Local number fluctuations in ordered and disordered phases of water across temperatures: Higher-order moments and degrees of tetrahedrality.

The isothermal compressibility (i.e., related to the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal under near-ambient conditions. This anomalous non-monotonic temperature dependence is due to a balance between thermal fluctuations and the formation of tetrahedral hydrogen-bond networks. Since tetrahedrality is a many-body property, it will also influence the higher-order moments of density fluctuations, including the skewness and kurtosis. To gain a more complete picture, we examine these higher-order moments that encapsulate many-body correlations using a recently developed, advanced platform for local density fluctuations. We study an extensive set of simulated phases of water across a range of temperatures (80-1600 K) with various degrees of tetrahedrality, including ice phases, equilibrium liquid water, supercritical water, and disordered nonequilibrium quenches. We find clear signatures of tetrahedrality in the higher-order moments, including the skewness and excess kurtosis, which scale for all cases with the degree of tetrahedrality. More importantly, this scaling behavior leads to non-monotonic temperature dependencies in the higher-order moments for both equilibrium and non-equilibrium phases. Specifically, under near-ambient conditions, the higher-order moments vanish most rapidly for large length scales, and the distribution quickly converges to a Gaussian in our metric. However, under non-ambient conditions, higher-order moments vanish more slowly and hence become more relevant, especially for improving information-theoretic approximations of hydrophobic solubility. The temperature non-monotonicity that we observe in the full distribution across length scales could shed light on water's nested anomalies, i.e., reveal new links between structural, dynamic, and thermodynamic anomalies.

Free-energy landscape and spinodals for the liquid-liquid transition of the TIP4P/2005 and TIP4P/Ice models of water.

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.

Melting curves of ice polymorphs in the vicinity of the liquid-liquid critical point.

The possible existence of a liquid-liquid critical point in deeply supercooled water has been a subject of debate due to the challenges associated with providing definitive experimental evidence. The pioneering work by Mishima and Stanley [Nature 392, 164-168 (1998)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected liquid-liquid transition and its associated critical point. Based on the continuous or discontinuous changes in the slope of the melting curves, Mishima [Phys. Rev. Lett. 85, 334 (2000)] suggested that the liquid-liquid critical point lies between the melting curves of ice III and ice V. We explore this conjecture using molecular dynamics simulations with a machine learning model based on ab initio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII and find that all of them are supercritical and do not intersect the liquid-liquid transition locus. We also find a pronounced, yet continuous, change in the slope of the melting lines upon crossing of the liquid locus of maximum compressibility. Finally, we analyze the literature in light of our findings and conclude that the scenario in which the melting curves are supercritical is favored by the most recent computational and experimental evidence. Although the preponderance of evidence is consistent with the existence of a second critical point in water, the behavior of ice polymorph melting lines does not provide strong evidence in support of this viewpoint, according to our calculations.

Anomalies and Local Structure of Liquid Water from Boiling to the Supercooled Regime as Predicted by the Many-Body MB-pol Model.

For the past 50 years, researchers have sought molecular models that can accurately reproduce water's microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ∼208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid water's physical properties across broad ranges of thermodynamic states, including the so-called water's "no man's land" which is difficult to probe experimentally.

Liquid-Liquid Transition in Water from First Principles.

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

Vapor-liquid equilibrium of water with the MB-pol many-body potential.

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water's solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor-liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400 K < T < 600 K, we calculated properties such as equilibrium coexistence densities, vapor-liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor-liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the intramolecular degrees of freedom. These results attest to the chemical accuracy of MB-pol and its high degree of transferability, thus enabling MB-pol's application across a large swath of water's phase diagram.

Manifestations of metastable criticality in the long-range structure of model water glasses.

Much attention has been devoted to water's metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index; water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids.

Signatures of a liquid-liquid transition in an ab initio deep neural network model for water.

The possible existence of a metastable liquid-liquid transition (LLT) and a corresponding liquid-liquid critical point (LLCP) in supercooled liquid water remains a topic of much debate. An LLT has been rigorously proved in three empirically parametrized molecular models of water, and evidence consistent with an LLT has been reported for several other such models. In contrast, experimental proof of this phenomenon has been elusive due to rapid ice nucleation under deeply supercooled conditions. In this work, we combined density functional theory (DFT), machine learning, and molecular simulations to shed additional light on the possible existence of an LLT in water. We trained a deep neural network (DNN) model to represent the ab initio potential energy surface of water from DFT calculations using the Strongly Constrained and Appropriately Normed (SCAN) functional. We then used advanced sampling simulations in the multithermal-multibaric ensemble to efficiently explore the thermophysical properties of the DNN model. The simulation results are consistent with the existence of an LLCP, although they do not constitute a rigorous proof thereof. We fit the simulation data to a two-state equation of state to provide an estimate of the LLCP's location. These combined results-obtained from a purely first-principles approach with no empirical parameters-are strongly suggestive of the existence of an LLT, bolstering the hypothesis that water can separate into two distinct liquid forms.

Experimental and theoretical evidence for molecular forces driving surface segregation in photonic colloidal assemblies.

Surface segregation in binary colloidal mixtures offers a simple way to control both surface and bulk properties without affecting their bulk composition. Here, we combine experiments and coarse-grained molecular dynamics (CG-MD) simulations to delineate the effects of particle chemistry and size on surface segregation in photonic colloidal assemblies from binary mixtures of melanin and silica particles of size ratio (D large /D small) ranging from 1.0 to ~2.2. We find that melanin and/or smaller particles segregate at the surface of micrometer-sized colloidal assemblies (supraballs) prepared by an emulsion process. Conversely, no such surface segregation occurs in films prepared by evaporative assembly. CG-MD simulations explain the experimental observations by showing that particles with the larger contact angle (melanin) are enriched at the supraball surface regardless of the relative strength of particle-interface interactions, a result with implications for the broad understanding and design of colloidal particle assemblies.

pyPRISM: A Computational Tool for Liquid-State Theory Calculations of Macromolecular Materials.

The Polymer Reference Interaction Site Model (PRISM) theory describes the equilibrium spatial-correlations of liquid-like polymer systems including melts, blends, solutions, block copolymers, ionomers, liquid crystalline polymers, and nanocomposites. Using PRISM theory, one can calculate thermodynamic (second virial coefficients, Flory-Huggins χ interaction parameters, potentials of mean force) and structural (pair correlation functions, structure factors) data for these macromolecular materials. Here, we present a Python-based, open-source framework, pyPRISM, for conducting PRISM theory calculations. This framework aims to simplify PRISM-based studies by providing a user-friendly scripting interface for setting up and numerically solving the PRISM equations. pyPRISM also provides data structures, functions, and classes that streamline PRISM calculations, allowing pyPRISM to be extended for use in other tasks, such as the coarse-graining of atomistic simulation force-fields or the modeling of experimental scattering data. The goal of this framework is to reduce the barrier to correctly and appropriately using PRISM theory and to provide a platform for rapid calculations of the structure and thermodynamics of polymeric fluids and nanocomposites.

Macromolecular 'size' and 'hardness' drives structure in solvent-swollen blends of linear, cyclic, and star polymers.

In this paper, we apply molecular simulation and liquid state theory to uncover the structure and thermodynamics of homopolymer blends of the same chemistry and varying chain architecture in the presence of explicit solvent species. We use hybrid Monte Carlo (MC)/molecular dynamics (MD) simulations in the Gibbs ensemble to study the swelling of ∼12 000 g mol-1 linear, cyclic, and 4-arm star polystyrene chains in toluene. Our simulations show that the macroscopic swelling response is indistinguishable between the various architectures and matches published experimental data for the solvent annealing of linear polystyrene by toluene vapor. We then use standard MD simulations in the NPT ensemble along with polymer reference interaction site model (PRISM) theory to calculate effective polymer-solvent and polymer-polymer Flory-Huggins interaction parameters (χeff) in these systems. As seen in the macroscopic swelling results, there are no significant differences in the polymer-solvent and polymer-polymer χeff between the various architectures. Despite similar macroscopic swelling and effective interaction parameters between various architectures, the pair correlation function between chain centers-of-mass indicates stronger correlations between cyclic or star chains in the linear-cyclic blends and linear-star blends, compared to linear chain-linear chain correlations. Furthermore, we note striking similarities in the chain-level correlations and the radius of gyration of cyclic and 4-arm star architectures of identical molecular weight. Our results indicate that the cyclic and star chains are 'smaller' and 'harder' than their linear counterparts, and through comparison with MD simulations of blends of soft spheres with varying hardness and size we suggest that these macromolecular characteristics are the source of the stronger cyclic-cyclic and star-star correlations.

Leveraging Gibbs Ensemble Molecular Dynamics and Hybrid Monte Carlo/Molecular Dynamics for Efficient Study of Phase Equilibria.

We describe an extension of the Gibbs ensemble molecular dynamics (GEMD) method for studying phase equilibria. Our modifications to GEMD allow for direct control over particle transfer between phases and improve the method's numerical stability. Additionally, we found that the modified GEMD approach had advantages in computational efficiency in comparison to a hybrid Monte Carlo (MC)/MD Gibbs ensemble scheme in the context of the single component Lennard-Jones fluid. We note that this increase in computational efficiency does not compromise the close agreement of phase equilibrium results between the two methods. However, numerical instabilities in the GEMD scheme hamper GEMD's use near the critical point. We propose that the computationally efficient GEMD simulations can be used to map out the majority of the phase window, with hybrid MC/MD used as a follow up for conditions under which GEMD may be unstable (e.g., near-critical behavior). In this manner, we can capitalize on the contrasting strengths of these two methods to enable the efficient study of phase equilibria for systems that present challenges for a purely stochastic GEMC method, such as dense or low temperature systems, and/or those with complex molecular topologies.