Autolab交流阻抗拟合方法简介

i I sin(t )
• Where φ is a phase angle.
Review of ac circuits
• A pure resistance R, E=IR, where the phase is zero. • A pure capacitance C, E • i sin(t )
Q=
CPE 常相元素 CONSTANT PHASE ELEMENT
SURFACE ROUGHNESS HETEROGENEOUS SURFACE
CIRCUIT ELEMENT
Z = 1/ (Q)n
n = 1 ONLY CAPACITANCE n = 0 ONLY RESISTANCE
Electrochemical Impedance spectroscopy
Electrochemical Impedance Spectroscopy
Resistance:
Z R
I E F 0
o
Capacitance:
Z
1 C
E I
F -90
o
Review of ac circuits
• Components along the ordinate are assigned as imaginary and along the abscissa are real, thus, we handle these parameters mathematically as “real” or “imaginary”.
1K
1K
1K
2
-2
-1
1 log(f)
2
3
4
0
Electrochemical Impedance spectroscopy
高频
单纯电阻: R
FRA test procedure with dummy cell: connect WE(e) R 5.0 90 75 FRA test procedure with dummy cell: connect WE(e) R
50 3.0
0.8K
/ ohm
40
-phas e / deg(+)
2.8
l og(Z)(o)
'' Z -
30 2.5 20
0.5K
0.3K
2.3 10
2.0
-2
-1
1 log(f)
2
3
4
0
0 0.1K
0.4K
0.6K Z' / ohm
0.9K
1.1K
Electrochemical Impedance spectroscopy
50 3.0 0.8K
-Z' ' / ohm
-phas e / deg(+)
R1 40
2.8
l og(Z)(o)
30 2.5 20
0.5K
0.3K 2.3 10
R1
0 0.1K 0.4K 0.6K Z' / ohm
R1+R2
R2
2.0 -2 -1 1 log(f) 2 3 4 0 0.9K 1.1K
5000
6000
7000
8000
Electrochemical Impedance spectroscopy
R(RQ)(RQ)
2.3M 2.0M 1.8M 1.5M 1.3M 1.0M 0.8M 0.5M 0.3M 0
) (Z )(o g l o m h o
R(Q[R(RQ)])
Faraday cage
A H Diff. ampl. I
s CE
B
+ + + + +
-
RE
G E
WE
C
D F
+ + + + +
-
Electrochemical Impedance spectroscopy
Capacitor double layer Solution Resistance
D
+ + + + +
+ + + + +
Electrochemical Impedance spectroscopy
理论
欧姆定律给出直流电位和直流电流的简单关系:
E=iR
(1)
当有交流参与时，关系式为:
Eac = iac Z
(2), 其中Z为阻抗
Electrochemical Impedance spectroscopy
Electrochemical Cell
E
-
Polarization Resistance
-
Electrochemical Impedance spectroscopy
Electrochemical Impedance Spectroscopy
FRA: Frequency Response I Analysis
I0
I0 + I sin ( t +
高频
单纯电容: C
低频
C 8 100 15M C
7 13M 6 75 10M 5
l og(Z)(o)
-phas e / deg(+)
/ ohm
4 50 3
8M
-Z' '
5M
2 3M 1 25 0 0
-1
-2
-1
0 log(f)
1
2
3
0
-3M -1M
2M
4M
7M
9M Z' / ohm
12M
14M
17M
50 5.5
5.0
-2
-1
0
1 log(f)
2
3
4
5
6
-Z' ' / ohm
0
3M
5M
8M Z' / ohm
10M
13M
15M
18M
20M
23M
Electrochemical Impedance spectroscopy
R(RC)
R1 C1 R2
高频
低频
R(RC) 3.3 R(RC)
C1
60
1.0K
19M
Electrochemical Impedance spectroscopy
高频
电阻与电容串联
[RC]
低频
R and C in serials [RC] 7.5 90 15M
ቤተ መጻሕፍቲ ባይዱ
R and C in serials [RC]
7.0
C
80 13M
6.5
70
60 6.0
l og(Z)(o)
-Z' ' / ohm
10M
50 5.5 40 5.0
-phase / deg(+)
8M
R
30
5M
4.5
20 3M
R
0 -1M
4.0
10
3.5
-2
-1
0
1 log(f)
2
3
4
5
6
0
2M
4M
7M
9M Z' / ohm
12M
14M
17M
19M
Electrochemical Impedance spectroscopy
高频
电阻与电容并联
(RC)
低频
R and C in parallel 7.5 (RC) 100 25M 23M 7.0 20M 75 6.5 18M 15M 13M 10M 8M 25 5M 4.5 3M 4.0 0 0 -3M
R and C in parallel (RC)
log(Z)(o)
6.0
-phase / deg(+)
Hoogovens cell, steel wit h coating.
Hoogovens cell, steel wit h coating. 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 Faraday cage 90 80 70 60
低频
4.5 65 4.0
l o g (Z)(o )
50
25
/ ohm -Z' '
-p h a s e
3.5
40
0
/ d e g (+)
3.0 15 2.5
-25
-50
2.0
-2
-1
1
log(f)
2
3
4
-10
-75
0
5K
10K
15K
20K
Z' / ohm
25K
30K
35K
40K
45K
50K
Electrochemical Impedance spectroscopy
Electrochemical Impedance spectroscopy
复合体系
这三种等效电路的曲线都一样! 必须结合实际体系来选择合适用的电路。
R(RC)( RC) Circuit 7000
6000
5000
-Z' ' / ohm
4000
3000
2000
1000
0 1000
2000
3000
4000 Z' / ohm
Z (R X C ) XC 1 tan F R RC
• The impedance is a kind of generalized resistance. The phase angle expresses the balance between capacitive and resistance components in the series circuit. For a pure resistance, φ=0; for a pure capacitance, φ=π/2; and for mixtures, intermediate phase angles are observed.
XC 2
• Where Xc is the capacitive reactance, 1/ωC • A comparison of R and Xc shows that Xc must carry dimensions of resistance, but the magnitude of Xc falls with increasing frequency.
E - jX C I • A voltage E is applied across R and C
E ER EC I ( R - jX C ) IZ • Where Z=R-jXc, called the impedance.
Review of ac circuits
• The magnitude of Z and phase angle are given by the following, respectively 2 2 1/ 2
Bode图: lg(Z)~lg(f) 和 φ~lg(f)
FRA test procedure with dummy cell: connect WE(c) 3.3 60
1.0K
Nyquist图: Z’ ~ -Z”
FRA test procedure with dummy cell: connect WE(c)
E0
Potentiostatic or galvanostatic measurements
E
E0 + E sin t
Review of ac circuits
• A purely sinusoidal voltage can be expressed as
e E sin t
• Where ω is the angular frequency, which is 2π times the conventional frequency in hertz. • The current lags the voltage, it can be expressed generally as
Electrochemical Impedance spectroscopy
HIGH FREQUENCY Cdl
D
Rsol
E
F
Rct
LOW FREQUENCY
Electrochemical Impedance spectroscopy
Electrochemical Impedance spectroscopy
Counter Electrode
POTENTIOSTAT GALVANOSTAT
A H Diff. ampl. I
Reference Electrode
sense Working Electrode
G
B
E
C
D
F
Electrochemical Impedance spectroscopy
POTENTIOSTAT GALVANOSTAT
n1 n = 0.8 QC
60 60.0 50 50.0
1K
40 40.0
-phas e / deg(+) -phas e / deg(+)
3
ohm / ohm ' / -Z' -Z' '
1K
l og(Z)(o)
30 30.0 3 20 20.0
0.K
2 10 10.0
0
0.K
0.K Z' / ohm
Cdl
( RC)
Rp
并联元件
[RC]
串联元件
Electrochemical Impedance spectroscopy
常用元件: 电阻 R
相位角: 0
0
Electrochemical Impedance spectroscopy
常用元件: 电容 C
相位角: 900
Electrochemical Impedance spectroscopy
PERFECT ELECTRODE =C
HETEROGENEOUS SURFACE = Q
Electrochemical Impedance spectroscopy
n=1 Q=C
FRA test procedure with dummy cell: connect WE(c) 1K
3 FRA test procedure with dummy cell: connect WE(c) 3