Dynamical inhomogeneity of quasi-liquid layers on ice: characteristic domain scale, vapor-pressure dependence, temperature-robust classification, and fast solid-like/liquid-like switching

The quasi-liquid layer (QLL) that premelts the surface of ice is dynamically inhomogeneous: molecules with similar mobility cluster into domains that continually exchange members, and within the simulation scale accessible to Yasuda et al. (2024) these dynamical domains show no characteristic length, while their long-range ordering varies with temperature and crystal face. That study explicitly left open four linked questions: (1) whether a characteristic in-plane domain length scale emerges beyond their ~23 nm all-atom slabs, and how atomic-scale dynamical inhomogeneity connects to mesoscale surface roughness and macroscale droplet/sheet formation; (2) how vapor pressure (over- and under-saturation), which is known to control QLL behavior, reshapes the in-layer dynamics; (3) how to classify surface molecules as solid-like or liquid-like in a way that remains valid at low temperature where a purely dynamics-based criterion fails; and (4) the nature of the fastest (sub-64 ps) switching events between dynamical states. No resolution of any of these four cores is known in the literature to date; the problem is open.

Background

Below the bulk melting point, the surface of ice is covered by a thin disordered film known as the quasi-liquid layer (QLL), a phenomenon called surface premelting. The QLL controls many distinctive properties of ice — atmospheric chemistry on snow and cloud crystals, ice friction, and the growth habits of snow crystals (Slater & Michaelides 2019; Nagata et al. 2019). Optical microscopy showed that under partial saturation the QLL is not uniform but consists of two coexisting phases, macroscopic liquid-like droplets and a thin wetting layer, whose morphology changes strongly with vapor supersaturation (Sazaki et al. 2012; Murata et al. 2016). X-ray and modeling studies established bilayer-by-bilayer melting of the topmost layers near the melting point (Sánchez et al. 2017), while grand-canonical simulations questioned how 'liquid' the equilibrium surface layer really is (Pickering et al. 2018) and large-scale simulations connected surface phase transitions to crystal growth habits (Llombart et al. 2020). Identifying which surface molecules are ice-like versus liquid-like is itself nontrivial: structure-based order parameters give inconsistent onsets of premelting (Qiu & Molinero 2018), and atomic-resolution atomic-force-microscopy imaging of the premelted ice Ih surface (Hong et al. 2024) resolved static structure but not molecular mobility. A theoretical perspective reconciling premelting onset and thickness controversies was given by MacDowell (2026), but it does not address in-plane dynamical heterogeneity. In this context, Yasuda, Endo, Arai and Yasuoka (Communications Chemistry 7, 117, 2024) performed all-atom molecular dynamics simulations of ice/vapor slabs of 432,000 TIP4P/Ice water molecules (a rigid four-site water model tuned to reproduce the ice melting point, ~269.8 K for this model), ~23 nm on a side, exposing the basal, primary prism, and secondary prism faces (the three principal crystallographic surfaces of hexagonal ice) at temperatures from ~209 to 269 K. Using a machine-learning pipeline in the graph-dynamical-network lineage (Xie et al. 2019), each surface molecule's 64 ps trajectory was mapped to a scalar dynamical descriptor $g(x)$ and classified as solid-like or liquid-like; the in-plane organization of these labels was quantified by the static structure factor $S(q)$ (the Fourier transform of density correlations, whose low-$q$ behavior reveals long-range order and characteristic domain sizes). They found that QLL molecules do not form a static mosaic of solid and liquid patches; instead, molecules with similar dynamics form transient dynamical domains — akin to the dynamical heterogeneity of supercooled liquids (the clustering of fast- and slow-moving molecules in liquids cooled well below their melting point) — whose members frequently switch state, with no maximum in $S(q)$ (i.e., no characteristic domain size) within the accessible window ($0.05\text{--}0.3$ Å$^{-1}$), and with long-range ordering that grows on cooling and differs between crystal faces. The authors state that finite size may mask a characteristic length, that vapor pressure was not controlled, that the dynamics-based classification degrades at low temperature because overall mobility decreases on cooling, and that 64 ps trajectories cannot resolve the fastest switching — these stated limitations are precisely the open problem.

Problem Statement

Determine the physical character of in-layer dynamical inhomogeneity in the quasi-liquid layers on the ice surface, by answering four linked questions, all four of which are required for a resolution, that jointly define one objective. (1) Length scale: does a characteristic in-plane dynamical domain size exist? This requires ice/vapor simulations (or equivalent measurements) whose in-plane extent is at least twice the ~23 nm edge of the 432,000-molecule TIP4P/Ice slabs of Yasuda et al. (2024), with a finite-size check across at least two cell sizes that the low-$q$ behavior of the static structure factor $S(q)$ of solid-like and liquid-like classified molecules does not merely track the cell edge, and a check whether $S(q)$ develops a maximum at low $q$, and quantifying the connection to larger scales by measuring the mesoscale surface roughness (surface-height variation above the molecular scale) together with the macroscale droplet/sheet structures (the coexisting liquid-like droplets and thin wetting layer observed experimentally) and stating an explicit relation between these observables and the atomic-scale dynamical inhomogeneity. (2) Thermodynamic control: how does vapor pressure reshape QLL in-layer dynamics — what changes in the dynamical-domain structure and switching when the surface is equilibrated under controlled over-saturated, saturated, and under-saturated conditions, each at a stated saturation ratio that is held fixed during equilibration, given that macroscale QLL structures are known to form under over- and under-saturation? (3) Temperature-robust classification: construct a classification of surface molecules into solid-like and liquid-like states that remains valid at low temperatures, validity here meaning that the labels keep separating the two populations against a reference that is independent of the classifier's construction, with the achieved classification accuracy reported, even where purely dynamics-based criteria fail because overall molecular mobility decreases upon cooling — for example by combining structural and dynamical information — and re-examine the domain structure with it. (4) Fast switching: resolve the fastest transitions between solid-like and liquid-like dynamical states, which lie below the ~64 ps trajectory windows used to define $g(x)$ and require a sampling time resolution at least an order of magnitude finer than that window, identifying their timescale, mechanism, and statistics. An answer should state, for each of the four questions, a conclusion supported by reproducible simulation or experimental evidence over the relevant scales, temperatures, and vapor conditions, together with the ranges each conclusion covers (cell or field-of-view size over which it was obtained, temperature, saturation ratio, and time resolution); a conclusion that omits these ranges, or covers only some of the four questions, is a partial result and does not resolve the task.

References

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