Initial-growth modes of nucleation droplets

Abstract

Using the theoretical formulation of Cahn and Hilliard and of Langer, we study the initial growth of nucleation droplets in systems with no conservation law for various dimensions and for an arbitrary distance from the coexistence curve. In the vicinity of the coexistence curve the nucleating droplets are compact at the center and growth occurs only at the droplet surface. Close to the classical spinodal the nucleating droplets are ramified and the growth occurs preferentially at the droplets’ center. The growth is always maximum where the second derivative of the free-energy density is negative, i.e., at unstable concentrations. The droplet profile for any specified field tends to a universal tanh(x) profile for large dimension. We argue that certain aspects of the droplet depend only on a single scaling field that combines dimensions and quench depth.