Impedance : From the experimental side - Bio-Logic … exp side - Background on EIS Experimental...
Transcript of Impedance : From the experimental side - Bio-Logic … exp side - Background on EIS Experimental...
Impedance : From the experimental side
EIS exp side - 1
EIS exp side -
Background on EIS Experimental set-up • Which instruments? • Connection • Experimental conditions • Cell
Monitoring software • Basic parameters (DC or AC voltage/current, frequency,...) • Advanced parameters (Drift, Multisinus, …) • Stack of cell
Analysis tools • Kramers-Kronig • Zfit • Mott-Schottky/capacity measurement
CONTENTS
2
TF – Some Basics -
BACKGROUND
Current response has a the same frequency with an amplitude dI and phase F Perturbation in potential, (it is also possible to perform the same in Galvano)
Increasing the frequency or amplitude moving away from the steady state Iss vs E curve
3
EIS exp side – Some Basics -
Nyquist diagram Bode diagram
The impedance is a complex number: Z = a + j b = Re(Z) + j Im(Z) (with j2= -1) Z = ρ(cosφ + j sinφ) with ρ the modulus and φ the phase
4
In the Nyquist plot, the impedance for each frequency is plotted in the complex plane -Im(Z) vs Re(Z).
In the Bode Plot, the modulus and the phase of the impedance are plotted against the frequency of the modulation.
BACKGROUND
Z = L[E(t)]/L[I(t)] L: Laplace Transform
How to optimize the setup?
EC-Lab -
• Which instruments for my measurements? • Connection • Experimental conditions • Cell
5
EIS exp side – Setup
Select the appropriate instrument … …in the optimized configuration i.e. low current option, high current option…
HCP-803 SP-300
THE APPROPRIATE INSTRUMENT
For a system with high impedance (such as a coating), SP-300 with ULC can be of interest
Z/O
hm
Z/O
hm
Frequency/kHz
SP-300 with ULC
Z/O
hm
Frequency/kHz
Frequency/kHz
6 Ref: Brochures
For a system with low impedance (such as battery, supercapacitor), select a potentiostat with a current booster.
Low current limit
High current limit
Stray capacitance limit
Bandwidth limit
Stray indcutance limit
EIS exp side – Setup
Protect the cell from any external disturbance
7
PEIS_5mV.mpr
-Im(Z) vs. Re(Z)
Re(Z)/kOhm
1050
-Im
(Z)/
kO
hm
6
5
4
3
2
1
0
-1
-2
Fq = 50 Hz
Use a Faraday cage connected to the earth of the potentiostat Especially for low current measurements.
Faraday cage
Earth
EXTERNAL PERTURBATION
50 / 60 Hz
f = 50 Hz
-Im(Z) vs. Re(Z)
PEIS_Cable_10m.mpr PEIS_Cable_1-5m.mpr # PEIS_Cable_2-5m.mpr PEIS_Cable_4m.mpr
Re(Z)/kOhm
1.510.5
-Im
(Z)/
kO
hm
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0199531 Hz
15842 Hz
1121 Hz
EIS exp side – Setup 8
EXTENDED CABLE
Why? • Because this affects the bandwith of the potentiostat. Error is higher. • Capacity of the extra cable is added. Specifications given are the specifications at the end of the leads of the standard cable.
0.1 1 10 100 1000 10000 100000
1
10
100
1000
1,5m
2,5m
4m
10m
|Z|/Ohms
f/(k
Hz)
TestBox1 1.5 m
2.5 m
4 m 10 m
Avoid extended cable Affect the EIS measurement especially at high frequencies
Ref: Tech Note 13
EIS exp side – Setup 9
EXTENDED CABLE
It is possible to evaluate the error thanks to EC-Lab: 1. Fit the resulting EIS data of 1.5 m
2. Use these fitted values as reference
3. Compare these reference values with the data obtained with 10 m cable (Plot the error data vs. frequency, for the 1.5 m cable and for the 10 m cable)
Ref: Tech Note 13
EIS exp side – Setup 10
EXTENDED CABLE
It is even clearer in the Bode plot
1- Fit of the EIS data obtained with 1.5 m cable
Ref: Tech Note 13
-Im(Z) vs. Re(Z)
PEIS_Cable_1-5m.mpr PEIS_Cable_1-5m_zfit.mpp #
Re(Z)/kOhm
54321
-Im
(Z)/
kO
hm
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
PEIS_Cable_1-5m.mpr : log (|Z|) vs. log (freq) PEIS_Cable_1-5m.mpr : Phase(Z) vs. log (freq) PEIS_Cable_1-5m_zfit.mpp : log (|Z|) vs. log (freq) PEIS_Cable_1-5m_zfit.mpp : Phase(Z) vs. log (freq)
PEIS_Cable_10m.mpr : log (|Z|) vs. log (freq) PEIS_Cable_10m.mpr : Phase(Z) vs. log (freq) #
log (freq/Hz)
420
log
(|Z
|/k
Oh
m)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
Ph
as
e(Z
)/de
g
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
EIS exp side – Setup 11
EXTENDED CABLE
10 m cable
1.5 m cable
Fit of 1.50 m cable
Modulus: line Phase: marker
Ref: Tech Note 13
PEIS_Cable_10m_zfit.mpp : f(Delta(|Z|)) vs. freq, log spacing PEIS_Cable_10m_zfit.mpp : Delta(Phase(Z)) vs. freq, log spacing
PEIS_Cable_1-5m_zfit.mpp : f(Delta(|Z|)) vs. freq, log spacing PEIS_Cable_1-5m_zfit.mpp : Delta(Phase(Z)) vs. freq, log spacing #
freq/Hz , log spacing
1 10 100 1,000 10,000 100,000
De
lta
(|Z
|)/%
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
De
lta(P
ha
se
(Z))/d
eg
90
80
70
60
50
40
30
20
10
0
EIS exp side – Setup 12
EXTENDED CABLE
10 m cable
1.5 m cable
Modulus: line Phase: marker
Ref: Tech Note 13
2. Use these fitted values as reference
3. Compare these reference values with the data obtained with 10 m cable (Plot the error data vs. frequency, for the 1.5 m cable and for the 10 m cable)
EIS exp side – Setup 13
CONNECTION (R contact)
Battery
2 m
Affects the measurement at low level of impedance. This is particularly relevant for battery, supercapacitor investigations…
Contact resistance is no more negligible for low impedance system. In that case, 4-point measurements has to be considered:
Ref2 + Ref3
CA1
Ref1
CA2
Ref: App Note 23
EIS exp side – Setup 14
Affects the measurement at low level of impedance. This is particularly relevant for battery, supercapacitor investigations…
Ref: App Note 23
CONNECTION (inductive effect)
Battery + wiring
Battery
Connectors
Battery
Equivalent circuit: R + L/R +R/Q 620 nH against 870 nH The length of the extra wiring is around 25 cm. Generally this is 10 nH/cm
-Im(Z) vs. Re(Z)
PEIS_01.mpr # PEIS w ithout R_01.mpr
Re(Z)/kOhm
321
-Im
(Z)/
kO
hm
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
200 kHz200 kHz
13 kHz13 kHz
EIS exp side – Setup 15
GEOMETRY OF THE CELL
Reduce ohmic drop of the cell by: - decreasing the distance between RE and WE - changing the Vycor glass of the RE - …
Affects the measurement of low impedance system at high frequency (battery, supercapa, …)
A resistor of 1 kOhm was added to mimick the ohmic drop
Ref: App Notes 27-29
-Im(Z) vs. Re(Z)
PEIS_01.mpr # PEIS w ithout R_01.mpr
Re(Z)/kOhm
321
-Im
(Z)/
kO
hm
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
200 kHz200 kHz
13 kHz13 kHz
Shift of 1 kOhm
EIS exp side – Setup 16
Determine/compensate the ohmic drop resistance thanks to ZIR technique (measure the Re(Z) at one frequency). Note that it is not possible to compensate ohmic drop for EIS measurement.
Ref: App Notes 27-29
GEOMETRY OF THE CELL
EIS exp side – Setup 17
TEMPERATURE EFFECT
TestBox3 circuit 2
R decreases when Temp increases
14°C
16°C
18°C 20°C
22°C 24°C
26°C
Control of temperature of the cell may be required.
For example, if one experiment is performed during the night and another one during the day, a difference between both spectra can be observed.
Ref: Tech Note 16
EIS exp side – Setup 18
FUNNY BEHAVIOR !!!
What’s that? Only artifact due to reference electrode impedance not negligible at high frequencies
PEIS_Funny_loop (Artifact)_Ferrocen_in_THF.mpr
-Im(Z) vs. Re(Z)
Re(Z)/kOhm
100500
-Im
(Z)/
kO
hm
100
90
80
70
60
50
40
30
20
10
0
-10
Fq = 643 Hz
341 kHz
42 kHz
2.8 MHz
Ref: Diard, Electrochim.Acta 2010, 55, 6, 1907-1911
EIS exp side – Setup 19
FUNNY BEHAVIOR !!!
Ref: Diard, Electrochim.Acta 2010, 55, 6, 1907-1911
C1
L2
R2 R1
R3
C3
This is due to the Ref Electrode
ZRef
EIS exp side – Setup 20
FUNNY BEHAVIOR !!!
Ref: Diard, Electrochim.Acta 2010, 55, 6, 1907-1911
WE CE
RE
Frequency/Hz
IZI/
Oh
m
Capacitor
Ref electrode
A solution:
RE
At high frequency the impedance of the capacitor is negligible Capacitor of ~ 1 µF
Pt wire
IZI = 1/(2πfC)
How to optimize the settings in EC-Lab® software?
EIS exp side
• Which techniques in EC-Lab®/EC-Lab® Express • Basic parameters (DC or AC voltage/current, frequency,...) • Advanced parameters (Drift, Multisinus, …) • Stack of cell
21
EIS exp side – Soft
EC-LAB TECHNIQUES
PEIS: control of the perturbation in voltage GEIS: control of the perturbation in current SPEIS: PEIS at several DC voltage bias SGEIS: GEIS at several DC current bias PEISW: PEIS at one frequency versus time
22 Ref: EC-Lab® manual
EIS exp side – Soft
OVERVIEW OF EIS TECHNIQUE
EDC/IDC: defines the bias level (bias current for galvano or bias voltage for potentio) DC level
Va/Ia: defines the amplitude of AC perturbation (be careful, it is an amplitude and not peak-to-peak or RMS amplitude)
Pw: offers the possibility to add a delay before the measurement at each frequency. This delay is defined as a part of the period. So the delay is longer for low frequencies.
Na: repeats Na measure(s) and average the values for each frequency.
E(t) = EDC + Va sin (2π f t)
fi/ff: initial /final frequency
23 Ref: EC-Lab® manual
I(t) = IDC + Ia sin (2π f t)
EIS exp side – Soft
AMPLITUDE (Va) -Im(Z) vs. Re(Z)
battery 10Ah_Va=0.5mV_pw =0_Na=1_no drift_separate_12.mpr
battery 10Ah_Va=10mV_pw =0_Na=1_no drift_separate_12.mpr #
Re (Z) /m Ohm
12108
-Im
(Z)/
mO
hm
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
Va = 0.5 mV
Va = 10 mV
The resulting current and potential value should be in agreement with the accuracy of the instrument.
Amplitude of the controlled signal (Va or Ia) should be: - high enough to induce a significant amplitude of the response - Small enough to keep the linear behavior of the cell.
24 Ref: App. Note 23
EIS exp side – Soft
AVERAGE (Na) -Im(Z) vs. Re(Z)
battery 10Ah_Va=0.5mV_pw =0_Na=36_drift_separate_repetition_12.mpr, cycle 1
batterie 10Ah_Va=0.5mV_pw =0_Na=1_no drift_separate_repetition_12.mpr, cycle 1 #
Re (Z) /m Ohm
1110987
-Im
(Z
)/m
Oh
m
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
Na = 36
Na = 1
This average process smoothes the random error of the measurement.
25 Ref: App. Note 23
Curve with Na = 36 is less noisy than the one with Na = 1. Noie is divided by the N1/2
-Im(Z) vs. Re(Z)
peis dummyCell Pw 2_07.mpr # peis dummyCell Pw 0_07.mpr
Re(Z)/kOhm
42
-Im
(Z)/
kO
hm
2.5
2
1.5
1
0.5
0
-0.5
EIS exp side – Soft
WAIT PERIOD (Pw)
Curve with Pw = 2 is less scattered than the one with Pw = 0. This result means that it is possible to slightly compensate a noisy shape of an EIS diagram just by increasing the Pw value and without disturbing the cell much. Memory effect of the system
Pw = 0
Important to activate this option when there is a big gap between two frequencies .
26 Ref: App. Note 23
Pw = 2
-Im(Z) vs. Re(Z)
peis dummyCell Pw 2_07.mpr # peis dummyCell Pw 0_07.mpr
Re(Z)/kOhm
2.682.662.64
-Im
(Z)/
kO
hm
1.675
1.67
1.665
1.66
1.655
1.65
1.645
1.64
1.635
28 Hz
EIS exp side – Soft
MULTISINE
27
Sum of sinus
Advantages: - Reduce time of the measurement (activated below 10 Hz) - Avoid drifts for non-steady state system on measurement at low frequency
Ref: App. Note 19
u(t) A cos(2fkk1
N
t Fk)
Minimize the crest factor (avoid too large exciation, this might result in a measurement in the non-linear response domain of the electrochemical cell):
EIS exp side – Soft
MULTISINE
28 Ref: App. Note 19
Same result…. ….for less time (5 mn instead of 20 mn)
Single Sine Multisinus
This is especially important for EIS at low frequency (such as battery)
EIS exp side – Soft
DRIFT
29
Theoretically, an EIS experiment has to be performed only on the system at its steady state but for slow system such as battery, this is almost never the case, so this option allows the user to perform EIS experiment on a system which is not yet in its steady state. This is a patented process. Note: Duration of the experiment will be twice longer.
Ref: App. Note 17
In its steady-state
Not in its steady-state
File048_02_PEIS.mpr
-Im(Z) vs. Re(Z)
Re(Z)/Ohm
300200
-Im
(Z)/
Oh
m
120
100
80
60
40
20
EIS exp side – Soft
DRIFT
30 Ref: App. Note 17
File048_02_PEIS.mpr
-Im(Z) vs. Re(Z)
Re(Z)/Ohm
3002001000
-Im
(Z)/
Oh
m150
100
50
0
284 Hz
0.439 Hz
After a pulse of current
File047_02_PEIS.mpr
-Im(Z) vs. Re(Z)
Re(Z)/Ohm
3002001000
-Im
(Z)/
Oh
m
150
100
50
0
284 Hz
0.436 Hz
File047_02_PEIS.mpr
-Im(Z) vs. Re(Z)
Re(Z)/Ohm
300250200
-Im
(Z)/
Oh
m
120
100
80
60
40
20
0
Without drift correction
stable
With drift correction
First EIS just after the current pulse is higher
Two other EIS (done after) are stable
EIS exp side – Soft
EIS ON COUNTER ELECTRODE
31
In « Cell Characteristics » tab:
For this kind of measurement, a three-electrode setup is required.
+ CA2/REF1
- CA1/REF3
REF2
ZWE ZCE
Simultaneous and independent measurment on the two sides of a system. Battery, fuel cell, supercapacitor with a ref electrode.
peis_ce_C14.mpr
-Im(Z) vs. Re(Z) -Im(Zce) vs. Re(Zce) #
Re (Zce ) /m Ohm
40302010
-Im
(Zc
e)/
mO
hm
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
EIS exp side – Soft 32
Counter Electrode Working Electrode
EIS ON COUNTER ELECTRODE
difference is not due to the battery but to the connection
EIS exp side – Soft
EIS ON STACK OF CELL
33
Ref1 Ref2 Ref3 Ref1 Ref2 Ref3
Ref1 CA2
Ref2+Ref3 CA1
+ -
Slave channel (only measures)
Master channel (control and measure
the whole stack)
Ref: App. Note 16
Simultaneously measurment on a whole stack and the behavior follow up of each cell. Battery, fuel cell, supercapacitor with a ref electrode.
EIS exp side – Soft
EIS ON STACK OF CELL
34
Stack of 12 elements Impedance of the stack (Zstack) is the sum of the impedance of each element (Z1, Z2, ...)
1 2 3 4 12
Z stack
Z1 Z2 Z3
Ref: App. Note 16
Some analysis tools of EC-Lab®
EIS exp side
• Kramers-Kronig • Zfit • Mott-Schottky/capacity measurement
35
EIS exp side - tools
This works only for non-truncated plot.
-Im(Z) vs. Re(Z)
-Im(Z) vs. Re(Z) PEIS_-0-35V_circuit3_kk.mpp
Re(Z)/kOhm
21
-Im
(Z)/
kO
hm
1
0.8
0.6
0.4
0.2
0
21.1 Hz
-Im(Z) vs. Re(Z)
-Im(Z) vs. Re(Z) PEIStruncated_-0-35V_circuit3_kk.mpp
Re(Z)/kOhm
10
-Im
(Z)/
kO
hm
1
0.8
0.6
0.4
0.2
0
21.7 Hz
KRAMERS-KRONIG
36 Ref: App. Note 15
Applicable Non-applicable
There is a relationship between Re(Z) and Im(Z) when: - causal, stable an dlinear time invariant system - when f 0 and f ∞
Checks the validity of the measurement
EIS exp side - tools
EIS DATA FITTING (ZFIT)
9 elements: - R: resistor, - L: self/inductor, - C: capacitor, - Q: constant Phase Element (CPE), - W: Warburg Element simulating the semi-infinite diffusion, - Wd: Warburg Diffusion Element simulating the convective diffusion, - M: restricted Linear Diffusion Element, - G: Gerischer Element.
37
Ref: Manual of EC-Lab®
EIS exp side - tools
EIS DATA FITTING (ZFIT)
Sel: if this parameter is checked the corresponding value will be used in the fit as defined value (non minimized)
Sign: selection of the sign allowed for the parameter. + and/or -.
Dev: confidence interval (like a standard deviation).
38 Ref: Manual of EC-Lab®
SGEIS_IMVS_zfitparam.mpp
R1/Ohm vs. <Ewe> # C1/F vs. <Ewe>
<Ewe>/V
10.80.6
R1
/Oh
m
65
60
55
50
45
40
35
30
25
20
15
10
5
C1/µF
200
190
180
170
160
150
140
130
120
110
100
Point 0, Cycle 1
Point 3, Cycle 4
Point 10, Cycle 11
EIS exp side - tools
EIS DATA FITTING (ZFIT)
39
Cycle: allow to fit one cycle or several cycles successively and allow one to follow the changes of the values with the cycles
Each point corresponds to one cycle of SPEIS (at different voltage)
Ref: App. Note 30
EIS exp side - tools
EIS DATA FITTING (ZFIT)
Re(Z)/Ohm
6040200
-Im
(Z)/
Oh
m
35
30
25
20
15
10
5
0
-5
Re(Z)/Ohm
100
50
0
-Im
(Z)/
Oh
m
60
40
20
0
-20
<Ewe>/V
1
0.8
0.6
40 Ref: App. Note 30
- Fit on several cycles
Follow up of the element values variations with time/potential/current..
EIS exp side - tools
EIS DATA FITTING (ZFIT)
41
Raw data
Fit data XXX_Zfitparam.mpp file is created
Ref: App. Note 30
- Fit on several cycles
EIS exp side - tools
EIS DATA FITTING (ZFIT)
Method: Algorithm used for the fit Iterations: Number of iteration 2 quality of the fit. 2/N is weighted.
42 Ref: Manual of EC-Lab®
SPEIS_7MHz to 1Hz__C_V_Charact.mpr.mpr
Cs-2 vs. <Ewe>
7.000 MHz
<Ewe>/V
1050
Cs
-2/n
F-2
1,600
1,400
1,200
1,000
800
600
400
200
EIS exp side - tools
MOTT-SCHOTTKY
Determination of the flatband potential and the donor density For semi-conductor, such as PV cell, …
1/Cs2 = f(Ewe)
43 Ref: App. Note 24
EIS exp side - tools
CAPACITY in the MPR FILE
If the equivalent circuit is modeled by R/Cp or R+Cs, the mpr file of the EIS techniques (PEIS, GEIS, SPEIS, SGEIS, PEISW) includes already the capacity value Cs and Cp.
Cp
Cs
44 Ref: App. Note 35
EIS exp side - tools
CAPACITY in the MPR FILE
Cp vs. <Ewe>, log spacing
SPEIS_7MHz to 1Hz_01.mpr SPEIS_7MHz to 1Hz_01.mprSPEIS_7MHz to 1Hz_01.mpr SPEIS_7MHz to 1Hz_01.mprSPEIS_7MHz to 1Hz_01.mpr # SPEIS 323 kHz_01.mpr
<Ewe>/V, log spacing
0,001 0,01 0,1 1 10
Cp
/pF
160
140
120
100
80
60
40
20
Fq = 7.0 MHz
Fq =3.2 MHz
Fq = 1.5 MHz
Fq < 323 kHz
C vs Voltage at several frequencies
This allows one to plot on-line (without Zfit), Cs or Cp versus voltage or time.
45 Ref: App. Note 35
EIS exp side
MORE INFO…….
Feel free to visit our web site, some application notes or EIS handbook may be helpful for your applications:
http://www.bio-logic.info/potentiostat/notesan.html
Thank you for your attention
Lets move to the instruments
46