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Quantitative analysis of GITT measurements of Li-S batteries
James Dibden, Nina Meddings, Nuria Garcia-Araez, and John R. Owen
1
Acknowledgements to Oxis and EPSRC for EP/M50662X/1 - CASE studentship, EP/P019099/1- MESS project co-funded by Innovate UK.
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2
time
Constant current pulse + relaxation step
-cu
rren
t
IRu
IRu
constant potential
after relaxation
ERELAX
time
-vo
lta
ge EPULSE
Cathode. thickness L
Li+ e-
cLi
depth
l 0 L
The Galvanostatic Intermittent Titration Technique - as applied to Li-ION
Li e Li Host
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3
The Galvanostatic Intermittent Titration Technique - as applied to Li-S
time
Constant current pulse + relaxation step
- cu
rren
t
IRu
IRu
constant potential
after relaxation
ERELAX
time
- v
olt
ag
e
EPULSE
Li
e-
c(LiSn)
depth
0 L
Li+
Li+ S
Sn-
OHARA
nS ne S
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GITT in Li-ion battery materials
4
Weppner and Huggins. J. Electrochem. Soc, 1977, 124, 1569-1578.
Chemical diffusion coefficient Equilibrium
voltage profile
224
PULSE
RELAX
E
ELD =
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Thermodynamically enhanced diffusion
5 Weppner and Huggins. J. Electrochem. Soc, 1977, 124, 1569-1578.
Enhancement factor:
Enhancement of the chemical diffusion coefficient
ln
ln
Li
Li
y Fd a dE
d c RT d
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GITT in Li-S cells ― complications
• Redox reactions in the liquid state
• Multiple polysulfide species (not fully identified)
• Polysulfide shuttle can cause self discharge
6
GITT in Li-S cells ― our approach
• Polysulfide shuttling avoided using a lithium selective membrane (Ohara)
• Equations derived for (complicated) solution redox reactions
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Plan
• Use GITT in Li-S cells to obtain quantitative information of:
– Mass transport rate (diffusion coefficient)
– Reaction rate (relaxation rate)
– Composition-dependent activity coefficients
7
Aim
• Validate our approach with a model redox system
• Apply it to cells containing dissolved sulfur
• Apply it to cells containing dissolved polysulfides
• Apply it to Li-S cells
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Validation
• Chemical diffusion coefficient determined by:
– Cyclic voltammetry
– Square-wave voltammetry
– Chronopotentiometry
– GITT
8
EtV2+ =
Model redox system:
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Cell design
9
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Results: Summary
10
0.01–2 mM EtV2+ in 0.1 M LiTFSI in Pyr14TFSI
Glassy carbon working electrode
Method D / cm2 s-1
Cyclic voltammetry 6.3 x 10-8
Chronopotentiometry 7.7 x 10-8
Square wave voltammetry 7.5 x 10-8
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Cyclic voltammetry
11
System is electrochemically reversible (~ 63 mV)
DEtV2+ = 6.3 x 10-8 cm2 s-1
2 mM EtV2+ in 0.1 M LiTFSI in Pyr14TFSI
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Chronopotentiometry
12
2 mM EtV2+ in 0.1 M LiTFSI in Pyr14TFSI
DEtV2+ = 7.7 x 10-8 cm2 s-1
Transition time:
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Square wave voltammetry
13
0.01–2 mM EtV2+ in 0.1 M LiTFSI in Pyr14TFSI
DEtV2+ = 7.5 x 10-8 cm2 s-1
2 mM
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GITT
14
2 mM EtV2+ in 0.1 M LiTFSI in Pyr14TFSI
Next: repeat the experiments with an smaller and thinner separator to decrease the electrolyte volume and thus increase cbulk.
30%
0.002
(0.6 mM)
mM 0 mV
surface
bulk RELAX
c
c E
224
PULSE
RELAX
E
ELD =
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Cell design
15
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Results: Summary
16
Method D / cm2 s-1
Cyclic voltammetry 2.2 x 10-6
Chronopotentiometry 2.4 x 10-6
GITT ≈2 x 10-6
5 mM EtV2+ in 1 M LiTFSI in DOL
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Cyclic voltammetry
17
5 mM EtV2+ in 1 M LiTFSI in DOL
System is electrochemically reversible (~ 60 mV)
DEtV2+ = 2.2 x 10-6 cm2 s-1
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Chronopotentiometry
18
DEtV2+ = 2.4 x 10-6 cm2 s-1
Glassy carbon C-coated Al foil
Transition time:
5 mM EtV2+ in 1 M LiTFSI in DOL
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GITT (1)
19
5 mM EtV2+ in 1 M LiTFSI in DOL
224
PULSE
RELAX
E
ELD =
Unrealistic variation of the chemical diffusion coefficient
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GITT (2)
20
Equilibrium voltage profile in agreement with Nernst equation
Evolution of voltage change induced by pulses is unexpected
5 mM EtV2+ in 1 M LiTFSI in DOL
224
PULSE
RELAX
E
ELD =
EtV2+ + e- →EtV+
20 ln EtV
EtV
cRTE E
F c
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GITT analysis
21
Fick’s first law: 0
0x
I cnFD
A x
Evolution of surface concentrations with time:
2 2 2
0 02x initial initial
EtV EtV EtV
I tc c c
AnF D
Assumption: EPULSE is proportional to c(x=0)
0 /bulk
I nFc
AL
Since
224
PULSE
RELAX
E
ELD =
2EtV e EtV
0 020x
EtV
I tc c x
AnF D
( 0)PULSEE k c x
and the proportionality constant is RELAX bulkE k c
It is concluded that: 2
PULSE RELAX
L tE E
D
And for t=:
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GITT analysis
22
Fick’s first law: 0
0x
I cnFD
A x
Evolution of surface concentrations with time:
2 2
0 02x initial
EtV EtV
I tc c
AnF D
2EtV e EtV
0 02x
EtV
I tc
AnF D
Assumption: EPULSE is calculated with the Nernst equation
0 /bulk
I nFc
AL
2
0
0
0ln
x
EtVPULSE x
EtV
cRTE E
nF c
and E0 is obtained from the equilibrium voltage profile (2.44V)
taking into account:
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GITT (3)
23
5 mM EtV2+ in 1 M LiTFSI in DOL
Pulse 1 Pulse 5 Pulse 15
The evolution of the voltage change induced by the pulse is in agreement with the Nernst equation
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Conclusions
24
• Theoretical framework to analyze GITT results of Li-S cells
• Validation of the evaluation of the diffusion coefficient by:
– Cyclic voltammetry
– Square wave voltammetry
– Chronopotentiometry
– GITT
• Next: GITT as diagnostic tool of Li-S cells