General view of a liquid-liquid phase transition

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.

Long-range, water-mediated interaction between a moderately active antifreeze protein molecule and the surface of ice

Using molecular dynamics simulations, we show that a molecule of moderately active antifreeze protein (type III AFP, QAE HPLC-12 isoform) is able to interact with ice in an indirect manner. This interaction occurs between the ice binding site (IBS) of the AFP III molecule and the surface of ice, and it is mediated by liquid water, which separates these surfaces. As a result, the AFP III molecule positions itself at a specific orientation and distance relative to the surface of ice, which enables the effective binding (via hydrogen bonds) of the molecule with the nascent ice surface. Our results show that the final adsorption of the AFP III molecule on the surface of ice is not achieved by chaotic diffusion movements, but it is preceded by a remote, water-mediated interaction between the IBS and the surface of ice. The key factor that determines the existence of this interaction is the ability of water molecules to spontaneously form large, high-volume aggregates that can be anchored to both the IBS of the AFP molecule and the surface of ice. The results presented in this work for AFP III are in full agreement with the ones obtained by us previously for hyperactive CfAFP, which indicates that the mechanism of the remote interaction of these molecules with ice remains unchanged despite significant differences in the molecular structure of their ice binding sites. For that reason, we can expect that also other types of AFPs interact with the ice surface according to an analogous mechanism.

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.

Two-Step Melting in a Bulk Crystal via Intermediate Metastable Liquid

The mechanism of melting is significant, as it links the structure and dynamics between crystal and liquid. In two dimensions, the crystal could first melt into a hexatic liquid before finally reaching a disordered liquid. However, such a hexatic liquid phase is unstable in three dimensions, and melting is recognized as a one-step process. Here we report a two-step melting process in a three-dimensional system, (S)-(+)-ibuprofen. The crystal melts through an indirect pathway that first transforms into an intermediate liquid phase exhibiting an extremely long lifetime followed by the transition to the ordinary liquid phase at a spinodal point with the occurrence of long-range fluctuations. Such observations suggest that the complexity of liquid could affect the transition pathway of melting. These results could lead us to hypothesize the existence of continuous melting in three dimensions.

Control of thermodynamic liquid-liquid phase transition in a fragility-tunable glassy model

We propose a distinguishable-particle glassy model suitable for the molecular dynamics simulation of structural glasses. This model can sensitively tune the kinetic fragility of supercooled liquids in a wide range by simply changing the distribution of particle interactions. In the model liquid, we observe the occurrence of thermodynamic liquid-liquid phase transitions above glass transition. The phase transition is facilitated by lowering fragility. Prior to the liquid-liquid phase transition, our simulations verify the existence of a constant-volume heat capacity maximum varying with fragility. We reveal the characteristics of the equilibrium potential energy landscape in liquids with different fragility. Within the Gaussian excitation model, the liquid-liquid transition as well as the response to fragility is reasonably interpreted in configuration space.

Mechanism of antifreeze protein functioning and the "anchored clathrate water" concept

In liquid water, there is a natural tendency to form aggregates that consist of water molecules linked by hydrogen bonds. Such spontaneously formed aggregates are surrounded by a "sea" of disordered water molecules, with both forms remaining in equilibrium. The process of creating water aggregates also takes place in the solvation water of proteins, but in this case, the interactions of water molecules with the protein surface shift the equilibrium of the process. In this paper, we analyze the structural properties of the solvation water in antifreeze proteins (AFPs). The results of molecular dynamics analysis with the use of various parameters related to the structure of solvation water on the protein surface are presented. We found that in the vicinity of the active region responsible for the binding of AFPs to ice, the equilibrium is clearly shifted toward the formation of "ice-like aggregates," and the solvation water has a more ordered ice-like structure. We have demonstrated that a reduction in the tendency to create "ice-like aggregates" results in a significant reduction in the antifreeze activity of the protein. We conclude that shifting the equilibrium in favor of the formation of "ice-like aggregates" in the solvation water in the active region is a prerequisite for the biological functionality of AFPs, at least for AFPs having a well-defined ice binding area. In addition, our results fully confirm the validity of the "anchored clathrate water" concept, formulated by Garnham et al. [Proc. Natl. Acad. Sci. U. S. A. 108, 7363 (2011)].

Tailoring Phosphonium Ionic Liquids for a Liquid-Liquid Phase Transition

The existence of more than one liquid state in a single-component system remains the most intriguing physical phenomenon. Herein, we explore the effect of cation self-assembly on ion dynamics in the vicinity of liquid-liquid and liquid-glass transition of tetraalkyl phosphonium ([P_mmm,n]⁺, m = 4, 6; n = 2-14) ionic liquids. We found that nonpolar local domains formed by 14-carbon alkyl chains are crucial in obtaining two supercooled states of different dynamics within a single ionic liquid. Although the nano-ordering, confirmed by Raman spectroscopy, still occurs for shorter alkyl chains (m = 6, n < 14), it does not bring calorimetric evidence of LLT. Instead, it results in peculiar behavior of ion dynamics near the liquid-glass transition and 20-times smaller size of the dynamic heterogeneity compared to imidazolium ionic liquids. These results represent a crucial step toward understanding the nature of the LLT phenomenon and offer insight into the design of efficient electrolytes based on ionic liquids revealing self-assembly behavior.

Structural Changes in Metallic Glass-Forming Liquids on Cooling and Subsequent Vitrification in Relationship with Their Properties

The present review is related to the studies of structural changes observed in metallic glass-forming liquids on cooling and subsequent vitrification in terms of radial distribution function and its analogues. These structural changes are discussed in relationship with liquid's properties, especially the relaxation time and viscosity. These changes are found to be directly responsible for liquid fragility: deviation of the temperature dependence of viscosity of a supercooled liquid from the Arrhenius equation through modification of the activation energy for viscous flow. Further studies of this phenomenon are necessary to provide direct mathematical correlation between the atomic structure and properties.

Pressure-induced liquid-liquid transition in a family of ionic materials

Liquid−liquid transition (LLT) between two disordered phases of single-component material remains one of the most intriguing physical phenomena. Here, we report a first-order LLT in a series of ionic liquids containing trihexyl(tetradecyl)phosphonium cation [P_666,14]⁺ and anions of different sizes and shapes, providing an insight into the structure-property relationships governing LLT. In addition to calorimetric proof of LLT, we report that ion dynamics exhibit anomalous behavior during the LLT, i.e., the conductivity relaxation times (τ_σ) are dramatically elongated, and their distribution becomes broader. This peculiar behavior is induced by isobaric cooling and isothermal compression, with the τ_σ(T_LL,P_LL) constant for a given system. The latter observation proves that LLT, in analogy to liquid-glass transition, has an isochronal character. Finally, the magnitude of discontinuity in a specific volume at LLT was estimated using the Clausius-Clapeyron equation.

Liquid−liquid transitions (LLTs) have been reported for some molecular systems but are difficult to observe under high pressure conditions. Here the authors report and characterize a first-order LLT in a series of ionic liquids containing the trihexyl(tetradecyl)phosphonium cation and anions of different sizes and shapes, using calorimetric and dielectric measurements.

Structural characteristics of low-density environments in liquid water

The existence of two structural forms in liquid water has been a point of discussion for a long time. A phase transition between these two forms of liquid water has been proposed based on evidence from molecular simulations, and experiments have also been very recently able to track the proposed transition of the low-density liquid form to the high-density liquid form. We propose to use the average angle an oxygen atom makes with its neighbors to describe the structural environment of a water molecule. The distribution of this order parameter is observed to have two peaks with one peak at ∼109.5^{∘}, corresponding to the internal angle of a regular tetrahedron, indicating tetrahedral arrangement. The other peak corresponds to an environment with a tighter arrangement of neighboring molecules. The distribution of O-O-O angles is decomposed into two skewed distributions to estimate the fractions of the two liquid forms in water. A good similarity is observed between the temperature and pressure trends of fractions of locally favored tetrahedral structure (LFTS) form estimated using the new order parameter and the reports in the literature, over a range of temperatures and pressures. We also compare the structural environments indicated by different order parameters and find that the order parameter proposed in this paper captures the structure of first solvation shell of the LFTS accurately.

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.

The microscopic transition process from high-density to low-density amorphous state of SnI4

A molecular crystalline SnI₄undergoes pressure-induced solid-state amorphization via molecular dissociation to the high-density amorphous (HDA) state, which we call Am-I. In the present study, we examine the reverse transition process from Am-I to the low-density amorphous (LDA) state, called Am-II. We first measure the structure factor on decompression from 30 GPa down to 1.1 GPa at room temperature, usingin situangle-dispersive synchrotron x-ray measurement and a diamond anvil cell. We then estimate the density, which exhibits an abrupt change between 3.3 and 3.0 GPa, indicating the HDA(Am-I)-to-LDA(Am-II) transition. We use the density and the molecular configuration generated from a molecular dynamics simulation as input to a reverse Monte Carlo fit. The fit vividly visualizes gradual molecular reassociation between 18 and 14 GPa within the Am-I region. The Am-I state can thus be divided into two states: the high-pressure Am-I state containing isolated Sn atoms and the low-pressure Am-I state consisting of deformed molecules connected by metallic I₂bonds. In the latter state, the molecular shape becomesC_3v-like just before the transition to Am-II, in which molecules recover the originalT_dsymmetry. This local symmetry change has been detected on the liquid-liquid transition of SnI₄, suggesting the strong coupling between the local symmetry and the global order parameter of density.

Kinematic Viscosity ofMulticomponent FeCuNbSiB-BasedMelts

The work investigated the temperature dependences of the kinematic viscosity for multicomponent melts of nanocrystalline soft magnetic alloys. It is shown that there is a linear relationship between the reduced activation energy of viscous flow E_a·(RT)⁻¹ and the pre-exponential factor ν₀. This ratio is universal for all quantities, the temperature dependence of which is expressed by the Arrhenius equation. It is shown that the activation energy of a viscous flow is linearly related to the cluster size on a natural logarithmic scale, and the melt viscosity increases with decreasing cluster size. The change in the Arrhenius plot in the anomalous zone on the temperature dependence of viscosity can be interpreted as a liquid–liquid structure transition, which begins with the disintegration of clusters and ends with the formation of a new cluster structure.

A theoretical investigation into the cooperativity effect on the TNT melting point under external electric field

External electric field has been regarded as an effective tool to induce the variation of melting points of molecular crystals. The melting point of 2,4,6-trinitrotoluene (TNT) was calculated by molecular dynamics simulations under external electric field, and the electric field effects on the cooperativity effects of the ternary (TNT)₃ were investigated at the M06-2X/6-311+G(d) and ωB97X-D/6-311++G(2d,p) levels. The results show that the melting points are decreased while the intermolecular interactions are strengthened under the external electric fields, suggesting that the intermolecular interactions cannot be used to explain the decreased melting points. A deduction based on the cooperativity effect is put forward: the enhanced cooperativity effects create the more serious defects in the melting process of the molecular crystal under the external electric fields, and simultaneously the local order parameters are decreased, leading to the decreased melting point. Thus, the cooperativity effect stemmed from the intermolecular C-H∙∙∙O H-bonding interactions controls the change of TNT melting point under the external electric field. Employing the information-theoretic approach (ITA), the origin of the cooperativity effects on the melting points of molecular crystal is revealed. This study opens a new way to challenge the problems involving the melting points for the molecular crystal under the external electric fields. However, note that above deduction needs to be improved; after all, the simple (TNT)₃ model cannot replace the crystal structure.

Modeling Elastically Mediated Liquid-Liquid Phase Separation

We propose a continuum theory of the liquid-liquid phase separation in an elastic network, where phase-separated microscopic droplets rich in one fluid component can form as an interplay of fluids mixing, droplet nucleation, network deformation, thermodynamic fluctuation, etc. We find that the size of the phase-separated droplets decreases with the shear modulus of the elastic network in the form of ∝[modulus]^{-1/3} and the number density of the droplet increases almost linearly with the shear modulus ∝[modulus], which are verified by the experimental observations. Phase diagrams in the space of (fluid constitution, mixture interaction, network modulus) are provided, which can help to understand similar phase separations in biological cells and also to guide fabrications of synthetic cells with desired phase properties.

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.

Structural Changes in Liquid Lithium under High Pressure

We have experimentally studied the effect of compression on the structure of liquid lithium (Li) by multiangle energy dispersive X-ray diffraction in a large-volume cupped-Drickamer-Toroidal cell. The structure factors, s(q), of liquid Li have been successfully determined under an isothermal compression at 600 ± 30 K and at pressures up to 11.5 GPa. The first peak position in s(q) is found to increase with increasing pressure and is showing an obvious slope change starting at ∼7.5 GPa. The slope change is interpreted as a structural change from bcc-like to fcc-like local ordering in liquid Li. At pressures above 8.7 GPa, the liquid Li becomes predominantly fcc-like up to the highest pressure of 11.5 GPa in this study. The observed structural changes in liquid Li are consistent with the recently determined melting curve of Li.

Role of hydrodynamics in liquid-liquid transition of a single-component substance

Liquid-liquid transition (LLT) is an unconventional transition between two liquid states in a single-component system. This phenomenon has recently attracted considerable attention not only because of its counterintuitive nature but also since it is crucial for our fundamental understanding of the liquid state. However, its physical understanding has remained elusive, particularly of the critical dynamics and phase-ordering kinetics. So far, the hydrodynamic degree of freedom, which is the most intrinsic kinetic feature of liquids, has been neglected in its theoretical description. Here we develop a Ginzburg-Landau-type kinetic theory of LLT taking it into account, based on a two-order parameter model. We examine slow critical fluctuations of the nonconserved order parameter coupled to the hydrodynamic degree of freedom in equilibrium. We also study the nonequilibrium process of LLT. We show both analytically and numerically that domain growth becomes faster (slower), depending upon the density decrease (increase) upon the transition, as a consequence of hydrodynamic flow induced by the density change. The coupling between nonconserved order parameter and hydrodynamic interaction results in anomalous domain growth in both nucleation-growth-type and spinodal-decomposition-type LLT. Our study highlights the characteristic features of hydrodynamic fluctuations and phase ordering during LLT under complex interplay among conserved and nonconserved order parameters and the hydrodynamic transport intrinsic to the liquid state.

Drastic enhancement of crystal nucleation in a molecular liquid by its liquid-liquid transition

Crystallization is one of the most familiar and fundamental phase transition phenomena. There is a possibility that crystallization may be enhanced by critical-like fluctuations associated with another nearby phase transition if the order parameter of the former is coupled to that of the latter; however, the mechanism of such order parameter coupling and its generality remain elusive due to the lack of experimental studies. Here we report experimental evidence for a nontrivial coupling between crystallization and liquid-liquid transition (LLT) for a molecular liquid, triphenyl phosphite. We find that the crystal nucleation frequency is drastically enhanced by short-time preannealing near but above the spinodal temperature of LLT. By successfully separating the thermodynamic and kinetic factors governing crystal nucleation, we show that this enhancement is induced by the lowering of the crystal-liquid interfacial energy due to the presence of critical-like order parameter fluctuations. This finding may be regarded as a fingerprint of the presence of LLT below the melting point. Thus, it may allow us not only to control the crystal nucleation frequency by LLT but also to unveil LLT hidden behind crystallization. This enhancement of nucleation frequency by critical-like fluctuations of another ordering phenomenon may be general to a variety of combinations of phase transitions. It would provide a way to control a crystal grain structure, which is a crucial control factor of mechanical and thermal properties of crystalline materials.

First-Order Liquid-Liquid Transition without Density Discontinuity in Molten Sodium Acetate Trihydrate and Its Influence on Crystallization

Liquid-liquid transition (LLT) refers to the phase transition among thermodynamically distinct liquid states with identical composition in analogy to the polymorphic transition in solid. The growing awareness of its significance to understanding the nature of liquid also provokes curiosity about its potential impact on crystallization. Here, we report a first-order liquid-liquid transition above liquidus temperature in the melt of sodium acetate trihydrate using nuclear magnetic resonance, differential scanning calorimetry, and high-precision density measurements, which show negligible change in density associated with the observed LLT. Further, the kinetics and products of crystallization are significantly influenced by LLT, providing a new way for the controlling crystallization pathway and realizing crystal polymorph selection.

Ice Nucleation of Confined Monolayer Water Conforms to Classical Nucleation Theory

We confirmed that monolayer water confined by parallel graphene sheets spontaneously crystallizes from a structurally and dynamically heterogeneous liquid phase under moderate supercooling via direct molecular dynamics simulation. Square-lattice-like geometric order is observed at the early stage of nucleation and is preserved during the entire nucleus growth process. The diffusion coefficient and free energy profile in the cluster space extracted from a Bayesian trajectory analysis agree well with the classical nucleation theory (CNT) prediction and yield thermodynamic quantities exhibiting linear temperature dependence. The effectiveness of maximum cluster size as the descriptor of ice nucleation dynamics in the CNT framework can be attributed to the dynamical time scale decoupling and strong structural pattern dependence of density fluctuation in the liquid phase.

Link between molecular mobility and order parameter during liquid-liquid transition of a molecular liquid

Liquid-liquid transition (LLT) is the transformation of one liquid to another via first-order phase transition. For example, LLT in a molecular liquid, triphenyl phosphite, is macroscopically the transformation from liquid I in a supercooled state to liquid II in a glassy state. Reflecting the transformation from the liquid to glassy state, the LLT is accompanied by considerable slowing down of overall molecular dynamics, but little is known about how this proceeds at a molecular level coupled with the evolution of the order parameter. We report such information by performing time-resolved simultaneous measurements of dielectric spectroscopy and phase contrast microscopy/Raman spectroscopy by using a dielectric cell with transparent electrodes. We find that the temporal change in molecular mobility crucially depends on whether LLT is nucleation growth type occurring in the metastable state or SD type occurring in the unstable state. Furthermore, our results suggest that the molecular mobility is controlled by the local order parameter: more specifically, the local activation energy of molecular rotation is controlled by the local fraction of locally favored structures formed in the liquid. Our study sheds light on the temporal change in the molecular dynamics during LLT and its link to the order parameter evolution.

Bond-counting potentials: A classical many-body model of covalent bonding with exact solutions in one dimension

We introduce "bond-counting" potentials, which provide an elementary description of covalent bonding. These simplistic potentials are intended for studies of the mechanisms behind a variety of phase transitions in elemental melts, including the liquid-liquid phase transitions (LLPTs) in phosphorus and bismuth. As a first study employing such potentials, an analytic solution of a one-dimensional model system is presented, including its thermodynamic properties and its structure factor. In the simplest case, the chemical valency of each atom is 1, and either single atoms or diatomic molecules are present. At low temperatures and moderate pressures, the system consists almost exclusively of molecules, and single atoms act as topological defects. A slightly more complicated case involves a valency of 2, with either single or double bonding. This system exhibits a first-order LLPT from a molecular to a polymeric phase as in phosphorus. In this case, the one-dimensional model system exhibits phase separation for finite-sized systems at low temperatures. A variant of this system also exhibits a nonequilibrium phase transformation upon heating the molecular condensed phase, qualitatively similar to boiling in white phosphorus.

Common microscopic structural origin for water's thermodynamic and dynamic anomalies

Water displays a vast array of unique properties, known as water's anomalies, whose origin remains subject to hot debate. Our aim in this article is to provide a unified microscopic physical picture of water's anomalies in terms of locally favored structures, encompassing both thermodynamic and dynamic anomalies, which are often attributed to different origins. We first identify locally favored structures via a microscopic structural descriptor that measures local translational order and provide direct evidence that they have a hierarchical impact on the anomalies. At each state point, the strength of thermodynamic anomalies is directly proportional to the amount of locally favored structures, while the dynamic properties of each molecule depend on the local structure surrounding both itself and its nearest neighbors. To incorporate this, we develop a novel hierarchical two-state model. We show by extensive simulations of two popular water models that both thermodynamic and kinetic anomalies can be almost perfectly explained by the temperature and pressure dependence of these local and non-local versions of the same structural descriptor, respectively. Moreover, our scenario makes three unique predictions in supercooled water, setting it apart from other scenarios: (1) Presence of an "Arrhenius-to-Arrhenius" crossover upon cooling, as the origin of the apparent "fragile-to-strong" transition; (2) maximum of dynamic heterogeneity around 20 K below the Widom line and far above the glass transition; (3) violation of the Stokes-Einstein-Debye relation at ∼2T _g, rather than 1.2T _g typical of normal glass-formers. These predictions are verified by recent measurement of water's diffusion at very low temperatures (point 1) and discoveries from our extensive simulations (points 2-3). We suggest that the same scenario may generally apply to water-like anomalies in liquids tending to form locally favored structures, including not only other important tetrahedral liquids such as silicon, germanium, and silica, but also metallic and chalcogenide liquids.

Impact of surface roughness on liquid-liquid transition

Liquid-liquid transition (LLT) in single-component liquids is one of the most mysterious phenomena in condensed matter. So far, this problem has attracted attention mainly from the fundamental viewpoint. We report the first experimental study on an impact of surface nanostructuring on LLT by using a surface treatment called rubbing, which is the key technology for the production of liquid crystal displays. We find that this rubbing treatment has a significant impact on the kinetics of LLT of an isotropic molecular liquid, triphenyl phosphite. For a liquid confined between rubbed surfaces, surface-induced barrierless formation of the liquid II phase is observed even in a metastable state, where there should be a barrier for nucleation of the liquid II phase in bulk. Thus, surface rubbing of substrates not only changes the ordering behavior but also significantly accelerates the kinetics. This spatiotemporal pattern modulation of LLT can be explained by a wedge-filling transition and the resulting drastic reduction of the nucleation barrier. However, this effect completely disappears in the unstable (spinodal) regime, indicating the absence of the activation barrier even for bulk LLT. This confirms the presence of nucleation-growth- and spinodal decomposition-type LLT, supporting the conclusion that LLT is truly a first-order transition with criticality. Our finding also opens up a new way to control the kinetics of LLT of a liquid confined in a solid cell by structuring its surface on a mesoscopic length scale, which may contribute to making LLT useful for microfluidics and other industrial applications.

The temperature dependence of intermediate range oxygen-oxygen correlations in liquid water

We analyze the recent temperature dependent oxygen-oxygen pair-distribution functions from experimental high-precision x-ray diffraction data of bulk water by Skinner et al. [J. Chem. Phys. 141, 214507 (2014)] with particular focus on the intermediate range where small, but significant, correlations are found out to 17 Å. The second peak in the pair-distribution function at 4.5 Å is connected to tetrahedral coordination and was shown by Skinner et al. to change behavior with temperature below the temperature of minimum isothermal compressibility. Here we show that this is associated also with a peak growing at 11 Å which strongly indicates a collective character of fluctuations leading to the enhanced compressibility at lower temperatures. We note that the peak at ∼13.2 Å exhibits a temperature dependence similar to that of the density with a maximum close to 277 K or 4 °C. We analyze simulations of the TIP4P/2005 water model in the same manner and find excellent agreement between simulations and experiment albeit with a temperature shift of ∼20 K.

Composition- and temperature-dependent liquid structures in Al-Cu alloys: an ab initio molecular dynamics and x-ray diffraction study

The composition- and temperature-dependent liquid structures in eight Al_rich-Cu binary alloys (from hypoeutectic Al₉₃Cu₇ to hypereutectic Al₇₀Cu₃₀) have been experimentally and computationally studied by x-ray diffraction (XRD) experiments and ab initio molecular dynamics (AIMD) simulations. The remarkable agreements of structure factors for all liquid Al_rich-Cu alloys obtained from high-temperature high-energy XRD measurements and AIMD simulations have been achieved, which consolidates the analyses of structural evolutions in Al_rich-Cu liquids during the cooling processing by AIMD simulations. The heat capacity of liquid Al_rich-Cu alloys continuously increases and presents no abnormal peak when reducing the temperature, which differs from the reported prediction for 55-atom Al_rich-Cu nanoliquids. The diffusivities of Al and Cu undergo an increasing deviation from Arrhenius behavior by tuning Cu concentration from 7 to 30 atomic percentages, correlated to the local ordering in these liquids by means of coordination number, bond-angle distribution, Honeycutt-Andersen index, bond-orientational order and Voronoi tessellation analyses. Upon cooling, the microstructure of the liquid Al_rich-Cu alloys inclines to form Al₂Cu crystal-like local atomic ordering, especially in the hypereutectic liquids. The favorable short-range ordering between Cu and Al atoms could cause the non-Arrhenius diffusion behavior.

The role of liquid–liquid transition in glass formation of CuZr alloys

The structure evolution during LLTs is beneficial to the glass forming ability (GFA) of Cu–Zr systems.

The reversibility and first-order nature of liquid-liquid transition in a molecular liquid

Liquid–liquid transition is an intriguing phenomenon in which a liquid transforms into another liquid via the first-order transition. For molecular liquids, however, it always takes place in a supercooled liquid state metastable against crystallization, which has led to a number of serious debates concerning its origin: liquid–liquid transition versus unusual nano-crystal formation. Thus, there have so far been no single example free from such debates, to the best of our knowledge. Here we show experimental evidence that the transition is truly liquid–liquid transition and not nano-crystallization for a molecular liquid, triphenyl phosphite. We kinetically isolate the reverse liquid-liquid transition from glass transition and crystallization with a high heating rate of flash differential scanning calorimetry, and prove the reversibility and first-order nature of liquid–liquid transition. Our finding not only deepens our physical understanding of liquid–liquid transition but may also initiate a phase of its research from both fundamental and applications viewpoints.

The nature of the phenomenon of so-called ‘liquid-liquid transitions' in molecular liquids is a long-standing debate. Here, the authors demonstrate the reversibility and first-order nature of the liquid-liquid transition in triphenyl phosphite via flash differential scanning calorimetry.

A liquid-liquid transition can exist in monatomic transition metals with a positive melting slope

Liquid-liquid transitions under high pressure are found in many elemental materials, but the transitions are known to be associated with either sp-valent materials or f-valent rare-earth elements, in which the maximum or a negative slope in the melting line is readily suggestive of the transition. Here we find a liquid-liquid transition with a positive melting slope in transition metal Ti from structural, electronic, and thermodynamic studies using ab-initio molecular dynamics calculations, showing diffusion anomaly, but no density anomaly. The origin of the transition in liquid Ti is a pressure-induced increase of local structures containing very short bonds with directionality in electronic configurations. This behavior appears to be characteristic of the early transition metals. In contrast, the late transition metal liquid Ni does not show the L-L transition with pressure. This result suggests that the possibility of the L-L transition decreases from early to late transition metals as electronic structures of late transition metals barely have a Jahn-Teller effect and bond directionality. Our results generalize that a phase transition in disordered materials is found with any valence band regardless of the sign of the melting slope, but related to the symmetry of electronic structures of constituent elements.

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Chiral Ordering in Supercooled Liquid Water and Amorphous Ice

The emergence of homochiral domains in supercooled liquid water is presented using molecular dynamics simulations. An individual water molecule possesses neither a chiral center nor a twisted conformation that can cause spontaneous chiral resolution. However, an aggregation of water molecules will naturally give rise to a collective chirality. Such homochiral domains possess obvious topological and geometrical orders and are energetically more stable than the average. However, homochiral domains cannot grow into macroscopic homogeneous structures due to geometrical frustrations arising from their icosahedral local order. Homochiral domains are the major constituent of supercooled liquid water and the origin of heterogeneity in that substance, and are expected to be enhanced in low-density amorphous ice at lower temperatures.

Time-Resolved Light Scattering Study on the Kinetics of the Liquid-Liquid Transition in Triphenyl Phosphite

There is experimental evidence suggesting the existence of a liquid-liquid transition (LLT) in a single-component liquid. However, none of this evidence is free from controversy, including the case of a molecular liquid, triphenyl phosphite, which we study here. Furthermore, the kinetics of LLT has been largely unexplored. Here we study the phase-transition dynamics of triphenyl phosphite in a supercooled liquid state by means of time-resolved polarized and depolarized small-angle light scattering to clarify whether the transition is a liquid-liquid transition (LLT) or merely nanocrystal formation. A part of this study was recently reported in another of our papers [Shimizu, R.; Kobayashi, M.; Tanaka, H. Phys. Rev. Lett. 2014, 112, 125702]. A detailed analysis of our experimental results of light scattering and the comparison with heat evolution during LLT have revealed the following facts. The polarized scattering from domains has a finite (nonzero) intensity in the low-wavenumber limit, and the time evolution of its average intensity is almost proportional to the square of the heat-releasing rate. The depolarized scattering intensity monotonically increases in the process of LLT during isothermal annealing above the spinodal temperature TSD but exhibits a peak below TSD. On the basis of these results, we suggest that the primary process is LLT, whose order parameter is of a nonconserved nature, but accompanies nanocrystal formation. In the NG-type LLT, the sharp interface between liquid II droplets and the liquid I matrix promotes nanocrystal formation there, whereas much less nanocrystal formation is induced in the SD-type LLT due to the lack of such sharp interfaces.

Evidence of liquid-liquid transition in glass-forming La50Al35Ni15 melt above liquidus temperature

Liquid-liquid transition, a phase transition of one liquid phase to another with the same composition, provides a key opportunity for investigating the relationship between liquid structures and dynamics. Here we report experimental evidences of a liquid-liquid transition in glass-forming La50Al35Ni15 melt above its liquidus temperature by (27)Al nuclear magnetic resonance including the temperature dependence of cage volume fluctuations and atomic diffusion. The observed dependence of the incubation time on the degree of undercooling is consistent with a first-order phase transition. Simulation results indicate that such transition is accompanied by the change of bond-orientational order without noticeable change in density. The temperature dependence of atomic diffusion revealed by simulations is also in agreement with experiments. These observations indicate the need of two-order parameters in describing phase transitions of liquids.

Tuning the Liquid-Liquid Transition by Modulating the Hydrogen-Bond Angular Flexibility in a Model for Water

We propose a simple extension of the well known ST2 model for water [F. H. Stillinger and A. Rahman, J. Chem. Phys. 60, 1545 (1974)] that allows for a continuous modification of the hydrogen-bond angular flexibility. We show that the bond flexibility affects the relative thermodynamic stability of the liquid and of the hexagonal (or cubic) ice. On increasing the flexibility, the liquid-liquid critical point, which in the original ST2 model is located in the no-man's land (i.e., the region where ice is the thermodynamically stable phase) progressively moves to a temperature where the liquid is more stable than ice. Our study definitively proves that the liquid-liquid transition in the ST2 model is a genuine phenomenon, of high relevance in all tetrahedral network-forming liquids, including water.

Mapping the intriguing transient morphologies and the demixing behavior in PS/PVME blends in the presence of rod-like nanoparticles

The demixing behavior, transient morphologies and mechanism of phase separation in PS/PVME blends were greatly altered in the presence of a very low concentration of rod-like particles (multiwall carbon nanotubes, MWNTs). This phenomenon is due to the specific interaction of one of the phases (PVME) with the anisotropic MWNTs, which creates a heterogeneous environment in the blend. This specific interaction alters the chain dynamics in the interfacial region as against the bulk. A comprehensive analysis using isochronal temperature sweep was performed to understand the demixing temperature in the blends. The evolution of phase morphology as a function of time and temperature was assessed by polarizing optical microscopy (POM), atomic force microscopy (AFM) and scanning electron microscopy (SEM). The addition of MWNTs increased the rheological demixing temperature and the spinodal temperature in almost all the compositions. The intriguing transient morphologies were mapped, which varied from nucleation and growth to coalescence-induced viscoelastic phase separation (C-VPS) in PVME-rich blends, to spinodal decomposition in the near-critical compositions, to transient gel-induced VPS (T-VPS) in the PS-rich compositions. Mapping of the morphology development displayed two types of fracture mechanisms: ductile fracture for near-critical compositions and brittle fracture for off-critical composition. The change in the phase separation mechanism in the presence of MWNTs was due to the variation in dynamic asymmetry brought about by these anisotropic particles. All these observations were correlated by POM, SEM and AFM studies. The length of the cooperatively rearranging region (CRR), as evaluated using modulated differential scanning calorimetry (MDSC) measurements, was found to be composition-independent. The observed variation of effective glass transition of PVME (low Tg component) on blending with PS (high Tg component) and by the addition of MWNTs accounts for the dynamic heterogeneity introduced by MWNTs in the system.

Microscopic identification of the order parameter governing liquid-liquid transition in a molecular liquid

A liquid-liquid transition (LLT) in a single-component substance is an unconventional phase transition from one liquid to another. LLT has recently attracted considerable attention because of its fundamental importance in our understanding of the liquid state. To access the order parameter governing LLT from a microscopic viewpoint, here we follow the structural evolution during the LLT of an organic molecular liquid, triphenyl phosphite (TPP), by time-resolved small- and wide-angle X-ray scattering measurements. We find that locally favored clusters, whose characteristic size is a few nanometers, are spontaneously formed and their number density monotonically increases during LLT. This strongly suggests that the order parameter of LLT is the number density of locally favored structures and of nonconserved nature. We also show that the locally favored structures are distinct from the crystal structure and these two types of orderings compete with each other. Thus, our study not only experimentally identifies the structural order parameter governing LLT, but also may settle a long-standing debate on the nature of the transition in TPP, i.e., whether the transition is LLT or merely microcrystal formation.

Order Parameter of the Liquid-Liquid Transition in a Molecular Liquid

Liquid-liquid transitions (LLTs) between amorphous phases of a single (chemically unchanged) liquid were predicted to occur in most molecular liquids but have only been observed in triphenyl phosphite (TPP) and n-butanol, and even these examples have been dismissed as "aborted crystallization". One of the foremost reasons that LLTs remain so controversial is the lack of an obvious order parameter, that is, a physical parameter characterizing the phase transition. Here, using the technique of fluorescence lifetime imaging, we show for the first time that the LLT in TPP is characterized by a change in polarity linked to changes in molecular ordering associated with crystal polymorphs. We conclude that the LLT in TPP is a phase transition associated with frustrated molecular clusters, explaining the paucity of examples of LLTs seen in nature.