Nucleation kinetics, size effects, and surface treatment

Abstract

The rate equations that describe nanoparticle formation have been derived on the basis of kinetic theory and statistical thermodynamics. In the formation processes, the critical size of the nucleus of the nanoparticle can be determined to be the nucleus generated under near-equilibrium conditions. Nanoparticles larger than the critical size can continue to grow; nanoparticles smaller than the critical size may become smaller by evaporation. However, under strongly nonequilibrium conditions such as the supersonic expansion of a neutral gas, the concept of a critical nucleus becomes irrelevant because the calculated critical size becomes smaller than the atomic diameter. Consideration of very small clusters from a kinetic standpoint is very important for understanding the early stages of nanoparticle formation under nonequilibrium conditions. In the present chapter, the rate equations that describe condensation and evaporation during nanoparticle formation and growth are described using molecular partition functions based on statistical thermodynamics. The equations are used to determine nanoparticle size, which accounts for the characteristics of the materials. The effects of size and surface treatment of nanoparticles are also described, the objective being practical application of this information.