Classical Kinetic Theory of Nucleation and Coarsening

Abstract

The purpose of this chapter is to explain the classical kinetic theory of nucleation in a context simpler than polymer crystallization. Many theories start by assuming that polymer crystallization is an activate d process involving crossing of a free energy barrier [1]. The latter separates two accessible stable states of the system such as monomer solution and crystal. This general setting for activated processes can be used to describe the formation of a crystal from a liquid cooled below its freezing point [2], precipitation and coarsening of binary alloys [3], colloidal crystallization [4] chemical reactions [5], polymer crystallization [1, 6, 7], etc. In all these cases, the theory of homogeneous isothermal nucleation provides a framework to study the processes of formation of nucleii from density fluctuations, and their growth until different nucleii impinge upon each other. In the early stages of these processes, nucleii of solid phase are formed and grow by incorporating particles from the surrounding liquid phase. There is a critical value for the radius of a nucleus that depends on a chemical drive potential, which is proportional to the supersaturation for small values thereof. In this limit, the critical radius is inversely proportional to the supersaturation. At the beginning of the nucleation process, nucleii have small critical radius and new clusters are being created at a non-negligible rate.