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