Revisiting classical nucleation theory: Insights into heterogeneous ice nucleation on nanoscale substrates

Heterogeneous nucleation plays a pivotal role in the ice nucleation process. Within the classical nucleation theory (CNT) framework, the heterogeneous nucleation rate is proportional to the substrate surface area, typically assuming infinite substrate surfaces. However, when the substrate size approaches the nanoscale, the nucleation rate deviates significantly from CNT predictions. This study presents a novel theoretical model that distinguishes the nanoscale substrate into central and edge regions, attributing different contributions to ice nucleation. We hypothesize that the edge width equals the critical size of the nucleus (r_{c}) and validate this hypothesis using molecular dynamics (MD) simulations with the coarse-grained water model (mW model) on circular and rectangular substrates of varying sizes. Our results demonstrate that the edge region impedes heterogeneous ice nucleation, with the MD calculated nucleation rates aligning well with our model. Furthermore, the statistical edge width matches the critical nucleus size r_{c}. By incorporating this refined model, our findings reconcile the nucleation rates with CNT predictions, offering new insights into heterogeneous ice nucleation at the nanoscale.