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

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

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

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

Degradation Mechanisms 10/28/2014 ECAT2014

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

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

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

Fitting Experimental Data Accelerated Stress Tests: potential cycling 0.6-0.9 V or 0.6-1.2 V vs. RHE triangular or square wave form 10/28/2014 ECAT2014

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fitting Experimental Data Accelerated Stress Test: square or triangular waveform (SW,TW) cycling between 0.6–0.9 V or 0.6-1.2 V vs. RHE 10/28/2014 ECAT2014

Particle Radius Distribution 10/28/2014 ECAT2014

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

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