Origin of the emergent fragile-to-strong transition in supercooled water

Isotope effects in supercooled H2O and D2O and a corresponding-states-like rescaling of the temperature and pressure

Water shows anomalous properties that are enhanced upon supercooling. The unusual behavior is observed in both H2O and D2O, however, with different temperature dependences for the two isotopes. It is often noted that comparing the properties of the isotopes at two different temperatures (i.e., a temperature shift) approximately accounts for many of the observations-with a temperature shift of 7.2 K in the temperature of maximum density being the most well-known example. However, the physical justification for such a shift is unclear. Motivated by recent work demonstrating a "corresponding-states-like" rescaling for water properties in three classical water models that all exhibit a liquid-liquid transition and critical point [Uralcan et al., J. Chem. Phys. 150, 064503 (2019)], the applicability of this approach for reconciling the differences in the temperature- and pressure-dependent thermodynamic properties of H2O and D2O is investigated here. Utilizing previously published data and equations-of-state for H2O and D2O, we show that the available data and models for these isotopes are consistent with such a low temperature correspondence. These observations provide support for the hypothesis that a liquid-liquid critical point, which is predicted to occur at low temperatures and high pressures, is the origin of many of water's anomalies.

Unraveling the dynamic slowdown in supercooled water: The role of dynamic disorder in jump motions

When a liquid is rapidly cooled below its melting point without inducing crystallization, its dynamics slow down significantly without noticeable structural changes. Elucidating the origin of this slowdown has been a long-standing challenge. Here, we report a theoretical investigation into the mechanism of the dynamic slowdown in supercooled water, a ubiquitous yet extraordinary substance characterized by various anomalous properties arising from local density fluctuations. Using molecular dynamics simulations, we found that the jump dynamics, which are elementary structural change processes, deviate from Poisson statistics with decreasing temperature. This deviation is attributed to slow variables competing with the jump motions, i.e., dynamic disorder. The present analysis of the dynamic disorder showed that the primary slow variable is the displacement of the fourth nearest oxygen atom of a jumping molecule, which occurs in an environment created by the fluctuations of molecules outside the first hydration shell. As the temperature decreases, the jump dynamics become slow and intermittent. These intermittent dynamics are attributed to the prolonged trapping of jumping molecules within extended and stable low-density domains. As the temperature continues to decrease, the number of slow variables increases due to the increased cooperative motions. Consequently, the jump dynamics proceed in a higher-dimensional space consisting of multiple slow variables, becoming slower and more intermittent. It is then conceivable that with further decreasing temperature, the slowing and intermittency of the jump dynamics intensify, eventually culminating in a glass transition.

Relating fragile-to-strong transition to fragile glass via lattice model simulations

Glass formers are, in general, classified as strong or fragile depending on whether their relaxation rates follow Arrhenius or super-Arrhenius temperature dependence. There are, however, notable exceptions, such as water, which exhibit a fragile-to-strong (FTS) transition and behave as fragile and strong, respectively, at high and low temperatures. In this work, the FTS transition is studied using a distinguishable-particle lattice model previously demonstrated to be capable of simulating both strong and fragile glasses [C.-S. Lee, M. Lulli, L.-H. Zhang, H.-Y. Deng, and C.-H. Lam, Phys. Rev. Lett. 125, 265703 (2020)0031-900710.1103/PhysRevLett.125.265703]. Starting with a bimodal pair-interaction distribution appropriate for fragile glasses, we show that by narrowing down the energy dispersion in the low-energy component of the distribution, a FTS transition is observed. The transition occurs at a temperature at which the stretching exponent of the relaxation is minimized, in agreement with previous molecular dynamics simulations.

Unraveling thermodynamic anomalies of water: A molecular simulation approach to probe the two-state theory with atomistic and coarse-grained water models

Thermodynamic and dynamic anomalies of water play a crucial role in supporting life on our planet. The two-state theory attributes these anomalies to a dynamic equilibrium between locally favored tetrahedral structures (LFTSs) and disordered normal liquid structures. This theory provides a straightforward, phenomenological explanation for water's unique thermodynamic and dynamic characteristics. To validate this two-state feature, it is critical to unequivocally identify these structural motifs in a dynamically fluctuating disordered liquid. In this study, we employ a recently introduced structural parameter (θavg) that characterizes the local angular order within the first coordination shell to identify these LFTSs through molecular dynamics simulations. We employ both realistic water models with a liquid-liquid critical point (LLCP) and a coarse-grained water model without an LLCP to study water's anomalies in low-pressure regions below 2 kbar. The two-state theory consistently describes water's thermodynamic anomalies in these models, both with and without an LLCP. This suggests that the anomalies predominantly result from the two-state features rather than criticality, particularly within experimentally accessible temperature-pressure regions.

An entropy trap model of thermodynamic anomalies for dual-amorphous water undergoing liquid-liquid phase transition

Water displays numerous anomalously thermodynamic behaviors. However, the working principles behind these anomalies are not well understood, and the liquid-liquid phase transition (LLPT) is often regarded as the potential reason. In this study, we developed an entropy trap model to characterize the thermodynamic LLPT in dual-amorphous water, i.e. having both low-density and high-density liquid water. From the Adam-Gibbs model and free-volume theory, thermodynamic behaviors of water have been described using the proposed model, in which the constitutive relationships among density, heat capacity, thermal expansivity and glass transition temperature have been formulated. Moreover, the glass transition and its connection to thermodynamic behaviors were also investigated for dual-amorphous water. Finally, experimental data reported in the literature were used to verify effectiveness of the proposed model. This study is expected to provide a physical insight into the anomalous thermodynamics of dual-amorphous water undergoing the LLPT.

A statistical mechanical model of supercooled water based on minimal clusters of correlated molecules

In this paper, we apply a theoretical model for fluid state thermodynamics to investigate simulated water in supercooled conditions. This model, which we recently proposed and applied to sub- and super-critical fluid water [Zanetti-Polzi et al., J. Chem. Phys. 156(4), 44506 (2022)], is based on a combination of the moment-generating functions of the enthalpy and volume fluctuations as provided by two gamma distributions and provides the free energy of the system as well as other relevant thermodynamic quantities. The application we make here provides a thermodynamic description of supercooled water fully consistent with that expected by crossing the liquid-liquid Widom line, indicating the presence of two distinct liquid states. In particular, the present model accurately reproduces the Widom line temperatures estimated with other two-state models and well describes the heat capacity anomalies. Differently from previous models, according to our description, a cluster of molecules that extends beyond the first hydration shell is necessary to discriminate between the statistical fluctuation regimes typical of the two liquid states.

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

We investigate a metallic glass-forming (GF) material (Al₉₀Sm₁₀) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, T_g. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u²〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u²〉 for heated crystalline Cu. This comparative analysis between H and 〈u²〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10^-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.

Self-diffusion and shear viscosity for the TIP4P/Ice water model

With an ever-increasing interest in water properties, many intermolecular force fields have been proposed to describe the behavior of water. Unfortunately, good models for liquid water usually cannot provide simultaneously an accurate melting point for ice. For this reason, the TIP4P/Ice model was developed for targeting the melting point and has become the preferred choice for simulating ice at coexistence. Unfortunately, available data for its dynamic properties in the liquid state are scarce. Therefore, we demonstrate a series of simulations aimed at the calculation of transport coefficients for the TIP4P/Ice model over a large range of thermodynamic conditions, ranging from T = 245 K to T = 350 K, for the temperature, and from p = 0 to p = 500 MPa, for the pressure. We have found that the self-diffusion (shear viscosity) exhibits smaller (increased) values than TIP4P/2005 and experiments. However, rescaling the temperature with respect to the triple point temperature, as in a corresponding states plot, we find that TIP4P/Ice compares very well with TIP4P/2005 and experiment. Such observations allow us to infer that despite the different original purposes of these two models examined here, one can benefit from a vast number of reports regarding the behavior of transport coefficients for the TIP4P/2005 model and utilize them following the routine described in this paper.

Hydrogen Bond Dynamics and Phase Transitions of Water inside Carbon Nanotubes

Water dynamics in nanochannels are altered by confinement, particularly in small carbon nanotubes (CNTs). However, the mechanisms behind these effects remain unclear. To address these issues, we carried out extensive molecular dynamics (MD) simulations to investigate the structure and dynamics of water inside CNTs of different sizes (length of 20 nm and diameters vary from 0.8 nm to 5.0 nm) at different temperatures (from 200 K to 420 K). The radial density profile of water inside CNTs shows a single peak near the CNT walls for small nanotubes. For CNTs with larger sizes, water molecules are arranged into coaxial tubular sheets, the number of which increases with the CNT size. Subdiffusive behavior is observed for ultranarrow CNTs with diameters of 0.8 nm and 1 nm. As the size of CNTs increases, Fickian diffusion becomes evident. The hydrogen bond correlation function of water inside CNT decays slower than in bulk water, and the decay rate decreases as we increase the diameter of the CNTs. In large CNTs, the hydrogen bond lifetime of the innermost layer is shorter than the other layers and depends on temperature. Additional analysis of our results reveals that water molecules along the CNT axis show a non-Arrhenius to Arrhenius diffusion crossover. In general, the diffusion transition temperature is higher than that of bulk water, but it depends on the size of the CNT.

Self-Diffusion in Confined Water: A Comparison between the Dynamics of Supercooled Water in Hydrophobic Carbon Nanotubes and Hydrophilic Porous Silica

Confined liquids are model systems for the study of the metastable supercooled state, especially for bulk water, in which the onset of crystallization below 230 K hinders the application of experimental techniques. Nevertheless, in addition to suppressing crystallization, confinement at the nanoscale drastically alters the properties of water. Evidently, the behavior of confined water depends critically on the nature of the confining environment and the interactions of confined water molecules with the confining matrix. A comparative study of the dynamics of water under hydrophobic and hydrophilic confinement could therefore help to clarify the underlying interactions. As we demonstrate in this work using a few representative results from the relevant literature, the accurate assessment of the translational mobility of water molecules, especially in the supercooled state, can unmistakably distinguish between the hydrophilic and hydrophobic nature of the confining environments. Among the numerous experimental methods currently available, we selected nuclear magnetic resonance (NMR) in a field gradient, which directly measures the macroscopic translational self-diffusion coefficient, and quasi-elastic neutron scattering (QENS), which can determine the microscopic translational dynamics of the water molecules. Dielectric relaxation, which probes the re-orientational degrees of freedom, are also discussed.

Manifestations of the structural origin of supercooled water’s anomalies in the heterogeneous relaxation on the potential energy landscape

Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models—based on the assumption of the existence of two types of competing local states (or, structures) in liquid water—have been extremely successful in describing water’s thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a predefined structural order parameter-free approach to unambiguously identify two types of competing local states—entropically and energetically favored—with significantly different structural and energetic features in the TIP4P/2005 liquid water. This identification is based on the heterogeneous structural relaxation of the system in the potential energy landscape (PEL) during the steepest-descent energy minimization. This heterogeneous relaxation is characterized using order parameters inspired by the spin-glass transition in frustrated magnetic systems. We have further established a direct relationship between the population fluctuation of the two states and the anomalous behavior of the heat capacity in supercooled water. The composition-dependent spatial distribution of the entropically favored local states shows an interesting crossover from a spanning network-like single cluster to the spatially delocalized clusters in the close vicinity of the Widom line. Additionally, this study establishes a direct relationship between the topographic features of the PEL and the water’s thermodynamic anomalies in the supercooled state and provides alternate markers (in addition to the locus of maxima of thermodynamic response functions) for the Widom line in the phase plane.

Screening and collective effects in randomly pinned fluids: a new theoretical framework

We propose a theoretical framework for the dynamics of bulk isotropic hard-sphere systems in the presence of randomly pinned particles and apply this theory to supercooled water to validate it. Structural relaxation is mainly governed by local and non-local activated process. As the pinned fraction grows, a local caging constraint becomes stronger and the long range collective aspect of relaxation is screened by immobile obstacles. Different responses of the local and cooperative motions results in subtle predictions for how the alpha relaxation time varies with pinning and density. Our theoretical analysis for the relaxation time of water with pinned molecules quantitatively well describe previous simulations. In addition, the thermal dependence of relaxation for unpinned bulk water is also consistent with prior computational and experimental data.

Modularly Integrated System for Spatiotemporally Separated Solar Energy Storage and Release

The sun is regarded as an endless source of clean energy. However, the intermittent supply and dynamically changeable demand of solar energy, as well as its uneven regional distribution, have been continually motivating the technological research of practical strategies to realize the spatiotemporally separated solar energy harvest and utilization. Accordingly, we here developed an integrated system for efficient solar energy capture, stable storage, and on-demand release, which corresponds to the intricate design of three distinct modules, namely, a photothermal conversion module, a latent heat storage module, and a mechanical trigger module. Moreover, efficient heat transfer and long-term supercooled stability necessitate interfacial passivation to coordinate the physical coupling of different modules. In addition to providing an integrated prototype that demonstrates a closed energy cycle in practice, this study may further inspire a new paradigm for advanced solar utilization in both theory and methodology.

Understanding the Fragile-to-Strong Transition in Silica from Microscopic Dynamics

In this work, we revisit the fragile-to-strong transition (FTS) in the simulated BKS silica from the perspective of microscopic dynamics in an effort to elucidate the dynamical behaviors of fragile and strong glass-forming liquids. Softness, which is a machine-learned feature from local atomic structures, is used to predict the microscopic activation energetics and long-term dynamics. The FTS is found to originate from a change in the temperature dependence of the microscopic activation energetics. Furthermore, results suggest there are two diffusion channels with different energy barriers in BKS silica. The fast dynamics at high temperatures is dominated by the channel with small energy barriers (<∼1  eV), which is controlled by the short-range order. The rapid closing of this diffusion channel when lowering temperature leads to the fragile behavior. On the other hand, the slow dynamics at low temperatures is dominated by the channel with large energy barriers controlled by the medium-range order. This slow diffusion channel changes only subtly with temperature, leading to the strong behavior. The distributions of barriers in the two channels show different temperature dependences, causing a crossover at ∼3100  K. This transition temperature in microscopic dynamics is consistent with the inflection point in the configurational entropy, suggesting there is a fundamental correlation between microscopic dynamics and thermodynamics.

Steady-like topology of the dynamical hydrogen bond network in supercooled water

We investigate the link between topology of the hydrogen bond network (HBN) and large-scale density fluctuations in water from ambient conditions to the glassy state. We observe a transition from a temperature-dependent topology at high temperatures, to a steady-like topology below the Widom temperature T_W ∼ 220 K signaling the fragile-to-strong crossover and the maximum in structural fluctuations. As a consequence of the steady topology, the network suppresses large-scale density fluctuations much more efficiently than at higher temperatures. Below T_W , the contribution of coordination defects of the kind A ₂ D ₁ (two acceptors and one donor) to the kinetics of the HBN becomes progressively more pronounced, suggesting that A ₂ D ₁ configurations may represent the main source of dynamical heterogeneities. Below the vitrification temperature, the freezing of rotational and translational degrees of freedom allow for an enhanced suppression of large-scale density fluctuations and the sample reaches the edges of nearly hyperuniformity. The formed network still hosts coordination defects, hence implying that nearly hyperuniformity goes beyond the classical continuous random network paradigm of tetrahedral networks and can emerge in scenarios much more complex than previously assumed. Our results unveil a hitherto undisclosed link between network topology and properties of water essential for better understanding water's rich and complex nature. Beyond implications for water, our findings pave the way to a better understanding of the physics of supercooled liquids and disordered hyperuniform networks at large.

Connection between water's dynamical and structural properties: Insights from ab initio simulations

SignificanceFirst-principles calculations, which explicitly account for the electronic structure of matter, can shed light on the molecular structure and dynamics of water in its supercooled state. In this work, we use density functional theory, which relies on a functional to describe electronic exchange and correlations, to evaluate which functional best describes the temperature evolution of bulk water transport coefficients. We also assess the validity of the Stokes-Einstein relation for all the functionals in the temperature range studied, and explore the link between structure and dynamics. Based on these results, we show how transport coefficients can be computed from structural descriptors, which require shorter simulation times to converge, and we point toward strategies to develop better functionals.

How do interfaces alter the dynamics of supercooled water?

The structure of liquid water in the proximity of an interface can deviate significantly from that of bulk water, with surface-induced structural perturbations typically converging to bulk values at about ∼1 nm from the interface. While these structural changes are well established it is, in contrast, less clear how an interface perturbs the dynamics of water molecules within the liquid. Here, through an extensive set of molecular dynamics simulations of supercooled bulk and interfacial water films and nano-droplets, we observe the formation of persistent, spatially extended dynamical domains in which the average mobility varies as a function of the distance from the interface. This is in stark contrast with the dynamical heterogeneity observed in bulk water, where these domains average out spatially over time. We also find that the dynamical response of water to an interface depends critically on the nature of the interface and on the choice of interface definition. Overall these results reveal a richness in the dynamics of interfacial water that opens up the prospect of tuning the dynamical response of water through specific modifications of the interface structure or confining material.

Isotope effects on the structural transformation and relaxation of deeply supercooled water

We have examined the structure of supercooled liquid D2O as a function of temperature between 185 and 255 K using pulsed laser heating to rapidly heat and cool the sample on a nanosecond timescale. The liquid structure can be represented as a linear combination of two structural motifs, with a transition between them described by a logistic function centered at 218 K with a width of 10 K. The relaxation to a metastable state, which occurred prior to crystallization, exhibited nonexponential kinetics with a rate that was dependent on the initial structural configuration. When the temperature is scaled by the temperature of maximum density, which is an isostructural point of the isotopologues, the structural transition and the non-equilibrium relaxation kinetics of D2O agree remarkably well with those for H2O.

Phase transition of supercooled water confined in cooperative two-state domain

The question of 'what is the structure of water?' has been regarded as one of the major scientific conundrums in condensed-matter physics due to the complex phase behavior and condensed structure of supercooled water. Great effort has been made so far using both theoretical analysis based on various mathematical models and computer simulations such as molecular dynamics and first-principle. However, these theoretical and simulation studies often do not have strong evidences of condensed-matter physics to support. In this study, a cooperative domain model is formulated to describe the dynamic phase transition of supercooled water between supercooled water and amorphous ice, both of which are composed of low- and high-density liquid water. Free volume theory is initially employed to identify the working principle of dynamic phase transition and its connection to glass transition in the supercooled water. Then a cooperative two-state model is developed to characterize the dynamic anomalies of supercooled water, including density, viscosity and self-diffusion coefficient. Finally, the proposed model is verified using the experimental results reported in literature.

The physics of empty liquids: from patchy particles to water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Folded network and structural transition in molten tin

The fundamental relationships between the structure and properties of liquids are far from being well understood. For instance, the structural origins of many liquid anomalies still remain unclear, but liquid-liquid transitions (LLT) are believed to hold a key. However, experimental demonstrations of LLTs have been rather challenging. Here, we report experimental and theoretical evidence of a second-order-like LLT in molten tin, one which favors a percolating covalent bond network at high temperatures. The observed structural transition originates from the fluctuating metallic/covalent behavior of atomic bonding, and consequently a new paradigm of liquid structure emerges. The liquid structure, described in the form of a folded network, bridges two well-established structural models for disordered systems, i.e., the random packing of hard-spheres and a continuous random network, offering a large structural midground for liquids and glasses. Our findings provide an unparalleled physical picture of the atomic arrangement for a plethora of liquids, shedding light on the thermodynamic and dynamic anomalies of liquids but also entailing far-reaching implications for studying liquid polyamorphism and dynamical transitions in liquids.

Unraveling the structural origin of liquid anomalies remains a challenging topic. Xu et al. propose a folded-network structural model for molten tin and provide insights into the observed second-order-like structural transition.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Supercooled nano-droplets of water confined in hydrophobic rubber

Hydrophobic elastomers are capable of absorbing a small amount of water that forms droplets around hydrophilic sites. These systems allow the study of confinement effects by a hydrophobic environment on the dynamics and thermodynamic behaviour of water molecules. The freezing-melting properties and the dynamics of water inside nano-droplets in butyl rubber are affected, as revealed by differential scanning calorimetry (DSC) and deuterium nuclear magnetic resonance (²H-NMR). Upon cooling down, all water crystalizes with a bimodal droplet population (d_a = 3.4 nm and d_b = 4.4 nm) in a temperature range associated with the droplet size distribution. However, the melting temperature is not shifted according to the Gibbs-Thomson equation. The relative decrease of the ²H-NMR longitudinal magnetization is not a single exponential and, by inverse Laplace transformation, it was deduced to be bimodal in agreement with the DSC measurements (T_1,a ∼ 10 ms and T_1,b ∼ 200 ms). The deduced correlation time of molecular reorientation is longer than that of bulk water and the behaviour with temperature follows the Vogel-Fulcher-Tammann (VFT) equations with a changing fragility as the droplet size is reduced when reducing hydration.

Conservation of the Stokes-Einstein relation in supercooled water

The Stokes-Einstein (SE) relation is commonly regarded as being breakdown in supercooled water. However, this conclusion is drawn by testing the validity of some variants of the SE relation rather than its original form, and it appears conflicting with the fact that supercooled water is in its local equilibrium. In this work, we show by molecular dynamics simulations that the Stokes-Einstein relation is indeed conserved in supercooled water. The inconsistency between the original SE relation and its variants comes from two facts: (1) the substitutes of the shear viscosity in the SE variants are only approximate relations; and (2) the effective hydrodynamic radius actually decreases with decreasing temperature, instead of being a constant as assumed in the SE variants.

Effect of Size and Temperature on Water Dynamics inside Carbon Nano-Tubes Studied by Molecular Dynamics Simulation

Water transport inside carbon nano-tubes (CNTs) has attracted considerable attention due to its nano-fluidic properties, its importance in nonporous systems, and the wide range of applications in membrane desalination and biological medicine. Recent studies show an enhancement of water diffusion inside nano-channels depending on the size of the nano-confinement. However, the underlying mechanism of this enhancement is not well understood yet. In this study, we performed Molecular Dynamics (MD) simulations to study water flow inside CNT systems. The length of CNTs considered in this study is 20 nm, but their diameters vary from 1 to 10 nm. The simulations are conducted at temperatures ranging from 260 K to 320 K. We observe that water molecules are arranged into coaxial water tubular sheets. The number of these tubular sheets depends on the CNT size. Further analysis reveals that the diffusion of water molecules along the CNT axis deviates from the Arrhenius temperature dependence. The non-Arrhenius relationship results from a fragile liquid-like water component persisting at low temperatures with fragility higher than that of the bulk water.

Large heat-capacity jump in cooling-heating of fragile glass from kinetic Monte Carlo simulations based on a two-state picture

The specific-heat capacity c_{v} of glass formers undergoes a hysteresis when subjected to a cooling-heating cycle, with a larger c_{v} and a more pronounced hysteresis for fragile glasses than for strong ones. Here we show that these experimental features, including the unusually large magnitude of c_{v} of fragile glasses, are well reproduced by kinetic Monte Carlo and equilibrium study of a distinguishable particle lattice model incorporating a two-state picture of particle interactions. The large c_{v} in fragile glasses is caused by a dramatic transfer of probabilistic weight from high-energy particle interactions to low-energy ones as temperature decreases.

Wide-angle X-ray scattering and molecular dynamics simulations of supercooled protein hydration water

Understanding the mechanism responsible for the protein low-temperature crossover observed at T≈ 220 K can help us improve current cryopreservation technologies. This crossover is associated with changes in the dynamics of the system, such as in the mean-squared displacement, whereas experimental evidence of structural changes is sparse. Here we investigate hydrated lysozyme proteins by using a combination of wide-angle X-ray scattering and molecular dynamics (MD) simulations. Experimentally we suppress crystallization by accurate control of the protein hydration level, which allows access to temperatures down to T = 175 K. The experimental data indicate that the scattering intensity peak at Q = 1.54 Å-1, attributed to interatomic distances, exhibits temperature-dependent changes upon cooling. In the MD simulations it is possible to decompose the water and protein contributions and we observe that, while the protein component is nearly temperature independent, the hydration water peak shifts in a fashion similar to that of bulk water. The observed trends are analysed by using the water-water and water-protein radial distribution functions, which indicate changes in the local probability density of hydration water.

Vitrification of octonary perylene mixtures with ultralow fragility

Strong glass formers with a low fragility are highly sought-after because of the technological importance of vitrification. In the case of organic molecules and polymers, the lowest fragility values have been reported for single-component materials. Here, we establish that mixing of organic molecules can result in a marked reduction in fragility. Individual bay-substituted perylene derivatives display a high fragility of more than 70. Instead, slowly cooled perylene mixtures with more than three components undergo a liquid-liquid transition and turn into a strong glass former. Octonary perylene mixtures display a fragility of 13 ± 2, which not only is a record low value for organic molecules but also lies below values reported for the strongest known inorganic glass formers. Our work opens an avenue for the design of ultrastrong organic glass formers, which can be anticipated to find use in pharmaceutical science and organic electronics.

Two States of Water Converge to One State below 215 K

Anomalies of water have been explained by the two-state water model. In the model, water becomes one state upon supercooling. However, water crystallizes completely below 235 K ("no man's land"). The structural origin of the anomalous of the water is hidden in the "no man's land". To understand the properties of water, the spectroscopic experiment in "Norman's land" is inevitable. Hence, we proposed a new soft-confinement method for standard nuclear magnetic resonance spectroscopy to explore the "no man's land". We found the singularity temperature (215 K) at ambient pressure. Water exists in one state below 215 K. Above 215 K, the two states of water are supercritical states of the liquid-liquid critical point. The current study provides a perspective to determine the liquid-liquid critical point of water existing in a high-pressure condition.

Transition pathway of hydrogen bond switching in supercooled water analyzed by the Markov state model

In this work, we examine hydrogen-bond (H-bond) switching by employing the Markov State Model (MSM). During the H-bond switching, a water hydrogen initially H-bonded with water oxygen becomes H-bonded to a different water oxygen. MSM analysis was applied to trajectories generated from molecular dynamics simulations of the TIP4P/2005 model from a room-temperature state to a supercooled state. We defined four basis states to characterize the configuration between two water molecules: H-bonded ("H"), unbound ("U"), weakly H-bonded ("w"), and alternative H-bonded ("a") states. A 16 × 16 MSM matrix was constructed, describing the transition probability between states composed of three water molecules. The mean first-passage time of the H-bond switching was estimated by calculating the total flux from the HU to UH states. It is demonstrated that the temperature dependence of the mean first-passage time is in accordance with that of the H-bond lifetime determined from the H-bond correlation function. Furthermore, the flux for the H-bond switching is decomposed into individual pathways that are characterized by different forms of H-bond configurations of trimers. The dominant pathway of the H-bond switching is found to be a direct one without passing through such intermediate states as "w" and "a," the existence of which becomes evident in supercooled water. The pathway through "w" indicates a large reorientation of the donor molecule. In contrast, the pathway through "a" utilizes the tetrahedral H-bond network, which is revealed by the further decomposition based on the H-bond number of the acceptor molecule.

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.

The subtle connections between water’s supercooled liquid and glassy states are difficult to characterize. Gartner et al. suggest with MD simulations that the long-range structure of glassy water may reflect signatures of water’s debated second critical point in the supercooled liquid.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

Structural relaxation and crystallization in supercooled water from 170 to 260 K

The origin of water's anomalous properties has been debated for decades. Resolution of the problem is hindered by a lack of experimental data in a crucial region of temperatures, T, and pressures where supercooled water rapidly crystallizes-a region often referred to as "no man's land." A recently developed technique where water is heated and cooled at rates greater than 10⁹ K/s now enables experiments in this region. Here, it is used to investigate the structural relaxation and crystallization of deeply supercooled water for 170 K < T < 260 K. Water's relaxation toward a new equilibrium structure depends on its initial structure with hyperquenched glassy water (HQW) typically relaxing more quickly than low-density amorphous solid water (LDA). For HQW and T > 230 K, simple exponential relaxation kinetics is observed. For HQW at lower temperatures, increasingly nonexponential relaxation is observed, which is consistent with the dynamics expected on a rough potential energy landscape. For LDA, approximately exponential relaxation is observed for T > 230 K and T < 200 K, with nonexponential relaxation only at intermediate temperatures. At all temperatures, water's structure can be reproduced by a linear combination of two, local structural motifs, and we show that a simple model accounts for the complex kinetics within this context. The relaxation time, τ _rel , is always shorter than the crystallization time, τ _xtal For HQW, the ratio, τ _xtal /τ _rel , goes through a minimum at ∼198 K where the ratio is about 60.

On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover

The problem of large-density variations in supercooled and ambient water has been widely discussed in the past years. Recent studies have indicated the possibility of nanometer-sized density variations on the subpicosecond and picosecond time scales. The nature of fluctuating density heterogeneities remains a highly debated issue. In the present work, we address the problem of possible association of such density variations with the dynamics of terahertz longitudinal acoustic-like modes in liquid water. Our study is based on the fact that the subpicosecond dynamics of liquid water are essentially governed by the structural relaxation. Using a mode coupling theory approach, we found that for typical values of parameters of liquid water, the dynamic mechanism coming from the combination of the structural relaxation process and the finiteness of the amplitude of terahertz longitudinal acoustic-like mode gives rise to a soliton-like collective mode on a temperature-dependent nanometer length scale. The characteristics of this mode are consistent with the estimates of the amplitudes and temperature-dependent correlation lengths of density fluctuations in liquid water obtained in experiments and simulations. Thus, the fully dynamic mechanism could contribute to the formation and dynamics of fluctuating density heterogeneities. The soliton-like collective excitations suggested by our analysis may be relevant to different phenomena connected with supercooled water and can be expected to be associated with some ultrafast biological processes.

Towards molecular movies with X-ray photon correlation spectroscopy

In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

Water diffusion in carbon nanotubes: Interplay between confinement, surface deformation, and temperature

In this article, we investigate, through molecular dynamics simulations, the diffusion behavior of the TIP4P/2005 water confined in pristine and deformed carbon nanotubes (armchair and zigzag). To analyze different diffusive mechanisms, the water temperature was varied as 210 ≤ T ≤ 380 K. The results of our simulations reveal that water presents a non-Arrhenius to Arrhenius diffusion crossover. The confinement shifts the diffusion transition to higher temperatures when compared with the bulk system. In addition, for narrower nanotubes, water diffuses in a single line, which leads to its mobility independent of the activation energy.

Could Chemical Reaction at the Molecular Level Show Distinction between Two Liquid-Water States? Study of the Excited-State Water-Catalyzed Proton Transfer Reaction Provides a Clue

The two liquid-water states, which lead to some anomalies when temperature crosses over 50 ± 10 °C at the atmospheric pressure, have been continuously catching popular attention. In this study, using the excited-state proton transfer (ESPT) catalyzed by water molecules as a prototypical reaction, we demonstrate that the kinetics of ESPT indeed is influenced by the two liquid-water states. In the water-catalyzed ESPT of 3-cyano-7-azaindole (3CAI), a repetitive and comprehensive temperature-dependent study of ESPT in H₂O from 0 to 90 °C shows anomalous behavior. The plot of the logarithm of ESPT rate constant as a function of inverse of absolute temperature deviates from a straight line. The convex-Arrhenius behavior manifests the activation free energy for water-assisted ESPT being dependent on temperature and hence the liquid water structure. To simplify the discussion, the plot is well fitted by using two straight lines that are crossed over in the vicinity of 40 °C. The free energy difference between water-solvated 3CAI and the 1:1 H₂O:3CAI complex is deduced to be 2.29 ± 0.04 and 1.96 ± 0.04 kcal·mol^-1 in the regions of 0-40 and 40-90 °C water, respectively, which also results in different frequency factors, i.e., the proton transfer/tunneling rates of (5.83 ± 0.36) × 10¹⁰ and (3.48 ± 0.27) × 10¹⁰ s^-1, respectively. In a qualitative manner, the results are then rationalized by the different types of H-bonding configuration as proposed for two liquid-water phases, rendering experimental evidence to support the different water phases in ambient temperatures at 1 bar.

Autonomously revealing hidden local structures in supercooled liquids

Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids. To explore this link, much research has been devoted to pinpointing local structures and order parameters that correlate strongly with dynamics. Here we use an unsupervised machine learning algorithm to identify structural heterogeneities in three archetypical glass formers—without using any dynamical information. In each system, the unsupervised machine learning approach autonomously designs a purely structural order parameter within a single snapshot. Comparing the structural order parameter with the dynamics, we find strong correlations with the dynamical heterogeneities. Moreover, the structural characteristics linked to slow particles disappear further away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.

The origin of dynamical slowdown in disordered materials remains elusive, especially in the absence of obvious structural changes. Boattini et al. use unsupervised machine learning to reveal correlations between structural and dynamical heterogeneity in supercooled liquids.

The anomalies and criticality of liquid water

The origin of water's anomalies has been a matter of long-standing debate. A two-state model, dating back to Röntgen, relies on the dynamical coexistence of two types of local structures-locally favored tetrahedral structure (LFTS) and disordered normal-liquid structure (DNLS)-in liquid water. Phenomenologically, this model not only explains water's thermodynamic anomalies but also can rationalize the existence of a liquid-liquid critical point (LLCP) if there is a cooperative formation of LFTS. We recently found direct evidence for the coexistence of LFTS and DNLS in the experimental structure factor of liquid water. However, the existence of the LLCP and its impact on water's properties has remained elusive, leaving the origin of water's anomalies unclear. Here we propose a unique strategy to locate the LLCP of liquid water. First, we make a comprehensive analysis of a large set of experimental structural, thermodynamic, and dynamic data based on our hierarchical two-state model. This model predicts that the two thermodynamic and dynamical fluctuation maxima lines should cross at the LLCP if it exists, which we confirm by hundred-microsecond simulations for model waters. Based on recent experimental results of the compressibility and diffusivity measurements in the no man's land, we reveal that the two lines cross around 184 K and 173 MPa for real water, suggesting the presence of the LLCP around there. Nevertheless, we find that the criticality is almost negligible in the experimentally accessible region of liquid water because it is too far from the LLCP. Our findings would provide a clue to settle the long-standing debate.

Reversible structural transformations in supercooled liquid water from 135 to 245 K

A fundamental understanding of the unusual properties of water remains elusive because of the limited data at the temperatures and pressures needed to decide among competing theories. We investigated the structural transformations of transiently heated supercooled water films, which evolved for several nanoseconds per pulse during fast laser heating before quenching to 70 kelvin (K). Water’s structure relaxed from its initial configuration to a steady-state configuration before appreciable crystallization. Over the full temperature range investigated, all structural changes were reversible and reproducible by a linear combination of high- and low-temperature structural motifs. The fraction of the liquid with the high-temperature motif decreased rapidly as the temperature decreased from 245 to 190 K, consistent with the predictions of two-state “mixture” models for supercooled water in the supercritical regime.

Dynamical Accuracy of Water Models on Supercooling

Molecular dynamics (MD) simulations are commonly used to explore the structural and dynamical properties of supercooled bulk water in the so-called "no man's land" (NML) (150-227 K), where crystallization occurs almost instantaneously. This approach has provided significant insight into experimentally inaccessible phenomena. In this paper, we compare the dynamics of simulations using one-, three-, and four-body water models to experimentally measured quasielastic neutron scattering spectra. We show that the agreement between simulated and experimental data becomes substantially worse with a decrease in temperature toward the deeply supercooled regime. It was found that it is mainly the nature of the local dynamics that is poorly reproduced, as opposed to the macroscopic properties such as the diffusion coefficient. This strongly implies that the molecular mechanism describing the water dynamics is poorly captured in the MD models, and simulated structural and dynamical properties of supercooled water in NML must be interpreted with care.

Anisotropic X-Ray Scattering of Transiently Oriented Water

We study the structural dynamics of liquid water by time-resolved anisotropic x-ray scattering under the optical Kerr effect condition. In this way, we can separate the anisotropic scattering decay of 160 fs from the delayed temperature increase of ∼0.1  K occurring at 1 ps and quantify transient changes in the O-O pair distribution function. Polarizable molecular dynamics simulations reproduce well the experiment, indicating transient alignment of molecules along the electric field, which shortens the nearest-neighbor distances. In addition, analysis of the simulated water local structure provides evidence that two hypothesized fluctuating water configurations exhibit different polarizability.