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In this work, we perform a systematic computer simulation study of ice premelting, and explore the thickness and structure of quasi-liquid layers formed at the interface of ice with substrates of different hydrophilicity. Our study shows that interfacial premelting occurs on neutral substrates of whatever hydrophilicity, forming films of limited thickness for substrates with contact angles larger than ca. 50$^\circ$ but exhibiting complete interfacial premelting at smaller contact angles. Contrary to most experimental studies, we focus not only on the premelting behavior with temperature, but also with pressure, which is a matter of relevance in important situations such as ice friction. Our study is guided within a rigorous framework of surface thermodynamics, demonstrating that the premelting film structure is a function of a single thermodynamic variable. By this token we are able to relate properties measured along an isobar, with premelting films at arbitrary temperature and pressure. We also find that adhesion strength in atomically smooth surfaces is one to two orders of magnitude larger than those found in experiments, and conjecture that the reason is substrate roughness and the presence of organic adsorbents. Our theoretical framework also allows us to exploit our results on interfacial premelting in order to gain insight into heterogeneous ice nucleation. We show that apolar smooth substrates of whatever hydrophilicity are unlikely nucleators, and that too large hydrophilicity conspires also against ice nucleation. Furthermore, we exploit statistical-thermodynamic framework to shed light into the nature of the surface intermolecular forces promoting interfacial premelting, and provide a model to predict quasi-liquid layer thickness as a function of the substrate's hydrophilicity with great potential applications in fields ranging from earth sciences to aircraft engineering.

A widely accepted phenomenological rule states that solids with free surfaces cannot be overheated. In this work we discuss this statement critically under the light of the statistical thermodynamics of interfacial roughening transitions. Our results show that the basal face of ice as described by the TIP4P/Ice model can remain mechanically stable for more than one hundred nanoseconds when overheated by 1 K, and for several hundreds of nanoseconds at smaller overheating despite the presence of a significant quasi-liquid layer at the surface. Such time scales, which are often of little experimental significance, can become a concern for the determination of melting points by computer simulations using the direct coexistence method. In the light of this observation, we reinterpret computer simulations of ice premelting and show that current results for the TIP4P/Ice model all imply a scenario of incomplete surface melting. Using a thermodynamic integration path, we reassess our own estimates for the Laplace pressure difference between water and vapor. These calculations are used to measure the disjoining pressure of premelting liquid films and allow us to confirm a minimum of the interfacial free energy at finite premelting thickness of about one nanometer., Comment: Manuscript as version of record except for minor edits

The ice surface is known for presenting a very small kinetic friction coefficient, but the origin of this property remains highly controversial to date. In this work, we revisit recent computer simulations of ice sliding on atomically smooth substrates, using newly calculated bulk viscosities for the TIP4P/Ice water model. The results show that spontaneously formed premelting films in static conditions exhibit an effective viscosity which is about twice the bulk viscosity. However, upon approaching sliding speeds in the order of m/s, the shear rate becomes very large, and the viscosities decrease by several orders of magnitude. This shows that premelting films can act as an efficient lubrication layer despite their small thickness, and illustrates an interesting interplay between confinement enhanced viscosities, and shear thinning. Our results suggest that the strongly thinned viscosities that operate under the high speed skating regime could largely reduce the amount of frictional heating., Comment: 5 pages, 1 figure

Experimental measurements of the surface tension of colloidal interfaces have long been in conflict with computer simulations. In this work we show that the surface tension of colloids as measured by surface fluctuations picks up a gravity dependent contribution which removes the discrepancy. The presence of this term puts a strong constraint on the structure of the interface which allows one to identify corrections to the fundamental equation of equilibrium capillarity and deduce bottom-up the microscopic origin of a growth model with close relation to the Kardar-Parisi-Zhang equation., Comment: 6 pages, two figures, one table + updated supplemental material

Studies have shown that math skills in early childhood are uniquely and strongly predictive of later outcomes across a range of domains and well into adulthood, including the likelihood of graduating from high school and college completion. The Making Pre-K Count and High 5s studies were designed to rigorously test the short- and long-term effects of improving children's math experiences in prekindergarten (pre-K) and kindergarten. Making Pre-K Count provided pre-K teachers in New York City with a high-quality, evidenced-based math curriculum (Building Blocks) and ongoing teacher training and coaching. The Making Pre-K Count study compared students who were exposed to this curriculum with their peers in pre-K as usual in public school and community-based sites. The High 5s math program was developed to offer children who had received Making Pre-K Count in pre-K in public schools hands-on, supplemental math enrichment in small groups, or clubs, outside of regular instructional time in kindergarten. The High 5s study compared students assigned to Making Pre-K Count in pre-K and High 5s in kindergarten with children assigned to Making Pre-K Count in pre-K and kindergarten as usual. Taken together, the Making Pre-K Count and High 5s studies present new evidence about the long-term effects of early math interventions on children's later outcomes. Early math enrichment experiences can lead to lasting gains for children across a variety of outcome domains, even years later. The findings suggest that high-quality early math instructional practices could make a difference, particularly for children with the greatest need.

With an ever-increasing interest in water properties, many intermolecular force fields have been proposed to describe the behavior of water. Unfortunately, good models for liquid water usually cannot provide simultaneously an accurate melting point for ice. For this reason, the TIP4P/Ice model was developed at targeting the melting point, and has become the preferred choice for simulating ice at coexistence. Unfortunately, available data for its dynamic properties in the liquid state are scarce. Therefore, we demonstrate a series of simulations aimed at the calculation of transport coefficients for the TIP4P/Ice model over a large range of thermodynamic conditions, ranging from $T=245$ K to $T=350$ K for the temperature and from $p=0$ to $p=500$ MPa for the pressure. We have found that the self-diffusion (shear viscosity) exhibits smaller (increased) values than TIP4P/2005 and experiments. However, rescaling the temperature with respect to the triple point temperature as in a corresponding states plot we find TIP4P/Ice compares very well with TIP4P/2005 and to experiment. Such observations allow us to infer that despite the different original purposes of these two models examined here, one can benefit from a vast number of reports regarding the behavior of transport coefficients for the TIP4P/2005 model and utilize them following the routine described in this paper.

The origin of ice slipperiness has been a matter of great controversy for more than a century, but an atomistic understanding of ice friction is still lacking. Here, we perform computer simulations of an atomically smooth substrate sliding on ice. In a large temperature range between 230 and 266 K, hydrophobic sliders exhibit a premelting layer similar to that found at the ice air interface. On the contrary, hydrophilic sliders show larger premelting and a strong increase of the first adsorption layer. The non equilibrium simulations show that premelting films of barely one nanometer thickness are sufficient to provide a lubricating quasi liquid layer with rheological properties similar to bulk undercooled water. Upon shearing, the films display a pattern consistent with lubricating Couette flow, but the boundary conditions at the wall vary strongly with the substrates interactions. Hydrophobic walls exhibit large slip, while hydrophilic walls obey stick boundary conditions with small negative slip. By compressing ice above atmospheric pressure, the lubricating layer grows continuously, and the rheological properties approach bulk-like behavior. Below 260 K, the equilibrium premelting films decrease significantly. However, a very large slip persists on the hydrophobic walls, while the increased friction on hydrophilic walls is sufficient to melt ice and create a lubrication layer in a few nanoseconds. Our results show the atomic scale frictional behavior of ice is a combination of spontaneous premelting, pressure melting and frictional heating., Comment: 9 pages, 4 figures + supplementary material, 24 pgs, 14 figures, 5 tables

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 emphasizes 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., Comment: 27 pages, 15 figures, 7 tables (including supplementary material)

The van der Waals force established between two surfaces plays a central role in many phenomena, such as adhesion or friction. However, the dependence of this forces on the distance of separation between plates is very complex. Two widely different non-retarded and retarded regimes are well known, but these have been traditionally studied separately. Much less is known about the important experimentally accesible cross-over regime. In this study, we provide analytical approximations for the van der Waals forces between two plates that interpolates exactly between the short distance and long distance behavior, and provides new insight into the crossover from London to Casimir forces at finite temperature. At short distance, where the behavior is dominated by non-retarded interactions, we work out a very accurate simplified approximation for the Hamaker constant which adopts analytical form for both the Drude and Lorentz models of dielectric response. We apply our analytical expressions for the study of forces between metallic plates, and observe very good agreement with exact results from numerical calculations. Our results show that contributions of interband transitions remain important in the experimentally accessible regime of decades nm for several metals, including gold., Comment: 10 pages, 3 figures, supplementary materials

This paper presents developed real-time simulation models for offshore wind turbine generators in compliance with industry standards. The critical control functions such as negative sequence injection, sequence current limit, voltage ride through, and power curtailments are designed to meet the industry requirements for future electromagnetic transient (EMT) testing and controls of offshore wind farms. Average-value and switching detailed models are developed in the Opal-RT real-time simulator. Real-time capabilities of these models are compared to show the effectiveness of the average-value model in terms of accuracy and computation efficiency. Studies of balanced and unbalanced faults illustrate the ability of the proposed turbine models to inject active and reactive currents during fault events. The models are validated against the second-generation generic wind turbine model proposed by Western Electricity Coordinating Council (WECC). Validation results reveal that the proposed models are aligned with the WECC generic model. In addition, the models provide an extended capability in mitigating the active power oscillation during unbalanced fault conditions.

Hypothesis: As a fluid approaches three phase coexistence, adsorption may take place by the successive formation of two intervening wetting films. The equilibrium thickness of these wetting layers is the result of a delicate balance of intermolecular forces, as dictated by an underlying interface potential. The van der Waals forces for the two variable adsorption layers may be formulated exactly from Dzyaloshinskii-Lifshitz-Pitaevskii theory, and analytical approximations may be derived that extent well beyond the validity of conventional Hamaker theory. Calculations: We consider the adsorption equilibrium of water vapor on Silver Iodide where both ice and a water layers can form simultaneously and compete for the vapor as the triple point is approached. We perform numerical calculations of Lifshitz theory for this complex system and work out analytical approximations which provide quantitative agreement with the numerical results. Findings: At the three phase contact line between AgI/water/air, surface forces promote growth of ice both on the AgI/air and the water/vapor interfaces, lending support to a contact nucleation mode of AgI in the atmosphere. Our approach provides a framework for the description of adsorption at three phase coexistence, and allows for the study of ice nucleation efficiency on atmospheric aerosols., Comment: Accepted Manuscript

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 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., Comment: 43 pages, 13 figures, including supplementary

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 prismatic facets exhibit an enigmatic temperature dependence, and crossover up to three times in a range between 0 and -40 C. Here we use large scale computer simulations to characterize the ice surface and identify a sequence of novel 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., Comment: 21 pages, 4 figures + supplementary material. A revised version to appear in Science Advances (In press) under a CC-BY license

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., Comment: 32 pages, 10 figures

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., Comment: 6 pages + 3 figures + supplementary file

In this paper we study the structure of the ice/vapor interface in the neighborhood of the triple point for the TIP4P/2005 model. We probe the fluctuations of the ice/film and film/vapor surfaces that separate the liquid film from the coexisting bulk phases at basal, primary prismatic and secondary prismatic planes. The results are interpreted using a coupled sine Gordon plus Interface Hamiltonian model. At large length-scales, the two bounding surfaces are correlated and behave as a single complex ice/vapor interface. For small length, on the contrary, the ice/film and film/vapor surfaces behave very much like independent ice/water and water/vapor interfaces. The study suggests that the basal facet of the TIP4P/2005 model is smooth, the prismatic facet is close to a roughening transition, and the secondary prismatic facet is rough. For the faceted basal face, our fluctuation analysis allows us to estimate the step free energy in good agreement with experiment. Our results allow for a quantitative characterization of the extent to which the adsorbed quasi-liquid layer behaves as water, and explains experimental observations which reveal similar activation energies for crystals grown in bulk vapor or bulk water., Comment: 39 pages, 7 figures