How ice grows from premelting films and water droplets

The growth and melting of ice are crucial in various processes, from snowflake precipitation to glacier dynamics and climate change. However, a complete understanding of ice growth remains elusive, with conflicting experimental measurements of growth rates. Classical crystal growth models based on vapor deposition and adatom migration don't account for premelting films observed at the ice/vapor interface near the triple point. These films, confirmed by experiments and simulations, significantly impact growth rates. The primary habit or aspect ratio of snow crystals changes dramatically with temperature and saturation, yet phenomenological models based on a kinetic anisotropy factor accurately describe these shapes. However, linking this factor to ambient conditions remains a challenge. Incorporating the premelting layer is essential to understand the dependence of growth rates on ambient conditions. The challenges in incorporating premelting films are also found in materials science, where partially stable liquid phases condense into droplets on the growing substrate, altering the growth mechanism. The problem is analogous to wetting theory, studying metastable liquid adsorption at the solid/vapor interface, but with the added complexity of the substrate reacting with the adsorbed film. This study combines computer simulations, equilibrium wetting theory, and thin-film modeling to describe ice surface kinetics near the triple point within a general framework for wetting on reactive substrates.

Existing research on ice growth rates has yielded conflicting results, often analyzed using classical crystal growth models that focus on direct deposition from the vapor phase and adatom migration. These models do not account for the premelting films experimentally observed on the ice surface near the triple point. Studies using various experimental techniques, along with computer simulations, consistently demonstrate the existence of a quasi-liquid layer of premelted ice, whose thickness increases as the triple point is approached. Attempts to incorporate this effect into classical models have met with limited success. Understanding snow crystal growth highlights the issue; these crystals exhibit diverse shapes dependent on temperature and saturation, accurately modeled using phenomenological approaches. However, a connection between the phenomenological parameters and ambient conditions remains elusive. The role of premelting films is also challenging to integrate into crystal growth theories in other materials science systems, particularly when liquid droplets condense on the growing substrate, fundamentally changing the growth mechanism. Equilibrium wetting theory offers a framework, but the substrate's reactivity complicates the application of these theories to out-of-equilibrium scenarios.

This research combines state-of-the-art computer simulations, equilibrium wetting theory, and thin-film modeling to describe ice growth kinetics near the triple point. The study begins by determining the interface potential for a water film adsorbed on ice. While experiments often report premelting layer thicknesses as a function of temperature, the process can also be viewed as vapor condensation. Premelting thickness is therefore a function of both temperature and vapor pressure. Ice in contact with water vapor is only in equilibrium along the sublimation line; premelting thickness away from this line can only be meaningfully characterized for small deviations, where condensation and freezing rates are equal. The authors calculate an approximate interface potential using an analysis of equilibrium surface fluctuations of ice along the sublimation line. The effective surface free energy is expressed as w(h;T) = g(h;T) – Api(T)h, where Api(T) is the pressure difference between liquid and vapor phases, and w(h;T) is calculated through simulations of solid/vapor equilibrium. The free energy is obtained from the fluctuation formula Δw(h;T) = –kTln P(h;T). Api(T) is calculated using thermodynamic integration. The TIP4P/Ice model is employed for simulations, providing accurate predictions of surface tensions. The results are fitted to a model that includes short-range and van der Waals contributions to the interface potential. The interface potential is used to construct a coarse-grained free energy (Hamiltonian) incorporating sine-Gordon and Capillary Wave physics with bulk fields. This Hamiltonian is used to study the dynamics of two interfaces, the solid-liquid and liquid-vapor surfaces. The evolution of these interfaces is treated using non-conserved gradient dynamics and a thin-film approximation, accounting for freezing/melting, condensation/evaporation, and advective fluxes. A kinetic phase diagram is generated by analyzing the dynamics equations, identifying key kinetic phase lines (kinetic coexistence, α → β transition, and kinetic spinodal). Extensive numerical simulations confirm the accuracy of the kinetic phase diagram. Model parameters, including kinetic growth coefficients, viscosity, surface tensions, etc., are obtained from gas kinetic theory, crystal growth theory, and literature data for water and ice.

The study reveals three distinct ice growth regimes as vapor saturation increases. First, at low saturation, growth proceeds via terrace spreading below a premelting film of well-defined thickness. The solid's motion is conveyed through the liquid to the outer liquid-vapor interface. Second, at intermediate saturations, droplets condense on the ice surface, and growth happens mainly beneath the droplets. A crater forms under the droplet. Third, at high saturations, the premelting layer thickness diverges, and growth occurs from below a bulk water phase. The different regimes are separated by well-defined kinetic phase lines, which can be mapped to an underlying equilibrium interface potential. The interface potential, obtained from computer simulations, exhibits two minima (α and β), corresponding to different film thicknesses. The study develops a kinetic phase diagram that plots pressure versus temperature, identifying regions of activated growth, continuous growth, and droplet formation. Three key kinetic phase lines are identified: the kinetic coexistence line (where Δpk = 0), the α → β kinetic transition line, and the kinetic spinodal line (where the film thickness diverges). The kinetic coexistence line marks the onset of droplet formation, occurring above the liquid-vapor coexistence line. The slope of the kinetic coexistence lines is determined by the ratio of kinetic coefficients, while the separation between lines depends on the minima's depth and energy separation. Numerical simulations confirm these findings, showing growth mechanisms in agreement with the kinetic phase diagram. Below the kinetic coexistence line, growth occurs through terrace spreading or nucleation and spread of terraces, depending on the thermodynamic driving force relative to the pinning field. Above the line, droplet formation and growth under droplets are observed. Above the kinetic α-β transition line, droplets form on top of a thicker β film, resembling experimental observations. Beyond the spinodal line, the film thickness diverges, and growth happens beneath a macroscopically thick wetting film.

The findings highlight the importance of considering the underlying substrate's behavior when analyzing the dynamics of the quasi-liquid layer. The complex dynamics of the buried solid surface is conveyed to the outer surface of the quasi-liquid film. Observations of terrace translation, spiral growth, and nucleation are consistent with the existence of a nanometer-thick premelting film. The transition from thin to thick film regimes significantly alters the crystal growth mechanism. In the thin-film regime, step growth is energetically expensive; in the thick-film regime, droplet condensation facilitates step formation, increasing the growth rate, especially at corners. This explains the preferential growth at crystal corners observed in experiments and might play a role in tip splitting. The discontinuous change in growth mechanisms combined with recent findings on temperature dependence of step-free energies could improve our understanding of snowflake growth. The model developed provides a valuable tool for predicting the ice growth mechanisms under various conditions and could be extended to study other reactive wetting systems.

This study provides a comprehensive model for ice growth that incorporates the effects of premelting films and droplet condensation. The model accurately predicts the different growth regimes observed experimentally, clarifying the relationship between ambient conditions and ice crystal morphology. Future research could focus on refining the model by incorporating more detailed descriptions of the ice surface structure and incorporating stochastic effects to study the nucleation process more accurately. Investigating the role of impurities and other atmospheric factors in influencing ice growth would also be beneficial.

The TIP4P/Ice model, while reasonably accurate, is a simplified representation of water and ice interactions. More sophisticated models, incorporating polarization effects and many-body interactions, could potentially provide further refinement. The model assumes small deviations from equilibrium; larger deviations may require a more complex treatment. The kinetic parameters used in the model are estimated from literature values; more precise measurements could improve the model's accuracy.