SOFC and Electrolysis Electrochemical Characterisation-Impedance Fundamentals
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1 SOFC and Electrolysis Electrochemical Characterisation-Impedance Fundamentals Søren Højgaard Jensen Fuel Cells and Solid State Chemistry Division Risø National Laboratory for Sustainable Energy Technical University of Denmark P.O. 49, DK-4000 Roskilde, Denmark Tel.: , Fax: ,
2 Outline Fysisk Kemi 2, Exercise 3 (1 hour) Pause (15 min) Chapter 4 in Mark E. Orazem and Bernard Tribollet, Electrochemical Impedance Spectroscopy, Willey, Hoboken, NJ, 2008 (15 min) Exercises in relation to chapter 4 (45 min) Pause (15 min) Chapter 7 in Mark E. Orazem and Bernard Tribollet, Electrochemical Impedance Spectroscopy, Willey, Hoboken, NJ, 2008 (30 min) Exercises in relation to chapter 7 2 (45 min)
3 Electrical Circuits Chapter 4 in EIS by Orazem and Tribollet, Wiley
4 Electrical Circuits Leon Chua
5 Electrical Circuits Chapter 4 in EIS by Orazem and Tribollet, Wiley
6 Electrical Circuits Chapter 4 in EIS by Orazem and Tribollet, Willey
7 Electrical Circuits -Inductor 7
8 Electrical Circuits -Exercise Derive the impedance of a capacitor 8
9 Electrical Circuits -Exercise 9
10 Electrical Circuits -Series and Parallel Connections Show this 10
11 Electrical Circuits -Exercise 1. Draw Nyquist plot and Bode plots of the impedances of a resistor, inductor and capacitor 2. Draw the impedance of in a Zr, Zl plot with Re = 1 Ohm, Rt = 2 Ohm and Cdl = 0.1 F 3. Exercise 4.1, 4.2, 4.3, 4.4, (extra 4.6) 11
12 Pause (15 minutes) 12
13 13
14 14
15 Applied Voltage: Faradaic current response: Capacitive current response: Charge Transfer resistance : Derive this 15
16 16
17 Equiv. circuit 17
18 Equiv. circuit What happens with max(i-i) for a constant ΔV when the frequency increases from 1 mhz to 10 khz? 18
19 Equiv. circuit 19
20 Why? 20
21 Why? 21
22 Experimental Methods Chapter 7 in EIS by Orazem and Tribollet, Wiley 2008 Lissajous curve 22
23 Experimental Methods Exercise Verify the equations 23
24 Experimental Methods Phase sensitive methods (Lock-in amplifier) Signal (AC current) Ref signal (square) Integration (one period) 24
25 Experimental Methods Phase sensitive methods (Lock-in amplifier) Signal (AC voltage) 25
26 Experimental Methods Single Phase Fourier Analysis Periodic signal: Complex repr.: Deriv of coeff.: 26
27 Experimental Methods Single Phase Fourier Analysis What is a1 and b1? a1= cos(phi) b1 = -sin(phi) cos2(x) = (1 + cos(2x))/2 27 cos(x)sin(x)=½sin(2x)
28 Experimental Methods Single Phase Fourier Analysis 28
29 Experimental Methods Single Phase Fourier Analysis 29
30 Experimental Methods Single Phase Fourier Analysis 30
31 31
32 32
33 Experimental Methods Single Phase Fourier Analysis 33
34 Pause 34
35 Gas Conversion Impedance Primdahl and Mogensen. JES 145, 2431 (1998) H2+½O2 H2O 35
36 Gas Conversion Impedance Primdahl and Mogensen. JES 145, 2431 (1998) PH 2O RT E = E0 + ln nf PH2 PO2 36
37 Gas Conversion Impedance Primdahl and Mogensen. JES 145, 2431 (1998) 37
38 Gas Conversion Impedance Primdahl and Mogensen. JES 145, 2431 (1998) 38
39 Gas Conversion Impedance Primdahl and Mogensen. JES 145, 2431 (1998) 39
40 Gas Conversion Impedance Primdahl and Mogensen. JES 145, 2431 (1998) Exercises 1. On Figure 6, the curves have a slope of app. 1 and -1. Why? Why are the curves not linear? 2. On Figure 5 the capacity increases with decreasing flow rate. Why does it increase? 3. The criterion for the expressions for Rg, Cg and fg is that xh2o<<xh2o and xh2<<xh2. Why is it so? 4. Extra: Read Appendix A 40
41 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 41
42 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 42
43 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 43
44 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 44
45 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) PH 2O RT E = E0 + ln nf PH2 PO2 45
46 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 46
47 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 47
48 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 48
49 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 49
50 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 50
51 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) 51
52 Gas Diffusion Impedance Chapter 5.4 in: Atlung og Jacobsen. Elektrokemi, DTU, Lyngby DK (2005) 52
53 Gas Diffusion Impedance Chapter 5.4 in: Atlung og Jacobsen. Elektrokemi, DTU, Lyngby DK (2005) 53
54 Gas Diffusion Impedance Chapter 5.4 in: Atlung og Jacobsen. Elektrokemi, DTU, Lyngby DK (2005) 54
55 Gas Diffusion Impedance Primdahl and Mogensen. JES 146, 2827 (1999) Exercises 1. Figure 7 (Primdahl, Diffusion, JES, 146, 2827 (1999)) show a linear dependency of the gas resistance. Why is it linear? 2. Read the appendix (Primdahl, Diffusion-paper) 55
An Introduction to Electrochemical Impedance Spectroscopy (EIS)
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