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Abstract. Heterogeneous ice nucleation is thought to be the primary pathway for the formation of ice in mixed-phase clouds, with the number of active ice-nucleating particles (INPs) increasing rapidly with decreasing temperature. Here, molecular-dynamics simulations of heterogeneous ice nucleation demonstrate that the ice nucleation rate is also sensitive to pressure and that negative pressure within supercooled water shifts freezing temperatures to higher temperatures. Negative pressure, or tension, occurs naturally in water capillary bridges and pores and can also result from water agitation. Capillary bridge simulations presented in this study confirm that negative Laplace pressure within the water increases heterogeneous-freezing temperatures. The increase in freezing temperatures with negative pressure is approximately linear within the atmospherically relevant range of 1 to −1000 atm. An equation describing the slope depends on the latent heat of freezing and the molar volume difference between liquid water and ice. Results indicate that negative pressures of −500 atm, which correspond to nanometer-scale water surface curvatures, lead to a roughly 4 K increase in heterogeneous-freezing temperatures. In mixed-phase clouds, this would result in an increase of approximately 1 order of magnitude in active INP concentrations. The findings presented here indicate that any process leading to negative pressure in supercooled water may play a role in ice formation, consistent with experimental evidence of enhanced ice nucleation due to surface geometry or mechanical agitation of water droplets. This points towards the potential for dynamic processes such as contact nucleation and droplet collision or breakup to increase ice nucleation rates through pressure perturbations. 

Heterogeneous ice nucleation is ubiquitous but its microscopic mechanisms can be extraordinarily complex even on a simple surface. Such complexity poses a challenge in modeling nucleation using advanced sampling methods. Here, we investigate heterogeneous ice nucleation on an FCC (211) surface by a forward flux sampling (FFS) method to understand how the complexity in nucleation pathways affects the accuracy of FFS. We first show the commonly adopted, size-based order parameter fails to describe heterogeneous ice nucleation on the FCC (211) surface. Inclusion of geometric anisotropy of ice nucleus as an additional descriptor is found to significantly improve the quality of the size-based order parameter for the current system. Subsequent application of this new order parameter in FFS identifies two competing ice nucleation pathways in the system: a primary-prism-planed (PPP) path and a secondary-prism-planed (SPP) path, both leading to the formation of hexagonal ice but with different crystalline orientations. Although the PPP pathway dominates ice nucleation on the FCC (211) surface, the occurrence of the less efficient SPP pathway, particularly its strong presence at the early stage of FFS, is found to yield a significant statistical uncertainty in the calculated FFS rate constant. We develop a two-path model that enables gaining a general, quantitative understanding of the impact of initial finite sampling on the reliability of FFS calculations in the presence of multiple nucleation pathways. Our study also suggests a few general strategies for improving the accuracy of FFS when exploring unknown but complex systems.