Theoretical Model for Ostwald Ripening of Nanoparticles with Size-Linear Capture Coefficients

The Ostwald ripening process in 3D and 2D systems has been studied in great detail over decades. In the application to surface nanoislands and nanodroplets, it is usually assumed that the capture coefficients of adatoms by supercritical nanoparticles of size s scale as sα, where the growth index α is smaller than unity. Here, we study theoretically the Ostwald ripening of 3D and 2D nanoparticles whose capture coefficients scale linearly with s. This case includes submonolayer surface islands that compete for the flux of highly diffusive adatoms upon termination of the material influx. We obtain analytical solutions for the size distributions using the Lifshitz-Slezov scaled variables. The distributions over size s and radius R are monotonically decreasing, and satisfy the normalization condition for different values of the Lifshitz-Slezov constant c. The obtained size distributions satisfy the Family-Vicsek scaling hypothesis, although the material influx is switched off. The model is validated by fitting the monotonically decreasing size distributions of Au nanoparticles that serve as catalysts for the vapor-liquid-solid growth of III-V nanowires on silicon substrates.