simulating the electrical double layer · edl capacitance varies as a function of – dielectric...
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Simulating the Electrical Double Layer
Guigen Zhang, Ph.D.
Dept. of Bioengineering, Dept. of Electrical & Computer Engineering
Institute for Biological Interfaces of Engineering
Clemson University
COMSOL Conference 2010 Boston Presented at the
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Overview
The drive to make supercharge capacitors Electrochemical based capacitor The structure of electrical double layer (EDL) The effect of EDL structure on electron transfer The EDL capacitor Conclusions
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The Electrochemical Society Interface, Fall 2008
Making Supercharge Capacitors
Overpotential (mV)
-600 -400 -200 0 200 400 600 800
Ca
pac
itan
ce (
F)
8
12
16
20
Nano
Overpotential (mV)
-600 -400 -200 0 200 400 600 800
Cap
acit
an
ce (
F)
1.0
1.5
2.0
2.5
3.0
Flat
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Electrochemical Based Capacitor
D. C. Grahame, 1947.
dAC /0
This topic has been a major interest in electrochemistry for about a century In 1997, the Electrochemical Society sponsored a symposium on the double layer to recognize the 50th anniversary of Grahame’s seminal work
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+
+
++
++
OHP
--------
Ψ0
x
Gouy-Chapman Model
Gouy-Chapman-Stern Model
Helmholtz Model
Problems with the classic theories on electrical double layer (EDL): 1. No electron transfer across the electrode/solution interface 2. Boltzmann distributions for ions in the solution 3. Electro-neutrality
d
AC 0
Diffuse zone
x - - - - - - - - -
+
+
+ +
+ + - -
- -
+
+
+ +
+ +
- -
- -
+
+
+ +
+ +
Diffuse layer
Bulk solution Stern Plane OHP, PET
- - - - - - - - - - -
x
- -
- -
Gouy plane
+
+
+ +
+ + - -
- -
+
+
+ +
+ +
- - + +
+ +
+ +
Compact layer
Electrical Double Layer (EDL)
The EDL structure
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Mass transport by diffusion and electromigration – Nernst-Planck equation
Electrostatics – Poisson equation
Reversible/irreversible systems – Butler-Volmer kinetics
Modeling the EDL Using COMSOL
IHP OHP
Electrolyte
1000 r0
Axis of in-plane symmetry
Axis of axisymmetry
u
v
A
0r
22 vur
21 ll
IHP OHP
Electrolyte
1000 r0
Axis of in-plane symmetry
Axis of axisymmetry
u
v
A
0r
22 vur
21 ll
)( VcDRT
FzcD
t
cii
i
ii
i
In the compact layer: In the solution:
)( 0 V0
i
iicz
1 zfk
bk
z ReO
]/)(exp[ '00 RTEVEFkk tf
]/)()1exp[( '00 RTEVEFkk tb
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Dielectric constant inside the compact layer
Modeling Using COMSOL
Distance (x)
Die
lectr
ic c
on
sta
nt (
x)
a b c
r0 r0 + l1
IHP OHP
B
Electrode surface
Electrolyte
2
1
Radial Distance (r)
PET
r0 + l1 + l2Distance (x)
Die
lectr
ic c
on
sta
nt (
x)
a b c
r0 r0 + l1
IHP OHP
B
Electrode surface
Electrolyte
2
1
Radial Distance (r)
PET
r0 + l1 + l2
rllr
llrrlrrrll
lrrrrr
2102
2101002122
2
100012
1
, )],([Scos
)],([Scosh
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The Size Factor of the EDL
r-r0 (nm)
0.0 0.2 0.4 0.6
Pot
entia
l (V
)
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
1 nm100 nm
A
(r-r0-)/
0.00 0.05 0.10 0.15 8.00 12.00
Pot
entia
l (V
)
-0.030
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
Potential
Con
cent
ratio
n (m
M)
0
1
2
3
4
5
6
Concentration1 nm100 nm
B
(nm) 820 (nm), 14 1001 diffusion
nm
diffusion
nm
(nm) 5.4 (nm), 8.1 1001 diffuse
nm
diffuse
nm
Diffuse Layer
Diffuse Layer
~13% ~0.5%
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E-E0' (V)-0.25 -0.20 -0.15 -0.10 -0.05 0.00
i/i d
L
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1nm10nm50nm100nm200nmz = -1z = +1Diffusion
-0.2-0.1 0.0 0.1 0.2
i/i dL
0.00.20.40.60.81.0
Electrode Radius (mm)0 100 200
0.90
0.95
1.00
1.05
1.10
Diffusionz=-1z=+1
E-E0'(V)
Insert-1 Insert-2
E-E0' (V)
-0.2 -0.1 0.0 0.1 0.2 0.3
i/i d
L
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Diffusion0.2nm0.4nm0.7nm
0.0 0.5 1.0 100.0
Con
cent
ratio
n (m
M)
0123456
Concentration
(r-r0-)/
Pote
ntia
l (V)
-0.12-0.10-0.08-0.06-0.04-0.020.000.02
Potential
Effect of compact layer thickness Effect of electrode size
EDL Effect on Electron Transfer
Note: “Diffusion” represents the case in which the EDL effect is not considered.
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Effects of EDL
Distance into Solution from PET (nm)
0 1 2 3 4 5 6
Pote
ntia
l (V)
-0.030
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
Con
cent
ratio
n (m
M)
0
1
2
3
4
5
PotentialConcentration0.33nm0.44nm0.55nm0.66nm
Distance into Solution from PET (nm)
0 1 2 3 4 5 6
Pote
ntia
l (V)
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
Con
cent
ratio
n (m
M)
0
1
2
3
4
5
PotentialConcentrationES=6ES=12ES=18ES=24
Distance into Solution from PET (nm)
0 2 4 6 8 10 12
Pote
ntia
l (V)
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
Con
cent
ratio
n (m
M)
0
1
2
3
4
5
PotentialConcentration0.00 M0.05 M0.50 M5.00 M
Distance into Solution from PET (nm)
0 2 4 6 8 10
Pote
ntia
l (V)
-0.04
-0.03
-0.02
-0.01
0.00
Con
cent
ratio
n (m
M)
0
1
2
3
4
5
PotentialConcentration0.5 nm1.0 nm5.0 nm10.0 nmFlat
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EDL Capacitance
Radius of Electrode (nm)1 10 100 1000
Capa
citan
ce (
F/cm
2 )
10
12
14
16
18
20
22
24
26
y=-4.21+28.66x/(0.42+x)
Size effect
2
0Cr E
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EDL Capacitance
Dielectric Constant at Electric Satuaration0 6 12 18 24
Cap
acita
nce
(F/
cm2 )
10
15
20
25
30
35
40
Distance (x)
Die
lec
tric
co
ns
tan
t (
x)
a b c
r0 r0 + l1
IHP OHP
B
Electrode surface
Electrolyte
2
1
Radial Distance (r)
PET
r0 + l1 + l2Distance (x)
Die
lec
tric
co
ns
tan
t (
x)
a b c
r0 r0 + l1
IHP OHP
B
Electrode surface
Electrolyte
2
1
Radial Distance (r)
PET
r0 + l1 + l2
Dielectric effect
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EDL Capacitance
Thickness of Compact Layer (nm)0.33 0.44 0.55 0.66
Capa
citan
ce (
F/cm
2 )
8
10
12
14
16
18
20
22
24Thickness effect
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EDL Capacitance
Concentration of Supporting Electrolyte (M)0 1 2 3 4 5 6
Cap
acita
nce
(F/
cm2 )
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
17.0
Electrolyte effect
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EDL Capacitance: A Surprise
D. C. Grahame, 1947.
Overpotential (V)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Cap
acit
an
ce (
F/c
m2)
11.365
11.370
11.375
11.380
11.385
With ETwithout ET
FEM
Overpotential (V)
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Ca
pa
cit
an
ce
(C
/CP
ZC)
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
MD
dAC /0
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Conclusions
EDL capacitance varies as a function of – Dielectric constant – Compact layer thickness – Electrode size – Electrolyte concentration
When redox is allowed, the capacitance-potential curve exhibits a dip feature near the potential of zero charge This study shed some new light into enhancing the supercharge capacitors
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Acknowledgement
National Science Foundation Bill & Melinda Gates Foundation
Thank You!