Underlying mechanisms in size control of uniform nanoparticles

Insights are given into underlying mechanisms for size control of uniform nanoparticles in liquid phases. At the outset, instead of the classical nucleation theories, which are hardly applicable to the size control of uniform particles, a fundamental equation for the nucleation of monodisperse particles, derived for their size control on the basis of the LaMer model, is introduced. This equation was derived on three assumptions: (1) There is a mass balance between the supply rate of solute and its consumption rate for nucleation and growth of the generated nuclei; (2) The supply rate of solute is independent of the subsequent precipitation events; (3) The nucleation rate is controlled only by the growth of the preformed nuclei at a fixed supply rate of solute. Thus, this nucleation theory is applicable to a system in which the precursor solute is supplied by slow irreversible generation in a closed system or by continuous feed from outside in an open system. However, it is inapplicable even if only one of these three assumptions is not fulfilled. Examples of applicable and inapplicable systems are listed, and finally discussion is focused on the underlying mechanisms of size control in some unique processes chosen from them, such as hydrolysis-induced precipitation of AgCl nanoparticles, double-jet precipitation of AgCl nanoparticles in a reverse micelle system to resolve the mechanism of particle formation in general reverse micelle systems, and a gel-sol process for the formation of nanoparticles of anatase TiO2.