Pre-ordering of interfacial water in the pathway of heterogeneous ice nucleation does not lead to a two-step crystallization mechanism

According to Classical Nucleation Theory (CNT), the transition from liquid to crystal occurs in a single activated step with a transition state controlled by the size of the crystal embryo. This picture has been challenged in the last two decades by several reports of two-step crystallization processes in which the liquid first produces pre-ordered or dense domains, within which the crystal nucleates in a second step. Pre-ordering preceding crystal nucleation has been recently reported in simulations of ice crystallization, raising the question of whether the mechanism of ice nucleation involves two steps. In this paper, we investigate the heterogeneous nucleation of ice on carbon surfaces. We use molecular simulations with efficient coarse-grained models combined with rare event sampling methods and free energy calculations to elucidate the role of pre-ordering of liquid water at the carbon surface in the reaction coordinate for heterogeneous nucleation. We find that ice nucleation proceeds through a classical mechanism, with a single barrier between liquid and crystal. The reaction coordinate that determines the crossing of the nucleation barrier is the size of the crystal nucleus, as predicted by CNT. Wetting of the critical ice nuclei within pre-ordered domains decreases the nucleation barrier, increasing the nucleation rates. The preferential pathway for crystallization involves the early creation of pre-ordered domains that are the birthplace of the ice crystallites but do not represent a minimum in the free energy pathway from liquid to ice. We conclude that a preferential pathway through an intermediate-order precursor does not necessarily result in a two-step mechanism.