Electric Charge Electric Charge & Current Current Electric Charge Current Chapter 20.
Insight Into Li/S Batteries: Institute of Elementary Kinetic ......2.4 Discharge CC charge CV charge...
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Institute of Technical Thermodynamics Insight Into Li/S Batteries: Elementary Kinetic Modeling and Impedance Simulation David N. Fronczek *,1,2,3 and Wolfgang G. Bessler 1,2,4 1 German Aerospace Center (DLR), Institute of Technical Thermodynamics, Stuttgart, Germany 2 Helmholtz Institute Ulm for Electrochemical Energy Storage (HIU), Ulm, Germany 3 Lawrence Berkeley National Laboratory, Berkeley, USA 4 From Sep. 2012: Offenburg University of Applied Sciences , Offenburg, Germany * [email protected] Motivation & Approach Summary & Conclusions Major challenges for lithium-sulfur (Li/S) batteries today 1 : • Complex multi-species, multi-reaction chemistry, precise charge/discharge mechanism unknown • Dissolution/precipitation of phases • Unstable electrolyte interface (continuously re-formed during cycling) A sound physically-based model of the Li/S cell can address all of the above and provide new and deeper insight into the Li/S cell. Model development and simulations are carried out using the DLR’s • Discharge behavior is governed by presence of solid reactant and product phases; amount and distribution of sulfur and Li 2 S change dramatically during cycling • Two plateau stages characterized by the presence of solid S 8 and Li 2 S, respectively • All sulfur is dissolved in the form of polysulfides of various length during the intermediate “dip” stage • The impedance of the cell is simulated based on the physico- chemical model (no equivalent circuit required) • Predicted energy density for this type of cell (per cathode weight and volume): 1300 Wh/l and 850 Wh/kg assuming quantitative Interface Electrode Repeat unit Cell 400 100 % Constant current discharge at various rates: in-house software DENIS 2 . Experimental activities at DLR and LBNL pro- vide data for model validation and calibration, see poster by Cañas et al.: In-Situ X-Ray Diffraction (XRD) Studies of Lithium-Sulfur Batteries Results and volume): 1300 Wh/l and 850 Wh/kg assuming quantitative conversion of S 8 to Li 2 S. Cell layout and reactions Geometry and reaction mechanism according to Kumaresan et al. 3 No side reactions are considered. Governing equations - Species production rates are modeled by Arrhenius law and thermodynamics: , - Faradaic current density follows from electron production rate: - Volume fractions of each phase: , where - = ∏ ∏ ∈ ∈ r j f j R j v j r R j v j f i i a k a k v s ´´ ´ & ∆ - - = φ α β RT zF RT E T k k exp exp act f f 0 f ∆ - = RT G k k exp r f ∑ ∑ + = n n n m m m l s F A s F i V , electron V , electron F & & i i i i M R t = ∂ ∂ ) ( ε ρ Model design Discharge behavior i i i i σ τ ε σ 2 eff = i i i i D D τ ε 2 eff = ∑ = m m m i i A s R V , & ) , ( , V 0 V , n m n m n m f A A ε ε ⋅ = Transport & phase management Volume fractions of the main cathode com- ponents during CCCV cycling: Impedance Simulated EIS at various SOC using potential step algorithm 5 : ( 29 V eff eff ∂ ∂ ∂ ∂ ∂ ∂ i i i i i i i i s M y c D y RT F z y c D y t c & + ∂ ∂ + ∂ ∂ = φ ε Discharge CC charge CV charge 2.4 2.6 0.01C 0.1C 1C / V - Total volume continuously adjusted to ensure constant pressure - Phase formation/dissolution and phase transition are handled as chemical reactions - Microstructural surface area of each phase: - where typically - Mass and charge transport: where and . For a detailed list of parameters, see ref. 4. Wissen für Morgen Knowledge for Tomorrow 0 100 200 300 400 0 100 200 300 Im / Ohm*cm 2 Re / Ohm*cm 2 100 % 99 % 75 % 50 % 25 % 3 % Concentrations of dissolved species during a discharge followed by a CCCV charge: References 1 Goodenough & Kim, J. Power Sources, 196 (2011), 6688–6694 2 Bessler et al., Electrochim. Acta, 53 (2007), 1782–1800 3 Kumaresan et al., J. Electrochem. Soc., 155 (2008), A576–A582 4 Neidhardt et al., J. Electrochem. Soc., in press (2012) 5 Bessler, J. Electrochem. Soc., 154 (2007), B1186–B1191 0 50 100 150 200 Volume fraction Time / h Carbon Sulfur Li 2 S Electrolyte 0.4 0.2 0.0 1.0 Discharge CC charge CV charge 0 400 800 1200 1600 1.8 2.0 2.2 1C Cell voltage / Discharge capacity / Ah/kg of S 8 10 -9 10 -6 10 -3 10 0 10 3 0 800 1600 800 0 Discharge capacity / Ah/kg of S 8 Concentration / mol/l Li + S 2- S 8(l) S 2- 4 S 2- 6 PF - 6 S 2- 2 S 2- 8
Transcript of Insight Into Li/S Batteries: Institute of Elementary Kinetic ......2.4 Discharge CC charge CV charge...
Institute of
Technical Thermodynamics
Insight Into Li/S Batteries:Elementary Kinetic Modeling and Impedance SimulationDavid N. Fronczek*,1,2,3 and Wolfgang G. Bessler1,2,4
1German Aerospace Center (DLR), Institute of Technical Thermodynamics, Stuttgart, Germany2Helmholtz Institute Ulm for Electrochemical Energy Storage (HIU), Ulm, Germany3Lawrence Berkeley National Laboratory, Berkeley, USA4From Sep. 2012: Offenburg University of Applied Sciences , Offenburg, Germany*[email protected]
Motivation & Approach Summary & Conclusions
Major challenges for lithium-sulfur (Li/S) batteries today1:• Complex multi-species, multi-reaction chemistry,
precise charge/discharge mechanism unknown• Dissolution/precipitation of phases• Unstable electrolyte interface (continuously re-formed during cycling)
A sound physically-based model of theLi/S cell can address all of theabove and provide newand deeper insightinto the Li/S cell.
Model development and simulations are carried out using the DLR’s
• Discharge behavior is governed by presence of solid reactant and
product phases; amount and distribution of sulfur and Li2S change
dramatically during cycling
• Two plateau stages characterized by the presence of solid S8 and
Li2S, respectively
• All sulfur is dissolved in the form of polysulfides of various length
during the intermediate “dip” stage
• The impedance of the cell is simulated based on the physico-
chemical model (no equivalent circuit required)
• Predicted energy density for this type of cell (per cathode weight
and volume): 1300 Wh/l and 850 Wh/kg assuming quantitative
Interface
Electrode
Repeat unit
Cell
400100 %
Constant current discharge at various rates:
in-house software DENIS2. Experimental activities at DLR and LBNL pro-vide data for model validation and calibration, see poster by Cañas et al.: In-Situ X-Ray Diffraction (XRD) Studies of Lithium-Sulfur Batteries
Results
and volume): 1300 Wh/l and 850 Wh/kg assuming quantitative
conversion of S8 to Li2S.
Cell layout and reactions
Geometry and reaction mechanism according to Kumaresan et al.3
No side reactions are considered.
Governing equations
- Species production rates are modeled by Arrhenius law and thermodynamics:
,
- Faradaic current density follows from electron production rate:
- Volume fractions of each phase:
, where
−= ∏∏
∈∈ r
j
f
j
Rj
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v
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&
∆−
−= φαβ
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RT
ETkk expexp
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∆−=RT
G
k
kexp
r
f
∑∑ +=n
nnm
mm lsFAsFi V,electron
V,electronF &&
ii
ii MRt
=∂
∂ )( ερ
Model design
Discharge behavior
i
i
ii
στ
εσ
2
eff =i
i
ii DD
τ
ε2
eff =
∑=m
mmii AsR V,&
),(,V0
V, nmnmnm fAA εε⋅=
Transport & phase management
Volume fractions of the main cathode com-ponents during CCCV cycling:
Impedance
Simulated EIS at various SOC using potential step algorithm5:
( ) Veffeff
∂∂
∂∂
∂∂
iiiiii
ii sM
ycD
yRT
Fz
y
cD
yt
c&+
∂∂+
∂∂= φε
Discharge CC charge CV charge2.4
2.6 0.01C
0.1C
1C
Cell
volt
age
/ V
- Total volume continuously adjusted to ensure constant pressure
- Phase formation/dissolution and phase transition are handled as chemical reactions
- Microstructural surface area of each phase:
- where typically
- Mass and charge transport:
where and .
For a detailed list of parameters, see ref. 4.
Wissen für Morgen
Knowledge for Tomorrow
0 100 200 300 400
0
100
200
300
Im
/ O
hm
*cm
2
Re / Ohm*cm2
100 %
99 %
75 %
50 %
25 %
3 %
Concentrations of dissolved species during a discharge followed by a CCCV charge:
References1Goodenough & Kim, J. Power Sources, 196 (2011), 6688–66942Bessler et al., Electrochim. Acta, 53 (2007), 1782–18003Kumaresan et al., J. Electrochem. Soc., 155 (2008), A576–A5824Neidhardt et al., J. Electrochem. Soc., in press (2012)5Bessler, J. Electrochem. Soc., 154 (2007), B1186–B1191
0 50 100 150 200
Vo
lum
e f
ract
ion
Time / h
Carbon
Sulfur
Li2S
Electrolyte
0.4
0.2
0.0
1.0
Discharge CC charge CV charge
0 400 800 1200 1600
1.8
2.0
2.2
2.4 1C
Cell
volt
age
/ V
Discharge capacity / Ah/kg of S8
10-9
10-6
10-3
100
103
0 800 1600 800 0
Discharge capacity / Ah/kg of S8
Con
cen
trati
on
/ m
ol/l
Li+
S2-
S8(l)
S2-4
S2-6PF-
6
S2-2
S2-8
