The Definition of “Critical Radius” for a Collection of Nanoparticles Undergoing Ostwald Ripening

An improved, exact analysis of surface Ostwald ripening of a collection of nanoparticles is presented in an effort to redefine the critical radius involved in the kinetic models of ripening. In a collection of supported particles of different sizes, the critical radius is the size of the particle that is in equilibrium with the surrounding adatom concentration. Such a particle neither grows nor shrinks due to Ostwald ripening, whereas larger particles grow and smaller particles shrink. We show that previous definitions of critical radius are applicable only for limiting regimes where the Kelvin equation has been linearized. We propose a more universally applicable definition of critical radius that satisfies the constraints of mass balance.