Chapter 15 - Advanced Nucleation Theories

Abstract

Classical nucleation theory provides a useful framework for understanding key elements of the nucleation process. However, the assumptions made in classical nucleation theory limit its ability to make quantitatively accurate prediction of nucleation rates for many real systems. Of particular concern is the calculation of an accurate work of cluster formation for generating a stable nucleus. Statistical mechanics provides a rigorous framework for constructing a detailed model of nucleation. Statistical mechanical models are constructed in the grand canonical ensemble to allow for nucleating clusters of different sizes. Successful application of statistical mechanical techniques requires having an accurate description of the interaction energies between particles. Diffuse interface theory represents a phenomenological correction to classical nucleation theory, considering a continuously varying free energy density across the liquid-nucleus interface. In this manner, a broad interface with continuously changing free energy density can be considered. However, diffuse interface theory itself does not provide a means for calculating the variation of the free energy density. Density functional theory is a more sophisticated approach, considering the free energy as a functional of the spatially inhomogeneous density. The variation in density is related to the change in free energy density, which is then used to calculate the work of nucleation. However, density functional theory cannot be used if the nucleating cluster and the matrix phase have the same values of density. The implicit glass model is a hybrid Monte Carlo-based approach for numerically simulating nucleation. The implicit glass model involves application of a generalized Born solvation model, which effectively replaces the liquid/glassy matrix with a continuous medium and enables the computations to focus on nucleating atomic clusters in the grand canonical ensemble.