Theoretical and numerical studies of nucleation kinetics

Abstract

Reconsideration on the concept of critical nucleus for single component systems leads to the result that the size n_k of a kinetic critical nucleus for which the probabilities of its decay and growth balance is not equal to the size n^* of the thermodynamic one for which the reversible work of nucleus formation takes the maximum value. n_k is in general smaller than n^*, and there exist two values for n_k, the larger is kinetically unstable but the smaller is stable. The difference between n^* and the larger n_k increases but the difference between the two values of n_k decreases with supersaturation and or temperature, and at the critical state two values of n_k coincide and it diminishes to 8/27 of n^* for three dimensional homogeneous nucleation and to 1/4 of n^* for two dimensional disc nucleation on a substrate. Beyond this critical state n_k does not exist and for a nucleus with any size the probabilty of growth is higher than that of decay. The height of the nucleation barrier, i.e., the reversible work of critical nucleus formation, is found to be the main parameter quantitatively controlling the distinction between n^* and n_k. It is shown that when the distinction between the two kinds of the critical nuclei is significant, the attachment and the detachment rates of monomers do not differ appreciably.