Liquid-liquid Transition Research Articles

Viscosity anomaly of a metallic glass-forming liquid under high pressure

Viscosity, as a critical property closely associated with the glass-forming ability of a liquid, has been extensively studied with varying temperatures. However, its pressure dependence has not been well explored yet due to experimental difficulties. Here, we measured the viscosity of a metallic glass-forming liquid, Zr46Cu37.6Ag8.4Al8, at pressures up to 6.1 GPa above the melting points by falling-sphere viscometry with ultrafast synchrotron x-ray imaging. Overall, the viscosity increases with pressure, while surprisingly, there is an abrupt drop between 3.2 GPa and 3.7 GPa, indicating the possible existence of a pressure-induced liquid-to-liquid transition. Pressure could change the short- and medium-range orders in the multicomponent glass-forming liquid, as suggested by the different crystalline outcomes after cooling to room temperature at high- and low-pressure ranges. Our work extended the viscosity investigation of metallic glass-forming liquids to the high-pressure regime, which will expand our understanding of liquid-liquid transitions and metallic glass formation.

Phase Diagram of Aqueous Solutions of LiCl: a Study of Concentration Effects on the Anomalies of Water

We perform molecular dynamics simulations in order to study thermodynamics and the structure of supercooled aqueous solutions of lithium chloride (LiCl) at concentrations c = 0.678 and 2.034 mol/kg. We model the solvent using the TIP4P/2005 potential and the ions using the Madrid-2019 force field, a force field particularly suited for studying this solution. We find that, for c = 0.678 mol/kg, the behavior of the equation of state, studied in the P-T plane, indicates the presence of a liquid-liquid phase transition, similar to what was previously found for bulk water. We estimate the position of the liquid-liquid critical point to be at Tc ≈ 174 K, Pc ≈ 1775 bar, and ρc ≈ 1.065 g/cm3. When the concentration is tripled to c = 2.034 mol/kg, no critical point is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-ions structure in the two solutions, and we find that at the concentrations examined the effect of ions on the water-water structure is not strong, and all the features found in bulk water are preserved. We also calculate the hydration number of the Li and Cl ions, and in line with experiments, we find the value of 4 for Li+ and between 5.5 and 6 for Cl-, confirming the good performances of the Madrid-2019 force field.

Modulating Liquid-Liquid Transitions and Glass Formation in Zeolitic Imidazolate Frameworks by Decoration with Electron-Withdrawing Cyano Groups.

The liquid phase of metal-organic frameworks (MOFs) is key for the preparation of melt-quenched bulk glasses as well as the shaping of these materials for various applications; however, only very few MOFs can be melted and transformed into stable glasses. Here, the solvothermal and mechanochemical preparation of a new series of functionalized derivatives of ZIF-4 (Zn(im)2, where im- = imidazolate and ZIF = zeolitic imidazolate framework) containing the cyano-functionalized imidazolate linkers CNim- (4-cynanoimidazolate) and dCNim- (4,5-dicyanoimidazolate) is reported. The strongly electron-withdrawing nature of the CN groups facilitates low-temperature melting of the materials (below 310 °C for some derivatives) and the formation of microporous ZIF glasses with remarkably low glass-transition temperatures (down to only about 250 °C) and strong resistance against recrystallization. Besides conventional ZIF-4, the CN-functionalized ZIFs are so far the only MOFs to show an exothermic framework collapse to a low-density liquid phase and a subsequent transition to a high-density liquid phase. By systematic adjustment of the fraction of cyano-functionalized linkers in the ZIFs, we derive fundamental insights into the thermodynamics of the unique polyamorphic nature of these glass formers as well as further design rules for the porosity of the ZIF glasses and the viscosity of their corresponding liquids. The results provide new insights into the unusual phenomenon of liquid-liquid transitions as well as a guide for the chemical diversification of meltable MOFs, likely with implications beyond the archetypal ZIF glass formers.

Solid-amorphous transition is related to the waterlike anomalies in a fluid without liquid-liquid phase transition.

The most accepted origin for the water anomalous behavior is the phase transition between two liquids (LLPT) in the supercooled regime connected to the glassy first order phase transition at lower temperatures. Two length scale potentials are an effective approach that has long been employed to understand the properties of fluids with waterlike anomalies and, more recently, the behavior of colloids and nanoparticles. These potentials can be parameterized to have distinct shapes, as a pure repulsive ramp, such as the model proposed by de Oliveira et al. [J. Chem. Phys. 124, 64901 (2006)]. This model has waterlike anomalies despite the absence of LLPT. To unravel how the waterlike anomalies are connected to the solid phases, we employ molecular dynamics simulations. We have analyzed the fluid-solid transition under cooling, with two solid crystalline phases, BCC and HCP, and two amorphous regions being observed. We show how the competition between the scales creates an amorphous cluster in the BCC crystal that leads to amorphization at low temperatures. A similar mechanism is found in the fluid phase, with the system changing from a BCC-like to an amorphous-like structure in the point where a maxima in kT is observed. With this, we can relate the competition between two fluid structures with the amorphous clusterization in the BCC phase. These findings help to understand the origins of waterlike behavior in systems without the liquid-liquid critical point.

Simulating a flexible water model as rigid: Best practices and lessons learned.

Two ways to create rigid versions of flexible models are explored. The rigid model can assume the Model's Geometry (MG) as if the molecule is not interacting with any other molecules or the ensemble averaged geometry (EG) under a particular thermodynamic condition. Although the MG model is more straightforward to create, it leads to relatively poor performance. The EG model behaves similarly to the corresponding flexible model (the FL model) and, in some cases, agrees even better with experiments. While the difference between the EG and the FL models is mostly a result of flexibility, the MG and EG models have different dipole moments as a result of an effective induction in the condensed phase. For the three water models studied, the property that shows the most difference is the temperature dependence of density. The MG version of the water model by adaptive force matching for ice and liquid does not possess a temperature of maximum density, which is attributed to a downshift of the putative liquid-liquid phase transition line, leading to the hypothesized second critical point of liquid water to manifest at negative pressure. A new three-phase coexistence method for determining the melting temperature of ice is also presented.

Effect of graphene substrate on melting of Cu nanoparticles

A nanoparticles-graphene-based composites (NGC) can be produced by placing a metallic nanoparticle on the graphene or its derivative carrier. Molecular dynamics simulations were employed to investigate the structural evolution of Cu NGC during rapid heating, in terms of the largest standard cluster analysis (LaSCA). It is found that the Cu nanoparticles melt through three stages of surface melting, split-melting and rapid melting, instead of shell by shell from surface to center. The grapheme substrate improves the structure stability by lowering potential energy and increasing the melting point of Cu nanoparticles; it not only leads to non-isotropic melting but also introduce a liquid-liquid transition after all fcc atoms decomposed. These findings provide important insights for the melting of NGCs and will guide their preparation, utilization, modification, and other technologies.

Kinetics and Mechanisms of Pressure-Induced Ice Amorphization and Polyamorphic Transitions in a Machine-Learned Coarse-Grained Water Model.

Water glasses have attracted considerable attention due to their potential connection to a liquid-liquid transition in supercooled water. Here we use molecular simulations to investigate the formation and phase behavior of water glasses using the machine-learned bond-order parameter (ML-BOP) water model. We produce glasses through hyperquenching of water, pressure-induced amorphization (PIA) of ice, and pressure-induced polyamorphic transformations. We find that PIA of polycrystalline ice occurs at a lower pressure than that of monocrystalline ice and through a different mechanism. The temperature dependence of the amorphization pressure of polycrystalline ice for ML-BOP agrees with that in experiments. We also find that ML-BOP accurately reproduces the density, coordination number, and structural features of low-density (LDA), high-density (HDA), and very high-density (VHDA) amorphous water glasses. ML-BOP accurately reproduces the experimental radial distribution function of LDA but overpredicts the minimum between the first two shells in high-density glasses. We examine the kinetics and mechanism of the transformation between low-density and high-density glasses and find that the sharp nature of these transitions in ML-BOP is similar to that in experiments and all-atom water models with a liquid-liquid transition. Transitions between ML-BOP glasses occur through a spinodal-like mechanism, similar to ice crystallization from LDA. Both glass-to-glass and glass-to-ice transformations have Avrami-Kolmogorov kinetics with exponent n = 1.5 ± 0.2 in experiments and simulations. Importantly, ML-BOP reproduces the competition between crystallization and HDA→LDA transition above the glass transition temperature Tg, and separation of their time scales below Tg, observed also in experiments. These findings demonstrate the ability of ML-BOP to accurately reproduce water properties across various regimes, making it a promising model for addressing the competition between polyamorphic transitions and crystallization in water and solutions.

Structural heterogeneity in levitated glassy alloys with different undercoolings

The structural evolution in the undercooled liquid plays an essential role in comprehending the crystallization mechanism, which is of benefit to understand the glass-forming ability (GFA), the thermal stability, and the development of glassy alloy (GA) with excellent properties. In this work, Zr61Ti2Cu25Al12 GAs with different undercooled states were obtained by means of electromagnetic levitation. The Zr61Ti2Cu25Al12 GA can achieve an undercooling degree of 226 K, which is larger than previously reported GAs. Calorimetric analysis indicates a more relaxed state occurs in the GA cooled from the larger undercooling. Hardness tests show that deep undercooling can lead to a significant increase in hardness compared to a low undercooling level. It might be attributed to a liquid-liquid transition, bringing out an obvious change in the atomic volume of the glassy phase. In addition, a pronounced ordered structure apparently exists when the system reaches the larger undercooling degree. Our findings provide a new perspective for the study of the undercooled liquid, and the solidification kinetics of GAs.

Single-molecule techniques to visualize and to characterize liquid-liquid phase separation and phase transition.

Biomolecules forming membraneless structures via liquid-liquid phase separation (LLPS) is a common event in living cells. Some liquid-like condensates can convert into solid-like aggregations, and such a phase transition process is related to some neurodegenerative diseases. Liquid-like condensates and solid-like aggregations usually exhibit distinctive fluidity and are commonly distinguished via their morphology and dynamic properties identified through ensemble methods. Emerging single-molecule techniques are a group of highly sensitive techniques, which can offer further mechanistic insights into LLPS and phase transition at the molecular level. Here, we summarize the working principles of several commonly used single-molecule techniques and demonstrate their unique power in manipulating LLPS, examining mechanical properties at the nanoscale, and monitoring dynamic and thermodynamic properties at the molecular level. Thus, single-molecule techniques are unique tools to characterize LLPS and liquid-to-solid phase transition under close-to-physiological conditions.

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.

Effect of bulky anions on the liquid-liquid phase transition in phosphonium ionic liquids: Ambient and high-pressure dielectric studies

Although the first-order liquid–liquid phase transition (LLT) has been reported to exist in various systems (i.e., phosphorus, silicon, water, triphenyl phosphite, etc.), it is still one of the most challenging problems in the field of physical science. Recently, we found that this phenomenon occurs in the family of trihexyl(tetradecyl)phosphonium [P666,14]+ based ionic liquids (ILs) with different anions (Wojnarowska et al in Nat Commun 13:1342, 2022). To understand the molecular structure–property relationships governing LLT, herein, we examine ion dynamics of two other quaternary phosphonium ILs containing long alkyl chains in cation and anion. We found that IL with the anion containing branched –O–(CH2)5–CH3 side chains does not reveal any signs of LLT, while IL with shorter alkyl chains in the anion brings a hidden LLT, i.e., it overlaps with the liquid-glass transition. Ambient pressure dielectric and viscosity measurements revealed a peculiar behavior of ion dynamics near Tg for IL with hidden LLT. Moreover, high-pressure studies have shown that IL with hidden LLT has relatively strong pressure sensitivity compared to the one without first-order phase transition. At the same time, the former exposes the inflection point indicating the concave-convex character of logτσ(P) dependences.

Stable Solid Molecular Hydrogen above 900K from a Machine-Learned Potential Trained with Diffusion Quantum MonteCarlo.

We survey the phase diagram of high-pressure molecular hydrogen with path integral molecular dynamics using a machine-learned interatomic potential trained with quantum MonteCarlo forces and energies. Besides the HCP and C2/c-24 phases, we find two new stable phases both with molecular centers in the Fmmm-4 structure, separated by a molecular orientation transition with temperature. The high temperature isotropic Fmmm-4 phase has a reentrant melting line with a maximum at higher temperature (1450K at 150GPa) than previously estimated and crosses the liquid-liquid transition line around 1200K and 200GPa.

Experimental observation of mesoscopic fluctuations to identify origin of thermodynamic anomalies of ambient liquid water

We report a new experimental approach for observing mesoscopic fluctuations underlying the thermodynamic anomalies of ambient liquid water. In this approach, two sound velocity measurements with different frequencies, namely inelastic X-ray scattering (IXS) in THz band and ultrasonic (US) in MHz band, are required to investigate the relaxation phenomenon with the characteristic frequency between the two aforementioned frequencies. We performed IXS measurements to obtain the IXS sound velocity of liquid water from the ambient conditions to the supercritical region of liquid-gas phase transition (LGT) and compared the results with the US sound velocity in the literature. We found that the ratio of the two sound velocities, Sf, which corresponds to the relaxation intensity, exhibits a simple but significant change. Two distinct rises were observed in the high-temperature and low-temperature regions, implying that two relaxation phenomena exist: in the high-temperature region, a peak was observed near the LGT critical ridge line, which was linked with changes in the density fluctuation and isochoric and isobaric specific heat capacities; in the low-temperature region, Sf increased toward the low-temperature region, which was linked with the change in the isochoric heat capacity. We concluded that these two relaxation phenomena are originated from critical fluctuations of liquid-gas phase transition (LGT) and liquid-liquid phase transition, respectively. The linkage between Sf and isochoric heat capacity in the low-temperature region proves that the relaxation is the cause of the well-known heat capacity anomaly of ambient liquid water. In this study, both LGT and LLT critical fluctuations were observed, and the relationship between thermodynamics and the critical fluctuations was comprehensively discussed.

Effect of a membrane protein condensation phase transition on reaction-diffusion kinetics.

Reversible biomolecular phase transitions, such as liquid-liquid phase transition in cytosolic proteins, and phosphorylation-driven condensation in membrane-bound systems have been cited as underlying mechanisms for numerous important cellular processes such as signal transduction. For example, condensation of the T cell signaling protein LAT, and, separately, Epidermal Growth Factor Receptor has been shown to elongate the membrane dwell time of the Ras-GEF SOS, enabling it to overcome a series of slow, membrane dependent activation steps. However, evidence from in-vitro reconstitution experiments suggests that formation of a condensed phase may not solely be beneficial to membrane-associated enzyme kinetics. SOS is both a scaffolding component, and a downstream effector of signaling condensates upstream of the Ras/Erk pathway. In such systems, its substrate Ras needs to have access to SOS for nucleotide exchange to take place. Sequestration of SOS proteins within a networked condensate may inhibit the ability of Ras to encounter SOS by diffusion. To investigate, we reconstitute protein condensation phase transitions consisting of the phosphotyrosine tails of either LAT or EGFR on supported lipid bilayers, along with the crosslinking components Grb2 and the PR domain of SOS to induce condensation. Under these conditions, single molecule TIRF microscopy can be used to localize and track membrane diffusion and partitioning between the condensed domains and surrounding sparse phase.

Liquid-liquid phase separation in supercooled water from ultrafast heating of low-density amorphous ice

Recent experiments continue to find evidence for a liquid-liquid phase transition (LLPT) in supercooled water, which would unify our understanding of the anomalous properties of liquid water and amorphous ice. These experiments are challenging because the proposed LLPT occurs under extreme metastable conditions where the liquid freezes to a crystal on a very short time scale. Here, we analyze models for the LLPT to show that coexistence of distinct high-density and low-density liquid phases may be observed by subjecting low-density amorphous (LDA) ice to ultrafast heating. We then describe experiments in which we heat LDA ice to near the predicted critical point of the LLPT by an ultrafast infrared laser pulse, following which we measure the structure factor using femtosecond x-ray laser pulses. Consistent with our predictions, we observe a LLPT occurring on a time scale < 100 ns and widely separated from ice formation, which begins at times >1 μs.

The coexistence region in the Van der Waals fluid and the liquid-liquid phase transitions.

Cellular membraneless organelles are thought to be droplets formed within the two-phase region corresponding to proteinaceous systems endowed with the liquid-liquid transition. However, their metastability requires an additional constraint-they arise in a certain region of density and temperature between the spinodal and binodal lines. Here, we consider the well-studied van der Waals fluid as a test model to work out criteria to determine the location of the spinodal line for situations in which the equation of state is not known. Our molecular dynamics studies indicate that this task can be accomplished by considering the specific heat, the surface tension and characteristics of the molecular clusters, such as the number of component chains and radius of gyration.

Critical fluctuations in liquid-liquid extraction organic phases controlled by extractant and diluent molecular structure.

Extractant aggregation in liquid-liquid extraction organic phases impacts extraction energetics and is related to the deleterious efficiency-limiting liquid-liquid phase transition known as third phase formation. Using small angle X-ray scattering, we find that structural heterogeneities across a wide range of compositions in binary mixtures of malonamide extractants and alkane diluents are well described by Ornstein-Zernike scattering. This suggests that structure in these simplified organic phases originates from the critical point associated with the liquid-liquid phase transition. To confirm this, we measure the temperature dependence of the organic phase structure, finding critical exponents consistent with the 3D Ising model. Molecular dynamics simulations were also consistent with this mechanism for extractant aggregation. Due to the absence of water or any other polar solutes required to form reverse-micellar-like nanostructures, these fluctuations are inherent to the binary extractant/diluent mixture. We also show how the molecular structure of the extractant and diluent modulate these critical concentration fluctuations by shifting the critical temperature: critical fluctuations are suppressed by increasing extractant alkyl tail lengths or decreasing diluent alkyl chain lengths. This is consistent with how extractant and diluent molecular structure are known to impact metal and acid loading capacity in many-component LLE organic phases, suggesting phase behavior of practical systems may be effectively studied in simplified organic phases. Overall, the explicit connection between molecular structure, aggregation and phase behavior demonstrated here will enable the design of more efficient separations processes.

Liquid-Liquid Transition in Water from First Principles.

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

Multiple Glass Transitions in Bismuth and Tin beyond Melting Temperatures

Liquid-liquid transitions were discovered above the melting temperature (Tm) in Bi and Sn up to 2 Tm, viewed as glass transitions at Tg = Tn+ &gt; Tm of composites nucleated at Tx &lt; Tm and fully melted at Tn+. A glassy fraction (f) disappeared at 784 K in Sn. (Tn+) increases with singular values of (f) depending on Tx with (f) attaining 100% at Tg = Tn+ = 2 Tm. The nonclassical model of homogeneous nucleation is used to predict Tx, Tn+ and the specific heat. The singular values of (f) leading to (Tn+) correspond to percolation thresholds of configurons in glassy phases. A phase diagram of glassy fractions occurring in molten elements is proposed. The same value of (Tx) can lead to multiple (Tg). Values of (Tg = Tn+) can be higher than (2 Tm) for Tx/Tm &lt; 0.7069. A specific heat equal to zero is predicted after cooling from T ≤ 2 Tm and would correspond to a glassy phase. Weak glassy fractions are nucleated near (Tn+) after full melting at (Tm) without transition at (Tx). Resistivity decreases were observed after thermal cycling between solid and liquid states with weak and successive values of (f) due to Tx/Tm &lt; 0.7069.

Liquid-liquid transition and inherited signatures in Zr-Cu-Ni-Al metallic glasses

Up to now, the research of liquid-liquid transition (LLT) has significantly improved the understanding of its liquid structure and evolution, which is crucial to addressing the longstanding problem with glass formation. However, it remains unclear how LLT affects the vitrification and structures of glasses, due to the challenge in experimentally exploring LLT in high-temperature melt well above the liquidus temperature. In the present study, an experiment is conducted to observe LLT in three Zr-Cu-Ni-Al melts at around 1450 K from both dynamic and thermodynamic perspectives. It is discovered that superheated fragility is closely associated with glass-forming ability. By controlling the melt temperature, two types of metallic glasses are obtained, showing difference in crystallization behaviors, which is attributed to the competition between crystal-like clusters and icosahedral-like clusters. Prior to the LLT, the formation of crystal-like clusters is dominant. Afterwards, the LLT promoted formation of icosahedral-like clusters becomes dominant. Due to the inherited signatures in glass, LLT is manifested by the changes in both medium-range order structure and short-range order structure. This study further reveals the pattern of microstructural evolution accompanied by LLT in high-temperature multi-component melts, which is conducive to the control on structure and properties of glasses from liquids.