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
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
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
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
+
+
++
++
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
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
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
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%
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.
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
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
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
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
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
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
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
Acknowledgement
National Science Foundation Bill & Melinda Gates Foundation
Thank You!