Liquid-liquid transition and ice crystallization in a machine-learned coarse-grained water model.

Mounting experimental evidence supports the existence of a liquid-liquid transition (LLT) in high-pressure supercooled water. However, fast crystallization of supercooled water has impeded identification of the LLT line TLL(p) in experiments. While the most accurate all-atom (AA) water models display a LLT, their computational cost limits investigations of its interplay with ice formation. Coarse-grained (CG) models provide over 100-fold computational efficiency gain over AA models, enabling the study of water crystallization, but have not yet shown to have a LLT. Here, we demonstrate that the CG machine-learned water model Machine-Learned Bond-Order Potential (ML-BOP) has a LLT that ends in a critical point at pc = 170 ± 10 MPa and Tc = 181 ± 3 K. The TLL(p) of ML-BOP is almost identical to the one of TIP4P/2005, adding to the similarity in the equation of state of liquid water in both models. Cooling simulations reveal that ice crystallization is fastest at the LLT and its supercritical continuation of maximum heat capacity, supporting a mechanistic relationship between the structural transformation of water to a low-density liquid (LDL) and ice formation. We find no signature of liquid-liquid criticality in the ice crystallization temperatures. ML-BOP replicates the competition between formation of LDL and ice observed in ultrafast experiments of decompression of the high-density liquid (HDL) into the region of stability of LDL. The simulations reveal that crystallization occurs prior to the coarsening of the HDL and LDL domains, obscuring the distinction between the highly metastable first-order LLT and pronounced structural fluctuations along its supercritical continuation.

Kinetics and Mechanisms of Pressure-Induced Ice Amorphization and Polyamorphic Transitions in a Machine-Learned Coarse-Grained Water Model.

Water glasses have attracted considerable attention due to their potential connection to a liquid-liquid transition in supercooled water. Here we use molecular simulations to investigate the formation and phase behavior of water glasses using the machine-learned bond-order parameter (ML-BOP) water model. We produce glasses through hyperquenching of water, pressure-induced amorphization (PIA) of ice, and pressure-induced polyamorphic transformations. We find that PIA of polycrystalline ice occurs at a lower pressure than that of monocrystalline ice and through a different mechanism. The temperature dependence of the amorphization pressure of polycrystalline ice for ML-BOP agrees with that in experiments. We also find that ML-BOP accurately reproduces the density, coordination number, and structural features of low-density (LDA), high-density (HDA), and very high-density (VHDA) amorphous water glasses. ML-BOP accurately reproduces the experimental radial distribution function of LDA but overpredicts the minimum between the first two shells in high-density glasses. We examine the kinetics and mechanism of the transformation between low-density and high-density glasses and find that the sharp nature of these transitions in ML-BOP is similar to that in experiments and all-atom water models with a liquid-liquid transition. Transitions between ML-BOP glasses occur through a spinodal-like mechanism, similar to ice crystallization from LDA. Both glass-to-glass and glass-to-ice transformations have Avrami-Kolmogorov kinetics with exponent n = 1.5 ± 0.2 in experiments and simulations. Importantly, ML-BOP reproduces the competition between crystallization and HDA→LDA transition above the glass transition temperature Tg, and separation of their time scales below Tg, observed also in experiments. These findings demonstrate the ability of ML-BOP to accurately reproduce water properties across various regimes, making it a promising model for addressing the competition between polyamorphic transitions and crystallization in water and solutions.

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions.

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

What Is the Smallest Zeolite That Could Be Synthesized?

Zeolites with a few unit cells are promising as catalyst and adsorbents. The quest to synthesize the smallest zeolites has recently resulted in 4 to 8 nm nanozeolites, about 2 to 4 unit cells. These findings pose the question of what is the smallest zeolite that could be obtained by hydrothermal synthesis. Here we address this question using molecular simulations and thermodynamic analysis. The simulations predict that amorphous precursors as small as 4 nm can crystallize zeolites, in agreement with the experiments. We find that interfacial forces dominate the structure of smaller particles, resulting in size-dependent compact isomers that have ring and pore distributions different from open framework zeolites. The instability of zeolites smaller than 3±0.5 nm precludes a classical mechanism of nucleation from solution or through assembly of small nanoslabs.

Polymorph Selection in Zeolite Synthesis Occurs after Nucleation.

Zeolites are porous crystals with extensive polymorphism. The hydrothermal synthesis of zeolites is a multistage process involving amorphous precursors that evolve continuously in solubility and local order toward those of the crystal. These results pose several questions: Why does a first-order transition appear as a continuous transformation? At which stage is the polymorph selected? How large are the barriers and critical sizes for zeolite nucleation? Here we address these questions using nucleation theory with experimental data. We find that the nucleation barriers and critical zeolite nuclei are extremely small at temperatures of hydrothermal synthesis, resulting in spinodal-like crystallization that produces a mosaic of tiny zeolitic crystallites that compete to grow inside each glassy precursor nanoparticle. The subnanometer size of the critical nuclei reveals that the selection between zeolite polymorphs occurs after the nucleation stage, during the growth and coarsening of the crystals around the excluded volume of the structure-directing agents.

Characterizing the Interplay between Polymer Solvation and Conformation.

Conformational transitions of flexible molecules, especially those driven by hydrophobic effects, tend to be hindered by desolvation barriers. For such transitions, it is thus important to characterize and understand the interplay between solvation and conformation. Using specialized molecular simulations, here we perform such a characterization for a hydrophobic polymer solvated in water. We find that an external potential, which unfavorably perturbs the polymer hydration waters, can trigger a coil-to-globule or collapse transition, and that the relative stabilities of the collapsed and extended states can be quantified by the strength of the requisite potential. Our results also provide mechanistic insights into the collapse transition, highlighting that the bottleneck to polymer collapse is the formation of a sufficiently large cluster, and the collective dewetting of such a cluster. We also study the collapse of the hydrophobic polymer in octane, a nonpolar solvent, and interestingly, we find that the mechanistic details of the transition are qualitatively similar to that in water.

Molecular simulation of osmometry in aqueous solutions of the BMIMCl ionic liquid: a potential route to force field parameterization of liquid mixtures.

Despite widespread development and use of ionic liquids (ILs) in both academic and industrial research, computational force fields (FFs) for most of those are not available for a precise description of inter-species interactions in aqueous environments. In the scope of this study, by means of molecular simulations, the osmotic coefficient of an aqueous solution of an IL is calculated and used as a basis to reparameterize popular IL-FFs existing in the literature. We first calculate the osmotic coefficients (at 298.15 K and 1 atm pressure) of aqueous solutions of 1-butyl-3-methylimidazolium chloride (BMIMCl), a generic IL, popularly used in biomass processing and the subsequent conversion to value-added intermediates. The performance of two popular atomic, nonpolarizable FFs developed for BMIMCl, one by Lopes, Pádua, and coworkers (FF-LP) and the other by Sambasivarao, Acevedo, and coworkers (FF-SA), when mixed with the SPC/E water model, is tested with respect to their ability to reproduce the experimental osmotic coefficient data. Interestingly, the osmotic coefficient is found to be increasing with a gradual increase in IL molality within the concentration range of our investigation, which is contrary to the experimental trend reported in the literature for the same IL-water mixture. Henceforth, necessary corrections to the nonbonded ion-ion and ion-water interactions are made to match the experimental osmotic coefficient. To further assess the reliability of the new FF, we extensively explore the thermodynamic (density, isothermal compressibility, and thermal expansion coefficient), dynamic (diffusivity and viscosity), and association/dissociation properties (rationalized with the help of radial distribution functions) with both the original and reparameterized FF for a wider range of concentrations up to a molality of 18.50 mol kg-1. The calculated quantities are compared against experimental data wherever available. The modified FF parameters exhibit significant improvements in terms of its ability to match experimental solution properties, such as density, viscosity, association/dissociation, etc. We report that excessive dissociation of BMIMCl in water is responsible for the shortcomings observed in the original FFs and improved prediction of physicochemical properties could be achieved using the modified FFs.

Molecular dynamics study of nanoscale organization and hydrogen bonding in binary mixtures of butylammonium nitrate ionic liquid and primary alcohols.

Molecular dynamics simulations are utilized here to explore the nanoscale morphology and the nature of hydrogen bonding in the equimolar mixtures of butylammonium nitrate protic ionic liquid with ethanol, propanol, and butanol. The X-ray scattering experimental study of Greaves et al. [Phys. Chem. Chem. Phys. 13, 13 501 (2011)] has evidenced that alkylammonium nitrate plus alcohol mixtures possess nanoscale structural order which becomes more pronounced as the chain length of the alcohol increases. Our analysis carried out using simulated total and partial X-ray scattering structure functions quantifies the basis of these observations. The partial structure functions highlight the off-phase density correlations of alcohol with both cation and anion in the low-q region. We demonstrate that the chain lengthening of alcohols offers significant variation in the structuring of the polar and apolar moieties in the mixtures. The inspection based on radial distribution functions manifests the non-linear hydrogen bonds of cations with nitrate anions as well as alcohol molecules. The alcohol's hydroxyl group prefers to form linear hydrogen bonds with anions and with other alcohol molecules. Incremented chain length of alcohol improves the extent of hydrogen bonding but does not alter their geometry. Spatial distribution functions delineate similar preferences. It shows stronger directional preferences of the hydroxyl group of alcohols than cation in the vicinity of an anion. Enhanced pair correlations associated with the terminal methyl carbons suggest aggregation of butanol chains in apolar domains. Triplet correlation functions (TCFs) are also used to evaluate the orientational preferences of the present polar moieties in the mixtures. Information based on TCFs for distribution of polar head group of cations and anions unveils the dominance of equilateral configurations over the less frequent isosceles configurations in all the three mixtures.

Probing the triplet correlation function in liquid water by experiments and molecular simulations.

Despite very significant developments in scattering experiments like X-ray and neutron diffraction, it has been challenging to elucidate the nature of tetrahedral molecular configurations in liquid water. A key question is whether the pair correlation functions, which can be obtained from scattering experiments, are sufficient to describe the tetrahedral ordering of water molecules. In our previous study (Dhabal et al., J. Chem. Phys., 2014, 141, 174504), using data-sets generated from reverse Monte Carlo and molecular dynamics simulations, we showed that the triplet correlation functions contain important information on the tetrahedrality of water in the liquid state. In the present study, X-ray scattering experiments and molecular dynamics (MD) simulations are used to link the isothermal pressure derivative of the structure factor with the triplet correlation functions for water. Triplet functions are determined for water up to 3.3 kbar at 298 K to display the effect of pressure on the water structure. The results suggest that triplet functions (H[combining tilde](q)) obtained using a rigid-body TIP4P/2005 water model are consistent with the experimental results. The triplet functions obtained in experiment as well as in simulations evince that in the case of tetrahedral liquids, exertion of higher pressure leads to a better agreement with the Kirkwood superposition approximation (KSA). We further validate this observation using the triplet correlation functions (g(3)(r,s,t)) calculated directly from simulation trajectory, revealing that both H[combining tilde](q) in q-space and g(3)(r,s,t) in real-space contain similar information on the tetrahedrality of liquids. This study demonstrates that the structure factor, even though it has only pair correlation information of the liquid structure, can shed light on three-body correlations in liquid water through its isothermal pressure derivative term.

Pressure-dependent morphology of trihexyl(tetradecyl)phosphonium ionic liquids: A molecular dynamics study.

In the present molecular dynamics study, we investigate the effects of increasing pressure on the structural morphology of trihexyl(tetradecyl)phosphonium bromide (P666,14+/Br-) and trihexyl(tetradecyl)phosphonium dicyanamide (P666,14+/DCA-) ionic liquids (ILs). Special attention was paid to how charge and polarity orderings, which are present in the microscopic structure of these ILs at ambient conditions, respond to very high external pressure. The simulated X-ray scattering structure functions, S(q)s, of the two systems reveal that both the characteristic orderings show appreciable responsiveness towards the applied pressure change. At a given pressure, a slight difference between the polarity ordering (PO), charge ordering (CO), and adjacency correlations (AC) for both the systems points towards different microscopic structure of the two ILs due to change in anion. Beyond a certain pressure, we observe emergence of a new low-q peak in the S(q)s of both the systems. The new peak is associated with formation of crystalline order in these systems at higher pressures and the real space length-scale corresponding to the crystalline order lies in between those of polarity- and charge-ordering. Beyond the transition pressure, the crystallinity of both the systems increases with increasing pressure and the corresponding length-scale shifts towards smaller values upon increasing pressure. We also observe that the extent of the usual polarity ordering decreases upon increasing pressure for both the P666,14+/Br- and P666,14+/DCA- systems. We demonstrate that the disappearance of the usual polarity peak is due to decreased polar-polar and apolar-apolar correlations and enhanced correlations between the charged and uncharged groups of the ions. This scenario is completely reversed for the components corresponding to the crystalline order, the polar-polar and apolar-apolar correlations are enhanced and polar-apolar correlations are diminished at higher pressure. In addition, the charge ordering peak, which is not so obvious from the total S(q) but from ionic and sub-ionic partial components of it, shifts towards lower q values for P666,14+/Br-. Instead, for the P666,14+/DCA-, at the highest pressure studied the CO peak occurs at a q-value higher than that at the ambient pressure.

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium.

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids.

Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW(23.15) or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S(trip), is also studied. S(trip) is a good entropy estimator for liquids where pair and triplet correlations are important such as Ge and Si, but loses accuracy for purely pair-dominated liquids, like LJ fluid, or near the crystallization temperature (T(thr)). Since local tetrahedral order is compatible with both liquid and crystalline states, the reorganisation of tetrahedral liquids is accompanied by a clear rise in the pair, triplet, and thermodynamic contributions to the heat capacity, resulting in the heat capacity anomaly. In contrast, the pair-dominated liquids show increasing dominance of triplet correlations on approaching crystallization but no sharp rise in either the pair or thermodynamic heat capacities.

Triplet correlation functions in liquid water.

Triplet correlations have been shown to play a crucial role in the transformation of simple liquids to anomalous tetrahedral fluids [M. Singh, D. Dhabal, A. H. Nguyen, V. Molinero, and C. Chakravarty, Phys. Rev. Lett. 112, 147801 (2014)]. Here we examine triplet correlation functions for water, arguably the most important tetrahedral liquid, under ambient conditions, using configurational ensembles derived from molecular dynamics (MD) simulations and reverse Monte Carlo (RMC) datasets fitted to experimental scattering data. Four different RMC data sets with widely varying hydrogen-bond topologies fitted to neutron and x-ray scattering data are considered [K. T. Wikfeldt, M. Leetmaa, M. P. Ljungberg, A. Nilsson, and L. G. M. Pettersson, J. Phys. Chem. B 113, 6246 (2009)]. Molecular dynamics simulations are performed for two rigid-body effective pair potentials (SPC/E and TIP4P/2005) and the monatomic water (mW) model. Triplet correlation functions are compared with other structural measures for tetrahedrality, such as the O-O-O angular distribution function and the local tetrahedral order distributions. In contrast to the pair correlation functions, which are identical for all the RMC ensembles, the O-O-O triplet correlation function can discriminate between ensembles with different degrees of tetrahedral network formation with the maximally symmetric, tetrahedral SYM dataset displaying distinct signatures of tetrahedrality similar to those obtained from atomistic simulations of the SPC/E model. Triplet correlations from the RMC datasets conform closely to the Kirkwood superposition approximation, while those from MD simulations show deviations within the first two neighbour shells. The possibilities for experimental estimation of triplet correlations of water and other tetrahedral liquids are discussed.

Triplet correlations dominate the transition from simple to tetrahedral liquids.

The total, triplet, and pair contributions to the entropy with increasing tetrahedrality are mapped out for the Stillinger-Weber liquids to demonstrate the qualitative and quantitative differences between triplet-dominated, tetrahedral liquids and pair-dominated, simple liquids with regard to supercooling and crystallization. The heat capacity anomaly of tetrahedral liquids originates in local ordering due to both pair and triplet correlations. The results suggest that structural correlations can be directly related to thermodynamic anomalies, phase changes, and self-assembly in other atomic and colloidal fluids.

Structural correlations and cooperative dynamics in supercooled liquids.

The relationships between diffusivity and the excess, pair and residual multiparticle contributions to the entropy are examined for Lennard-Jones liquids and binary glassformers, in the context of approximate inverse power law mappings of simple liquids. In the dense liquid where diffusivities are controlled by collisions and cage relaxations, Rosenfeld-type excess entropy scaling of diffusivities is found to hold for both crystallizing as well as vitrifying liquids. The crucial differences between the two categories of liquids emerge only when local cooperative effects in the dynamics result in significant caging effects in the time-dependent behaviour of the single-particle mean square displacement. In the case of glassformers, onset of such local cooperativity coincides with onset of deviations from Rosenfeld-type excess entropy scaling of diffusivities and increasing spatiotemporal heterogeneity. In contrast, for two- and three-dimensional liquids with a propensity to crystallise, the onset of local cooperative dynamics is sufficient to trigger crystallization provided that the liquid is sufficiently supercooled that the free energy barrier to nucleation of the solid phase is negligible. The state points corresponding to onset of transient caging effects can be associated with typical values, within reasonable bounds, of the excess, pair, and residual multiparticle entropy as a consequence of the isomorph-invariant character of the excess entropy, diffusivity and related static and dynamic correlation functions.

Water and other tetrahedral liquids: order, anomalies and solvation.

In order to understand the common features of tetrahedral liquids with water-like anomalies, the relationship between local order and anomalies has been studied using molecular dynamics simulations for three categories of such liquids: (a) atomistic rigid-body models for water (TIP4P, TIP4P/2005, mTIP3P, SPC/E), (b) ionic melts, BeF(2) (TRIM model) and SiO(2) (BKS potential) and (c) Stillinger-Weber liquids parametrized to model water (mW) and silicon. Rigid-body, atomistic models for water and the Stillinger-Weber liquids show a strong correlation between tetrahedral and pair correlation order and the temperature for the onset of the density anomaly is close to the melting temperature. In contrast, the ionic melts show weaker and more variable degrees of correlation between tetrahedral and pair correlation metrics, and the onset temperature for the density anomaly is more than twice the melting temperature. In the case of water, the relationship between water-like anomalies and solvation is studied by examining the hydration of spherical solutes (Na(+), Cl(-), Ar) in water models with different temperature regimes of anomalies (SPC/E, TIP4P and mTIP3P). For both ionic and nonpolar solutes, the local structure and energy of water molecules is essentially the same as in bulk water beyond the second-neighbour shell. The local order and binding energy of water molecules are not perturbed by the presence of a hydrophobic solute. In the case of ionic solutes, the perturbation is largely localized within the first hydration shell. The binding energies for the ions are strongly dependent on the water models and clearly indicate that the geometry of the partial charge distributions, and the associated multipole moments, play an important role. However the anomalous behaviour of the water network has been found to be unimportant for polar solvation.