Liquid–liquid transition and polyamorphism

Distinguish microphase-separated structures of diblock copolymers using local order parameters

The microphase-separated structures of block copolymers are inherently highly ordered local structures, commonly characterized by differences in domain width and curvature. By focusing on diblock copolymers, we propose local order parameters (LOPs) that accurately distinguish between adjacent microphase-separated structures on the phase diagram. We used the Molecular Assembly structure Learning package for Identifying Order parameters (MALIO) to evaluate the structure classification performance of 186 candidate LOPs. MALIO calculates the numerical values of all candidate LOPs for the input microphase-separated structures to create a dataset, and then performs supervised machine learning to select the best LOPs quickly and systematically. We evaluated the robustness of the selected LOPs in terms of classification accuracy against variations in miscibility and fraction of block. The minimum local area size required for LOPs to achieve their classification performances is closely related to the characteristic sizes of the microphase-separated structures. The proposed LOPs are potentially applicable over a large area on the phase diagram.

Numerical evidence for the existence of three different stable liquid water structures as indicated by local order parameter

Structures of liquid water are controversial not only in supercooled polyamorphism but also in stable bulk liquids in the high temperature and pressure range. Several experimental studies in bulk liquid have assumed the existence of three different liquid water structures. If indeed the three liquid water structures are different, they should be clearly distinguished by some measure other than density that characterizes the difference in structural order. In this study, whether the three different bulk liquid water structures are real or not is numerically verified based on molecular simulations using a reliable water molecular model. Since these liquid water structures have been suggested to be related to three different crystal structures (i.e., ice Ih, III, and V), liquid structures are sampled from the vicinity of the ice Ih-liquid coexistence point, the ice III-V-liquid triple point, and the ice V-VI-liquid triple point, respectively. An attempt is made to introduce local order parameters (LOPs) as an indicator to distinguish these structures. A fast and exhaustive LOP search is performed by the molecular assembly structure learning package for Identifying order parameters. The selected LOP distinguishes the molecular structures of three different stable liquid waters with high accuracy, providing numerical evidence that these structural orders differ from each other. Furthermore, regions of the liquid water structures are drawn on a phase diagram using the LOP, demonstrating their consistency with experimental studies.

Liquid-Liquid Transition in a Bose Fluid near Collapse

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this Letter, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum Monte Carlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter η describing its strength. If η exceeds a characteristic value η_{c}, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for η≲η_{c}, finding-in addition to a liquid-vapor transition-a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As η approaches η_{c}, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for η larger than η_{c} our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.

Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating

We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3 K and 1-500 bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25 bar does not freeze down to 0.1 K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5 K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3 K at 40-50 bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.

Crystallization and the liquid-liquid critical point in nonbonded modified-WAC models

For decades, it has been known that Liquid-Liquid Critical Points (LLCPs) can exist in one-component liquids, yet a comprehensive understanding of the conditions under which they arise remains elusive. To better comprehend the possible interplay between the LLCP and the crystalline phase, we conduct molecular dynamics simulations using the nonbonded family of modified-WAC (mWAC) models, which are known to exhibit a LLCP for certain parameter values. By comparing different versions of the mWAC model-those featuring a LLCP and those lacking one-we identify several key differences between the models relating to crystallization. Those models that do have a LLCP are found to have multiple stable crystalline phases, one of them being a solid-state ionic conductor similar to superionic ice. Moreover, we find that for models that do not have a LLCP, the liquid becomes a glass at a larger range of temperatures, possibly preventing the occurrence of a LLCP. Further studies are required to determine if these results are general or model-specific.

High-pressure X-ray photon correlation spectroscopy at fourth-generation synchrotron sources

A new experimental setup combining X-ray photon correlation spectroscopy (XPCS) in the hard X-ray regime and a high-pressure sample environment has been developed to monitor the pressure dependence of the internal motion of complex systems down to the atomic scale in the multi-gigapascal range, from room temperature to 600 K. The high flux of coherent high-energy X-rays at fourth-generation synchrotron sources solves the problems caused by the absorption of diamond anvil cells used to generate high pressure, enabling the measurement of the intermediate scattering function over six orders of magnitude in time, from 10-3 s to 103 s. The constraints posed by the high-pressure generation such as the preservation of X-ray coherence, as well as the sample, pressure and temperature stability, are discussed, and the feasibility of high-pressure XPCS is demonstrated through results obtained on metallic glasses.

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.

Beyond Local Structures in Critical Supercooled Water through Unsupervised Learning

The presence of a second critical point in water has been a topic of intense investigation for the last few decades. The molecular origins underlying this phenomenon are typically rationalized in terms of the competition between local high-density (HD) and low-density (LD) structures. Their identification often requires designing parameters that are subject to human intervention. Herein, we use unsupervised learning to discover structures in atomistic simulations of water close to the liquid-liquid critical point (LLCP). Encoding the information on the environment using local descriptors, we do not find evidence for two distinct thermodynamic structures. In contrast, when we deploy nonlocal descriptors that probe instead heterogeneities on the nanometer length scale, this leads to the emergence of LD and HD domains rationalizing the microscopic origins of the density fluctuations close to criticality.

Tuning the low-temperature phase behavior of aqueous ionic liquids

Water's anomalous behavior is often explained using a two-liquid model, where two types of water, high-density liquid (HDL) and low-density liquid (LDL), can be separated via a liquid-liquid phase transition (LLPT) at low temperature. Mixtures of water and the ionic liquid hydrazinium trifluoroacetate were suggested to also show an LLPT but with the advantage that there is no rapid ice crystallization hampering its observation. It remains controversial whether these solutions exhibit an LLPT or are instead associated with complex phase separation phenomena. We here show detailed low-temperature calorimetry and diffraction experiments on aqueous solutions containing hydrazinium trifluoroacetate and other similar ionic liquids, all at a solute mole fraction of x = 0.175. Hydrazinium trifluoroacetate, ammonium trifluoroacetate, ethylammonium trifluoroacetate and hydrazinium pentafluoropropionate all boast exothermic transitions unrelated to crystallization as well as remarkable structural changes upon cooling into the glassy state. We propose a model inspired by micelle formation and decomposition in surfactant solutions, which is complemented by MD simulations and allows rationalizing the rich phase behavior of our mixtures during cooling. The fundamental aspect of the model is the hydrophobic nature of fluorinated anions that enables aggregation, which is reversed upon cooling and culminates in the remarkable exothermic first-order transition observed at low temperature. That is, we assign the first-order transition not to an LLPT but to phase-separations similar to the ones when falling below the Krafft temperature. All other solutions merely show simple vitrification behavior. Still, they exhibit distinct differences in liquid fragility, which is decreased continuously with decreasing hydrophobicity of the anions. This might enable the systematic tuning of ionic liquids with the goal of designing aqueous solutions of specific fragility.

Prediction of water anomalous properties by introducing the two-state theory in SAFT

Water is one of the most abundant substances on earth, but it is still not entirely understood. It shows unusual behavior, and its properties present characteristic extrema unlike any other fluid. This unusual behavior has been linked to the two-state theory of water, which proposes that water forms different clusters, one with a high density and one with a low density, which may even form two distinct phases at low temperatures. Models incorporating the two-state theory manage to capture the unusual extrema of water, unlike traditional equations of state, which fail. In this work, we have derived the framework to incorporate the two-state theory of water into the Statistical-Associating-Fluid-Theory (SAFT). More specifically, we have assumed that water is an ideal solution of high density water molecules and low density water molecules that are in chemical equilibrium. Using this assumption, we have generalized the association term SAFT to allow for the simultaneous existence of the two water types, which have the same physical parameters but different association properties. We have incorporated the newly derived association term in the context of the Perturbed Chain-SAFT (PC-SAFT). The new model is referred to as PC-SAFT-Two-State (PC-SAFT-TS). Using PC-SAFT-TS, we have succeeded in predicting the characteristic extrema of water, such as its density and speed of sound maximum, etc., without loss of accuracy compared to the original PC-SAFT. This new framework is readily extended to mixtures, and PC-SAFT-TS manages to capture the solubility minimum of hydrocarbons in water in a straightforward manner.

Identification of local structures in water from supercooled to ambient conditions

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.

Size Dependent Phase Transformation of Liquid Gallium

As the most popular liquid metal (LM), gallium (Ga) and its alloys are emerging as functional materials due to their unique combination of fluidic and metallic properties near room temperature. As an important branch of utilizing LMs, micro- and submicron-particles of Ga-based LM are widely employed in wearable electronics, catalysis, energy, and biomedicine. Meanwhile, the phase transition is crucial not only for the applications based on this reversible transformation process, but also for the solidification temperature at which fluid properties are lost. While Ga has several solid phases and exhibits unusual size-dependent phase behavior. This complex process makes the phase transition and undercooling of Ga uncontrollable, which considerably affects the application performance. In this work, extensive (nano-)calorimetry experiments are performed to investigate the polymorph selection mechanism during liquid Ga crystallization. It is surprisingly found that the crystallization temperature and crystallization pathway to either α -Ga or β -Ga can be effectively engineered by thermal treatment and droplet size. The polymorph selection process is suggested to be highly relevant to the capability of forming covalent bonds in the equilibrium supercooled liquid. The observation of two different crystallization pathways depending on the annealing temperature may indicate that there exist two different liquid phases in Ga.

High-dimensional order parameters and neural network classifiers applied to amorphous ices

Amorphous ice phases are key constituents of water's complex structural landscape. This study investigates the polyamorphic nature of water, focusing on the complexities within low-density amorphous ice (LDA), high-density amorphous ice, and the recently discovered medium-density amorphous ice (MDA). We use rotationally invariant, high-dimensional order parameters to capture a wide spectrum of local symmetries for the characterization of local oxygen environments. We train a neural network to classify these local environments and investigate the distinctiveness of MDA within the structural landscape of amorphous ice. Our results highlight the difficulty in accurately differentiating MDA from LDA due to structural similarities. Beyond water, our methodology can be applied to investigate the structural properties and phases of disordered materials.

Structure and polymerization of liquid sulfur across the λ-transition

The anomalous λ-transition of liquid sulfur, which is supposed to be related to the transformation of eight-membered sulfur rings into long polymeric chains, has attracted considerable attention. However, a detailed description of the underlying dynamical polymerization process is still missing. Here, we study the structures and the mechanism of the polymerization processes of liquid sulfur across the λ-transition as well as its reverse process of formation of the rings. We do so by performing ab initio-quality molecular dynamics simulations thanks to a combination of machine learning potentials and state-of-the-art enhanced sampling techniques. With our approach, we obtain structural results that are in good agreement with the experiments and we report precious dynamical insights into the mechanisms involved in the process.

Liquid-Liquid Crossover in Water Model: Local Structure vs Kinetics of Hydrogen Bonds

In equilibrium and supercooled liquids, polymorphism is manifested by thermodynamic regions defined in the phase diagram, which are predominantly of different short- and medium-range order (local structure). It is found that on the phase diagram of the water model, the thermodynamic region corresponding to the equilibrium liquid phase is divided by a line of the smooth liquid-liquid crossover. In the case of the water model TIP4P/2005, this crossover is revealed by various local order parameters and corresponds to pressures on the order of 3150 ± 350 atm at ambient temperature. In the vicinity of the crossover, the dynamics of water molecules change significantly, which is reflected, in particular, in the fact that the self-diffusion coefficient reaches its maximum values. In addition, changes in the structure also manifest themselves in changes in the kinetics of hydrogen bonding, which are captured by values of such quantities as the average lifetime of hydrogen bonding, the average lifetimes of different local coordination numbers, and the frequencies of changes in different local coordination numbers. An interpretation of the hydrogen bond kinetics in terms of the free energy landscape concept in the space of possible coordination numbers is proposed.

Microscopic mechanisms of pressure-induced amorphous-amorphous transitions and crystallisation in silicon

Some low-coordination materials, including water, silica, and silicon, exhibit polyamorphism, having multiple amorphous forms. However, the microscopic mechanism and kinetic pathway of amorphous-amorphous transition (AAT) remain largely unknown. Here, we use a state-of-the-art machine-learning potential and local structural analysis to investigate the microscopic kinetics of AAT in silicon after a rapid pressure change. We find that the transition from low-density-amorphous (LDA) to high-density-amorphous (HDA) occurs through nucleation and growth, resulting in non-spherical interfaces that underscore the mechanical nature of AAT. In contrast, the reverse transition occurs through spinodal decomposition. Further pressurisation transforms LDA into very-high-density amorphous (VHDA), with HDA serving as an intermediate state. Notably, the final amorphous states are inherently unstable, transitioning into crystals. Our findings demonstrate that AAT and crystallisation are driven by joint thermodynamic and mechanical instabilities, assisted by preordering, occurring without diffusion. This unique mechanical and diffusion-less nature distinguishes AAT from liquid-liquid transitions.

A Second Glass Transition Observed in Single-Component Homogeneous Liquids Due to Intramolecular Vitrification

On supercooling a liquid, the viscosity rises rapidly until at the glass transition it vitrifies into an amorphous solid accompanied by a steep drop in the heat capacity. Therefore, a pure homogeneous liquid is not expected to display more than one glass transition. Here we show that a family of single-component homogeneous molecular liquids, titanium tetraalkoxides, exhibit two calorimetric glass transitions of comparable magnitude, one of which is the conventional glass transition associated with dynamic arrest of the bulk liquid properties, while the other is associated with the freezing out of intramolecular degrees of freedom. Such intramolecular vitrification is likely to be found in molecules in which low-frequency terahertz intramolecular motion is coupled to the surrounding liquid. These results imply that intramolecular barrier-crossing processes, typically associated with chemical reactivity, do not necessarily follow the Arrhenius law but may freeze out at a finite temperature.

Remarkably Stable Glassy GeS2 Densified at 8.3 GPa: Hidden Polyamorphism, Contrasting Optical Properties, Raman and DFT Studies, and Advanced Applications

Glassy GeS2, densified at 8.3 GPa, exhibits a strongly reduced bandgap, predominantly tetrahedral Ge environment, enhanced chemical disorder and partial 3-fold coordination of both germanium and sulfur, assuming two possible reaction paths under high pressure: (i) a simple dissociation 2Ge-S ⇄ Ge-Ge + S-S and (ii) a chemical disproportionation GeS2 ⇄ GeS + S. The observed electronic and structural changes remain intact for at least seven years under ambient conditions but are gradually evolving upon heating. The relaxation kinetics at elevated temperatures, up to the glass transition temperature Tg, suggests that complete recovery of the densified glassy GeS2 over a typical operational T-range of optoelectronic devices will take many thousands of years. The observed logarithmic relaxation and nearly infinite recovery time at room temperature raise questions about the nature of millennia-long phenomena in densified GeS2. Two alternative explanations will be discussed: (1) hidden polyamorphism and (2) continuous structural and chemical changes under high pressure. These investigations offer valuable insights into the behavior of glassy GeS2 under extreme conditions and its potential applications in optoelectronic devices and other advanced technologies.

Anisotropy in spinodal-like dynamics of unknown water at ice V-water interface

Experimentally demonstrating the existence of waters with local structures unlike that of common water is critical for understanding both the origin of the mysterious properties of water and liquid polymorphism in single component liquids. At the interfaces between water and ices Ih, III, and VI grown/melted under pressure, we previously discovered low- and high-density unknown waters, that are immiscible with the surrounding water. Here, we show, by in-situ optical microscopy, that an unknown water appears at the ice V-water interface via spinodal-like dynamics. The dewetting dynamics of the unknown water indicate that its characteristic velocity is ~ 90 m/s. The time evolution of the characteristic length of the spinodal-like undulation suggests that the dynamics may be described by a common model for spinodal decomposition of an immiscible liquid mixture. Spinodal-like dewetting dynamics of the unknown water transiently showed anisotropy, implying the property of a liquid crystal.

Nanocrystallites Modulate Intermolecular Interactions in Cryoprotected Protein Solutions

Studying protein interactions at low temperatures has important implications for optimizing cryostorage processes of biological tissue, food, and protein-based drugs. One of the major issues is related to the formation of ice nanocrystals, which can occur even in the presence of cryoprotectants and can lead to protein denaturation. The presence of ice nanocrystals in protein solutions poses several challenges since, contrary to microscopic ice crystals, they can be difficult to resolve and can complicate the interpretation of experimental data. Here, using a combination of small- and wide-angle X-ray scattering (SAXS and WAXS), we investigate the structural evolution of concentrated lysozyme solutions in a cryoprotected glycerol-water mixture from room temperature (T = 300 K) down to cryogenic temperatures (T = 195 K). Upon cooling, we observe a transition near the melting temperature of the solution (T ≈ 245 K), which manifests both in the temperature dependence of the scattering intensity peak position reflecting protein-protein length scales (SAXS) and the interatomic distances within the solvent (WAXS). Upon thermal cycling, a hysteresis is observed in the scattering intensity, which is attributed to the formation of nanocrystallites in the order of 10 nm. The experimental data are well described by the two-Yukawa model, which indicates temperature-dependent changes in the short-range attraction of the protein-protein interaction potential. Our results demonstrate that the nanocrystal growth yields effectively stronger protein-protein attraction and influences the protein pair distribution function beyond the first coordination shell.

Intermediate-range order governs dynamics in dense colloidal liquids

The conventional wisdom is that liquids are completely disordered and lack nontrivial structure beyond nearest-neighbor distances. Recent observations have upended this view and demonstrated that the microstructure in liquids is surprisingly rich and plays a critical role in numerous physical, biological, and industrial processes. However, approaches to uncover this structure are either system-specific or yield results that are not physically intuitive. Here, through single-particle resolved three-dimensional confocal microscope imaging and the use of a recently introduced four-point correlation function, we show that bidisperse colloidal liquids have a highly nontrivial structure comprising alternating layers with icosahedral and dodecahedral order, which extends well beyond nearest-neighbor distances and grows with supercooling. By quantifying the dynamics of the system on the particle level, we establish that it is this intermediate-range order, and not the short-range order, which has a one-to-one correlation with dynamical heterogeneities, a property directly related to the relaxation dynamics of glassy liquids. Our experimental findings provide a direct and much sought-after link between the structure and dynamics of liquids and pave the way for probing the consequences of this intermediate-range order in other liquid state processes.

Generic maximum-valence model for fluid polyamorphism

Recently, a maximal-valence model has been proposed to model a liquid-liquid phase transition induced by polymerization in sulfur. In this paper we present a simple generic model to describe liquid polyamorphism in single-component fluids using a maximum-valence approach for any arbitrary coordination number. The model contains three types of interactions: (i) atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) additional repulsive forces between atoms with maximal valence and atoms with any valence. This additional repulsion generates liquid-liquid phase separation and the region of the negative heat expansion coefficient (density anomaly) on a P-T phase diagram. We show the existence of liquid-liquid phase transitions for dimerization, polymerization, gelation, and network formation for corresponding coordination numbers z=1,2,...,6 and discuss the limits of this generic model for producing fluid polyamorphism.

Correlated Fluctuations of Structural Indicators Close to the Liquid-Liquid Transition in Supercooled Water

Multiple numerical studies have unambiguously shown the existence of a liquid-liquid critical point in supercooled states for different numerical models of water, and various structural indicators have been put forward to describe the transformation associated with this phase transition. Here we analyze numerical simulations of near-critical supercooled water to compare the behavior of several of such indicators with critical density fluctuations. We show that close to the critical point most indicators are strongly correlated to density, and some of them even display identical distributions of fluctuations. These indicators probe the exact same free energy landscape, therefore providing a thermodynamic description of critical supercooled water which is identical to that provided by the density order parameter. This implies that close to the critical point, there is a tight coupling between many, only apparently distinct, structural degrees of freedom.

Thermal Conductivity of Solid Triphenyl Phosphite

The thermal conductivity, κ, of solid triphenyl phosphite was measured by using the transient hot-wire method, and its temperature and pressure dependencies were analyzed to understand heat transfer processes in the solid polymorphic phases, as well as in the glass and the exotic glacial state. Phase transformations and the structural order of the phases are discussed, and a transitional pressure-temperature diagram of triphenyl phosphite is presented. The thermal conductivity of both the crystalline and disordered states is described within the theory of two-channel heat transfer by phonons and diffusons in dielectric solids. In the glass and glacial states, the weakly temperature-dependent (glass-like) κ is described well by the term associated with heat conduction of diffusons only, and it can be represented by an Arrhenius-type function. In the crystal phases, the strongly temperature-dependent (crystal-like) κ associated with heat transfer by phonons is weakened by significant heat transfer by diffusons, and the extent of the two contributions is reflected in the temperature dependence of κ. We find that the contribution of diffusons in the crystal phases depends on pressure in the same way as that in amorphous states, thus indicating that the same mechanism is responsible for this channel of heat transfer in crystals and amorphous states.

Thermodynamic modeling of fluid polyamorphism in hydrogen at extreme conditions

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid–fluid phase transition (FFPT) in high-pressure hydrogen between insulating and conducting high-density fluids. This transition is induced by the reversible dimerization/dissociation of the molecular and atomistic states of hydrogen. In this work, we present the first attempt to thermodynamically model the FFPT in hydrogen at extreme conditions. Our predictions for the phase coexistence and the reaction equilibrium of the two alternative forms of fluid hydrogen are based on experimental data and supported by the results of simulations. Remarkably, we find that the law of corresponding states can be utilized to construct a unified equation of state combining the available computational results for different models of hydrogen and the experimental data.

Water's Unusual Thermodynamics in the Realm of Physical Chemistry

While it is known since the early work by Edsall, Frank and Evans, Kauzmann, and others that the thermodynamics of solvation of nonpolar solutes in water is unusual and has implications for the thermodynamics of protein folding, only recently have its connections with the unusual temperature dependence of the density of solvent water been illuminated. Such density behavior is, in turn, one of the manifestations of a nonstandard thermodynamic pattern contemplating a second, liquid-liquid critical point at conditions of temperature and pressure at which water exists as a deeply supercooled liquid. Recent experimental and computational work unambiguously points toward the existence of such a critical point, thereby providing concrete answers to the questions posed by the 1976 pioneering experiments by Speedy and Angell and the associated "liquid-liquid transition hypothesis" posited in 1992 by Stanley and co-workers. Challenges of this phenomenology to the branch of Statistical Mechanics remain.

Liquid-liquid phase transition in deeply supercooled Stillinger-Weber silicon

The existence of a phase transition between two distinct liquid phases in single-component network-forming liquids (e.g. water, silica, silicon) has elicited considerable scientific interest. The challenge, both for experiments and simulations, is that the liquid-liquid phase transition (LLPT) occurs under deeply supercooled conditions, where crystallization occurs very rapidly. Thus, early evidence from numerical equation of state studies was challenged with the argument that slow spontaneous crystallization had been misinterpreted as evidence of a second liquid state. Rigorous free-energy calculations have subsequently confirmed the existence of a LLPT in some models of water, and exciting new experimental evidence has since supported these computational results. Similar results have so far not been found for silicon. Here, we present results from free-energy calculations performed for silicon modeled with the classical, empirical Stillinger-Weber-potential. Through a careful study employing state-of-the-art constrained simulation protocols and numerous checks for thermodynamic consistency, we find that there are two distinct metastable liquid states and a phase transition. Our results resolve a long-standing debate concerning the existence of a liquid-liquid transition in supercooled liquid silicon and address key questions regarding the nature of the phase transition and the associated critical point.

Structural changes across thermodynamic maxima in supercooled liquid tellurium: A water-like scenario

Liquid polymorphism is an intriguing phenomenon that has been found in a few single-component systems, the most famous being water. By supercooling liquid Te to more than 130 K below its melting point and performing simultaneous small-angle and wide-angle X-ray scattering measurements, we observe clear maxima in its thermodynamic response functions around 615 K, suggesting the possible existence of liquid polymorphism. A close look at the underlying structural evolution shows the development of intermediate-range order upon cooling, most strongly around the thermodynamic maxima, which we attribute to bond-orientational ordering. The striking similarities between our results and those of water, despite the lack of hydrogen-bonding and tetrahedrality in Te, indicate that water-like anomalies may be a general phenomenon among liquid systems with competing bond- and density-ordering.

Modeling fluid polyamorphism through a maximum-valence approach

We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: (i) Atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) atoms with maximal valence attract or repel each other stronger than other atoms, thus generating liquid-liquid separation. As an example, we qualitatively compare this model with the behavior of liquid sulfur and show that condition (iii) generates a liquid-liquid phase transition in addition to the liquid-gas phase transition.

Liquid-Liquid Criticality in the WAIL Water Model

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 parametrized 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 [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.

Low- and High-Density Unknown Waters at Ice-Water Interfaces

Experimental confirmation of liquid polymorphs of water, high-density liquid (HDL) and low-density liquid (LDL), is desired for understanding not only the liquid state of matter but also the origin of the mysterious properties of water. However, this remains challenging because the liquid-liquid critical point of water lies in experimentally inaccessible supercooling conditions known as "no man's land". Here, we show by in situ optical microscopy that droplets and layers of low- and high-density unknown waters (LDUW and HDUW) appear macroscopically depending upon ice polymorphs at non-equilibrium interfaces between water and ices under experimentally accessible (de)pressurization conditions. These unknown waters were found to have characteristic velocities (about 20 and 100 m/s for LDUW and HDUW, respectively) different from water (about 40 m/s) and quasi-liquid layers (QLLs) (about 2 and 0.2 m/s for droplet and layer forms of QLLs, respectively). Our discoveries provide insight on liquid polymorphism of water.

Interplay of vitrification and ice formation in a cryoprotectant aqueous solution at low temperature

The proneness of water to crystallize is a major obstacle to understanding its putative exotic behavior in the supercooled state. It also represents a strong practical limitation to cryopreservation of biological systems. Adding some concentration of glycerol, which has a cryoprotective effect preventing, to some degree, water crystallization, has been proposed as a possible way out, provided the concentration is small enough for water to retain some of its bulk character and/or for limiting the damage caused by glycerol on living organisms. Contrary to previous expectations, we show that, in the “marginal” glycerol molar concentration ≈ 18%, at which vitrification is possible with no crystallization on rapid cooling, water crystallizes upon isothermal annealing even below the calorimetric glass transition of the solution. Through a time-resolved polarized neutron scattering investigation, we extract key parameters, size and shape of the ice crystallites, fraction of water that crystallizes, and crystallization time, which are important for cryoprotection, as a function of the annealing temperature. We also characterize the nature of the out-of-equilibrium liquid phases that are present at low temperature, providing more arguments against the presence of an isocompositional liquid–liquid transition. Finally, we propose a rule of thumb to estimate the lower temperature limit below which water crystallization does not occur in aqueous solutions.

Phase transitions affected by natural and forceful molecular interconversion

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g., the equilibrium interconversion of enantiomers) or forcefully (e.g., via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we phenomenologically generalize the Cahn–Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.

Oxygen NMR of high-density and low-density amorphous ice

Using oxygen-17 as a nuclear probe, spin relaxometry was applied to study the high-density and low-density states of amorphous ice, covering temperatures below and somewhat above their glass transitions. These findings are put in perspective with results from deuteron nuclear magnetic resonance and with calculations based on dielectrically detected correlation times. This comparison reveals the presence of a wide distribution of correlation times. Furthermore, oxygen-17 central-transition echo spectra were recorded for wide ranges of temperature and pulse spacing. The spectra cannot be described by a single set of quadrupolar parameters, suggesting a distribution of H–O–H opening angles that is broader for high-density than for low-density amorphous ice. Simulations of the pulse separation dependent spin-echo spectra for various scenarios demonstrate that a small-step frequency diffusion process, assigned to the presence of homonuclear oxygen–oxygen interactions, determines the shape evolution of the pulse-separation-dependent spectra.

Multiple Melting Temperatures in Glass-Forming Melts

All materials are vitrified by fast quenching even monoatomic substances. Second melting temperatures accompanied by weak exothermic or endothermic heat are often observed at Tn+ after remelting them above the equilibrium thermodynamic melting transition at Tm. These temperatures, Tn+, are due to the breaking of bonds (configurons formation) or antibonds depending on the thermal history, which is explained by using a nonclassical nucleation equation. Their multiple existence in monoatomic elements is now demonstrated by molecular dynamics simulations and still predicted. Proposed equations show that crystallization enthalpy is reduced at the temperature Tx due to new vitrification of noncrystallized parts and their melting at Tn+. These glassy parts, being equal above Tx to singular values or to their sum, are melted at various temperatures Tn+ and attain 100% in Cu46Zr46Al8 and 86.7% in bismuth. These first order transitions at Tn+ are either reversible or irreversible, depending on the formation of super atoms, either solid or liquid.

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.

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Minimal Microscopic Model for Liquid Polyamorphism and Waterlike Anomalies

Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Unveiling the phase diagram of the noninterconverting binary mixture gives unprecedented insight on the phase behaviors accessible to the interconverting fluid, such as a liquid-liquid transition with a critical point, or a singularity-free scenario, exhibiting thermodynamic anomalies without polyamorphism. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with waterlike anomalies.

Structure of High-Pressure Supercooled and Glassy Water

We numerically investigate the structure of deep supercooled and glassy water under pressure, covering the range of densities corresponding to the experimentally produced high- and very-high-density amorphous phases. At T=188  K, a continuous increase in density is observed on varying pressure from 2.5 to 13 kbar, with no signs of first-order transitions. Exploiting a recently proposed approach to the analysis of the radial distribution function-based on topological properties of the hydrogen-bond network-we are able to identify well-defined local geometries that involve pairs of molecules separated by multiple hydrogen bonds, specific to the high- and very-high-density structures.

The liquid-amorphous phase transition, slow dynamics and dynamical heterogeneity for bulk iron: a molecular dynamics simulation

Based on molecular dynamics (MD) simulations, we investigate the liquid-amorphous phase transition, slow dynamic and dynamical heterogeneity (DH) for bulk iron in temperatures ranging 300-2300 K. The structure of obtained models is explored through the pair radial distribution function (PRDF) and simplex statistics. It was shown that the splitting of a PRDF second peak appears when the liquid transforms to an amorphous solid. This feature is originated from the transformation of simplexes from strongly-to weakly-distorted tetrahedron type. Further, we reveal that the diffusivity in the liquid is realized through the local density fluctuations (LDF) which are strongly correlated with each other. The diffusion coefficient is found to be a product of the rate of LDF act and mean square displacement of particles per LDF act. The later quantity mainly contributes to the slow dynamics and DH in the liquid. We found that the mobile atom clusters move during relaxation time, but mobile atoms do not tend to leave their cluster. Our work is expected to contribute a pathway to determine the liquid-amorphous phase transition and DH heterogeneity of bulk metal.

Mechanics, Ionics, and Optics of Metal-Organic Framework and Coordination Polymer Glasses

Melt and glassy states of coordination polymers (CPs)/metal-organic frameworks (MOFs) have gained attention as a new class of amorphous materials. Many bridging ligands such as azolate, nitrile, thiocyanide, thiolate, pyridine, sulfonate, and amide are available to construct crystals with melting temperatures in the range of 60-593 °C. Here, we discuss the mechanism of crystal melting, glass structures, and mechanical properties by considering both experimental and theoretical studies. High and exclusive H⁺ or Li⁺ conductivities in moldable CP glasses have been proven in the all-solid-state devices such as fuel cells or secondary batteries. Transparent glasses with wide composition and available dopants are also attractive for nonlinear optics, photoconductivity, emission, and light-harvesting. The ongoing challenge in the field is to develop the design principles of CP/MOF melts and glasses, corresponding functions of mass (ion, electron, photon, phonon, and so forth). transport and conversion, and the integration of devices with the use of their tunable mechanical properties.

Experimental evidence for glass polymorphism in vitrified water droplets

The question of whether a first-order liquid-to-liquid transition is at the origin of water’s anomalous properties has been controversial since the pioneering experiments by Mishima et al. in 1985 and molecular simulations by Poole et al. in 1992. Since then, experiments aimed at shedding light on this question have been performed using amorphous ices made from crystalline ice, fueling criticism about their crystal-like nature. In the present study, we avoid crystalline ice at any time of the experiment yet still observe a first-order glass-to-glass transition in vitrified liquid droplets. This makes the strong case for glass polymorphism and the direct thermodynamic connection to the liquid-to-liquid transition at higher temperatures, dismissing the criticism voiced for three decades.

The nature of amorphous ices has been debated for more than 35 years. In essence, the question is whether they are related to ice polymorphs or to liquids. The fact that amorphous ices are traditionally prepared from crystalline ice via pressure-induced amorphization has made a clear distinction tricky. In this work, we vitrify liquid droplets through cooling at ≥10⁶ K ⋅ s⁻¹ and pressurize the glassy deposit. We observe a first order–like densification upon pressurization and recover a high-density glass. The two glasses resemble low- and high-density amorphous ice in terms of both structure and thermal properties. Vitrified water shows all features that have been reported for amorphous ices made from crystalline ice. The only difference is that the hyperquenched and pressurized deposit shows slightly different crystallization kinetics to ice I upon heating at ambient pressure. This implies a thermodynamically continuous connection of amorphous ices with liquids, not crystals.

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.

Internal resistive heating of non-metallic samples to 3000 K and >60 GPa in the diamond anvil cell

High pressure-temperature experiments provide information on the phase diagrams and physical characteristics of matter at extreme conditions and offer a synthesis pathway for novel materials with useful properties. Experiments recreating the conditions of planetary interiors provide important constraints on the physical properties of constituent phases and are key to developing models of planetary processes and interpreting geophysical observations. The laser-heated diamond anvil cell (DAC) is currently the only technique capable of routinely accessing the Earth's lower-mantle geotherm for experiments on non-metallic samples, but large temperature uncertainties and poor temperature stability limit the accuracy of measured data and prohibits analyses requiring long acquisition times. We have developed a novel internal resistive heating (IRH) technique for the DAC and demonstrate stable heating of non-metallic samples up to 3000 K and 64 GPa, as confirmed by in situ synchrotron x-ray diffraction and simultaneous spectroradiometric temperature measurement. The temperature generated in our IRH-DAC can be precisely controlled and is extremely stable, with less than 20 K variation over several hours without any user intervention, resulting in temperature uncertainties an order of magnitude smaller than those in typical laser-heating experiments. Our IRH-DAC design, with its simple geometry, provides a new and highly accessible tool for investigating materials at extreme conditions. It is well suited for the rapid collection of high-resolution P-V-T data, precise demarcation of phase boundaries, and experiments requiring long acquisition times at high temperature. Our IRH technique is ideally placed to exploit the move toward coherent nano-focused x-ray beams at next-generation synchrotron sources.

Structural and topological changes across the liquid-liquid transition in water

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.