Premelting-Induced Smoothening of the Ice-Vapor Interface

Exploring surface properties and premelting in crystals

Crystal surfaces play a pivotal role in governing various significant processes, such as adsorption, nucleation, wetting, friction, and wear. A fundamental property that influences these processes is the surface free energy, γ. We have directly calculated γ(T) for low-index faces of Lennard-Jones (LJ), germanium, and silicon crystals along their sublimation lines using the computational cleavage technique. Our calculations agree well with experimental values for Si(111) and Ge(111), highlighting the accuracy of the method and models used. For LJ crystals, we identified a premelting onset at Tpm = 0.75Tm, marked by a sharp increase in atom mobility within the second outermost surface layer. Notably, Tpm closely aligned with the endpoint of the LJ melting line at negative pressures, Tend = 0.76Tm. We hypothesize that the emergence and coexistence of a liquid film atop the LJ crystal at Tpm < T < Tm correspond to the metastable melting line under negative pressures experienced by stretched crystal surfaces. Furthermore, our study of thin LJ crystal slabs reveals that premelting-induced failure leads to recrystallization below the homogeneous freezing limit, offering a promising avenue to explore crystal nucleation and growth at extremely deep supercoolings. Finally, no evidence of premelting was detected in the model crystals of Ge and Si, which is consistent with the experimental observations. Overall, our findings offer valuable insights into crystal surface phenomena at the atomic scale.

van der Waals induced ice growth on partially melted ice nuclei in mist and fog

Ice nucleation and formation play pivotal roles across various domains, from environmental science to food engineering. However, the exact ice formation mechanisms remain incompletely understood. This study introduces a novel ice formation process, which can be either heterogeneous or homogeneous, depending on the initial conditions. The process initiates ice crystal growth from a nucleus composed of a micron-sized partially melted ice particle. We explore the role of van der Waals (Lifshitz)-free energy and its resulting stress in the accumulation of ice at the interface with water vapor. Our analysis suggests that this process could lead to thicknesses ranging from nanometers to micrometers, depending on the size and degree of initial melting of the ice nucleus. We provide evidence for the growth of thin ice layers instead of liquid water films on a partially melted ice-vapor interface, offering some insights into mist and fog formation. We also link it to potential atmospheric and astrogeophysical applications.

Different pathways to anomalous stabilization of ice layers on methane hydrates

We explore the Casimir-Lifshitz free-energy theory for surface freezing of methane gas hydrates near the freezing point of water. The theory enables us to explore different pathways, resulting in anomalous (stabilizing) ice layers on methane hydrate surfaces via energy minimization. Notably, we will contrast the gas hydrate material properties, under which thin ice films can form in water vapor, with those previously predicted to be required in the presence of liquid water. It is predicted that methane hydrates in water vapor near the freezing point of water nucleate ice films, instead of water films.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.

Effect of sodium chloride adsorption on the surface premelting of ice

We characterise the structural properties of the quasi-liquid layer (QLL) at two low-index ice surfaces in the presence of sodium chloride (Na⁺/Cl^-) ions by molecular dynamics simulations. We find that the presence of a high surface density of Na⁺/Cl^- pairs changes the surface melting behaviour from step-wise to gradual melting. The ions lead to an overall increase of the thickness and the disorder of the QLL, and to a low-temperature roughening transition of the air-ice interface. The local molecular structure of the QLL is similar to that of liquid water, and the differences between the basal and primary prismatic surface are attenuated by the presence of Na⁺/Cl^- pairs. These changes modify the crystal growth rates of different facets and the solvation environment at the surface of sea-water ice with a potential impact on light scattering and environmental chemical reactions.

Intermolecular forces at ice and water interfaces: premelting, surface freezing and regelation

Using Lifshitz theory we assess the role of van der Waals forces at interfaces of ice and water. The results are combined with measured structural forces from computer simulations to develop a quantitative model of the surface free energy of premelting films. This input is employed within the framework of wetting theory and allows us to predict qualitatively the behavior of quasi-liquid layer thickness as a function of ambient conditions. Our results emphasize the significance of vapor pressure. The ice vapor interface is shown to exhibit only incomplete premelting, but the situation can shift to a state of complete surface melting above water saturation. The results obtained serve also to assess the role of subsurface freezing at the water-vapor interface, and we show that intermolecular forces favor subsurface ice nucleation only in conditions of water undersaturation. We show ice regelation at ambient pressure may be explained as a process of capillary freezing, without the need to invoke the action of bulk pressure melting. Our results for van der Waals forces are exploited in order to gauge dispersion interactions in empirical point charge models of water.

Premelting layer during ice growth: role of clusters

The premelting layer plays an important role in ice growth, but there is a significant gap in our knowledge between the atomistic premelting surface structure and the macroscopic growth mechanism. In this work, using large-scale molecular dynamics simulation, we reveal the existence of clusters on the premelting surface, as an intermediate feature bridging the gap. We show the spontaneous formation and evolution of clusters, and they form a stable distribution determined by the growth rate. We demonstrate how this stable distribution is related to the growth mode of ice, connected by the growth of clusters. We come to a bilayer-by-bilayer growth mode at simulation-reachable high growth rates, but another mechanism, namely "cluster stacking", is speculated to exist at lower growth rates. This work builds a connection between the microscopic structure of the premelting layer and the macroscopic growth of ice, making a step forward toward the full understanding of premelting and ice growth.

Impact of surface nanostructure and wettability on interfacial ice physics

Ice accumulation on solid surfaces is a severe problem for safety and functioning of a large variety of engineering systems, and its control is an enormous challenge that influences the safety and reliability of many technological applications. The use of molecular dynamics (MD) simulations is popular, but as ice nucleation is a rare event when compared to simulation timescales, the simulations need to be accelerated to force ice to form on a surface, which affects the accuracy and/or applicability of the results obtained. Here, we present an alternative seeded MD simulation approach, which reduces the computational cost while still ensuring accurate simulations of ice growth on surfaces. In addition, this approach enables, for the first time, brute-force all-atom water simulations of ice growth on surfaces unfavorable for nucleation within MD timescales. Using this approach, we investigate the effect of surface wettability and structure on ice growth in the crucial surface-ice interfacial region. Our main findings are that the surface structure can induce a flat or buckled overlayer to form within the liquid, and this transition is mediated by surface wettability. The first overlayer and the bulk ice compete to structure the intermediate water layers between them, the relative influence of which is traced using density heat maps and diffusivity measurements. This work provides new understanding on the role of the surface properties on the structure and dynamics of ice growth, and we also present a useful framework for future research on surface icing simulations.

Edge premelting of two-dimensional ices

The surface of a three-dimensional ice crystal naturally has a quasi-liquid layer (QLL) at temperatures below its bulk melting point, due to a phenomenon called surface premelting. Here, we show that the edges of a two-dimensional (2D) bilayer hexagonal ice adsorbed on solid surfaces undergo premelting as well, resulting in the formation of quasi-liquid bands (QLBs) at the edges. Our extensive molecular dynamics simulations show that the QLB exhibits structure and dynamics indistinguishable from the bilayer liquid phase, acting as a lower-dimensional analog of the QLL on the bulk ice. We further find that at low temperatures, the width of the QLBs at armchair-type edges of the 2D ice is almost identical to that at zigzag-type edges but becomes far greater than the latter at temperatures near the melting point. The chirality-dependent edge premelting of 2D ices should add an important new ingredient to the heterogeneity of premelting.

How ice grows from premelting films and water droplets

Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer liquid-vapor interface. At higher saturations water droplets condense, a large crater forms below, and freezing proceeds undetectably beneath the droplet. Our approach is a general framework that naturally models freezing close to three phase coexistence and provides a first principle theory of ice growth and melting which may prove useful in the geosciences.

Surface phase transitions and crystal habits of ice in the atmosphere

With climate modeling predicting a raise of at least 2°C by year 2100, the fate of ice has become a serious concern, but we still do not understand how ice grows (or melts). In the atmosphere, crystal growth rates of basal and prism facets exhibit an enigmatic temperature dependence and crossover up to three times in a range between 0° and -40°. Here, we use large-scale computer simulations to characterize the ice surface and identify a sequence of previously unidentified phase transitions on the main facets of ice crystallites. Unexpectedly, we find that as temperature is increased, the crystal surface transforms from a disordered phase with proliferation of steps to a smooth phase with small step density. This causes the anomalous increase of step free energies and provides the long sought explanation for the enigmatic crossover of snow crystal growth rates found in the atmosphere.

Rounded Layering Transitions on the Surface of Ice

Understanding the wetting properties of premelting films requires knowledge of the film's equation of state, which is not usually available. Here we calculate the disjoining pressure curve of premelting films and perform a detailed thermodynamic characterization of premelting behavior on ice. Analysis of the density profiles reveals the signature of weak layering phenomena, from one to two and from two to three water molecular layers. However, disjoining pressure curves, which closely follow expectations from a renormalized mean field liquid state theory, show that there are no layering phase transitions in the thermodynamic sense along the sublimation line. Instead, we find that transitions at mean field level are rounded due to capillary wave fluctuations. We see signatures that true first order layering transitions could arise at low temperatures, for pressures between the metastable line of water-vapor coexistence and the sublimation line. The extrapolation of the disjoining pressure curve above water-vapor saturation displays a true first order phase transition from a thin to a thick film consistent with experimental observations.

Premelting of ice adsorbed on a rock surface

Considering ice-premelting on a quartz rock surface (i.e. silica) we calculate the Lifshitz excess pressures in a four layer system with rock–ice–water–air.

Structure and water attachment rates of ice in the atmosphere: role of nitrogen

In this work we perform computer simulations of the ice surface in order to elucidate the role of nitrogen in the crystal growth rates and crystal habits of snow in the atmosphere. In pure water vapor at temperatures typical of ice crystal formation in cirrus clouds, we find that basal and primary prismatic facets exhibit a layer of premelted ice, with thickness in the subnanometer range. For partial pressures of 1 bar, well above the expected values in the troposphere, we find that only small amounts of nitrogen are adsorbed. The adsorption takes place onto the premelted surface, and hardly any nitrogen dissolves within the premelting film. The premelting film thickness does not change either. We quantify the resulting change of the ice/vapor surface tension to be in the hundredth of mN m^-1 and find that the structure of the pristine ice surface is not changed in a significant manner. We perform a trajectory analysis of colliding water molecules, and find that the attachment rates from direct ballistic collision are very close to unity irrespective of the nitrogen pressure. Nitrogen is however at sufficient density to deflect a fraction of trajectories with smaller distance than the mean free path. Our results show explicitly that the reported differences in growth rates measured in pure water vapor and a controlled nitrogen atmosphere are not related to a significant disruption of the ice surface due to nitrogen adsorption. On the contrary, we show clearly from our trajectory analysis that nitrogen slows down the crystal growth rates due to collisions between water molecules with bulk nitrogen gas. This clarifies the long standing controversy of the role of inert gases on crystal growth rates and demonstrates their influence is solely related to the diffusion limited flow of water vapor across the gas phase.

Binding potentials for vapour nanobubbles on surfaces using density functional theory

We calculate density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes et al (2015 J. Chem. Phys. 142 074702) to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness h of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as h is varied and thereby determine the binding potential as a function of h. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.

Fluctuation spectroscopy of surface melting of ice with and without impurities

Water is ubiquitous, and the surface properties of ice have been studied for some time, due to their importance. A liquidlike layer (LLL) is known to exist on ice, below the melting point. We use surface thermal fluctuation spectroscopy to study the LLL, including its thickness, for pure ice, and for ice with impurities. We find that the properties of the LLL are experimentally those of liquid water, with thickness much smaller than previous results. We also find that impurities cause the LLL to be thicker, and quite inhomogeneous, with properties depending on the dopant.

How Do Ice Crystals Grow inside Quasiliquid Layers?

A microscopic understanding of crystal-melt interfaces, inseparably involved in the dynamics of crystallization, is a long-standing challenge in condensed matter physics. Here, using an advanced optical microscopy, we directly visualize growing interfaces between ice basal faces and quasiliquid layers (QLLs) during ice crystal growth. This system serves as a model for studying the molecular incorporation process of the crystal growth from a supercooled melt (the so-called melt growth), often hidden by inevitable latent heat diffusion and/or the extremely high crystal growth rate. We reveal that the growth of basal faces inside QLLs proceeds layer by layer via two-dimensional nucleation of monomolecular islands. We also find that the lateral growth rate of the islands is well described by the Wilson-Frenkel law, taking into account the slowing down of the dynamics of water molecules interfaced with ice. These results clearly indicate that, after averaging surface molecular fluctuations, the layer by layer stacking still survives even at the topmost layer on basal faces, which supports the kink-step-terrace picture even for the melt growth.

Why Is It So Difficult to Identify the Onset of Ice Premelting?

Premelting of ice at temperatures below 0 °C is of fundamental importance for environmental processes. Various experimental techniques have been used to investigate the temperature at which liquid-like water first appears at the ice-vapor interface, reporting onset temperatures from -160 to -2 °C. The signals that identify liquid-like order at the ice-vapor interface in these studies, however, do not show a sharp initiation with temperature. That is at odds with the expected first-order nature of surface phase transitions, and consistent with recent large-scale molecular simulations that show the first premelted layer to be sparse and to develop continuously over a wide range of temperatures. Here we perform a thermodynamic analysis to elucidate the origin of the continuous formation of the first layer of liquid at the ice-vapor interface. We conclude that a negative value of the line tension of the ice-liquid-vapor three-phase contact line is responsible for the continuous character of the transition and the sparse nature of the liquid-like domains in the incomplete first layer.

Anomalous diffusion of water molecules at grain boundaries in ice Ih

Using ab initio and classical molecular dynamics simulations, we study pre-melting phenomena in pristine coincident-site-lattice grain boundaries (GBs) in proton-disordered hexagonal ice Ih at temperatures just below the melting point Tm. Concerning pre-melt-layer thicknesses, the results are consistent with the available experimental estimates for low-disorder impurity-free GBs. With regard to molecular mobility, the simulations provide a key new insight: the translational motion of the water molecules is found to be subdiffusive for time scales from ∼10 ns up to at least 0.1 μs. Moreover, the fact that the anomalous diffusion occurs even at temperatures just below Tm where the bulk supercooled liquid still diffuses normally suggests that it is related to the confinement of the GB pre-melt layers by the surrounding crystalline environment. Furthermore, we show that this behavior can be characterized by continuous-time random walk models in which the waiting-time distributions decay according to power-laws that are very similar to those describing dynamics in glass-forming systems.

Role of Salt, Pressure, and Water Activity on Homogeneous Ice Nucleation

Pure water can be substantially supercooled below the melting temperature without transforming into ice. The achievable supercooling can be enhanced by adding solutes or by applying hydrostatic pressure. Avoiding ice formation is of great importance in the cryopreservation of food or biological samples. In this Letter, we investigate the similarity between the effects of pressure and salt on ice formation using a combination of state-of-the-art simulation techniques. We find that both hinder ice formation by increasing the energetic cost of creating the ice-fluid interface. Moreover, we examine the widely accepted proposal that the ice nucleation rate for different pressures and solute concentrations can be mapped through the activity of water [ Koop , L. ; Tsias , P. Nature , 2000 , 406 , 611 ]. We show that such a proposal is not consistent with the nucleation rates predicted in our simulations because it does not include all parameters affecting ice nucleation. Therefore, even though salt and pressure have a qualitatively similar effect on ice formation, they cannot be quantitatively mapped onto one another.

Growth kinetics and morphology of snowflakes in supersaturated atmosphere using a three-dimensional phase-field model

Simulating ice crystal growth is a major issue for meteorology and aircraft safety. Yet, very few models currently succeed in reproducing correctly the diversity of snow crystal forms, and link the model parameters to thermodynamic quantities. Here, we demonstrate that the new three-dimensional phase-field model developed in Demange et al. [npj Comput. Mater. 3, 1 (2017)2057-396010.1038/s41524-017-0015-1] is capable of reproducing properly the morphology and growth kinetics of snowflakes in supersaturated atmosphere. Aside from that, we show that the growth dynamics of snow crystals satisfies the selection theory, consistently with previous experimental observations. Finally, we link the parameters of the phase-field model to atmospheric parameters.