Nucleation, Growth, and Coarsening -- A Global View on Aggregation

Abstract

We present a new model of homogeneous aggregation that contains the essential physical ideas of the classical predecessors, the Becker-Doring and Lifshitz-Slyovoz models. These classical models, which give different predictions, are asymptotic limits of the new model at small and large cluster sizes (respectively). Since the new theory is valid for large and small clusters, it allows for a complete description of the nucleation process; predicting the Zeldovich nucleation rate, and the diffusion limited growth of large clusters. By retaining the physically valid ingredients from both models, we can explain the seeming incompatibilities and arbitrary choices of the classical models. We solve the equations of our new model asymptotically in the small super-saturation limit. The solution exhibits three successive `eras': nucleation, growth, and coarsening, each with its specific scales of time and cluster size. During the nucleation era, the bulk of the clusters are formed by favorable fluctuations over a free energy barrier, according to the analysis by Zeldovich. During the Growth era no new clusters are created, and the expansion of the existing ones continues. Eventually the coarsening era begins. During this competitive attrition process, smaller clusters dissolve and fuel the further growth of the larger survivors. By resolving the preceding creation and growth eras, our analysis gives explicitly the characteristic time and cluster size of the coarsening era, and a unique selection of the long time, self-similar cluster size distribution.