Plastic crystal phases of simple water models

Diversity-driven, efficient exploration of a MOF design space to optimize MOF properties

Metal-organic frameworks (MOFs) promise to engender technology-enabling properties for numerous applications. However, one significant challenge in MOF development is their overwhelmingly large design space, which is intractable to fully explore even computationally. To find diverse optimal MOF designs without exploring the full design space, we develop Vendi Bayesian optimization (VBO), a new algorithm that combines traditional Bayesian optimization with the Vendi score, a recently introduced interpretable diversity measure. Both Bayesian optimization and the Vendi score require a kernel similarity function, we therefore also introduce a novel similarity function in the space of MOFs that accounts for both chemical and structural features. This new similarity metric enables VBO to find optimal MOFs with properties that may depend on both chemistry and structure. We statistically assessed VBO by its ability to optimize three NH3-adsorption dependent performance metrics that depend, to different degrees, on MOF chemistry and structure. With ten simulated campaigns done for each metric, VBO consistently outperformed random search to find high-performing designs within a 1000-MOF subset for (i) NH3 storage, (ii) NH3 removal from membrane plasma reactors, and (iii) NH3 capture from air. Then, with one campaign dedicated to finding optimal MOFs for NH3 storage in a "hybrid" ∼10 000-MOF database, we identify twelve extant and eight hypothesized MOF designs with potentially record-breaking working capacity ΔN NH3 between 300 K and 400 K at 1 bar. Specifically, the best MOF designs are predicted to (i) achieve ΔN NH3 values between 23.6 and 29.3 mmol g-1, potentially surpassing those that MOFs previously experimentally tested for NH3 adsorption would have at the proposed operation conditions, (ii) be thermally stable at the operation conditions and (iii) require only ca. 10% of the energy content in NH3 to release the stored molecule from the MOF. Finally, the analysis of the generated simulation data during the search indicates that a pore size of around 10 Å, a heat of adsorption around 33 kJ mol-1, and the presence of Ca could be part of MOF design rules that could help optimize NH3 working capacity at the proposed operation conditions.

Substantial breakdown of the hydrogen-bonding network, local density inhomogeneities and fluid-liquid structural transitions in supercritical octanol-1: A molecular dynamics investigation

Molecular dynamics simulations have been employed to explore the hydrogen-bonding structure and dynamics in supercritical octanol-1 at a near-critical temperature and up to high densities and pressures. A substantial breakdown of the hydrogen-bonding network when going from ambient-liquid to supercritical conditions is revealed. The fraction of the non-hydrogen bonded molecules significantly increases in supercritical octanol-1, and a substantial decrease in the intermittent hydrogen-bond lifetime is observed. This behavior is also reflected on the maximum local density augmentation, which is comparable to the values obtained for non-polar and non-hydrogen bonded fluids. The existence of a structural transition from an inhomogeneous fluid phase to a soft-liquid one at densities higher than 2.0 ρc is also revealed. At higher densities, a significant change in the reorientational relaxation process is observed, reflected on the significant increase in the ratio of the Legendre reorientational times τ1R/τ2R. The latter becomes much higher than the value predicted by the Debye model of diffusive reorientation and the corresponding ratio for ambient liquid octanol-1. The non-polar tail of octanol-1 under supercritical conditions reorients more slowly in comparison with the polar tail. Interestingly, the opposite behavior is observed for the ambient liquid, further verifying the strong effect of the breakdown of the hydrogen bonding network on the properties of supercritical octanol-1. In accordance with the above-mentioned findings, the static dielectric constant of supercritical octanol-1 is very low even at high densities and pressures, comparable to the values obtained for non-polar and non-hydrogen bonded fluids.

Hydrogen-bond linking is crucial for growing ice VII embryos

We use molecular dynamics simulations to examine the homogeneous nucleation of ice VII from metastable liquid water. An unsupervised machine learning classification identifies two distinct local structures composing Ice VII nuclei. The seeding method, combined with the classical nucleation theory (CNT), predicts the solid-liquid interfacial free energy, consistent with the value from the mold integration method. Meanwhile, the nucleation rates estimated from the CNT framework and brute force spontaneous nucleations are inconsistent, and we discuss the reasons for this discrepancy. Structural and dynamical heterogeneities suggest that the potential birthplace for an ice VII embryo is relatively ordered, although not necessarily relatively immobile. Moreover, we demonstrate that without the formation of hydrogen-bond links, ice VII embryos do not grow.

Close-Packed Ices in Nanopores

Water molecules in any of the ice polymorphs organize themselves into a perfect four-coordinated hydrogen-bond network at the expense of dense packing. Even at high pressures, there seems to be no way to reconcile the ice rules with the close packing. Here, we report several close-packed ice phases in carbon nanotubes obtained from molecular dynamics simulations of two different water models. Typically they are in plastic states at high temperatures and are transformed into the hydrogen-ordered ice, keeping their close-packed structures at lower temperatures. The close-packed structures of water molecules in carbon nanotubes are identified with those of spheres in a cylinder. We present design principles of hydrogen-ordered, close-packed structures of ice in nanotubes, which suggest many possible dense ice forms with or without nonzero polarization. In fact, some of the simulated ices are found to exhibit ferroelectric ordering upon cooling.

Electrolyte Permeability in Plastic Ice VII

Deep brines in water-rich planets form when electrolytes diffuse from the rocky interior through layers of thick dense ice such as ice VII and the hypothesized plastic ice VII. We perform classical molecular dynamics simulations of Li⁺, Na⁺, and K⁺ alkali ions and F^- and Cl^- halide ions in plastic ice VII at conditions similar to water-rich super-Earths, icy moons, and ocean worlds. We find that plastic ice VII is permeable to electrolytes on geological timescales. Diffusion occurs via jumps between adjacent voids in the bcc crystal structure and is governed by molecular rotations. An exception to this mechanism is Na⁺ which, at variance with other ions, can substitute water molecules on lattice positions. The bulk modulus of pristine plastic ice VII is dependent on the pace of molecular rotations: when the rotations are slow, the bulk modulus is 1 order of magnitude lower compared to the bulk modulus at conditions of fast rotations, hence providing direct evidence of the role of molecular rotations in determining elastic properties. Electrolytes affect the bulk modulus only at high-concentration conditions and slow molecular rotations. Our results show that plastic ice VII may facilitate the development of brines in water-rich planets and ocean worlds, with a clear significance for their potential to support exobiology and for the chemical evolution of their aqueous reservoirs.

Molecular rotations trigger a glass-to-plastic fcc heterogeneous crystallization in high-pressure water

We report a molecular dynamics study of the heterogeneous crystallization of high-pressure glassy water using (plastic) ice VII as a substrate. We focus on the thermodynamic conditions P ∈ [6-8] GPa and T ∈ [100-500] K, at which (plastic) ice VII and glassy water are supposed to coexist in several (exo)planets and icy moons. We find that (plastic) ice VII undergoes a martensitic phase transition to a (plastic) fcc crystal. Depending on the molecular rotational lifetime τ, we identify three rotational regimes: for τ > 20 ps, crystallization does not occur; for τ ∼ 15 ps, we observe a very sluggish crystallization and the formation of a considerable amount of icosahedral environments trapped in a highly defective crystal or in the residual glassy matrix; and for τ < 10 ps, crystallization takes place smoothly, resulting in an almost defect-free plastic fcc solid. The presence of icosahedral environments at intermediate τ is of particular interest as it shows that such a geometry, otherwise ephemeral at lower pressures, is, indeed, present in water. We justify the presence of icosahedral structures based on geometrical arguments. Our results represent the first study of heterogeneous crystallization occurring at thermodynamic conditions of relevance for planetary science and unveil the role of molecular rotations in achieving it. Our findings (i) show that the stability of plastic ice VII, widely reported in the literature, should be reconsidered in favor of plastic fcc, (ii) provide a rationale for the role of molecular rotations in achieving heterogeneous crystallization, and (iii) represent the first evidence of long-living icosahedral structures in water. Therefore, our work pushes forward our understanding of the properties of water.

Observation of a Plastic Crystal in Water-Ammonia Mixtures under High Pressure and Temperature

Solid mixtures of ammonia and water, the so-called ammonia hydrates, are thought to be major components of solar and extra-solar icy planets. We present here a thorough characterization of the recently reported high pressure (P)-temperature (T) phase VII of ammonia monohydrate (AMH) using Raman spectroscopy, X-ray diffraction, and quasi-elastic neutron scattering (QENS) experiments in the ranges 4-10 GPa, 450-600 K. Our results show that AMH-VII exhibits common structural features with the disordered ionico-molecular alloy (DIMA) phase, stable above 7.5 GPa at 300 K: both present a substitutional disorder of water and ammonia over the sites of a body-centered cubic lattice and are partially ionic. The two phases however markedly differ in their hydrogen dynamics, and QENS measurements show that AMH-VII is characterized by free molecular rotations around the lattice positions which are quenched in the DIMA phase. AMH-VII is thus a peculiar crystalline solid in that it combines three types of disorder: substitutional, compositional, and rotational.

Fingerprints of the Crossing of the Frenkel and Melting Line on the Properties of High-Pressure Supercritical Water

Using molecular dynamics simulations in combination with the two-phase thermodynamic model, we reveal novel characteristic fingerprints of the crossing of the Frenkel and melting line on the properties of high-pressure water at a near-critical temperature (1.03T_c). The crossing of the Frenkel line at about 1.17 GPa is characterized by a crossover in the rotational and translational entropy ratio S^rot/S^trans, indicating a change in the coupling between translational and rotational motions which is also reflected in the shape of the rotational density of states. The observed isosbestic points in the translational and rotational density of states are also blue-shifted at density and pressure conditions higher than the ones corresponding to the Frenkel line. The first-order phase transition from a rigid liquid to a face-centered cubic plastic crystal phase at about 8.5 GPa is reflected in the discontinuous changes in the translational and rotational entropy, particularly in the significant increase of the ratio S^rot/S^trans. A noticeable discontinuous increase of the dielectric constant has also been revealed when crossing this melting line, which is attributed to the different arrangement of the water molecules in the plastic crystal phase. The reorientational dynamics in the plastic crystal phase is faster in comparison with the "rigid" liquid-like phase, but it remains unchanged upon a further pressure increase in the range of 8.5-11 GPa.

Temperature- and pressure-dependence of the hydrogen bond network in plastic ice VII

We model, via classical molecular dynamics simulations, the plastic phase of ice VII across a wide range of the phase diagram of interest for planetary investigations. Although structural and dynamical properties of plastic ice VII are mostly independent on the thermodynamic conditions, the hydrogen bond network (HBN) acquires a diverse spectrum of topologies distinctly different from that of liquid water and of ice VII simulated at the same pressure. We observe that the HBN topology of plastic ice carries some degree of similarity with the crystal phase, stronger at thermodynamic conditions proximal to ice VII, and gradually lessening upon approaching the liquid state. Our results enrich our understanding of the properties of water at high pressure and high temperature, and may help in rationalizing the geology of

High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII

Simultaneous high-temperature and high-pressure studies reveal phase transformation of bulk liquid water to an ice-VII-like structure having an eight coordination. It was demonstrated through this numerical study that the observed high-temperature and high-pressure phase of water obtained upon shock compression and equilibration has high rotational diffusion and thereby the hydrogen dynamics of these crystal structures are significantly complex compared with ice VII. The current work provides new characterization methods for the numerically observed plastic crystal phase of ice at the boundary of the liquid water and ice VII phases in which the molecules have a defined lattice position but rotate freely. It is anticipated that the present work will provide important data and guide new theoretical and experimental investigations in the search for plastic crystal phases of water. The power spectra plots of bulk liquid water subjected to different temperature and pressure conditions have also been presented in this numerical study, demonstrating significant differences between these high-temperature and high-pressure shock-equilibrated phases and those of pure ice VII at 10 GPa and liquid water at ambient temperature and pressure, as well as at elevated pressures and temperatures.

On the Different Faces of the Supercritical Phase of Water at a Near-Critical Temperature: Pressure-Induced Structural Transitions Ranging from a Gaslike Fluid to a Plastic Crystal Polymorph

The present study reports a systematic analysis of a wide variety of structural, thermodynamic, and dynamic properties of supercritical water along the near-critical isotherm of T = 1.03T_c and up to extreme pressures, using molecular dynamics and Monte Carlo simulations. The methodology employed provides solid evidence about the existence of a structural transition from a liquidlike fluid to a compressed, tightly packed liquid, in the density and pressure region around 3.4ρ_c and 1.17 GPa, introducing an alternative approach to locate the crossing of the Frenkel line. Around 8.5 GPa another transition to a face-centered-cubic plastic crystal polymorph with density 5.178ρ_c is also observed, further confirmed by Gibbs free energy calculations using the two-phase thermodynamic model. The isobaric heat capacity maximum, closely related to the crossing of the Widom line, has also been observed around 0.8ρ_c, where the local density augmentation is also maximized. Another structural transition has been observed at 0.2ρ_c, related to the transformation of the fluid to a dilute gas at lower densities. These findings indicate that a near-critical isotherm can be divided into different domains where supercritical water exhibits distinct behavior, ranging from a gaslike one to a plastic crystal one.

Phase Diagram of a Deep Potential Water Model

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII^{''} and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

Solvation of simple ions in water at extreme conditions

The interaction of ions and water at high pressure and temperature plays a critical role in Earth and planetary science yet remains poorly understood. Aqueous fluids affect geochemical properties ranging from water phase stability to mineral solubility and reactivity. Here, we report first-principles molecular dynamics simulations of mono-valent ions (Li⁺, K⁺, Cl^-) as well as NaCl in liquid water at temperatures and pressures relevant to the Earth's upper mantle (11 GPa, 1000 K) and concentrations in the dilute limit (0.44-0.88 m), in the regime of ocean salinity. We find that, at extreme conditions, the average structural and vibrational properties of water are weakly affected by the presence of ions, beyond the first solvation shell, similar to what was observed at ambient conditions. We also find that the ionic conductivity of the liquid increases in the presence of ions by less than an order of magnitude and that the dielectric constant is moderately reduced by at most ∼10% at these conditions. Our findings may aid in the parameterization of deep earth water models developed to describe water-rock reactions.

Structure and dynamics of water plastic crystals from computer simulations

Water has a rich phase diagram with several crystals, as confirmed by experiments. High-pressure and high-temperature water is of interest for Earth's mantle and exoplanetary investigations. It is in this region of the phase diagram of water that new plastic crystal phases of water have been revealed via computer simulations by both classical forcefields and ab initio calculations. However, these plastic phases still remain elusive in experiments. Here, we present a complete characterization of the structure, dynamics, and thermodynamics of the computational plastic crystal phases of water using molecular dynamics and the two-phase thermodynamic method and uncover the interplay between them. The relaxation times of different reorientational correlation functions are obtained for the hypothetical body-centered-cubic and face-centered-cubic plastic crystal phases of water at T = 440 K and P = 8 GPa. Results are compared to a high pressure liquid and ice VII phases to improve the understanding of the plastic crystal phases. Entropy results indicate that the fcc crystal is more stable compared to the bcc structure under the studied conditions.

Melting Curve and Isostructural Solid Transition in Superionic Ice

The phase diagram and melting curve of water ice is investigated up to 45 GPa and 1600 K by synchrotron x-ray diffraction in the resistively and laser heated diamond anvil cell. Our melting data evidence a triple point at 14.6 GPa, 850 K. The latter is shown to be related to a first-order solid transition from the dynamically disordered form of ice VII, denoted ice VII^{'}, toward a high-temperature phase with the same bcc oxygen lattice but larger volume and higher entropy. Our experiments are compared to ab initio molecular dynamics simulations, enabling us to identify the high-temperature bcc phase with the predicted superionic ice VII^{''} phase [J.-A. Hernandez and R. Caracas, Phys. Rev. Lett. 117, 135503 (2016).PRLTAO0031-900710.1103/PhysRevLett.117.135503].

Coexistence of plastic and partially diffusive phases in a helium-methane compound

Helium and methane are major components of giant icy planets and are abundant in the universe. However, helium is the most inert element in the periodic table and methane is one of the most hydrophobic molecules, thus whether they can react with each other is of fundamental importance. Here, our crystal structure searches and first-principles calculations predict that a He3CH4 compound is stable over a wide range of pressures from 55 to 155 GPa and a HeCH4 compound becomes stable around 105 GPa. As nice examples of pure van der Waals crystals, the insertion of helium atoms changes the original packing of pure methane molecules and also largely hinders the polymerization of methane at higher pressures. After analyzing the diffusive properties during the melting of He3CH4 at high pressure and high temperature, in addition to a plastic methane phase, we have discovered an unusual phase which exhibits coexistence of diffusive helium and plastic methane. In addition, the range of the diffusive behavior within the helium-methane phase diagram is found to be much narrower compared to that of previously predicted helium-water compounds. This may be due to the weaker van der Waals interactions between methane molecules compared to those in helium-water compounds, and that the helium-methane compound melts more easily.

Structure and phase behavior of high-density ice from molecular-dynamics simulations with the ReaxFF potential

We report a molecular dynamics simulation study of dense ice modeled by the reactive force field (ReaxFF) potential, focusing on the possibility of phase changes between crystalline and plastic phases as observed in earlier simulation studies with rigid water models. It is demonstrated that the present model system exhibits phase transitions, or crossovers, among ice VII and two plastic ices with face-centered cubic (fcc) and body-centered cubic (bcc) lattice structures. The phase diagram derived from the ReaxFF potential is different from those of the rigid water models in that the bcc plastic phase lies on the high-pressure side of ice VII and does the fcc plastic phase on the low-pressure side of ice VII. The phase boundary between the fcc and bcc plastic phases on the pressure, temperature plane extends to the high-temperature region from the triple point of ice VII, fcc plastic, and bcc plastic phases. Proton hopping, i.e., delocalization of a proton, along between two neighboring oxygen atoms in dense ice is observed for the ReaxFF potential but only at pressures and temperatures both much higher than those at which ice VII-plastic ice transitions are observed.

Computational Prediction of Novel Ice Phases: A Perspective

Although computational prediction of new ice phases is a niche field in water science, the scientific subject itself is representative of two important areas in physical chemistry, namely, statistical thermodynamics and molecular simulations. The prediction of a variety of novel ice phases has also attracted general public interest since the 1980s. In particular, the prediction of low-dimensional ice phases has gained momentum since the confirmation of a number of low-dimensional "computer ice" phases in the laboratory over the past decade. In this Perspective, the research advancements in computational prediction of novel ice phases over the past few years are reviewed. Particular attention is placed on new ice phases whose physical properties or dimensional structures are distinctly different from conventional bulk ices. Specific topics include the (i) formation of superionic ices, (ii) electrofreezing of water under high pressure and in a high external electric field, (iii) prediction of low-density porous ice at strongly negative pressure, (iv) ab initio computational study of two-dimensional (2D) ice under nanoscale confinement, and (v) 2D ices formed on a solid surface near ambient temperature without nanoscale confinement. Clearly, the formation of most of these novel ice phases demands certain extreme conditions. Ongoing challenges and new opportunities for predicting new ice phases from either classical molecular dynamics simulation or high-level ab initio computation are discussed.

Plastic and superionic phases in ammonia-water mixtures at high pressures and temperatures

The interiors of giant icy planets depend on the properties of hot, dense mixtures of the molecular ices water, ammonia, and methane. Here, we discuss results from first-principles molecular dynamics simulations up to 500 GPa and 7000 K for four different ammonia-water mixtures that correspond to the stable stoichiometries found in solid ammonia hydrates. We show that all mixtures support the formation of plastic and superionic phases at elevated pressures and temperatures, before eventually melting into molecular or ionic liquids. All mixtures' melting lines are found to be close to the isentropes of Uranus and Neptune. Through local structure analyses we trace and compare the evolution of chemical composition and longevity of chemical species across the thermally activated states. Under specific conditions we find that protons can be less mobile in the fluid state than in the (colder, solid) superionic regime.

Lennard-Jones Parameters Determined to Reproduce the Solubility of NaCl and KCl in SPC/E, TIP3P, and TIP4P/2005 Water

Most classical nonpolarizable ion potential models underestimate the solubility values of NaCl and KCl in water significantly. We determine Lennard-Jones parameters of Na⁺, K⁺, and Cl^- that reproduce the solubility as well as the hydration free energy in dilute aqueous solutions for three water potential models, SPC/E, TIP3P, and TIP4P/2005. The ion-oxygen distance in the solution and the cation-anion distance in salt are also considered in the parametrization. In addition to the target properties, the hydration enthalpy, hydration entropy, self-diffusion coefficient, coordination number, lattice energy, enthalpy of solution, density, viscosity, and number of contact ion pairs are calculated for comparison with 17 frequently used or recently developed ion potential models. The overall performance of each ion model is represented by a global score using a scheme that was originally developed for comparison of water potential models. The global score is better for our models than for the other 17 models not only because of the quite good prediction for the solubility but also because of the relatively small deviation from the experimental value for many of the other properties.

Anomalous hydrogen dynamics of the ice VII-VIII transition revealed by high-pressure neutron diffraction

Above 2 GPa the phase diagram of water simplifies considerably and exhibits only two solid phases up to 60 GPa, ice VII and ice VIII. The two phases are related to each other by hydrogen ordering, with the oxygen sublattice being essentially the same. Here we present neutron diffraction data to 15 GPa which reveal that the rate of hydrogen ordering at the ice VII-VIII transition decreases strongly with pressure to reach timescales of minutes at 10 GPa. Surprisingly, the ordering process becomes more rapid again upon further compression. We show that such an unusual change in transition rate can be explained by a slowing down of the rotational dynamics of water molecules with a simultaneous increase of translational motion of hydrogen under pressure, as previously suspected. The observed cross-over in the hydrogen dynamics in ice is likely the origin of various hitherto unexplained anomalies of ice VII in the 10-15 GPa range reported by Raman spectroscopy, X-ray diffraction, and proton conductivity.

On the role of intermolecular vibrational motions for ice polymorphs. II. Atomic vibrational amplitudes and localization of phonons in ordered and disordered ices

We investigate the vibrational amplitudes and the degree of the phonon localization in 19 ice forms, both crystalline and amorphous, by a quasi-harmonic approximation with a reliable classical intermolecular interaction model for water. The amplitude in the low pressure ices increases with compression, while the opposite trend is observed in the medium and high pressure ices. The amplitude of the oxygen atom does not differ from that of hydrogen in low pressure ices apart from the contribution from the zero-point vibrations. This is accounted for by the coherent but opposite phase motions in the mixed translational and rotational vibrations. A decoupling of translation-dominant and rotation-dominant motions significantly reduces the vibrational amplitudes in any ice form. The amplitudes in ice III are found to be much larger than any other crystalline ice form. In order to investigate the vibrational mode characteristics, the moment ratio of the atomic displacements for individual phonon modes, called the inverse participation ratio, is calculated and the degree of the phonon localization in crystalline and amorphous ices is discussed. It is found that the phonon modes in the hydrogen-ordered ice forms are remarkably spread over the entire crystal having propagative or diffusive characteristic, while many localized modes appear at the edges of the vibrational bands, called dissipative modes, in the hydrogen-disordered counterparts. The degree of localization is little pronounced in low density amorphous and high density amorphous due to disordering of oxygen atoms.

Thermodynamics, dynamics, and structure of supercritical water at extreme conditions

Molecular dynamics (MD) simulations to understand the thermodynamic, dynamic, and structural changes in supercritical water across the Frenkel line and the melting line have been performed.

Translational and Rotational Diffusion in Liquid Water at Very High Pressure: A Simulation Study

Translational and rotational diffusion coefficients of liquid water have been computed from molecular dynamics simulation with a recent polarizable potential at 298, 400, and 550 K at very high pressure. At 298 K, the model reproduces the initial increase and the occurrence of a maximum for the translational and rotational diffusion coefficients when the pressure increases. At 400 and 550 K, translational and rotational diffusion coefficients are found to monotonically decrease when pressure increases in the gigapascal range, with the translational coefficient decreasing faster than the rotational one. At 400 K, such an evolution of the rotational diffusion coefficient contrasts with quasielastic neutron scattering results predicting a near independence of the rotational diffusion with a pressure increase above ≃0.5 GPa. An interpretation is proposed to explain this discrepancy. The pressure dependence of the translation-rotation coupling is analyzed. The anisotropy of rotational diffusion is investigated by computing the rotational diffusion tensor in a molecular system of axes and the reorientational correlation times of rank 1 and rank 2 of the inertia axes and of the OH bond vector. Deviation of the simulation data with respect to the predictions of the isotropic Debye model of rotational diffusion are quantified and can be used to estimate experimental rotational diffusion coefficients from experimental reorientational correlation times.

On the role of intermolecular vibrational motions for ice polymorphs I: Volumetric properties of crystalline and amorphous ices

Intermolecular vibrations and volumetric properties are investigated using the quasiharmonic approximation with the TIP4P/2005, TIP4P/Ice, and SPC/E potential models for most of the known crystalline and amorphous ice forms that have hydrogen-disordering. The ice forms examined here cover low pressure ices (hexagonal and cubic ice I, XVI, and hypothetical dtc ice), medium pressure ices (III, IV, V, VI, XII, hydrogen-disordered variant of ice II), and high pressure ice (VII) as well as the low density and the high density amorphous forms. We focus on the thermal expansivities and the isothermal compressibilities in the low temperature regime over a wide range of pressures calculated via the intermolecular vibrational free energies. Negative thermal expansivity appears only in the low pressure ice forms. The sign of the thermal expansivity is elucidated in terms of the mode Grüneisen parameters of the low frequency intermolecular vibrational motions. Although the band structure for the low frequency region of the vibrational density of state in the medium pressure ice has a close resemblance to that in the low pressure ice, its response against volume variation is opposite. We reveal that the mixing of translational and rotational motions in the low frequency modes plays a crucial role in the appearance of the negative thermal expansivity in the low pressure ice forms. The medium pressure ices can be further divided into two groups in terms of the hydrogen-bond network flexibility, which is manifested in the properties on the molecular rearrangement against volume variation, notably the isothermal compressibility.

Homology Modeling-Based in Silico Affinity Maturation Improves the Affinity of a Nanobody

Affinity maturation and rational design have a raised importance in the application of nanobody (VHH), and its unique structure guaranteed these processes quickly done in vitro. An anti-CD47 nanobody, Nb02, was screened via a synthetic phage display library with 278 nM of K_D value. In this study, a new strategy based on homology modeling and Rational Mutation Hotspots Design Protocol (RMHDP) was presented for building a fast and efficient platform for nanobody affinity maturation. A three-dimensional analytical structural model of Nb02 was constructed and then docked with the antigen, the CD47 extracellular domain (CD47^ext). Mutants with high binding affinity are predicted by the scoring of nanobody-antigen complexes based on molecular dynamics trajectories and simulation. Ultimately, an improved mutant with an 87.4-fold affinity (3.2 nM) and 7.36 °C higher thermal stability was obtained. These findings might contribute to computational affinity maturation of nanobodies via homology modeling using the recent advancements in computational power. The add-in of aromatic residues which formed aromatic-aromatic interaction plays a pivotal role in affinity and thermostability improvement. In a word, the methods used in this study might provide a reference for rapid and efficient in vitro affinity maturation of nanobodies.

Salt- and gas-filled ices under planetary conditions

In recent years, evidence has emerged that solid water can contain substantial amounts of guest species, such as small gas molecules-in gas hydrate structures-or ions-in salty ice structures-and that these 'filled' ice structures can be stable under pressures of tens of Gigapascals and temperatures of hundreds of Kelvins. The inclusion of guest species can strongly modify the density, vibrational, diffusive and conductivity properties of ice under high pressure, and promote novel exotic properties. In this review, we discuss our experimental findings and molecular dynamics simulation results on the structures formed by salt- and gas-filled ices, their unusual properties, and the unexpected dynamical phenomena observed under pressure and temperature conditions relevant for planetary interiors modelling. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Room temperature electrofreezing of water yields a missing dense ice phase in the phase diagram

Water can freeze into diverse ice polymorphs depending on the external conditions such as temperature (T) and pressure (P). Herein, molecular dynamics simulations show evidence of a high-density orthorhombic phase, termed ice χ, forming spontaneously from liquid water at room temperature under high-pressure and high external electric field. Using free-energy computations based on the Einstein molecule approach, we show that ice χ is an additional phase introduced to the state-of-the-art T–P phase diagram. The χ phase is the most stable structure in the high-pressure/low-temperature region, located between ice II and ice VI, and next to ice V exhibiting two triple points at 6.06 kbar/131.23 K and 9.45 kbar/144.24 K, respectively. A possible explanation for the missing ice phase in the T–P phase diagram is that ice χ is a rare polarized ferroelectric phase, whose nucleation/growth occurs only under very high electric fields.

Water can crystallize in different ice polymorphs according to temperature and pressure conditions. Here the authors predict by molecular dynamics simulations a new ice phase spontaneously forming at room temperature under high pressure and high electric field.

The effect of polymorphism on the structural, dynamic and dielectric properties of plastic crystal water: A molecular dynamics simulation perspective

We have employed molecular dynamics simulations based on the TIP4P/2005 water model to investigate the local structural, dynamical, and dielectric properties of the two recently reported body-centered-cubic and face-centered-cubic plastic crystal phases of water. Our results reveal significant differences in the local orientational structure and rotational dynamics of water molecules for the two polymorphs. The probability distributions of trigonal and tetrahedral order parameters exhibit a multi-modal structure, implying the existence of significant local orientational heterogeneities, particularly in the face-centered-cubic phase. The calculated hydrogen bond statistics and dynamics provide further indications of the existence of a strongly heterogeneous and rapidly interconverting local orientational structural network in both polymorphs. We have observed a hindered molecular rotation, much more pronounced in the body-centered-cubic phase, which is reflected by the decay of the fourth-order Legendre reorientational correlation functions and angular Van Hove functions. Molecular rotation, however, is additionally hindered in the high-pressure liquid compared to the plastic crystal phase. The results obtained also reveal significant differences in the dielectric properties of the polymorphs due to the different dipolar orientational correlation characterizing each phase.

Ab initio spectroscopy and ionic conductivity of water under Earth mantle conditions

The phase diagram of water at extreme conditions plays a critical role in Earth and planetary science, yet remains poorly understood. Here we report a first-principles investigation of the liquid at high temperature, between 11 GPa and 20 GPa-a region where numerous controversial results have been reported over the past three decades. Our results are consistent with the recent estimates of the water melting line below 1,000 K and show that on the 1,000-K isotherm the liquid is rapidly dissociating and recombining through a bimolecular mechanism. We found that short-lived ionic species act as charge carriers, giving rise to an ionic conductivity that at 11 GPa and 20 GPa is six and seven orders of magnitude larger, respectively, than at ambient conditions. Conductivity calculations were performed entirely from first principles, with no a priori assumptions on the nature of charge carriers. Despite frequent dissociative events, we observed that hydrogen bonding persists at high pressure, up to at least 20 GPa. Our computed Raman spectra, which are in excellent agreement with experiment, show no distinctive signatures of the hydronium and hydroxide ions present in our simulations. Instead, we found that infrared spectra are sensitive probes of molecular dissociation, exhibiting a broad band below the OH stretching mode ascribable to vibrations of complex ions.

Rapid freezing of water under dynamic compression

Understanding the behavior of materials at extreme pressures is a central issue in fields like aerodynamics, astronomy, and geology, as well as for advancing technological grand challenges such as inertial confinement fusion. Dynamic compression experiments to probe high-pressure states often encounter rapid phase transitions that may cause the materials to behave in unexpected ways, and understanding the kinetics of these phase transitions remains an area of great interest. In this review, we examine experimental and theoretical/computational efforts to study the freezing kinetics of water to a high-pressure solid phase known as ice VII. We first present a detailed analysis of dynamic compression experiments in which water has been observed to freeze on sub-microsecond time scales to ice VII. This is followed by a discussion of the limitations of currently available molecular and continuum simulation methods in modeling these experiments. We then describe how our phase transition kinetics models, which are based on classical nucleation theory, provide a more physics-based framework that overcomes some of these limitations. Finally, we give suggestions on future experimental and modeling work on the liquid-ice VII transition, including an outline of the development of a predictive multiscale model in which molecular and continuum simulations are intimately coupled.

Thermal conductivity of ice polymorphs: a computational study

Thermal transport in ice features an unusual response. In addition to its intrinsic scientific interest, an understanding of the mechanisms determining the thermal conductivity of ice might be relevant in climate modelling and planetary science. Accurate microscopic models can provide important molecular insight into these mechanisms. In this work, we quantify using molecular simulations and state of the art forcefields, the thermal conductivity of ice Ih, VI, VII and a plastic phase that has been proposed very recently at pressures in the GPa range. The TIP4P models used in this study underestimate significantly the thermal conductivity of ice Ih and ice VII, while they show good agreement with experimental measurements of ice VI. The discrepancies observed are examined by investigating the temperature dependence of the thermal conductivity. The simulations indicate that the models are too anharmonic and they potentially feature a higher structural disorder than the experimental systems. We suggest that at high pressures the simulated thermal conductivities can be rationalized in terms of the performance of the models in predicting the equation of state of ice. The thermal conductivity of the plastic phase is very similar to that of the coexisting ice VII. Since the water molecules in the plastic phase feature orientational disorder, these results indicate that the hydrogen bond network does not play a significant role in defining the thermal transport mechanisms of ice at high pressures.

Phase Diagram of TIP4P/2005 Water at High Pressure

We report a new ice phase that forms spontaneously at the interface between ice VII and liquid water in molecular dynamics simulations of TIP4P/2005 water. The new phase is structurally quite similar to an ice phase originally found to be a precursor in the course of the homogeneous nucleation of ice VII in liquid water. A part of the water molecules in these ice phases can rotate easily because the number of hydrogen bonds in them is less than four, and thus they can be regarded as partial plastic phases. A rough estimate suggests that these phases are thermodynamically more stable than either ice VI or ice VII for 3 GPa < P < 18 GPa at T = 300 K. Although the partial plastic phases would be metastable states at any point in the phase diagram of real water, they might be realized experimentally with the aid of dopants and/or solid surfaces.

Compression Freezing Kinetics of Water to Ice VII

Time-resolved x-ray diffraction (XRD) of compressed liquid water shows transformation to ice VII in 6 nsec, revealing crystallization rather than amorphous solidification during compression freezing. Application of classical nucleation theory indicates heterogeneous nucleation and one-dimensional (e.g., needlelike) growth. These first XRD data demonstrate rapid growth kinetics of ice VII with implications for fundamental physics of diffusion-mediated crystallization and thermodynamic modeling of collision or impact events on ice-rich planetary bodies.

Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.

Ice VII from aqueous salt solutions: From a glass to a crystal with broken H-bonds

It has been known for decades that certain aqueous salt solutions of LiCl and LiBr readily form glasses when cooled to below ≈160 K. This fact has recently been exploited to produce a « salty » high-pressure ice form: When the glass is compressed at low temperatures to pressures higher than 4 GPa and subsequently warmed, it crystallizes into ice VII with the ionic species trapped inside the ice lattice. Here we report the extreme limit of salt incorporation into ice VII, using high pressure neutron diffraction and molecular dynamics simulations. We show that high-pressure crystallisation of aqueous solutions of LiCl∙RH₂O and LiBr∙RH₂O with R = 5.6 leads to solids with strongly expanded volume, a destruction of the hydrogen-bond network with an isotropic distribution of water-dipole moments, as well as a crystal-to-amorphous transition on decompression. This highly unusual behaviour constitutes an interesting pathway from a glass to a crystal where translational periodicity is restored but the rotational degrees of freedom remaining completely random.

Continuous melting through a hexatic phase in confined bilayer water

Liquid water is not only of obvious importance but also extremely intriguing, displaying many anomalies that still challenge our understanding of such an a priori simple system. The same is true when looking at nanoconfined water: The liquid between constituents in a cell is confined to such dimensions, and there is already evidence that such water can behave very differently from its bulk counterpart. A striking finding has been reported from computer simulations for two-dimensionally confined water: The liquid displays continuous or discontinuous melting depending on its density. In order to understand this behavior, we have analyzed the melting exhibited by a bilayer of nanoconfined water by means of molecular dynamics simulations. At high density we observe the continuous melting to be related to the phase change of the oxygens only, with the hydrogens remaining liquidlike throughout. Moreover, we find an intermediate hexatic phase for the oxygens between the liquid and a triangular solid ice phase, following the Kosterlitz-Thouless-Halperin-Nelson-Young theory for two-dimensional melting. The liquid itself tends to maintain the local structure of the triangular ice, with its two layers being strongly correlated yet with very slow exchange of matter. The decoupling in the behavior of the oxygens and hydrogens gives rise to a regime in which the complexity of water seems to disappear, resulting in what resembles a simple monoatomic liquid. This intrinsic tendency of our simulated water may be useful for understanding novel behaviors in other confined and interfacial water systems.

Effect of salt on the H-bond symmetrization in ice

The richness of the phase diagram of water reduces drastically at very high pressures where only two molecular phases, proton-disordered ice VII and proton-ordered ice VIII, are known. Both phases transform to the centered hydrogen bond atomic phase ice X above about 60 GPa, i.e., at pressures experienced in the interior of large ice bodies in the universe, such as Saturn and Neptune, where nonmolecular ice is thought to be the most abundant phase of water. In this work, we investigate, by Raman spectroscopy up to megabar pressures and ab initio simulations, how the transformation of ice VII in ice X is affected by the presence of salt inclusions in the ice lattice. Considerable amounts of salt can be included in ice VII structure under pressure via rock-ice interaction at depth and processes occurring during planetary accretion. Our study reveals that the presence of salt hinders proton order and hydrogen bond symmetrization, and pushes ice VII to ice X transformation to higher and higher pressures as the concentration of salt is increased.

Fabrication of polyhedral particles from spherical colloids and their self-assembly into rotator phases

Particle shape is a critical parameter that plays an important role in self-assembly, for example, in designing targeted complex structures with desired properties. Over the last decades, an unprecedented range of monodisperse nanoparticle systems with control over the shape of the particles have become available. In contrast, the choice of micrometer-sized colloidal building blocks of particles with flat facets, that is, particles with polygonal shapes, is significantly more limited. This can be attributed to the fact that in contrast to nanoparticles, the larger colloids are significantly harder to synthesize as single crystals. It is now shown that a very simple building block, such as a micrometer-sized polymeric spherical colloidal particle, is already enough to fabricate particles with regularly placed flat facets, including completely polygonal shapes with sharp edges. As an illustration that the yields are high enough for further self-assembly studies, the formation of three-dimensional rotator phases of fluorescently labelled, micrometer-sized, and charged rhombic dodecahedron particles was demonstrated. This method for fabricating polyhedral particles opens a new avenue for designing new materials.

Melting temperatures of H2O up to 72 GPa measured in a diamond anvil cell using CO2 laser heating technique

The melting curve of H2O from 49 to 72 GPa was determined by using a laser-heated diamond anvil cell. Double-sided CO2 laser heating technique was employed in order to heat the sample directly. Discontinuous changes of the heating efficiency attributed to the H2O melting were observed between 49 and 72 GPa. The obtained melting temperatures at 49 and 72 GPa are 1200 and 1410 K, respectively. We found that the slope of the melting curve significantly decreases with increasing pressure, only 5 K/GPa at 72 GPa while 44 K/GPa at 49 GPa. Our results suggest that the melting curve does not intersect with the isentropes of Uranus and Neptune, and hence, H2O should remain in the liquid state even at the pressure and temperature conditions found deep within Uranus and Neptune.