Distribution Kinetics Modeling of Nucleation, Growth, and Aggregation Processes

Certain emerging fields of nanotechnology depend on self-assembly processes that lead to molecular structures which are organized and ordered or disorganized and disordered. Many such processes can be understood as combinations of nucleation, reversible growth, and reversible aggregation. We develop a descriptive theoretical framework through population balances for the cluster mass distribution and show the formulation of its mass moments. Calculations for relaxation to equilibrium show the effects of aggregation, deaggregation, dissolution, cluster growth by monomer addition, and nucleation, as either single processes or various combinations. Competition among the processes yields a variety of different behaviors that have been observed in nature and in the laboratory. Problems that can hinder self-organization processes include coarsening (Ostwald ripening) and glasslike phase transition (noncrystalline solidification). Both of these and other processes can be described by the kinetics of cluster distributions and the dynamics of their moments.