1. Model-based Analysis of PEFC Catalyst Degradation Mechanisms
Thomas Kadyk, Steven G. Rinaldo, Michael Eikerling
International Symposium on Electrocatalysis

2. Literature: In-Situ Degradation
Correlation between
decay in cell voltage and ECSA loss
P.J. Ferreira et al. J. Electrochem. Soc. 152(11):A2256 (2005)
10/28/2014
ECAT2014

3. Literature: Ex-Situ Degradation
Correlation between changes in
particle radius distribution (PRD)
and ECSA loss
→ theoretical link between PRD
evolution and ECSA loss
K.J.J. Mayrhofer et al. Electrochem. Comm. 10:1144 (2008)
10/28/2014
ECAT2014

4. Outline Catalyst Layer Degradation Model
Fitting Experimental Accelerated Stress Tests
Model Based Analysis
Conclusions and Summary
10/28/2014
ECAT2014

5. Degradation Mechanisms
10/28/2014
ECAT2014

6. dissolution and redeposition [1,2]
Model Equations
dissolution and redeposition [1,2]
coagulation [3]
detachment
dimensionless, normalized particle radius distribution
rate of particle radius change
particle creation and extinction terms
detachment rate, assumed radius independent
[1] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19:35 (1961)
[2]C. Wagner, Z. Elektrochem. 65:581 (1961)
[3] V. Smoluchowski, Z. Phys. Chem. 92:129 (1917)
[Steven G. Rinaldo, PhD Thesis, SFU, 2013)
10/28/2014
ECAT2014

7. Kinetics of Dissolution and Redeposition
Pt mass balance
assumption: c(t=0) = 0
characteristic radius
surface tension
mass moment
[1] D. Talapin, A. Rogach, M. Haase, H. Weller, J. Phys. Chem. B 105:12278 (2001)
10/28/2014
ECAT2014

8. Kinetics of Coagulation
particles formed:
particles coagulating:
radius of particle formed from merging of two particles with radii and
coagulation rate kernel, assumed constant (random collisions)
[1] V. Smoluchowski, Z. Phys. Chem. 92:129 (1917)
10/28/2014
ECAT2014

9. Fitting Experimental Data
Accelerated Stress Tests:
potential cycling V or V vs. RHE
triangular or square wave form
10/28/2014
ECAT2014

10. Fitting Experimental Data
Starting Point for Fit:
fitting of single mechanisms separately
dissolution and redeposition: 𝑅 0 0 , 𝑘 𝑑𝑖𝑠 0 , 𝑘 𝑟𝑑𝑝 0
coagulation: 𝑘 𝑐𝑔𝑙 0
detachment: 𝑘 𝑑𝑒𝑡 0
start point for single mechanism fit screened over 5-8 orders of magnitude
Fit of 0.9V data converged into 2 parameter sets for dissolution/redeposition
2 start points for 0.9V fits
10/28/2014
ECAT2014

11. Fitting Experimental Data
For 0.9V full model fits converged to 2 parameter sets
low dissolution and high coagulation
high dissolution and low coagulation
Additional tests with varied start parameters
0.9 V
dependency of the fit on start parameters
ambiguity of dissolution/redeposition and coagulation
detachment always negligible
1.2 V
fit converge into approximately the same solution
10/28/2014
ECAT2014

12. Analyzing Individual Mechansism’s Contributions
PRD change of
each mechanism
ECSA loss from each mechanism
10/28/2014
ECAT2014

13. e.g. coagulation term cycle number↑ number of cycles r [m]
particles lost or gained
ECSA loss
10/28/2014
ECAT2014

14. Square Wave 0.9V time (cycles) time (cycles) time (cycles)
deconvoluting individual mechanism’s contributions
45% ECSA loss due to dissolution/redeposition
2.5% ECSA loss due to coagulation
negligible ECSA loss due to detachment
time (cycles)
10/28/2014
ECAT2014

15. Square Wave 1.2V time (cycles) time (cycles) time (cycles)
dynamic interplay between mechanisms
rapid initial dissolution of small particles
later regaining of ECSA due to redeposition caused by disturbance of the dissolution-redeposition equilibrium due to the other mechanisms
time (cycles)
10/28/2014
ECAT2014

16. Summary and Conclusions
Degradation model linking PRD and ECSA loss
dissolution and redeposition
coagulation
detachment
Fitting experimental accelerated stress tests
ambiguity of dissolution/redeposition and coagulation at low upper potential limit
Model-based analysis
deconvolute individual mechanism’s contribution to ECSA loss
dynamic interaction of mechanisms
10/28/2014
ECAT2014

17. Model-based Analysis of PEFC Catalyst Degradation Mechanisms
Thank you for your attention!
Model-based Analysis of PEFC Catalyst Degradation Mechanisms
Thomas Kadyk, Michael Eikerling
International Symposium on Electrocatalysis

18. coagulation term t↑ time (cycles) r [m] time (cycles) 10/28/2014
ECAT2014
time (cycles)

19. Square Wave 1.2V time (cycles) time (cycles) time (cycles)
10/28/2014
ECAT2014

20. Triangular Wave 1.2V time (cycles) time (cycles) time (cycles)
10/28/2014
ECAT2014

21. Square Wave 0.9V time (cycles) time (cycles) time (cycles)
10/28/2014
ECAT2014

22. Triangular Wave 0.9V time (cycles) time (cycles) time (cycles)
10/28/2014
ECAT2014

23. Square Wave 0.9V – 2nd Start Point
time (cycles)
time (cycles)
time (cycles)
time (cycles)
10/28/2014
ECAT2014

24. Triangular Wave 0.9V – 2nd Start Point
time (cycles)
time (cycles)
time (cycles)
time (cycles)
10/28/2014
ECAT2014

25. Fitting Experimental Data
Accelerated Stress Test:
square or triangular waveform (SW,TW) cycling between 0.6–0.9 V or V vs. RHE
10/28/2014
ECAT2014

26. Particle Radius Distribution
10/28/2014
ECAT2014

27. Solving Coupled Model: Numerical Issues
Convergence problems for SN → 0
ODE solver (variable-order solver based on numerical differentiation formulas [1])
Numerical mass loss for coagulation
improved numerical integration
Speed up code
[1] L.F. Shampine et al. SIAM J. Sci. Comput. 18:1 (1997)
10/28/2014
ECAT2014

28. Fitting Strategy least-squares method
heuristic, derivative-free Nelder-Mead simplex algorithm [1]
Starting Point:
fitting of single mechanisms separately
dissolution and redeposition: 𝑅 0 0 , 𝑘 𝑑𝑖𝑠 0 , 𝑘 𝑟𝑑𝑝 0
coagulation: 𝑘 𝑐𝑔𝑙 0
detachment: 𝑘 𝑑𝑒𝑡 0
using those parameters as starting point
[1] J.C. Lagarias et al., SIAM J. Optim. 9(1):112 (1998)
10/28/2014
ECAT2014