Estimation of Nucleation Barriers from Simulations of Crystal Nuclei Surrounded by Fluid in Equilibrium

Nucleation rates for homogeneous nucleation are commonly estimated in terms of an Arrhenius law involving the nucleation barrier, written in terms of a competition of the contribution in surface free energy of the nucleus and the free energy gain proportional to the nucleus volume. For crystal nuclei this “classical nucleation theory” is hampered by the problem that the nucleus in general is non spherical, since the interfacial excess free energy depends on the orientation of the interface relative to the crystal axes. This problem can be avoided by analyzing the equilibrium of a crystal nucleus surrounded by fluid in a small simulation box in thermal equilibrium. Estimating the fluid pressure and the chemical potential, as well as the volume of the nucleus, suffices to obtain the nucleation barrier, if the equation of state of the pure phases as well as the coexistence pressure are known. This method is demonstrated to work using a coarse-grained model for colloids with an effective attraction due to small polymers, comparing two choices of the attraction strength.