Nonmonotonic dynamics in Lifshitz-Slyozov-Wagner theory: Ostwald ripening in nanoparticle catalysts

摘要

Nanoparticle catalysts dispersed on high-surface-area electronic support materials are used in a wide rangenof applications. Nano-sized particles afford a high active surface area per unit volume of an electrocatalyticnmedium. However, the gain in active surface area for desired surface reactions is offset in part by enhancednrates of degradation processes that cause losses in catalyst mass, catalyst surface area, and electrocatalyticnactivity. A dynamic model of surface-area-loss phenomena based on the theories of Lifshitz and Slyozov [J.nPhys. Chem. Solids 19, 35 (1961)], Wagner [Z. Elektrochem. 65, 581 (1961)], and Smoluchowski [Z. Phys.nChem. 92, 129 (1917)] is presented. A population balance equation in particle space accounts for nanoparticlendissolution, redeposition, and coagulation. It relates kinetic rates of these processes to the evolution of the particlesizendistribution and its moments. Our analysis of the temporal dynamics of the number density, mean radii,nsurface area, and mass moments focuses on the important case of reaction-limited Ostwald ripening. Transientnsolutions reveal unique scaling relationships between the moments of the evolving distribution. Diagnostic criterianestablished from the scaling relationships are applied to previously published experimental degradation data fornsupported nanoparticle catalysts in polymer electrolyte fuel cells.