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We quantify the statistical properties of the potential energy landscape for a recently proposed machine learning coarse grained model for water, machine learning-bond-order potential [Chan et al., Nat. Commun. 10, 379 (2019)]. We find that the landscape can be accurately modeled as a Gaussian landscape at all densities. The resulting landscape-based free-energy expression accurately describes the model properties in a very wide range of temperatures and densities. The density dependence of the Gaussian landscape parameters [total number of inherent structures (ISs), characteristic IS energy scale, and variance of the IS energy distribution] predicts the presence of a liquid–liquid transition located close to P = 1750 ± 100 bars and T = 181.5 ± 1 K. [ABSTRACT FROM AUTHOR]

Continued increases in computational power now make it possible to evaluate the free-energy landscape associated with the first-order liquid–liquid transition in realistic models of water for which an accurate estimate of the liquid–liquid critical point exists, and to explore its change with pressure near the coexistence line. We report the results of 50 μs-long NPT umbrella sampling simulations for two realistic models for water, TIP4P/2005 and TIP4P/ice, 3–9 K below their critical temperatures. The free energy profile at different pressures clearly shows the presence of two well-defined free energy basins and makes it possible to identify the liquid–liquid spinodal points, the limits of stability that define the (temperature dependent) pressure range within which two distinct free energy basins exist. The results show that for temperatures less than 10 K below the critical temperature, metastable states are possible across a very limited pressure interval, information that is relevant to the interpretation of experiments probing the metastable phase behavior of deeply supercooled water in the so-called no-man's land. [ABSTRACT FROM AUTHOR]

Studies of water thermodynamics have long been tied to the identification of two distinct families of local structures, whose competition could explain the origin of the many thermodynamic anomalies and the hypothesized liquid–liquid critical point in water. Despite the many successes and insights gained, the structural indicators proposed throughout the years were not able to unequivocally identify these two families over a wide range of conditions. We show that a recently introduced indicator, Ψ, which exploits information on the hydrogen bond network connectivity, can reliably identify these two distinct local environments over a wide range of thermodynamic conditions (188–300 K and 0–13 kbar) and that close to the liquid–liquid critical point, the spatial correlations of density fluctuations are identical to those of the Ψ indicator. Our results strongly support the idea that water thermodynamic properties arise from the competition between two distinct and identifiable local environments. [ABSTRACT FROM AUTHOR]

Nucleation in systems with a metastable liquid–gas critical point is the prototypical example of a two-step nucleation process in which the appearance of the critical nucleus is preceded by the formation of a liquid-like density fluctuation. So far, the majority of studies on colloidal and protein crystallization have focused on one-component systems, and we are lacking a clear description of two-step nucleation processes in multicomponent systems, where critical fluctuations involve coupled density and concentration inhomogeneities. Here, we examine the nucleation process of a binary mixture of patchy particles designed to nucleate into a diamond lattice. By combining Gibbs-ensemble simulations and direct nucleation simulations over a wide range of thermodynamic conditions, we are able to pin down the role of the liquid–gas metastable phase diagram on the nucleation process. In particular, we show that the strongest enhancement of crystallization occurs at an azeotropic point with the same stoichiometric composition of the crystal. [ABSTRACT FROM AUTHOR]

The representation of complex systems as networks has become a critical tool across many fields of science. In the context of physical networks, such as biological neural networks, vascular networks, or network liquids where the nodes and edges occupy volume in three-dimensional space, the question of how they become densely packed is of special importance. Here, we investigate a model network liquid, which is known to densify via two successive liquid-liquid phase transitions (LLPTs). We elucidate the importance of rings--cyclic paths formed by bonded particles in the networks--and their spatial disposition in understanding the structural changes that underpin the increase in density across the LLPTs. Our analyses demonstrate that the densification of these networks is primarily driven by the formation of linked rings, and the LLPTs correspond to a hierarchy of topological transitions where rings form the fundamental building blocks. We envisage entanglement to emerge as a general mechanism for densification, with wide implications for the embedding of physical networks, especially in confined spaces. [ABSTRACT FROM AUTHOR]

We present a neural network (NN) potential based on a new set of atomic fingerprints built upon two- and three-body contributions that probe distances and local orientational order, respectively. Compared with the existing NN potentials, the atomic fingerprints depend on a small set of tunable parameters that are trained together with the NN weights. In addition to simplifying the selection of the atomic fingerprints, this strategy can also considerably increase the overall accuracy of the network representation. To tackle the simultaneous training of the atomic fingerprint parameters and NN weights, we adopt an annealing protocol that progressively cycles the learning rate, significantly improving the accuracy of the NN potential. We test the performance of the network potential against the mW model of water, which is a classical three-body potential that well captures the anomalies of the liquid phase. Trained on just three state points, the NN potential is able to reproduce the mW model in a very wide range of densities and temperatures, from negative pressures to several GPa, capturing the transition from an open random tetrahedral network to a dense interpenetrated network. The NN potential also reproduces very well properties for which it was not explicitly trained, such as dynamical properties and the structure of the stable crystalline phases of mW. [ABSTRACT FROM AUTHOR]

The hypothesis that the anomalous behavior of liquid water is related to the existence of a second critical point in deeply supercooled states has long been the subject of intense debate. Recent, sophisticated experiments designed to observe the transformation between the two subcritical liquids on nano- and microsecond time scales, along with demanding numerical simulations based on classical (rigid) models parameterized to reproduce thermodynamic properties of water, have provided support to this hypothesis. A stronger numerical proof requires demonstrating that the critical point, which occurs at temperatures and pressures far from those at which the models were optimized, is robust with respect to model parameterization, specifically with respect to incorporating additional physical effects. Here, we show that a liquid–liquid critical point can be rigorously located also in the WAIL model of water [Pinnick et al., J. Chem. Phys. 137, 014510 (2012)], a model parameterized using ab initio calculations only. The model incorporates two features not present in many previously studied water models: It is both flexible and polarizable, properties which can significantly influence the phase behavior of water. The observation of the critical point in a model in which the water–water interaction is estimated using only quantum ab initio calculations provides strong support to the viewpoint according to which the existence of two distinct liquids is a robust feature in the free energy landscape of supercooled water. [ABSTRACT FROM AUTHOR]

It has recently been shown that the TIP4P/Ice model of water can be studied numerically in metastable equilibrium at and below its liquid–liquid critical temperature. We report here simulations along a subcritical isotherm, for which two liquid states with the same pressure and temperature but different density can be equilibrated. This allows for a clear visualization of the structural changes taking place across the transition. We specifically focus on how the topological properties of the H-bond network change across the liquid–liquid transition. Our results demonstrate that the structure of the high-density liquid, characterized by the existence of interstitial molecules and commonly explained in terms of the collapse of the second neighbor shell, actually originates from the folding back of long rings, bringing pairs of molecules separated by several hydrogen-bonds close by in space. [ABSTRACT FROM AUTHOR]

Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former. [ABSTRACT FROM AUTHOR]

The origin of water anomalies hides in an experimentally inaccessible region of the phase diagram known as no-man's land, bounded at low temperature by the domain of stability of amorphous glasses, and at high temperature by the homogeneous nucleation line, below which liquid water loses its metastability. The existence of at least two different forms of glass on one side, i.e., the low-density amorphous (LDA) and the high-density amorphous (HDA) ices, and of one anomalous liquid on the other side, points to a hidden connection between these states, whose understanding has the potential to uncover what happens in no-man's land and shed light on the complex nature of water's behavior. Here, we develop a Neural Network scheme capable of discerning local structures beyond tetrahedrality. Applied over a wide region of the water's phase diagram, we show that the local structures that characterize both LDA and HDA amorphous phases are indeed embedded in the supercooled liquid phase. Remarkably, the rapid increase in the LDA-like population with supercooling occurs in the same temperature and pressure region where thermodynamic fluctuations are maximized, linking these structures with water's anomalies. At the same time, the population of HDA-like environments rapidly increases with pressure, becoming the majority component at high density. Our results show that both LDA and HDA are genuine glasses, and provide a microscopic connection between the non-equilibrium and equilibrium phase diagrams of water. [ABSTRACT FROM AUTHOR]

We introduce a parameter-free structural indicator to classify local environments of water molecules in stable and supercooled liquid states, which reveals a clear two-peak distribution of local properties. The majority of molecules are tetrahedrally coordinated (T molecules), via low-energy hydrogen bonds. The minority component, whose relative concentration decreases with a decrease in the temperature at constant pressure, is characterized by prevalently three-coordinated molecules, giving rise to a distorted local network around them (D molecules). The inter-conversion between T and D molecules explains the increasing specific heat at constant pressure on cooling. The local structure around a T molecule resembles the one found experimentally in low-density amorphous ice (a network structure mostly composed by T molecules), while the local structure around a D molecule is reminiscent of the structural properties of high-density amorphous ice (a network structure composed by a mixture of T and D molecules). [ABSTRACT FROM AUTHOR]

The control over the self-assembly of complex structures is a long-standing challenge of material science, especially at the colloidal scale, as the desired assembly pathway is often kinetically derailed by the formation of amorphous aggregates. Here, we investigate in detail the problem of the self-assembly of the three Archimedean shells with five contact points per vertex, i.e., the icosahedron, the snub cube, and the snub dodecahedron. We use patchy particles with five interaction sites (or patches) as model for the building blocks and recast the assembly problem as a Boolean satisfiability problem (SAT) for the patch–patch interactions. This allows us to find effective designs for all targets and to selectively suppress unwanted structures. By tuning the geometrical arrangement and the specific interactions of the patches, we demonstrate that lowering the symmetry of the building blocks reduces the number of competing structures, which in turn can considerably increase the yield of the target structure. These results cement SATassembly as an invaluable tool to solve inverse design problems. [ABSTRACT FROM AUTHOR]

Here, we revisit the assembly of colloidal tetrahedral patchy particles. Previous studies have shown that the crystallization of diamond from the fluid phase depends more critically on patch width than on the interaction range: particles with patches narrower than 40° crystallize readily and those with wide patches form disordered glass states. We find that the crystalline structure formed from the fluid also depends on the patch width. Whereas particles with intermediate patches assemble into diamond (random stacking of cubic and hexagonal diamond layers), particles with narrow patches (with width ≈20° or less) crystallize frequently into clathrates. Free energy calculations show that clathrates are never (in the pressure-temperature plane) thermodynamically more stable than diamond. The assembly of clathrate structures is thus attributed to kinetic factors that originate from the thermodynamic stabilization of pentagonal rings with respect to hexagonal ones as patches become more directional. These pentagonal rings present in the fluid phase assemble into sII clathrate or into large clusters containing 100 particles and exhibiting icosahedral symmetry. These clusters then grow by interpenetration. Still, the organization of these clusters into extended ordered structures was never observed in the simulations. [ABSTRACT FROM AUTHOR]

The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here, we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) using computer simulations of the TIP4P/2005 molecular model of water. We find that the properties of the PEL sampled by the system during the LDA-HDA transformation exhibit anomalous behavior. In particular, at conditions where the change in density during the LDA-HDA transformation is approximately discontinuous, reminiscent of a first-order phase transition, we find that (i) the inherent structure (IS) energy, eIS(V), is a concave function of the volume and (ii) the IS pressure, PIS(V), exhibits a van der Waals-like loop. In addition, the curvature of the PEL at the IS is anomalous, a nonmonotonic function of V. In agreement with previous studies, our work suggests that conditions (i) and (ii) are necessary (but not sufficient) signatures of the PEL for the LDA-HDA transformation to be reminiscent of a first-order phase transition. We also find that one can identify two different regions of the PEL, one associated with LDA and another with HDA. Our computer simulations are performed using a wide range of compression/decompression and cooling rates. In particular, our slowest cooling rate (0.01 K/ns) is within the experimental rates employed in hyperquenching experiments to produce LDA. Interestingly, the LDA-HDA transformation pressure that we obtain at T = 80 K and at different rates extrapolates remarkably well to the corresponding experimental pressure. [ABSTRACT FROM AUTHOR]

The stability-limit conjecture (SLC) proposes that the liquid spinodal of water returns to positive pressure in the supercooled region and that the apparent divergence of water's thermodynamic response functions as temperature decreases are explained by the approach to this re-entrant spinodal. Subsequently, it has been argued that the predictions of the SLC are inconsistent with general thermodynamic principles. Here, we reconsider the thermodynamic viability of the SLC by examining a model equation of state for water which was first studied to clarify the relationship of the SLC to the proposed liquid-liquid phase transition in supercooled water. By demonstrating that a binodal may terminate on a spinodal at a point that is not a critical point, we show that the SLC is thermodynamically permissible in a system that has both a liquid-gas and a liquid-liquid phase transition. We also describe and clarify other unusual thermodynamic behavior that may arise in such a system, particularly that associated with the so-called "critical-point-free" scenario for a liquid-liquid phase transition, which may apply to the case of liquid Si. [ABSTRACT FROM AUTHOR]

We study the evolution of dynamic fluctuations averaged over different space lengths and time scales to characterize spatially and temporally heterogeneous behavior of TIP4P/2005 water in liquid and supercooled states. Analyzing a 250 000 molecules simulated system, we provide evidence of the existence, upon supercooling, of a significant enhancement of spatially localized dynamic fluctuations stemming from regions of correlated mobile molecules. We show that both the magnitude of the departure from the value expected for the system-size dependence of an uncorrelated system and the system size at which such a trivial regime is finally recovered clearly increase upon supercooling. This provides a means to estimate an upper limit to the maximum length scale of influence of the regions of correlated mobile molecules. Notably, such an upper limit grows two orders of magnitude on cooling, reaching a value corresponding to a few thousand molecules at the lowest investigated temperature. [ABSTRACT FROM AUTHOR]

Nanoscale or colloidal particles are important in many realms of science and technology. They can dramatically change the properties of materials, imparting solid-like behaviour to a wide variety of complex [...]

A re-entrant gas-liquid spinodal was proposed as a possible explanation of the apparent divergence of the compressibility and specific heat off supercooling water. Such a counter-intuitive possibility, e.g., a liquid that becomes unstable to gas-like fluctuations on cooling at positive pressure, has never been observed, neither in real substances nor in off-lattice simulations. More recently, such a reentrant scenario has been dismissed on the premise that the re-entrant spinodal would collide with the gas-liquid coexisting curve (binodal) in the pressure-temperature plane. Here we study, numerically and analytically, two previously introduced one-component patchy particle models that both show (i) a re-entrant limit of stability of the liquid phase and (ii) a re-entrant binodal, providing a neat in silico (and in charta) realization of such unconventional thermodynamic scenario. [ABSTRACT FROM AUTHOR]