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.

Direct observation of reversible liquid-liquid transition in a trehalose aqueous solution

Recent studies on liquid water suggest that the two liquid waters exist in the supercooled temperature region and that their existence relates to the anomalous behavior of low-temperature liquid water such as the maximum density at 4 °C. However, the experimental investigation of two liquid waters is difficult because of the rapid crystallization. In this study, a reversible liquid–liquid transition in a trehalose aqueous solution by the change in pressure was observed directly. This result suggests strongly that two liquid waters exist in the aqueous solution. This study has implications for wide fields related to liquid water, such as solution chemistry, cryobiology, meteorology, and food engineering.

Water forms two glassy waters, low-density and high-density amorphs, which undergo a reversible polyamorphic transition with the change in pressure. The two glassy waters transform into the different liquids, low-density liquid (LDL) and high-density liquid (HDL), at high temperatures. It is predicted that the two liquid waters also undergo a liquid–liquid transition (LLT). However, the reversible LLT, particularly the LDL-to-HDL transition, has not been observed directly due to rapid crystallization. Here, I prepared a glassy dilute trehalose aqueous solution (0.020 molar fraction) without segregation and measured the isothermal volume change at 0.01 to 1.00 GPa below 160 K. The polyamorphic transition and the glass-to-liquid transition for the high-density and low-density solutions were examined, and the liquid region where both LDL and HDL existed was determined. The results show that the reversible polyamorphic transition induced by the pressure change above 140 K is the LLT. That is, the transition from LDL to HDL is observed. Moreover, the pressure hysteresis of LLT suggests strongly that the LLT has a first-order nature. The direct observation of the reversible LLT in the trehalose aqueous solution has implications for understanding not only the liquid–liquid critical point hypothesis of pure water but also the relation between aqueous solution and water polyamorphism.

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.

The effect of shear on the liquid-liquid transition and crystallization of the undercooled Zr41.2Ti13.8Cu12.5Ni10.0Be22.5(Vit1) bulk metallic glass forming alloy

An entropy driven liquid-liquid transition (LLT) from a fragile (less ordered) to a strong (highly ordered) liquid occurs in the phase during undercooling. In this work, we show that this ordering transition as well as the applied shear rate affect the onset of crystallization. By recording simultaneously melt viscosity and temperature profiles, we quantitatively determine the shift in the upper part of the time-temperature-transformation diagram of Vit1 to shorter times with increasing shear rate. This acceleration in nucleation rate can be explained by the classical nucleation theory of crystals only if we take into consideration the effect of both shear flow and equilibrium viscosity. A critical assessment of the results concludes that shearing must first trigger the nucleation of the strong liquid from the fragile liquid and that the crystallization proceeds in a second step from the strong liquid. The fragile-to-strong transition decreases the configurational entropy of the liquid leading to a smaller interfacial energy between liquid and crystal, thus reducing the activation barrier for crystallization.

Evidence of a liquid-liquid transition in a glass-forming ionic liquid

A liquid-liquid transition (LLT) is a transformation from one liquid to another through a first-order transition. The LLT is fundamental to the understanding of the liquid state and has been reported in a few materials such as silicon, phosphorus, triphenyl phosphite, and water. Furthermore, it has been suggested that the unique properties of materials such as water, which is critical for life on the planet, are linked to the existence of the LLT. However, the experimental evidence for the existence of an LLT in many molecular liquids remains controversial, due to the prevalence and high propensity of the materials to crystallize. Here, we show evidence of an LLT in a glass-forming trihexyltetradecylphosphonium borohydride ionic liquid that shows no tendency to crystallize under normal laboratory conditions. We observe a step-like increase in the static dielectric permittivity at the transition. Furthermore, the sizes of nonpolar local domains and ion-coordination numbers deduced from wide-angle X-ray scattering also change abruptly at the LLT. We independently corroborate these changes in local organization using Raman spectroscopy. The experimental access to the evolution of local order and structural dynamics across a liquid-liquid transition opens up unprecedented possibilities to understand the nature of the liquid state.

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

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

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.

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.

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.

Supercooled and glassy water: Metastable liquid(s), amorphous solid(s), and a no-man's land

We review the recent research on supercooled and glassy water, focusing on the possible origins of its complex behavior. We stress the central role played by the strong directionality of the water-water interaction and by the competition between local energy, local entropy, and local density. In this context we discuss the phenomenon of polyamorphism (i.e., the existence of more than one disordered solid state), emphasizing both the role of the preparation protocols and the transformation between the different disordered ices. Finally, we present the ongoing debate on the possibility of linking polyamorphism with a liquid-liquid transition that could take place in the no-man's land, the temperature-pressure window in which homogeneous nucleation prevents the investigation of water in its metastable liquid form.

Diffusive dynamics during the high-to-low density transition in amorphous ice

Water exists in high- and low-density amorphous ice forms (HDA and LDA), which could correspond to the glassy states of high- (HDL) and low-density liquid (LDL) in the metastable part of the phase diagram. However, the nature of both the glass transition and the high-to-low-density transition are debated and new experimental evidence is needed. Here we combine wide-angle X-ray scattering (WAXS) with X-ray photon-correlation spectroscopy (XPCS) in the small-angle X-ray scattering (SAXS) geometry to probe both the structural and dynamical properties during the high-to-low-density transition in amorphous ice at 1 bar. By analyzing the structure factor and the radial distribution function, the coexistence of two structurally distinct domains is observed at T = 125 K. XPCS probes the dynamics in momentum space, which in the SAXS geometry reflects structural relaxation on the nanometer length scale. The dynamics of HDA are characterized by a slow component with a large time constant, arising from viscoelastic relaxation and stress release from nanometer-sized heterogeneities. Above 110 K a faster, strongly temperature-dependent component appears, with momentum transfer dependence pointing toward nanoscale diffusion. This dynamical component slows down after transition into the low-density form at 130 K, but remains diffusive. The diffusive character of both the high- and low-density forms is discussed among different interpretations and the results are most consistent with the hypothesis of a liquid-liquid transition in the ultraviscous regime.

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.

Observation of fragile-to-strong dynamic crossover in protein hydration water

At low temperatures, proteins exist in a glassy state, a state that has no conformational flexibility and shows no biological functions. In a hydrated protein, at temperatures greater-- similar 220 K, this flexibility is restored, and the protein is able to sample more conformational substates, thus becoming biologically functional. This "dynamical" transition of protein is believed to be triggered by its strong coupling with the hydration water, which also shows a similar dynamic transition. Here we demonstrate experimentally that this sudden switch in dynamic behavior of the hydration water on lysozyme occurs precisely at 220 K and can be described as a fragile-to-strong dynamic crossover. At the fragile-to-strong dynamic crossover, the structure of hydration water makes a transition from predominantly high-density (more fluid state) to low-density (less fluid state) forms derived from the existence of the second critical point at an elevated pressure.