Shaping the Future
Near-surface ion distribution
and buffer effects
during electrochemical reactions
MIR@W day: Modelling and simulation
of electrochemical flows in Lithium-ion
batteries
Dr. Michael AUINGER
MIR@W day
Zeeman Building, University of Warwick
Coventry CV4 7AL, United Kingdom
30th November, 2015
Shaping the Future
The Beauty of Thermochemical
Simulations
MIR@W day: Modelling and simulation
of electrochemical flows in Lithium-ion
batteries
Dr. Michael AUINGER
MIR@W day
Zeeman Building, University of Warwick
Coventry CV4 7AL, United Kingdom
30th November, 2015
The Steels Processing Group
Prof. S. Seetharaman
Physical Metallurgy
C. Davis
B. Shollock
Mechanics
Coatings
R. Dashwood
Director
P. Srirangam
R. Bhagat
M. Auinger
in-situ
EChem.
Modelling
The Hierarchy of Modelling
The Hierarchy of Modelling
4
Macro-Scale Models
Process Flows
Microstructure Evolution
Large-Scale FEM Simulations
m – 100mm
Micro-Scale FEM Simulations
Phase Formation and Oxidation
100mm - 1mm
Surfaces and Interfaces
Molecular Dynamics
10mm – 10nm
generate missing
thermodynamic (and
kinetic) data
DFT Calculations
< 10nm
Accurate Data for
Properties
Theoretical Model and Discussion
ion diffusion
migration in an
electric field
chemical
equilibrium
convection
P. Skladal, Analytica Chimica Acta
727 (2012) 41– 46.
PCCP 13 (2011) 16384-16394.
Programme Algorithm
element transport
dt
= div Di  x,T  .ci  x, t   zi . i  x,T  .ci  x, t  . x, t  
electrochemical potential Fe / V
dci  x, t 
chemical reaction
2.0
1.5
3+
Fe
Fe 2O3
1.0
0.5
0.0
2+
Fe
-0.5
-1.0
-1.5
0.0
Fe 3O4
+
Fe
3.5
[Fe(OH)] Fe(OH)
2
7.0
10.5
14.0
pH-value
Oxid. Met. 76 (2011) 247-258.
Electrochemistry & surface pH-values
PCCP 13 (2011) 16384-16394.
Experimental RDE-Setup
Working electrode:
polycrystalline Pt disc
(0.196 cm²), embedded in Teflon
Counter electrode:
graphite rod
Reference electrode:
saturated Ag/AgCl
50ml Teflon 3-compartment cell
Uncompensated resistance < 2Ω
parameters controlled via
LabVIEW
Parameters and Diffusion Layer
calculated surface pH-value
14
1.0
12
10
8
6
4
400 rpm
900 rpm
1 600 rpm
2 500 rpm
0.5
2
0
1
Levich Equation:
(a)
 eff 
0.0
-2

c H  H  c OH  OH
c H  cOH




1
2


-0.5
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Electrode potential / VSHE
0.25
(b)
0.00
-0.25
pH 4.1
-0.50
pH 3.
-0.75
0
500
9
1000 1500 2000 2500 3000 3500
diffusion layer thickness eff / µm
current density j / mA cm
1
 i  1.6126 D i3 ν 6 ω
60
400 rpm
900 rpm
1 600 rpm
2 500 rpm
50
40
H
+
 OH
30
-
20
10
0
2
4
6
8
10
12
14
pH value of solution
-1
Electrode rotation rate  / min
PCCP 13 (2011) 16384-16394.
Unbuffered Aqueous Solution
calculated surface pH-value
14
1.0
12
10
8
6
4
bulk pH-value
pH 1
pH 4
pH 7
pH 10
pH 13
0
14
10
10
8
6
4
2
0
simulation
1
-2
0.1
current density j / mA cm
current density j / mA cm
12
simulation
-2
0.5
calculated surface pH-value
2
0.0
-0.5
-1.0
1.0
experiment
0.01
1E-3
1E-4
10
experiment
1
0.5
0.1
0.0
bulk pH-value
pH 1
pH 4
pH 7
pH 10
pH 13
0.01
-0.5
1E-3
-1.0
-0.8
-0.6
-0.4
-0.2
1E-4
0.0
-0.8
-0.6
Electrode potential / V SHE
unbuffered solution:
-0.4
-0.2
0.0
Electrode potential / VSHE
jH 
OH


F
 eff

 1
1
solution
 surface  solution

c

D
 D H  csurface
 KW
H
H
OH

cH

 cH






PCCP 13 (2011) 16384-16394.
Local Corrosion Effects
Figure: Cyclic voltammograms in unbuffered solutions of different pH-value.
Local Corrosion Effects
Figure: Cyclic voltammograms in unbuffered solution of pH 7.
Electrochemistry & Pickling
= −58
An applied voltage of -58 mV
(vs SHE) corresponds to:
pH =
7 and
10-12 bar H2
pH =
5 and
10-8 bar H2
pH =
1 and
1 bar H2
pH =
0 and
100 bar H2
=
− (29
+
log( (
2))
“Solubility” at extreme Conditions
different internet sources – GOOGLE search
Acetate Buffered Solution
CH3COO- + H+
CH3COOH
j  jH
 D Ac K S D HAc c solution
 D Ac K S 
c 0Buffer F  D HAc c surface
H
H




 eff 
K S  c surface
K S  c solution

H
H


OH 

0.020
solid lines:
1mM acetate
dashed lines: without buffer
concentration c / mol m
-3
0.015
0.010
0.005
eff
0.000
1.0
0.5
eff
0.0
0
5
10
15
20
25
30
distance from electrode surface x / µm
PCCP 13 (2011) 16384-16394.
concentration
General Transport Scheme
+
H
-
OH
eff
H2
-
e
HR
+
H
-
H2O
concentration
OH
H2O
2-
H2R
H2R
-
-
HR
R
HR
-
2-
R
eff
distance from electrode surface x / µm
PCCP 13 (2011) 16384-16394.
Phosphate Buffered Solution
125
concentration c / mol m
-3
100
75
50
25
eff
0
100
80
60
40
20
0
H3PO4
-
H2PO4
2-
HPO4
3-
eff
0
5
10
15
20
PO4
25
30
distance from electrode surface x / µm
j  jH
j Buffer

OH 
 jBuffer
K S1
K S1 K S2
K S1 K S2 K S3

3D

D

D

3
D

1
2
3
4
c ( x ), H
c (2x ), H
c3( x ), H
c 0Buffer F 

K
K K
K K K
 eff 
1  S1  S12 S2  S1 3 S2 S3

c ( x ), H
c ( x ), H
c ( x ), H







x 0






 x 
PCCP 13 (2011) 16384-16394.
eff
The Use of Mathematics
www.abstrusegoose.com
The Use of Mathematics
www.abstrusegoose.com
The Use of Mathematics
www.abstrusegoose.com
Summary
Near-surface ion distribution and buffer effects during
electrochemical reaction
M. Auinger, I. Katsounaros, J.C. Meier, S.O. Klemm,
P.U. Biedermann, A.A. Topalov, M. Rowherder,
K.J.J. Mayrhofer
PCCP 13 (2011) 16384-16394.
The effective surface pH during reactions at the solid-liquid interface
I. Katsounaros, J.C. Meier, S.O. Klemm, A.A. Topalov,
P.U. Biedermann, M. Auinger, K.J.J. Mayrhofer
Electrochem. Commun. 13 (2011) 634-637.
Hydrogen Transport in non-ideal Crystalline Materials
M. Auinger, Chem. Phys. Chem. 15 (2014) 2893-2902.
Acknowledgement
K. Mayrhofer, J.C. Meier, A.A. Topalov, I. Katsounaros,
D. Kurz, A. Mingers