Sibley, Llombart, Noya, Archer and MacDowell (Nat. Commun. 12, 239, 2021) built a mesoscopic thin-film (gradient-dynamics) model of ice growth near the triple point in which the thermodynamic input is the interface potential g(h)g(h) of the quasi-liquid premelting film and the kinetic inputs are interfacial transfer coefficients, chiefly the liquid-vapor coefficient klvk_{\mathrm{lv}}, and predicted a kinetic phase diagram with activated-growth, thin-film, and droplet-condensation regimes, including droplet-induced cratering and hidden freezing beneath droplets. The model's load-bearing inputs are still not independently determined, and its central predictions remain untested: g(h)g(h) is fitted from non-polarizable TIP4P/Ice simulations valid to about 1 nm plus Lifshitz-type extrapolations, and klvk_{\mathrm{lv}} was tuned to empirical slopes of the kinetic coexistence line. This problem asks for the completion and validation of that theory: a converged ab initio or many-body (or validated many-body-trained) determination of g(h)g(h) beyond ∼1\sim 1 nm establishing the balance of short-range oscillatory forces and long-range van der Waals tails, an independent experimental or microscopic determination of the kinetic coefficients, direct experimental tests of the predicted kinetic phase lines and of droplet-induced cratering and hidden freezing, and extension of the framework beyond the clean basal facet to prism faces, their roughening transition, and impurity/dislocation effects. Substantial but only partial progress has been reported on each of these items, and no published work is known to resolve any of them.

Background

Close to the triple point (0.01 ∘C0.01~^\circ\mathrm{C}, 612 Pa, where solid, liquid and vapor water coexist), the surface of ice is covered by a nanometer-thick disordered film, the quasi-liquid layer or premelting film, which controls growth and melting rates. Classical models of crystal growth from the vapor (terrace nucleation, spiral growth, and roughening — the temperature-dependent loss of facetedness of a crystal face) do not account for this film. In wetting physics the thermodynamics of such a film is encoded in the interface potential g(h)g(h), the effective free-energy cost per unit area of a liquid film of thickness hh adsorbed on the solid: minima of g(h)g(h) pin equilibrium film thicknesses, and a minimum at finite thickness coexisting with a negative tail implies partial wetting, i.e. liquid droplets coexisting with a thin film on the solid surface. For ice, the short-range part of g(h)g(h) exhibits damped oscillations with a molecular period, set by layering, while long-range retarded and non-retarded van der Waals (dispersion) forces, computable from the dielectric response functions of ice and water via Lifshitz theory as parameterized by Elbaum and Schick (Phys. Rev. Lett. 66, 1713, 1991), add an algebraic −Bh−3-B h^{-3} tail; the shallow minima of order 10−5 J m−210^{-5}\ \mathrm{J\,m^{-2}} that result explain why droplets and thin films coexist on ice just below 0 ∘C0~^\circ\mathrm{C}. Sibley, Llombart, Noya, Archer and MacDowell (Nat. Commun. 12, 239, 2021) coupled such an interface potential, obtained from molecular dynamics simulations of the TIP4P/Ice model (a fixed-point-charge, non-polarizable water potential) in the range 210-270 K, to a gradient-dynamics thin-film model that evolves both the solid-liquid and liquid-vapor interfaces, with interfacial kinetics described by transfer coefficients: kslk_{\mathrm{sl}} for freezing at the buried solid-liquid boundary and klvk_{\mathrm{lv}} for condensation/evaporation at the outer liquid-vapor boundary. Steady states of this model organize into a kinetic phase diagram in pressure-temperature space, bounded by kinetic phase lines — the kinetic coexistence line, a kinetic α→β\alpha\to\beta transition line (between the thin-film state α\alpha and the droplet state β\beta), and a kinetic spinodal — separating a thin-film regime (growth by step nucleation and terrace spreading, with the buried solid motion conveyed through the film to the visible outer surface, as in the Kuroda-Lacmann model of vapor growth, J. Cryst. Growth 56, 189, 1982) from a droplet regime in which condensing droplets dig craters into the ice and freezing proceeds hidden beneath them, consistent with classical growth-rate measurements such as Lamb and Scott (J. Cryst. Growth 12, 21, 1972). The authors themselves state the limitations that define this problem: the interface potential is simulation-fitted only up to ∼1\sim 1 nm and constrained by extrapolation, because converged electronic-structure or explicit many-body/polarizable simulations at the required system sizes appear unfeasible; klvk_{\mathrm{lv}} was chosen to match empirical slopes of the kinetic coexistence line, introducing model-dependence in line locations and time scales; only an ideal clean basal facet is treated, with impurities and dislocations (which enable spiral growth and can eliminate the activated-growth regime) unmodeled; extension to prism faces, whose roughening transition lies near 269 K (Elbaum, Phys. Rev. Lett. 67, 2982, 1991), and to wider temperature ranges is future work; and experimental verification of the predictions — droplet-induced cratering, hidden freezing beneath droplets, and the kinetic phase lines — is suggested but open.

Problem Statement

The mesoscopic kinetic theory of ice growth from premelting films (Sibley et al., Nat. Commun. 12, 239, 2021) predicts a kinetic phase diagram — bounded by the kinetic coexistence, kinetic α→β\alpha\to\beta transition, and kinetic spinodal lines — separating activated thin-film growth from a droplet regime with droplet-induced cratering and freezing hidden beneath droplets, but its load-bearing inputs are fitted rather than independently known and its central predictions are unverified. The problem is to complete and validate this theory by: (1) determining the interface potential g(h)g(h) of the premelting film on the basal face of ice at thicknesses beyond ∼1\sim 1 nm from converged ab initio or explicit many-body/polarizable calculations (or machine-learning potentials validated at that level), establishing quantitatively the balance between short-range oscillatory/many-body forces and the long-range van der Waals tail rather than fitting it, so that the shallow minima of g(h)g(h) that control the saturation regime are predicted microscopically; (2) determining the interfacial kinetic coefficients — in particular the liquid-vapor transfer coefficient klvk_{\mathrm{lv}}, and consistently the solid-liquid coefficient kslk_{\mathrm{sl}} — independently of the empirical slopes of the kinetic coexistence line, and propagating these independently obtained parameters into the thin-film model to establish the quantitative locations of the kinetic phase lines and their time scales; (3) testing the model's falsifiable predictions experimentally near three-phase coexistence: direct observation (e.g. by advanced optical microscopy) of droplet-induced cratering, of hidden freezing beneath condensing droplets, and of the predicted kinetic phase lines, together with targeted measurements of premelting film thickness versus vapor pressure near coexistence; and (4) extending the same framework beyond the ideal clean basal facet to other crystallographic planes — prism faces and their roughening transition — and to realistic samples incorporating impurities, dislocations, and other defect sources of heterogeneous nucleation that can eliminate the activated-growth regime. These components serve one objective: replacing the fitted inputs and untested predictions of the kinetic growth model with independently measured microscopic foundations and experimental validation, so that ice growth and melting near the triple point become quantitatively predictable from first principles. The four components are independent sub-goals: the task is resolved by any single one of (1)-(4) carried to its stated standard, while the remaining items stay open.

References

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