Pore-Scale Transport Resolved Model Incorporating Cathode Microstructure and Peroxide
Growth in Lithium-Air Batteries
Complex Fluids &
Multiphase Transport
Laboratory
Charles Andersena , Han Hua, Gang Qiua, Vibha Kalrab, and Ying Suna
a Department of Mechanical Engineering and Mechanics, Drexel University
b Department of Chemical and Biological Engineering, Drexel University
50%
90%
0
O2
Li+
Li-ion technology in electric
The
Li-air
cell
has
a
solid
lithium
anode
and
a
vehicles is limited to ~100
miles. Li-air battery are high cathode in electrolyte. The discharge reaction
forms
insoluble
lithium
peroxide
(Li
O
)
2
2
energy density alternatives.
depositions on the cathode.
Methodology
Pore-scale modeling
Li
Porous Electrode
400 nm
Li2O2
Li
e
Pore-Scale
Volume-averaged

2 RT
 ln f 

t  11 

FC Li
  ln C Li 
t
t
  DLi   ,   
F
F
Li+
O2
Electrolyte
High conductivity for ultra-thin
Li2O2 layer due to electron tunneling
Critical film thickness (δcrit =12nm)
when Li2O2 becomes insulating
Δx
Framework
Parallel computing with
Message Passing
Interface (MPI)
eElectrode
C– Concentration (mol m-3)
D –Diffusion coefficient (m2 s-1)
f - Activity coefficient
F – Faraday’s constant (C mol-1)
I0 – Current density (A m-2)
N – Mass flux (mol m-2 s-1)
R – Universal gas constant (J mol-1 K-1)
T – Temperature (K)
t+ - Transference number
α – Transfer coefficient
ϕ – Electric potential (V)
κ – Electrolytic conductivity (S m-1)
η – Overpotential (V)
𝜎 – Electrode conductivity (S m-1)
Li2O2
High Fidelity Geometry
Explicitly model 3 distinct
electrode/electrolyte/Li2O2
phases
Pore-scale simulation
via massively parallel
supercomputers
Model Development
Simulate pore-scale
mass/charge transport &
Li2O2 growth
2.2
2.0
Simulation, present work
Experiment, Lu et al. 20118[3]
1.8
0
1000
1500
2000
2.4
2.2
2.0
2500
1.8
3000
0
1000
Specific capacity (mAh g-1C)
Porosity : 85%
Specific Surface Area: 100 m2/gc
Local current density: 2.5 mA/m2
2.8
2.8
2.6
2.4
ilocal =0.5 mA/m2
2
ilocal =1.0 mA/m
ilocal =2.5 mA/m2
2.6
2.4
2.2
kc = 3.63×10-10mol m-2s-1
kc = 3.63×10-9mol m-2s-1
2.0
2
kc = 3.63×10-8mol m-2s-1
ilocal =20 mA/m
0
500
1.8
1000 1500 2000 2500 3000 3500
0
Electrolyte
3000
•Li2O2 grows when it reaches saturation
concentration
Electrolyte
Non-pore-blocking
2500
Pore-blocking
2000
Simulation w/ nanostructures
Simulation w/ bare fin
Insulation limit
10
20
30
40
Nanostructured
electrode
(0<S<40nm)
Loss of surface area
Li2O2
2000
2500
3000
A higher reaction rate constant
improves the cell voltage.
Lower current density yields higher
voltage and longer discharge time
2.6
Loss of active area
Pore-blocking
Electrolyte
S=4nm
Li2O2
Loss of active area
Electrode
Electrolyte
Li2O2
Active area
not lost
2.4
H = 4nm
H = 10nm
H = 20nm
H = 50nm
2.2
2.0
H
Bare fin electrode
(S=40nm)
Loss of surface area
Lower specific capacity
Lower specific capacity
H=50nm
H=4nm
S
S=36nm
1.8
0
1000
2000
3000
4000
5000
6000
Specific capacity (mAh g-1C)
Electrode
Li2O2 growth
t
1500
Specific capacity (mAh g-1C)
Specific capacity (mA h/g)
Li2O2
Cmax
2O2
1000
Pore-blocking
Electrolyte
Electrode
Electrode
CLi
500
2.8
3500
Bare fin electrode
(S=0nm)
2e-
4000
Effect of Reaction Rate constant
3.0
2.0
3000
Constant conductivity doesn’t capture flat
initial voltage and sudden voltage drop.
3.0
2.2
2000
Specific capacity (mAh g-1C)
Effect of Applied Current
1.8
Structure to Property
Study impact of
nanostructure & Li2O2
growth on performance
500
3=107 -17.83
Spacing of nanostructure, S(nm)
2Li+ O
2
Drexel Research Day May 1 2015
2.6
2.4
1.6
 3= 10-10 S/m
Effect of Nanostructure Spacing Effect of Nanostructure Height
Li2O2
Δy
Optimization: change
nanostructure
conditions
Pore-blocking
0
BV
2O2
I o  
CO2   F 
 F 

Butler-Volmer Boundary Condition N  kc
exp
   exp
 

Cref   RT 
 RT 
Flux of species resulting from
  solid  electrolyte  U 0
electrochemical reactions
1500
CLi
Current
Collector
Butler-Volmer Boundary
Reaction assumption
Condition
Finite volume method
Thickness dependent
conductivity
•As reactions occur at the
electrolyte/electrode
interface Li2O2 “fills up”
each voxel during discharge
Constants
Electrode
Simulation Domain Homogenous continuum
Multiphase
Microstructures
Volume-averaged
Fully resolved
Li2O2 formation
Porosity change
Explicitly modeled
Peroxide growth
modeling
Continuous BC
Specific Capacity, Q(mAhg-1c)
Lu et al 2013 [1]
Adams et al 2013 [2]
As
2
The diffusivity of Li+ and O2 through Li2O2 is less than
conductivity of e- through Li2O2 and reactions will occur at
electrolyte/Li2O2 surface.
~
~
0   
2
2.6
x
C


2 Li  O2  2e  Li2O2
Li2O2 Deposits
0   CLi   
y
2
 3= 10-11 S/m
Cell voltage (V)
Li
Li
2.8
2.8
Cell voltage (V)
5
5000
I o  
O2
Effect of Li2O2 Conductivity
Cell voltage (V)
C
e- Li+
Air
CO2 = C0
Matching:
V
e-
Validation
Cell voltage (V)
10
10000
Theoretical
Practical
% Efficiency
S = 4nm
14.5%
Results
Species Transport
Electrolyte
CO2
C Li
2
2
2
  C Li   
 DO2  CO2
t
t
Li2O2
Charge Transport
Electrode
S = 20nm
13%
Charge
Discharge
e-
S = 30nm
Energy Density (Wh/g)
15000
15
Governing Equations
Cell voltage (V)
Motivation
Specific discharge capacity increases
with nanostructure spacing.
Larger spacing prevents pore-blocking
and loss of active area.
Larger nanostructure height yields
higher voltage and larger specific
capacity due to increased active surface
area.
References
[1] Y.-C. Lu, B. M. Gallant, D. G. Kwabi, J. R. Harding, R. R. Mitchell, M. S. Whittingham, and Y. Shao-Horn, Energy & Environmental Science, 6, 750 (2013).
[2] B. D.Adams, C. Radtke, R. Black, M. L. Trudeau,K. Zaghib, and L. F.Nazar, Energy & Environmental Science, 6, 1772 (2013).
[3] Y.-C. Lu, D. G. Kwabi, K. P. C. Yao, J. R. Harding, J. Zhou, L. Zuin, and Y. Shao-Horn, Energy & Environmental Science, 4, 2999 (2011).