Phase-field model for deposition process of platinum nanoparticles on carbon substrate

Platinum supported on a carbon carrier is widely used as a catalyst for polymer electrolyte membrane fuel cells. The catalytic activity is significantly affected by the size distribution and morphologies of the platinum particles. The objective of this study is to extend the phase-field approach to describe the formation process of platinum particles onto the substrate. The microstructural evolution of a nanoparticle was represented by the temporal evolution of the field variables related to the platinum concentration, long-range crystallographic ordering and phase transition. First-principles calculations were performed in order to estimate the interaction energies between several different types of platinum clusters and a graphene sheet. The platinum density profile concentrated over the substrate surface led to the formation of three-dimensional islands in accordance with the Volmer-Weber mode of growth. The size distributions of the platinum particles were sensitive to the heterogeneity of the substrate surface and to the competitive nucleation and growth processes.