(544c) On the Challenge of Sampling Multiple Nucleation Pathways: A Case Study of Heterogeneous Ice Nucleation on FCC (211) Surface

Heterogeneous ice nucleation plays a significant role in a variety of fields ranging from global climate change to drug production, yet its microscopic mechanisms can be remarkably intricate even on a simple surface. Such complexity poses a challenge in modeling nucleation using advanced sampling methods. In this study, we explore heterogeneous ice nucleation on the FCC (211) surface with a lattice constant of 4.158 Ã… using a forward flux sampling (FFS) approach¹ based on mW model². We demonstrate that the commonly employed size-based order parameter fails to describe heterogeneous ice nucleation on the FCC (211) surface, which yields an ensemble of phase points that are virtually composed of “disk-like” seeds that cannot grow into ice. To overcome the issue, we develop a new order parameter λ_k by integrating a geometric constraint on ice seed by computing its maximum ratio in the resolved components of the radius of gyration k.

The new order parameter is found to significantly improve the quality of FFS in the current system³. With a proper range of geometric constraints, the calculated nucleation rates are found to be nearly invariant with a k_cut between 3 and 5, while a small k_cut (<2) places a very strong geometric constraint leading to a lower nucleation rate. The quality of the λ_k was further verified by pB histogram analysis at the critical sizes identified at different k_cut. Interestingly, structural analysis of nucleation trajectories shows co-existence of two distinct nucleation pathways. One is a primary-prism-planed (PPP) path that was previously identified in direct MD simulations^4,5. The other pathway, which was absent from direct MD simulations on FCC (211) surface with the lattice constant of 4.158 Ã…, yields the secondary-prism-planed (SPP) path of Ih. PPP and SPP both lead to the formation of hexagonal ice but with distinct crystalline orientations. The 4-order of magnitude difference in growth probability of PPP and SPP showed that nucleation of ice on the FCC (211) surface is dominated by PPP, which explains the absence of SPP in previous direct simulations⁵.

Although the PPP path has a significantly higher nucleation rate than the SPP path, the less-efficient SPP path is found to overwhelm the ensemble of configurations collected at the early milestones of FFS modeling, which contributes to the substantial statistical uncertainty in the FFS rate constant calculations and exhibits an undesirable dependence on the choice of FFS parameters.

To address this sampling issue, we develop a two-path model to understand how the collection of initial sampling at λ₀, for example, initial milestones and the number of initial configurations, influence the reliability of FFS computations when two competing nucleation pathways are involved. The two-path model, which considers the co-existence of a fast and a slow route in one system, provides a comprehensive, quantitative understanding of the dependence of the final rate constant in FFS on the initial weights and the difference in the growth probabilities of both routes. Such dependence highlights the challenge of modeling crystal nucleation in the presence of multiple pathways, particularly in pursuit of a quantitative description of the key rate constant that governs the true nucleation dynamics. Our study also suggests a few general strategies for improving the accuracy of FFS when exploring unknown but complex systems.

Acknowledgement:

The work is supported by NSF through award CBET-2053330.

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