A theoretical model for digestive ripening

Recently, gram quantities of monodisperse gold or silver nanoparticles were reported to be produced through a digestive ripening process, in which colloidal particles of size from 2 to 40 nm are transformed to nearly monodisperse particles of 4–5 nm diameter. Digestive ripening, an example for inverse Ostwald ripening, is a puzzling phenomenon since it appears to avoid the usual capillary consequence, i.e., reduction of interfacial free energy. This paper presents a theoretical model which accounts for the self-assembled monodisperse state of such nanoparticles by considering the effect of charges, and therefore electrostatic energy, in the coarsening behavior of the particles. An appropriate Gibbs–Thomson equation is first derived, and then particle growth rates are calculated. The results show that success of a monodisperse state depends on, among other things, the initial particle distribution, and the size distribution at equilibrium follows some of the thermodynamic principles observed in binary phase diagrams of alloy systems.