Using machine learning with atomistic surface and local water features to predict heterogeneous ice nucleation

Heterogeneous ice nucleation (HIN) has applications in climate science, nanotechnology, and cryopreservation. Ice nucleation on the earth's surface or in the atmosphere usually occurs heterogeneously involving foreign substrates, known as ice nucleating particles (INPs). Experiments identify good INPs but lack sufficient microscopic resolution to answer the basic question: What makes a good INP? We employ molecular dynamics (MD) simulations in combination with machine learning (ML) to address this question. Often, the large amount of computational cost required to cross the nucleation barrier and observe HIN in MD simulations is a practical limitation. We use information obtained from short MD simulations of atomistic surface and water models to predict the likelihood of HIN. We consider 153 atomistic substrates with some surfaces differing in elemental composition and others only in terms of lattice parameters, surface morphology, or surface charges. A range of water features near the surface (local) are extracted from short MD simulations over a time interval (≤300 ns) where ice nucleation has not initiated. Three ML classification models, Random Forest (RF), support vector machine, and Gaussian process classification are considered, and the accuracies achieved by all three approaches lie within their statistical uncertainties. Including local water features is essential for accurate prediction. The accuracy of our best RF classification model obtained including both surface and local water features is 0.89 ± 0.05. A similar accuracy can be achieved including only local water features, suggesting that the important surface properties are largely captured by the local water features. Some important features identified by ML analysis are local icelike structures, water density and polarization profiles perpendicular to the surface, and the two-dimensional lattice match to ice. We expect that this work, with its strong focus on realistic surface models, will serve as a guide to the identification or design of substrates that can promote or discourage ice nucleation.

The limit of macroscopic homogeneous ice nucleation at the nanoscale

Nucleation in small volumes of water has garnered renewed interest due to the relevance of pore condensation and freezing under conditions of low partial pressures of water, such as in the upper troposphere. Molecular simulations can in principle provide insight on this process at the molecular scale that is challenging to achieve experimentally. However, there are discrepancies in the literature as to whether the rate in confined systems is enhanced or suppressed relative to bulk water at the same temperature and pressure. In this study, we investigate the extent to which the size of the critical nucleus and the rate at which it grows in thin films of water are affected by the thickness of the film. Our results suggest that nucleation remains bulk-like in films that are barely large enough accommodate a critical nucleus. This conclusion seems robust to the presence of physical confining boundaries. We also discuss the difficulties in unambiguously determining homogeneous nucleation rates in nanoscale systems, owing to the challenges in defining the volume. Our results suggest any impact on a film's thickness on the rate is largely inconsequential for present day experiments.

Characterizing Surface Ice-Philicity Using Molecular Simulations and Enhanced Sampling

The formation of ice, which plays an important role in diverse contexts ranging from cryopreservation to atmospheric science, is often mediated by solid surfaces. Although surfaces that interact favorably with ice (relative to liquid water) can facilitate ice formation by lowering nucleation barriers, the molecular characteristics that confer icephilicity to a surface are complex and incompletely understood. To address this challenge, here we introduce a robust and computationally efficient method for characterizing surface ice-philicity that combines molecular simulations and enhanced sampling techniques to quantify the free energetic cost of increasing surface-ice contact at the expense of surface-water contact. Using this method to characterize the ice-philicity of a family of model surfaces that are lattice matched with ice but vary in their polarity, we find that the nonpolar surfaces are moderately ice-phobic, whereas the polar surfaces are highly ice-philic. In contrast, for surfaces that display no complementarity to the ice lattice, we find that ice-philicity is independent of surface polarity and that both nonpolar and polar surfaces are moderately ice-phobic. Our work thus provides a prescription for quantitatively characterizing surface ice-philicity and sheds light on how ice-philicity is influenced by lattice matching and polarity.

A theory for the stabilization of polar crystal surfaces by a liquid environment

Polar crystal surfaces play an important role in the functionality of many materials and have been studied extensively over many decades. In this article, a theoretical framework is presented that extends existing theories by placing the surrounding solution environment on an equal footing with the crystal itself; this is advantageous, e.g., when considering processes such as crystal growth from solution. By considering the polar crystal as a stack of parallel plate capacitors immersed in a solution environment, the equilibrium adsorbed surface charge density is derived by minimizing the free energy of the system. In analogy to the well-known diverging surface energy of a polar crystal surface at zero temperature, for a crystal in solution it is shown that the "polar catastrophe" manifests as a diverging free energy cost to perturb the system from equilibrium. Going further than existing theories, the present formulation predicts that fluctuations in the adsorbed surface charge density become increasingly suppressed with increasing crystal thickness. We also show how, in the slab geometry often employed in both theoretical and computational studies of interfaces, an electric displacement field emerges as an electrostatic boundary condition, the origins of which are rooted in the slab geometry itself, rather than the use of periodic boundary conditions. This aspect of the work provides a firmer theoretical basis for the recent observation that standard "slab corrections" fail to correctly describe, even qualitatively, polar crystal surfaces in solution.

Accurate prediction of ice nucleation from room temperature water

Crystal nucleation is one of the most fundamental processes in the physical sciences and almost always occurs heterogeneously with the aid of a nucleating substrate. No example of nucleation is more ubiquitous and impactful than the formation of ice, vital to fields as diverse as geology, biology, aeronautics, and climate science. However, despite considerable effort, we still cannot predict a priori the efficacy of a nucleating agent. Here we utilize deep learning methods to accurately predict nucleation ability from images of room temperature liquid water-generated from molecular dynamics simulations-on a broad range of substrates. The resulting model, named IcePic, can rapidly and accurately infer nucleation ability, eliminating the requirement for either notoriously expensive simulations or direct experimental measurement. In an online poll, IcePic was found to significantly outperform humans in predicting the ice nucleating efficacy of materials. By analyzing the typical errors made by humans, as well as the application of reverse interpretation methods, physical insights into the role the water contact layer plays in ice nucleation have been obtained. Moving forward, we suggest that IcePic can be used as an easy, cheap, and rapid way to discern the nucleation ability of substrates, also with potential for learning other properties related to interfacial water.

Chemical Nature of Heterogeneous Electrofreezing of Supercooled Water Revealed on Polar (Pyroelectric) Surfaces

The ability to control the icing temperature of supercooled water (SCW) is of supreme importance in subfields of pure and applied sciences. The ice freezing of SCW can be influenced heterogeneously by electric effects, a process known as electrofreezing. This effect was first discovered during the 19th century; however, its mechanism is still under debate. In this Account we demonstrate, by capitalizing on the properties of polar crystals, that heterogeneous electrofreezing of SCW is a chemical process influenced by an electric field and specific ions. Polar crystals possess a net dipole moment. In addition, they are pyroelectric, displaying short-lived surface charges at their hemihedral faces at the two poles of the crystals as a result of temperature changes. Accordingly, during cooling or heating, an electric field is created, which is negated by the attraction of compensating charges from the environment. This process had an impact in the following experiments. The icing temperatures of SCW within crevices of polar crystals are higher in comparison to icing temperatures within crevices of nonpolar analogs. The role played by the electric effect was extricated from other effects by the performance of icing experiments on the surfaces of pyroelectric quasi-amorphous SrTiO₃. During those studies it was found that on positively charged surfaces the icing temperature of SCW is elevated, whereas on negatively charged surfaces it is reduced. Following investigations discovered that the icing temperature of SCW is impacted by an ionic current created within a hydrated layer on top of hydrophilic faces residing parallel to the polar axes of the crystals. In the absence of such current on analogous hydrophobic surfaces, the pyroelectric effect does not influence the icing temperature of SCW. Those results implied that electrofreezing of SCW is a process influenced by specific compensating ions attracted by the pyroelectric field from the aqueous solution. When freezing experiments are performed in an open atmosphere, bicarbonate and hydronium ions, created by the dissolution of atmospheric CO₂ in water, influence the icing temperature. The bicarbonate ions, when attracted by positively charged pyroelectric surfaces, elevate the icing temperature, whereas their counterparts, hydronium ions, when attracted by the negatively charged surfaces reduce the icing temperature. Molecular dynamic simulations suggested that bicarbonate ions, concentrated within the near positively charged interfacial layer, self-assemble with water molecules to create stabilized slightly distorted “ice-like” hexagonal assemblies which mimic the hexagons of the crystals of ice. This occurs by replacing, within those ice-like hexagons, two hydrogen bonds of water by C–O bonds of the HCO₃^– ion. On the basis of these simulations, it was predicted and experimentally confirmed that other trigonal planar ions such as NO₃^–, guanidinium⁺, and the quasi-hexagonal biguanidinium⁺ ion elevate the icing temperature. These ions were coined as “ice makers”. Other ions including hydronium, Cl^–, and SO₄^–2 interfere with the formation of ice-like assemblies and operate as “ice breakers”. The higher icing temperatures induced within the crevices of the hydrophobic polar crystals in comparison to the nonpolar analogs can be attributed to the proton ordering of the water molecules. In contrast, the icing temperatures on related hydrophilic surfaces are influenced both by compensating charges and by proton ordering.

Can molecular simulations reliably compare homogeneous and heterogeneous ice nucleation?

In principle, the answer to the posed titular question is undoubtedly "yes." But in practice, requisite reference data for homogeneous systems have been obtained with a treatment of intermolecular interactions that is different from that typically employed for heterogeneous systems. In this article, we assess the impact of the choice of truncation scheme when comparing water in homogeneous and inhomogeneous environments. Specifically, we use explicit free energy calculations and a simple mean field analysis to demonstrate that using the "cut-and-shift" version of the Lennard-Jones potential (common to most simple point charge models of water) results in a systematic increase in the melting temperature of ice I_h. In addition, by drawing an analogy between a change in cutoff and a change in pressure, we use existing literature data for homogeneous ice nucleation at negative pressures to suggest that enhancements due to heterogeneous nucleation may have been overestimated by several orders of magnitude.

Self-consistent determination of long-range electrostatics in neural network potentials

Machine learning has the potential to revolutionize the field of molecular simulation through the development of efficient and accurate models of interatomic interactions. Neural networks can model interactions with the accuracy of quantum mechanics-based calculations, but with a fraction of the cost, enabling simulations of large systems over long timescales. However, implicit in the construction of neural network potentials is an assumption of locality, wherein atomic arrangements on the nanometer-scale are used to learn interatomic interactions. Because of this assumption, the resulting neural network models cannot describe long-range interactions that play critical roles in dielectric screening and chemical reactivity. Here, we address this issue by introducing the self-consistent field neural network - a general approach for learning the long-range response of molecular systems in neural network potentials that relies on a physically meaningful separation of the interatomic interactions - and demonstrate its utility by modeling liquid water with and without applied fields.

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.

Molecular understanding of ion rejection in the freezing of aqueous solutions

In this work, we investigate the microscopic mechanism of ion rejection phenomena during the freezing of aqueous NaCl solutions through molecular dynamics simulations. It is found that the hydration energy for the ion-water interaction is stronger than that between ions and ice, which is the fundamental reason giving rise to the phenomenon of ion rejection. The probability of ions being rejected by ice is determined by the competition between the energy barrier at the ice-water interface and the thermal effect. The ion rejection rate increases with increasing temperature. Furthermore, it is found that the rejection rate of Na+ is higher than that of Cl- because of the relatively large hydration energy difference between Na+-water and Na+-ice interactions. The role of temperature in the applications of ion rejection in freeze desalination is also discussed.

Macroscopic surface charges from microscopic simulations

Attaining accurate average structural properties in a molecular simulation should be considered a prerequisite if one aims to elicit meaningful insights into a system's behavior. For charged surfaces in contact with an electrolyte solution, an obvious example is the density profile of ions along the direction normal to the surface. Here, we demonstrate that, in the slab geometry typically used in simulations, imposing an electric displacement field D determines the integrated surface charge density of adsorbed ions at charged interfaces. This allows us to obtain macroscopic surface charge densities irrespective of the slab thickness used in our simulations. We also show that the commonly used Yeh-Berkowitz method and the "mirrored slab" geometry both impose vanishing integrated surface charge densities. We present results both for relatively simple rocksalt (1 1 1) interfaces and the more complex case of kaolinite's basal faces in contact with an aqueous electrolyte solution.

Effects of Inorganic Ions on Ice Nucleation by the Al Surface of Kaolinite Immersed in Water

Molecular dynamics simulations are employed to investigate the influence of inorganic salts on ice nucleation by the Al surface of kaolinite, terminated with hydroxyl groups. Seven salt solutions (LiI(Cl), NaI(Cl), KI(Cl), and NH₄I) are considered. Simulations were performed at 300 K to obtain equilibrium surface-ion and surface-water density profiles. These simulations show no specific ion adsorption at the kaolinite surface. There are weak surface-ion correlations, with cations preferring to be closer to the surface than the anions. At a supercooling of 26 K (taking account of freezing point depression), 1 M salt solutions slowed ice nucleation by a factor of 2-3 compared with pure water and significantly reduced the rate of ice growth after nucleation. All salt solutions had similar influences on ice nucleation, and no specific ion effects were identified. Ice nucleation simulations for 1 M NaI(Cl), KI(Cl), and LiI solutions were performed for a range of temperatures. In all cases, the supercooling required for ice nucleation was larger by ∼1-6 K, after accounting for freezing point depression, than that required for pure water. For 1 M LiI solution an earlier laboratory study using kaolin as ice nucleating particles (INP) reported that the supercooling required for ice nucleation was ∼11 K smaller than that required for pure water. Our simulation results are not consistent with this finding. In this paper, we report new laboratory results for 1 M LiI solution employing kaolinite as INP. In our experiments ice nucleation in the LiI solution required the same supercooling as pure water, which is more consistent with our simulations.

Hydrogen polarity of interfacial water regulates heterogeneous ice nucleation

Using all-atomic molecular dynamics (MD) simulations, we show that the structure of interfacial water (IW) induced by substrates characterizes the ability of a substrate to nucleate ice. We probe the shape and structure of ice nuclei and the corresponding supercooling temperatures to measure the ability of IW with various hydrogen polarities for ice nucleation, and find that the hydrogen polarization of IW even with the ice-like oxygen lattice increases the contact angle of the ice nucleus on IW, thus lifting the free energy barrier of heterogeneous ice nucleation. The results show that not only the oxygen lattice order but the hydrogen disorder of IW on substrates are required to effectively facilitate the freezing of top water.

A force field of Li+, Na+, K+, Mg2+, Ca2+, Cl-, and SO4 2- in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions

In this work, a force field for several ions in water is proposed. In particular, we consider the cations Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ and the anions Cl^- and SO₄ ^2-. These ions were selected as they appear in the composition of seawater, and they are also found in biological systems. The force field proposed (denoted as Madrid-2019) is nonpolarizable, and both water molecules and sulfate anions are rigid. For water, we use the TIP4P/2005 model. The main idea behind this work is to further explore the possibility of using scaled charges for describing ionic solutions. Monovalent and divalent ions are modeled using charges of 0.85 and 1.7, respectively (in electron units). The model allows a very accurate description of the densities of the solutions up to high concentrations. It also gives good predictions of viscosities up to 3 m concentrations. Calculated structural properties are also in reasonable agreement with the experiment. We have checked that no crystallization occurred in the simulations at concentrations similar to the solubility limit. A test for ternary mixtures shows that the force field provides excellent performance at an affordable computer cost. In summary, the use of scaled charges, which could be regarded as an effective and simple way of accounting for polarization (at least to a certain extend), improves the overall description of ionic systems in water. However, for purely ionic systems, scaled charges will not adequately describe neither the solid nor the melt.