Large-scale molecular dynamics with the coarse-grained ML-mW water model showed that premelting and freezing of the ice Ih basal surface proceed through nucleation-like transitions between long-lived superheated and supercooled surface states, promoted by natural surface inhomogeneity (holes) and partially arrested during freezing by liquid-like boundaries between nuclei of different stacking order. However, the premelting onset and even the order of the surface transition differ qualitatively across water force fields, the fate of the stacking-mismatch boundaries and the low-temperature kinetic arrest of the quasi-liquid layer are unmeasured, and the bridge from molecular-scale hole/cluster coarsening to the micrometer-scale surface inhomogeneity seen in experiments is unbuilt. The open problem is to establish a physically faithful, model-independent account of ice-surface premelting/freezing transition dynamics: an efficient, ice-surface-accurate water potential (classical or ab initio-trained) and its use to re-evaluate onset, order, pathways, metastable lifetimes, stacking-boundary fate, kinetic arrest, orientation and termination dependence, and the quantitative molecular-to-mesoscopic connection.

Background

Premelting is the formation of a thin disordered surface film — the quasi-liquid layer (QLL) — on ice below the bulk melting point TmT_m; it governs snow-crystal habit, atmospheric chemistry on ice, and ice friction. Ice Ih exposes a basal (0001) face and primary (10-10) and secondary (11-20) prismatic faces, each a stack of molecular bilayers. 'Stacking disorder' refers to random sequencing of hexagonal (Ih) and cubic (Ic) stacking of those bilayers; nuclei formed independently on one surface can adopt different stacking orders, and where they meet the lattice mismatch can remain liquid-like. Simulating surface transitions is hard because the relevant fluctuations are nanometres wide and require system sizes of tens of nanometres and trajectories of order 100 ns, which rules out most explicit-hydrogen models. Water 'force fields' (interaction potentials) used include the monatomic coarse-grained mW model, its reparameterization ML-mW, and fixed-point-charge models such as TIP4P/Ice. Cui and Chen (Phys. Rev. B 108, 045413, 2023) found with ML-mW that the basal-face premelting transition is first-order-like, with an onset a few kelvin below TmT_m, coexisting supercooled and superheated surface states that interconvert by nucleation, holes in the first bilayer catalysing premelting (but not freezing) nuclei, and freezing sometimes leaving persistent liquid-like boundaries between nuclei of different stacking order. The same work showed (Supplemental Material) that at 180–220 K in TIP4P/Ice neither the solid nor the premelted surface equilibrates within 100 ns, with QLL diffusion becoming glass-like, implying that apparent premelting 'onsets' can be kinetic artifacts; prismatic faces showed continuous premelting unlike the basal face. These conclusions are model-dependent by the authors' own assessment: mW premelts continuously, TIP4P/Ice shows premelting down to about 200 K with incomplete surface melting (a finite film at TmT_m stabilized by dispersion forces), and reported onsets across simulations differ by tens of kelvin. Related context: Llombart, Noya and MacDowell (Sci. Adv. 6, eaay9322, 2020) found a sequence of surface phase transitions on basal and prism faces of TIP4P/Ice; Baran et al. (Mol. Phys. 122, e2388800, 2024) showed the TIP4P/Ice basal face survives over 100 ns at +1 K superheating, so superheating metastability is real but model-specific; MacDowell's recent synthesis (J. Chem. Phys. 164, 030901, 2026) advocates an equilibrium picture of incomplete surface melting with a sub-nanometre film, with diverging films arising only out of equilibrium. Atomic-resolution experiments with atomic force microscopy (AFM) (Hong et al., Nature 630, 375–380, 2024) and the AFM-plus-machine-learning discovery of an amorphous ice layer between 121 and 180 K beneath the QLL (Tang et al., Phys. Rev. X 15, 041048, 2025) keep revising the low-temperature surface picture. High-fidelity potentials now exist — machine-learning potentials trained on density-functional-theory (DFT) calculations (Piaggi et al., PNAS 119, e2207294119, 2022, for bulk homogeneous nucleation; Zeng and Gao, Crystals 14, 737, 2024, for a 1024-molecule ice–vapor slab; Berrens et al., JACS Au 5, 1173–1183, 2025, and Rashmi and Paesani, JACS 147, 1903–1910, 2025, for spectroscopy of the air–ice interface) — but none combines ice-surface accuracy with the scale and time needed to re-examine transition dynamics, which is exactly what the source work identified as the prerequisite for a definitive conclusion.

Problem Statement

Establish a physically faithful, model-independent account of the premelting/freezing transition dynamics of ice Ih surfaces, as requested by Cui and Chen (Phys. Rev. B 108, 045413, 2023). Concretely: (1) develop or identify an efficient water potential — classical or ab initio-trained machine-learned — that is quantitatively reliable for ice-surface thermodynamics and kinetics (validated against surface free energies, disjoining pressures, or premelting film behavior, with melting point known to better than about 1 K), and use it at the tens-of-nanometres, 100-ns-plus scale to re-evaluate whether the basal-face premelting transition is continuous or first-order-like, whether the premelting film stays incomplete (finite at TmT_m) or diverges, its true onset temperature, and the nucleation-like pathways with superheating/supercooling metastable lifetimes; (2) determine the fate of the liquid-like boundaries that form between nuclei of different stacking order when the quasi-liquid layer freezes — whether they heal, persist, or coarsen, on what timescale, as a function of temperature and hole/cluster geometry; (3) quantify how low-temperature kinetic arrest (glass-like QLL diffusion, non-equilibrium surface states surviving beyond 100 ns) controls apparent premelting onsets, including whether multiple operationally distinct onsets exist for the same model depending on the observable; (4) map the orientation dependence of the transition pathways and metastability across the basal and the primary and secondary prismatic faces, including the effect of non-ideal terminations (excess molecules, growth/evaporation conditions); and (5) connect molecular-scale hole and cluster coarsening quantitatively to the micrometer-scale surface inhomogeneity and droplet formation observed experimentally. A complete answer addresses all five parts above and, as their synthesis, states which features of the ML-mW picture — first-order-like basal premelting a few kelvin below TmT_m, hole-assisted nucleation, stacking-mismatch arrest of freezing — are robust surface physics and which are model artifacts, with evidence transferable across independent water models and, where possible, against surface-sensitive experiment.

References

  1. Shifan Cui and Haoxiang Chen, "Transition dynamics and metastable states during premelting and freezing of ice surfaces", Phys. Rev. B 108, 045413 (2023), DOI 10.1103/PhysRevB.108.045413, arXiv:2211.01787, https://doi.org/10.1103/PhysRevB.108.045413
  2. Pablo Llombart, Eva G. Noya, David N. Sibley, Andrew J. Archer, and Luis G. MacDowell, "Rounded Layering Transitions on the Surface of Ice", Phys. Rev. Lett. 124, 065702 (2020), DOI 10.1103/PhysRevLett.124.065702, https://arxiv.org/abs/2003.02945
  3. Pablo Llombart, Eva G. Noya, and Luis G. MacDowell, "Surface phase transitions and crystal habits of ice in the atmosphere", Sci. Adv. 6, eaay9322 (2020), DOI 10.1126/sciadv.aay9322, https://doi.org/10.1126/sciadv.aay9322
  4. Łukasz Baran, Pablo Llombart, Eva G. Noya, and Luis G. MacDowell, "Is it possible to overheat ice? The activated melting of TIP4P/Ice at solid–vapour coexistence", Mol. Phys. 122, e2388800 (2024), DOI 10.1080/00268976.2024.2388800, arXiv:2406.16574, https://doi.org/10.1080/00268976.2024.2388800
  5. Luis G. MacDowell, "The key physics of ice premelting", J. Chem. Phys. 164, 030901 (2026), DOI 10.1063/5.0302303, arXiv:2509.13221, https://doi.org/10.1063/5.0302303
  6. Jiani Hong, Ye Tian, Tiancheng Liang, Xinmeng Liu, Yizhi Song, Dong Guan, Zixiang Yan, Jiadong Guo, Binze Tang, Duanyun Cao, Jing Guo, Ji Chen, Ding Pan, Li-Mei Xu, En-Ge Wang, and Ying Jiang, "Imaging surface structure and premelting of ice Ih with atomic resolution", Nature 630, 375–380 (2024), DOI 10.1038/s41586-024-07427-8, https://doi.org/10.1038/s41586-024-07427-8
  7. Binze Tang, Chon-Hei Lo, Tiancheng Liang, Jiani Hong, Mian Qin, Yizhi Song, Duanyun Cao, Ying Jiang, and Limei Xu, "Unveiling the Amorphous Ice Layer during Premelting Using AFM Integrating Machine Learning", Phys. Rev. X 15, 041048 (2025), DOI 10.1103/9fzf-y9n9, arXiv:2512.15772, https://doi.org/10.1103/9fzf-y9n9
  8. Limin Zeng and Ang Gao, "Exploring the Premelting Transition through Molecular Simulations Powered by Neural Network Potentials", Crystals 14, 737 (2024), DOI 10.3390/cryst14080737, https://doi.org/10.3390/cryst14080737
  9. Richa Rashmi and Francesco Paesani, "Dissecting the Molecular Structure of the Air/Ice Interface from Quantum Simulations of the Sum-Frequency Generation Spectrum", J. Am. Chem. Soc. 147, 1903–1910 (2025), DOI 10.1021/jacs.4c14610, https://doi.org/10.1021/jacs.4c14610
  10. Margaret L. Berrens, Marcos F. Calegari Andrade, John T. Fourkas, Tuan Anh Pham, and Davide Donadio, "Molecular Fingerprints of Ice Surfaces in Sum Frequency Generation Spectra: A First-Principles Machine Learning Study", JACS Au 5, 1173–1183 (2025), DOI 10.1021/jacsau.4c00957, arXiv:2410.19980, https://doi.org/10.1021/jacsau.4c00957
  11. Jihong Shi, Maxwell Fulford, Matteo Salvalaglio, and Carla Molteni, "Unveiling the face-dependent ice growth kinetics: Insights from molecular dynamics on the basal and prism surfaces", J. Chem. Phys. 162, 054714 (2025), DOI 10.1063/5.0240795, arXiv:2410.07050, https://doi.org/10.1063/5.0240795
  12. Pablo M. Piaggi, Jack Weis, Athanassios Z. Panagiotopoulos, Pablo G. Debenedetti, and Roberto Car, "Homogeneous ice nucleation in an ab initio machine-learning model of water", Proc. Natl. Acad. Sci. U.S.A. 119, e2207294119 (2022), DOI 10.1073/pnas.2207294119, arXiv:2203.01376, https://doi.org/10.1073/pnas.2207294119
  13. Xudan Huang, Zifeng Yuan, Chon-Hei Lo, Huacong Sun, Lei Liao, Hongbo Han, Wenxi Li, Wenlong Wang, Zhi Xu, Lei Liu, Xuedong Bai, Limei Xu, Enge Wang, and Lifen Wang, "Kinetics of Stacking-Order Evolution during Heterogeneous Ice Formation", Phys. Rev. Lett. 136, 088001 (2026), DOI 10.1103/gns5-686v, arXiv:2603.00440, https://doi.org/10.1103/gns5-686v
  14. Shifan Cui, Haoxiang Chen, and Zhengpu Zhao, "Premelting layer during ice growth: role of clusters", Phys. Chem. Chem. Phys. 24, 15330–15339 (2022), DOI 10.1039/D2CP00412G, arXiv:2111.14146, https://doi.org/10.1039/D2CP00412G