Platinum Coarsening: Multiscale Analysis and Asymptotics in Proton Exchange Membrane Fuel Cells

We conduct a multiscale analysis on a physics based platinum oxide model for a proton exchange membrane fuel cell to derive a long time scaling law for the evolution of the electrochemically active surface area (ECSA). Under conditions where platinum coarsening is the main mode of ECSA loss, we derive the normalised ECSA will evolve at long times as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">nECSA</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≈</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mroot> <mml:mrow> <mml:mi>κ</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:mroot> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> for a decay rate κ . The exponent p may either be 2 or 3 depending on whether platinum coarsening is limited by the rate of deposition, or the rate of transport to the surface of a platinum particle. This physics based asymptotic expression yields straightforward methods that enable lifetime prediction of load/unload driven degradation on the cathode catalyst layer from a sparse set of data. This scaling law is then compared with several experiments and found to be in good agreement.