Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation

Mapping the influence of impurity interaction energy on nucleation in a lattice-gas model of solute precipitation

We study nucleation in the two dimensional Ising lattice-gas model of solute precipitation in the presence of randomly placed static and dynamic impurities. Impurity-solute and impurity-solvent interaction energies are varied whilst keeping other interaction energies fixed. In the case of static impurities, we observe a monotonic decrease in the nucleation rate when the difference between impurity-solute and impurity-solvent interaction energies is increased. The nucleation rate saturates to a minimum value with increasing interaction energy difference when the impurity density is low. However the nucleation rate does not saturate for high impurity densities. Similar behaviour is observed with dynamic impurities both at low and high densities. We explore a broad range of both symmetric and anti-symmetric interactions with impurities and map the regime for which the impurities act as a surfactant, decreasing the surface energy of the nucleating phase. We also characterise different nucleation regimes observed at different values of interaction energy. These include additional regimes where impurities play the role of inert-spectators, bulk-stabilizers or cluster together to create heterogeneous nucleation sites for solute clusters to form.

A statistical analysis of the first stages of freezing and melting of Lennard-Jones particles: Number and size distributions of transient nuclei

The freezing/melting transition is at the heart of many natural and industrial processes. In the classical picture, the transition proceeds via the nucleation of the new phase, which has to overcome a barrier associated with the free energy cost of the growing nucleus. The total nucleation rate is also influenced by a kinetic factor, which somehow depends on the number of attempts to create a nucleus, that translates into a significant density of proto-nuclei in the system. These transient tiny nuclei are not accessible to experiments, but they can be observed in molecular simulations, and their number and size distributions can be acquired and analyzed. The number distributions are carefully characterized as a function of the system size, showing the expected behavior, with limited spurious effects due to the finite simulation box. It is also shown that the proto-nuclei do exist even in the stable phase, in agreement with the fact that the (unfavorable) volume contribution to their free energy is negligible in the first stages of nucleation. Moreover, the number and size distributions evolve continuously between the stable and the metastable phases, in particular when crossing the coexistence temperature. The size distributions associated with any nucleus and with the largest one have also been calculated, and their relationship recently established for bubbles in a liquid [Puibasset, J. Chem. Phys. 157, 191102 (2022)] has been shown to apply here. This is an important relation for free energy barrier calculations with biased molecular simulations.