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*david.fronczek@dlr.de

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

v

jrRj

v

jfii akakvs´´´

&

∆−

−= φαβ

RT

zF

RT

ETkk expexp

actff

0f

∆−=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