Molecular simulations show that sodium and calcium chloride adsorbed on the ice surface form quasi-liquid brine films whose thickness is increased by a factor of two or more relative to the pure-water premelting layer, with salt concentrations bounded by the bulk liquidus line and converging to it as the ice-brine-vapor triple point is approached. However, because these simulations are closed (canonical) with respect to water and salt, they cannot decide whether, in the open thermodynamic limit where both species can exchange with reservoirs, such films remain finite equilibrium surface states (partial wetting) or grow without bound (complete wetting by brine). Determining the equilibrium wetting behavior of the ice|brine|vapor system - equivalently, the sign of the effective interface potential at three-phase coexistence - for at least one salt, at a three-phase coexistence state between the eutectic and the melting point, is an open problem in the interfacial physics of ice, directly relevant to how the surfaces of sea ice and saline snow are modeled.

Background

Below its melting point, the surface of ice is covered by a disordered, liquid-like film known as the quasi-liquid layer (QLL), a phenomenon called surface premelting; its thickness and thermodynamic status remain actively debated (Dash, Rempel and Wettlaufer, Rev. Mod. Phys. 78, 695 (2006); Slater and Michaelides, Nat. Rev. Chem. 3, 172 (2019)). In the language of wetting physics, the key question for a solid-vapor interface is whether the premelted film stays microscopically finite at three-phase coexistence (incomplete surface melting, i.e. partial wetting) or diverges without bound as the triple point is approached (complete surface melting, i.e. complete wetting). The distinction is decided by the sign of the effective interface potential, the free energy per unit area of a liquid film of thickness hh between solid and vapor: a minimum at finite hh gives a stable finite film, while a monotonically decreasing potential drives unbounded growth. For pure water, both a Lifshitz-theory treatment of van der Waals (long-range dispersion) forces (Luengo-Márquez, Izquierdo-Ruiz and MacDowell, J. Chem. Phys. 157, 044704 (2022)), which predicts only incomplete premelting at ice-vapor coexistence, and recent contact-angle experiments (Demmenie et al., Phys. Rev. Fluids 10, 054002 (2025)), which find a nonzero contact angle of water on ice near 0 degrees Celsius, support partial wetting. In coarse wetting terms, the spreading coefficient S=γsv−(γsl+γlv)S=\gamma_{sv}-(\gamma_{sl}+\gamma_{lv}) (the free-energy gain per area of inserting a macroscopic liquid film between solid and vapor, with γ\gamma the interfacial tensions) is negative for pure water on ice near the triple point.

Soluble impurities change this picture. Salts such as NaCl and CaCl2 are the dominant impurities of sea ice, and thermodynamics dictates that at equilibrium a brine layer in contact with ice has a salt concentration fixed by the liquidus line of the salt-water phase diagram (the curve giving the freezing temperature as a function of concentration), down to the eutectic point (about -21 degrees Celsius for NaCl-water), below which ice, solid salt hydrate, and solution coexist. Experiments on ice/brine mixtures (Cho et al., J. Phys. Chem. B 106, 11226 (2002)) and impurity-premelting theory (Wettlaufer, Phys. Rev. Lett. 82, 2516 (1999)) show that impurities can strongly enhance premelting, and molecular dynamics (MD) studies (Hudait, Allen and Molinero, J. Am. Chem. Soc. 139, 10095 (2017); Berrens, Bononi and Donadio, Phys. Chem. Chem. Phys. 24, 20932 (2022)) confirm that adsorbed NaCl thickens and disorders the QLL. A grand-canonical ensemble is one in which the simulation cell exchanges particles with an ideal reservoir at fixed chemical potentials μ\mu, so that the amount of water and salt is not conserved; this is the ensemble that faithfully represents an ice surface in contact with an atmosphere and external brine reservoirs.

The study that raised the present question (Baran and MacDowell, J. Colloid Interface Sci. 721, 140764 (2026); preprint arXiv:2512.21929 (2025)) performed closed, total-content-conserving MD simulations of TIP4P/Ice ice (a four-site rigid water model tuned for the ice phase) with NaCl or CaCl2 ions described by the Madrid-2019 scaled-charge force field (an ion model whose formal charges are reduced by a factor of 0.85 to approximate electronic polarization), at temperatures from 250 K to 265 K and salt coverages of 0.55 to 2.2 salt molecules per square nanometer. Using a geometrical definition of the film thickness and an effective film concentration, they showed that the briny QLL is a genuine surface state whose concentration lies in the immiscibility gap of the bulk phase diagram and approaches the liquidus line tangentially near the triple point. At 265 K the highest-coverage NaCl films and an intermediate-coverage CaCl2 film attain the liquidus concentration, meaning the system sits at or exceedingly close to three-phase ice-brine-vapor coexistence. There, exactly two open-system outcomes are possible: the film remains at finite thickness (the brine does not wet ice), or the film grows without bound (complete wetting by brine). The authors state explicitly that deciding between these outcomes would require simulations in a grand-canonical system, where arbitrary amounts of either salt or water are allowed so that the system chooses the thermodynamic state without finite system size constraints; no such simulations exist. The same study also acknowledges, as separable limitations, that its simulations cannot describe the below-eutectic regime where salt precipitation is expected, that the scaled-charge force field underestimates ionic diffusion and slows equilibration kinetics, that the CaCl2 highest-coverage films fully melted the simulation slab (a finite-size limitation), and that ion incorporation into the ice lattice introduces a small systematic error in the effective concentration measure.

Problem Statement

For the ice-salt-water vapor system, determine the equilibrium wetting behavior of the ice-vapor interface by brine at the ice-brine-vapor three-phase line in the open thermodynamic limit, where water and salt can exchange with reservoirs at fixed chemical potentials. For at least one salt (NaCl or CaCl2), at an ice-brine-vapor three-phase coexistence state between the eutectic point and the melting point, establish whether the premelted brine film - whose composition approaches the liquidus concentration as three-phase coexistence is reached - converges to a finite equilibrium thickness (partial wetting: a genuine finite surface state) or grows without bound as coexistence is approached (complete wetting by brine). Equivalently, determine the sign of the effective interface potential, or the sign of the spreading coefficient S=γiv−(γib+γbv)S=\gamma_{iv}-(\gamma_{ib}+\gamma_{bv}) with γiv\gamma_{iv}, γib\gamma_{ib}, γbv\gamma_{bv} the ice-vapor, ice-brine, and brine-vapor interfacial tensions, for the coexistence state in question. The answer should state, for the salt and model or system studied, which of the two thermodynamic outcomes occurs, and quantify the equilibrium film thickness behavior or interface potential on which the conclusion rests.

References

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