
2.4
9
2.5
2.6
2.7
Potential vs. Li I Li IVI
3.3.1
Diglyme Exchange Current Density from Galvanostatic Polarization
Sulfur Conc. (Molar)
Exchange Current Density (mA/cm2 s)
2.5
3
4
5
0.467
0.696
0.956
1.145
53