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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.

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.

We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.

When aged below the glass transition temperature, Tg , the density of a glass cannot exceed that of the metastable super-cooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL ) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

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.

Femtosecond x-ray laser pulses were used to probe micrometer-sized water droplets that were cooled down to 227 kelvin in vacuum. Isothermal compressibility and correlation length were extracted from x-ray scattering at the low–momentum transfer region. The temperature dependence of these thermodynamic response and correlation functions shows maxima at 229 kelvin for water and 233 kelvin for heavy water. In addition, we observed that the liquids undergo the fastest growth of tetrahedral structures at similar temperatures. These observations point to the existence of a Widom line, defined as the locus of maximum correlation length emanating from a critical point at positive pressures in the deeply supercooled regime. The difference in the maximum value of the isothermal compressibility between the two isotopes shows the importance of nuclear quantum effects.

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 liquid–liquid transition (LLT) in a single-component liquid reflects changes in the liquid structure on the molecular level. In the case of ionic liquids (ILs), a hierarchical liquid structure is present due to charge-alternation constraints and segregation of nonpolar alkyl chains. We present experimental evidence of structural reorganization in a glass-forming IL corresponding to an LLT. The change in liquid structure correlates to changes in the dynamics and dielectric properties of the IL, which may be useful for potential applications. 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.

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.

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. Whereas the amorphous solids are long-lived and slowly aging glasses, their melting can lead quickly to the formation of crystalline ice. Further, melting of the higher density amorphous solid at low pressures takes place in steps, transitioning to the lower-density glass before accessing a nonequilibrium liquid from which ice coarsens.