Growth laws for surfactant-coated nanocrystals: Ostwald ripening and size focusing

The growth of surfactant-coated nanocrystals is examined theoretically. A new single-particle growth rate is derived that explicitly models monomer diffusion through the layer of surfactant molecules, different from diffusion through bulk solution. From the single-particle growth rate, new theories for Ostwald ripening and size focusing are developed. Long surfactant molecules can strongly affect the dynamics of both growth regimes, depending on the mobility of monomers through the surfactant layer. It is implied that size focusing of nanocrystals that are coated with a well-chosen surfactant species can (in the maximal limit) be made much more monodisperse than the equivalent nanocrystals that are bare. This new maximal limit of size focusing could permit new optimized syntheses of monodisperse nanocrystals through the choice of appropriate surfactant molecules.