Below the bulk melting point, the surface of ice is coated by a premelted, quasi-liquid layer (QLL) a few molecules thick whose onset temperature, thickness, and dynamics have been debated for more than a century. In layer-resolved molecular dynamics simulations of three low-index faces of ice Ih (TIP4P/Ice model, 200–270 K), Kling, Kling and Donadio found that only the outermost molecular layer diffuses, with an Arrhenius activation energy of about 40 kJ/mol — roughly four times the value of about 11.5 kJ/mol extracted from tribological (friction) measurements on ice — while structurally disordered subsurface layers remain immobile on the simulated timescales, and the surface layer's mobility freezes out gradually on cooling in a glass-like way. The paper left open whether subsurface layers become fully liquid at longer times, why simulated diffusion barriers conflict with friction experiments, whether the gradual arrest is a genuine two-dimensional interfacial glass transition or an artifact of pinning to the crystalline substrate, and whether experimental observables can be computed accurately enough to reconcile conflicting measurements. Later work has substantially resolved the last thread's methodology — machine-learned and many-body quantum-accurate potentials now reproduce temperature-dependent sum-frequency-generation spectra of the air/ice interface — and argues the equilibrium film is sub-nanometer (incomplete surface melting). The open problem is the layer-resolved dynamics of the QLL: timescales of interlayer exchange and normal diffusion, transport activation energies versus tribology, the nature of dynamical arrest, and quantitative, cross-technique reconciliation of the experimental record through quantum-accurate prediction of observables.

Background

The surface of ice below 0 °C is partially disordered: a premelted film of water, the quasi-liquid layer (QLL), coats the crystal. Premelting influences atmospheric heterogeneous chemistry on ice and snow, the growth habit of snow crystals, and the slipperiness of ice. Yet for over a century the basic parameters of the QLL — the temperature at which it first appears, its equilibrium thickness as a function of temperature and vapor pressure, and how closely its molecules resemble bulk supercooled water — have remained contentious: measured onset temperatures range from below 200 K to nearly 273 K, and reported thicknesses at a given temperature range from sub-nanometer to tens of nanometers. Part of the conflict arises because different probes sense different aspects of the surface: vibrational sum-frequency generation (SFG) spectroscopy, a surface-specific nonlinear optical technique that reads out the vibrational spectrum of non-centrosymmetric interfacial layers; X-ray and helium-atom scattering; ellipsometry; and optical microscopy — often performed at different vapor pressures and on different crystallographic faces of hexagonal ice Ih (the basal face and two prismatic faces).

Kling, Kling and Donadio (J. Phys. Chem. C 122, 24780 (2018)) characterized the QLL by classical molecular dynamics (MD) with the TIP4P/Ice rigid point-charge water model, a force field chosen because it is thermodynamically consistent for ice. Resolving the slab into molecular layers, they found that between 200 and 270 K only the outermost layer is diffusive (the onset of approximately normal diffusion, defined by a fitted exponent η>0.8\eta>0.8 of the mean-square displacement (MSD) versus time, lies between 230 and 260 K depending on the face), while the structurally disordered subsurface (second) layers show negligible MSD on sub-nanosecond windows — their motion is subdiffusive, i.e. the MSD grows slower than linearly in time, as in glass-forming liquids. Three findings frame the present problem. First, top-layer diffusion is thermally activated with Arrhenius activation energy EA≈40E_A\approx 40 kJ/mol (basal and primary prismatic faces), about four times the EA≈11.5E_A\approx 11.5 kJ/mol that Weber et al. extracted from tribological (friction) measurements on ice; since TIP4P/Ice reproduces the bulk-water activation energy, a mere force-field artifact is unlikely. Second, the MSD exponent of the surface layer decreases gradually on cooling — with no sharp drop as would accompany a first-order transition — resembling a glass transition, although the glass transition of bulk supercooled water is predicted far lower (130–150 K); the authors attributed the arrest to pinning by the ordered crystalline subsurface template, and could not decide with tens-to-hundreds-of-nanoseconds trajectories whether this is a genuine glass transition of a quasi-two-dimensional interfacial liquid, a finite-time phenomenon, or whether subsurface layers acquire normal (layer-exchanging) diffusivity at times beyond the simulated window. Third, they concluded that resolving the conflicting experimental pictures requires computing the actual experimental observables (SFG spectra, scattering intensities) from transferable, quantum-chemically accurate models rather than from empirical point-charge potentials.

Subsequent work restructured parts of this problem. Combined SFG experiments and simulations found evidence for a discrete one-to-two-bilayer jump of the QLL on the basal face near 257 K — ice Ih is built from stacked molecular bilayers, so the premelted film can thicken in bilayer-height steps; disjoining-pressure calculations — the disjoining pressure is the free-energy cost per unit area of maintaining a film at a given thickness, and it controls the equilibrium film thickness — then showed that such layering transitions along the sublimation line are rounded by capillary waves (thermal fluctuations of the interface) rather than thermodynamically sharp; and analyses based on wetting physics and intermolecular (Lifshitz) dispersion forces argue the equilibrium ice–vapor interface exhibits incomplete surface melting, with a film of order one nanometer near the triple point, thicker films being out-of-equilibrium kinetic growth phenomena. Machine-learned potentials trained on ab initio data, and many-body quantum-accurate potentials such as MB-pol (a water potential fitted to high-level ab initio data through a many-body expansion of the intermolecular interactions), now reproduce the librational (hindered-rotational) and stretch-region SFG spectra of the air/ice interface and its temperature evolution without empirical adjustment. What this later literature has not delivered is the layer-resolved dynamics: the timescales of interlayer exchange and normal diffusion in the premelted film, quantum-accurate transport activation energies that can be confronted with the tribological value, a decision on the glass-transition-versus-pinning question, and a quantitative reconciliation — not just a qualitative synthesis — of the spread of measured QLL onset temperatures and thicknesses across techniques, faces, and vapor-pressure conditions.

Problem Statement

Determine, with transferable quantum-chemically accurate models (many-body or machine-learned potentials, including nuclear quantum effects — the quantum delocalization of the light hydrogen nuclei, which modifies hydrogen bonding — where relevant), with sufficiently long or enhanced-sampling (rare-event or accelerated) simulation, and where possible with experiment, the layer-resolved dynamical state of the premelted surface of hexagonal ice (ice Ih), as one objective with four jointly supporting parts: (i) whether structurally disordered subsurface (second and deeper) layers become genuinely liquid — exhibiting normal self-diffusion and finite interlayer exchange — and at which temperatures and timescales this occurs, beyond the tens-to-hundreds-of-nanoseconds window of the source simulations, or whether their mobility remains locked to the crystalline template at all accessible timescales; (ii) the transport coefficients of the quasi-liquid layer (in-plane and normal diffusion coefficients and their Arrhenius activation energies) from quantum-accurate models, and whether the roughly fourfold discrepancy between simulated diffusion barriers (about 40 kJ/mol) and the tribological activation energy (about 11.5 kJ/mol, extracted from friction experiments on ice) reflects a model error or genuinely different physics such as nonequilibrium shear, frictional heating, or confinement by the sliding counterface; (iii) whether the gradual dynamical arrest of the surface layer on cooling — the mean-square-displacement exponent decreasing continuously with no first-order-like drop — is a true glass transition of a quasi-two-dimensional, substrate-modified liquid or a finite-time phenomenon produced by pinning to the crystalline subsurface, decided by the scaling of long-time correlation functions, structural heterogeneities, and metabasin statistics (hopping between long-lived basins of the energy landscape, a hallmark of glassy dynamics) rather than by trajectory length alone; and (iv) whether the same models predict explicit experimental observables — vibrational sum-frequency-generation (SFG) spectra, X-ray and helium scattering, reflectivity — accurately enough to reconcile quantitatively the spread of reported QLL onset temperatures (below 200 K to nearly 273 K) and thicknesses (sub-nanometer to tens of nanometers) across techniques, crystal faces, and vapor-pressure conditions, including the kinetically formed quasi-liquid phases observed by optical microscopy. The common objective is a quantitative, layer-resolved, experimentally validated theory of the quasi-liquid layer on ice.

References

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