Thermodynamic behaviour of supercritical matter

Crossover from gas-like to liquid-like molecular diffusion in a simple supercritical fluid

According to textbooks, no physical observable can be discerned allowing to distinguish a liquid from a gas beyond the critical point. Yet, several proposals have been put forward challenging this view and various transition boundaries between a gas-like and a liquid-like behaviour, including the so-called Widom and Frenkel lines, and percolation line, have been suggested to delineate the supercritical state space. Here we report observation of a crossover from gas-like (Gaussian) to liquid-like (Lorentzian) self-dynamic structure factor by incoherent quasi-elastic neutron scattering measurements on supercritical fluid methane as a function of pressure, along the 200 K isotherm. The molecular self-diffusion coefficient was derived from the best Gaussian (at low pressures) or Lorentzian (at high pressures) fits to the neutron spectra. The Gaussian-to-Lorentzian crossover is progressive and takes place at about the Widom line intercept (59 bar). At considerably higher pressures, a liquid-like jump diffusion mechanism properly describes the supercritical fluid on both sides of the Frenkel line. The present observation of a gas-like to liquid-like crossover in the self dynamics of a simple supercritical fluid confirms emerging views on the unexpectedly complex physics of the supercritical state, and could have planet-wide implications and possible industrial applications in green chemistry.

Thermodynamic crossovers in supercritical fluids

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions.

Kinetic temperature and pressure of an active Tonks gas

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.

Supercritical fluids behave as complex networks

Supercritical fluids play a key role in environmental, geological, and celestial processes, and are of great importance to many scientific and engineering applications. They exhibit strong variations in thermodynamic response functions, which has been hypothesized to stem from the microstructural behavior. However, a direct connection between thermodynamic conditions and the microstructural behavior, as described by molecular clusters, remains an outstanding issue. By utilizing a first-principles-based criterion and self-similarity analysis, we identify energetically localized molecular clusters whose size distribution and connectivity exhibit self-similarity in the extended supercritical phase space. We show that the structural response of these clusters follows a complex network behavior whose dynamics arises from the energetics of isotropic molecular interactions. Furthermore, we demonstrate that a hidden variable network model can accurately describe the structural and dynamical response of supercritical fluids. These results highlight the need for constitutive models and provide a basis to relate the fluid microstructure to thermodynamic response functions.

Inhomogeneity Effects on Reactions in Supercritical Fluids: A Computational Study on the Pyrolysis of n-Decane

Supercritical fluids exhibit peculiar inhomogeneity, which strongly affects reaction behaviors in them. However, explanations for inhomogeneity and its effect on reactions are both ambiguous so far. Here, we provide an atomic-level understanding of inhomogeneity effects on reactions via the computational method, with the example of n-decane pyrolysis under supercritical conditions. We describe the characteristic pyrolysis behaviors through collective variable-driven hyperdynamics (CVHD) simulations and explain the inhomogeneity of supercritical n-decane as the coexistence of gas-like and liquid-like atoms by a trained machine learning classifier. Due to their specific local environment, the appearance of liquid-like atoms under supercritical conditions significantly increases the type and frequency of bimolecular reactions and eventually causes changes in product distributions. Future research with this method is expected to extend the effect of inhomogeneity on other reactions under supercritical conditions or other condensed phases.

Fingerprints of the Crossing of the Frenkel and Melting Line on the Properties of High-Pressure Supercritical Water

Using molecular dynamics simulations in combination with the two-phase thermodynamic model, we reveal novel characteristic fingerprints of the crossing of the Frenkel and melting line on the properties of high-pressure water at a near-critical temperature (1.03T_c). The crossing of the Frenkel line at about 1.17 GPa is characterized by a crossover in the rotational and translational entropy ratio S^rot/S^trans, indicating a change in the coupling between translational and rotational motions which is also reflected in the shape of the rotational density of states. The observed isosbestic points in the translational and rotational density of states are also blue-shifted at density and pressure conditions higher than the ones corresponding to the Frenkel line. The first-order phase transition from a rigid liquid to a face-centered cubic plastic crystal phase at about 8.5 GPa is reflected in the discontinuous changes in the translational and rotational entropy, particularly in the significant increase of the ratio S^rot/S^trans. A noticeable discontinuous increase of the dielectric constant has also been revealed when crossing this melting line, which is attributed to the different arrangement of the water molecules in the plastic crystal phase. The reorientational dynamics in the plastic crystal phase is faster in comparison with the "rigid" liquid-like phase, but it remains unchanged upon a further pressure increase in the range of 8.5-11 GPa.

The Phonon Theory of Liquids and Biological Fluids: Developments and Applications

Among the three basic states of matter (solid, liquid, and gas), the liquid state has always eluded general theoretical approaches for describing liquid energy and heat capacity. In this Viewpoint, we derive the phonon theory of liquids and biological fluids stemming from Frenkel's microscopic picture of the liquid state. Specifically, the theory predicts the existence of phonon gaps in vibrational spectra of liquids and a thermodynamic boundary in the supercritical state. Direct experimental evidence reaffirming these theoretical predictions was achieved through a combination of techniques using static compression X-ray diffraction and inelastic X-ray scattering on deeply supercritical argon in a diamond anvil cell. Furthermore, these findings inspired and then led to the discovery of phonon gaps in liquid crystals (mesogens), block copolymers, and biological membranes. Importantly, phonon gaps define viscoelastic crossovers in cellular membranes responsible for lipid self-diffusion, lateral molecular-level stress propagation, and passive transmembrane transport of small molecules and solutes. Finally, molecular interactions mediated by external stimuli result in synaptic activity controlling biological membranes' plasticity resulting in learning and memory. Therefore, we also discuss learning and memory effects─equally important for neuroscience as well as for the development of neuromorphic devices─facilitated in biological membranes by external stimuli.

On the Different Faces of the Supercritical Phase of Water at a Near-Critical Temperature: Pressure-Induced Structural Transitions Ranging from a Gaslike Fluid to a Plastic Crystal Polymorph

The present study reports a systematic analysis of a wide variety of structural, thermodynamic, and dynamic properties of supercritical water along the near-critical isotherm of T = 1.03T_c and up to extreme pressures, using molecular dynamics and Monte Carlo simulations. The methodology employed provides solid evidence about the existence of a structural transition from a liquidlike fluid to a compressed, tightly packed liquid, in the density and pressure region around 3.4ρ_c and 1.17 GPa, introducing an alternative approach to locate the crossing of the Frenkel line. Around 8.5 GPa another transition to a face-centered-cubic plastic crystal polymorph with density 5.178ρ_c is also observed, further confirmed by Gibbs free energy calculations using the two-phase thermodynamic model. The isobaric heat capacity maximum, closely related to the crossing of the Widom line, has also been observed around 0.8ρ_c, where the local density augmentation is also maximized. Another structural transition has been observed at 0.2ρ_c, related to the transformation of the fluid to a dilute gas at lower densities. These findings indicate that a near-critical isotherm can be divided into different domains where supercritical water exhibits distinct behavior, ranging from a gaslike one to a plastic crystal one.

Phase distribution including a bubblelike region in supercritical fluid

Pseudoboiling in supercritical fluid (SF) has been paid great attention in recent years. Available works mainly focus on thermodynamics analysis. Fewer studies were reported on the spatial time phase distribution. Here, SF is investigated in a multiphase fluid framework using molecular dynamics (MD) simulations. A simulation box contains 10 976 argon atoms, with periodic boundary conditions applied on all the box surfaces. Pressure and temperature are well controlled. Based on MD simulation results, an onset pseudoboiling temperature T^{-} and a termination pseudoboiling temperature T^{+} are defined using the neighboring molecules method, the radial distribution function method, and the two-body excess entropy method. The two transition temperatures divide the whole phase diagram into three regimes of liquidlike, two-phase-like (TPL), and gaslike, and the MD determined T^{-} and T^{+} well matched the thermodynamics-determined values. In the TPL regime, nanovoids are observed to have two distinct characteristics: (1) Particles are sparsely distributed to have gas density inside the void, but are densely populated to have liquid density outside the void. (2) Voids have a curved interface. These characteristics are very similar to bubble characteristics in subcritical pressure. Hence, voids in the supercritical state are called "bubblelike" in this paper. Nonlinear dynamics demonstrates chaotic behavior in the TPL regime, similar to the two-phase regime in the subcritical domain. The above findings give strong evidence that SF in the TPL regime consists of a mixture of bubblelike voids and surrounding liquids. Our work highlights the multiphase feature of a SF, hence, the well-established multiphase theory in subcritical pressures can be introduced to handle the complex SF.

Dynamic Crossover in Fluids: From Hard Spheres to Molecules

We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liquid-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to molecules' translation, is exactly equal to a collective property, the contribution to viscosity due to molecular interactions. Such a definition is shown to be consistent with the one based on the minima of the kinematic viscosity. For the hard sphere, this is shown to be an exact solution. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the critical point, and for all studied fluids, it is well captured by the critical excess entropy curve for atomic fluids, emphasizing the link between transport properties and local structure.

The "isothermal" compressibility of active matter

We demonstrate that the mechanically defined "isothermal" compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure-a combination of the collision and unique swim pressures-is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior.

Phonon-mediated lipid raft formation in biological membranes

Short-wavelength collective molecular motions, also known as phonons, have recently attracted much interest in revealing dynamic properties of biological membranes through the use of neutron and X-ray scattering, infrared and Raman spectroscopies, and molecular dynamics simulations. Experimentally detecting unique vibrational patterns such as, shear phonon excitations, viscoelastic crossovers, transverse acoustic phonon gaps, and continuous and truncated optical phonon modes in cellular membranes, to name a few, has proven non-trivial. Here, we review recent advances in liquid thermodynamics that have resulted in the development of the phonon theory of liquids. The theory has important predictions regarding the shear vibrational spectra of fluids, namely the emergence of viscoelastic crossovers and transverse acoustic phonon gaps. Furthermore, we show that these vibrational patterns are common in soft (non-crystalline) materials, including, but not limited to liquids, colloids, liquid crystals (mesogens), block copolymers, and biological membranes. The existence of viscoelastic crossovers and acoustic phonon gaps define the self-diffusion properties of cellular membranes and provide a molecular picture of the transient nature of lipid rafts (Bolmatov et al., 2020). Importantly, the timescales (picoseconds) for the formation and dissolution of transient lipid rafts match the lifetime of the formation and breakdown of interfacial water hydrogen bonds. Apart from acoustic propagating phonon modes, biological membranes can also support more energetic non-propagating optical phonon excitations, also known as standing waves or breathing modes. Importantly, optical phonons can be truncated due to the existence of finite size nanodomains made up of strongly correlated lipid-cholesterol molecular pairs. These strongly coupled molecular pairs can serve as nucleation centers for the formation of stable rafts at larger length scales, due to correlations of spontaneous fluctuations (Onsager's regression hypothesis). Finally and importantly, molecular level viscoelastic crossovers, acoustic phonon gaps, and continuous and truncated optical phonon modes may offer insights as to how lipid-lipid and lipid-protein interactions enable biological function.

Molecular dynamics simulation study used in systems with supercritical water

Supercritical water (SCW) is a green solvent. The supercritical fluids have been increasingly concerned and studied in many areas such as SCW gasification, biofuel production, SCW hydrothermal conversion, organic wastes treatment and utilization, nanotechnology, etc. Because of the severe circumstances and rapid reactions in supercritical water, it is difficult for experimental researchers to disentangle various fundamental reaction steps from the intermediate and product distributions. From this perspective, molecular dynamics (MD) simulation based on quantum chemistry is an efficient tool for studying and exploring complex molecular systems. In recent years, molecular simulations and quantum chemical calculations have become powerful for illustrating the possible internal mechanism of a complex system. However, now there is no literature about the overview of MD simulation study of the system with SCW. Therefore, in this paper, an overview of MD simulation investigation applied in various systems with SCW is presented. In the current review we explore diverse research areas. Namely, the applications of MD simulation on investigating the properties of SCW, pyrolysis/gasification systems with SCW, dissolution systems and oxidation systems with SCW were summarized. And the corresponding problems in diverse systems were discussed. Furthermore, the advances and problems in MD simulation study were also discussed. Finally, possible directions for future research were outlined. This work is expected to be one reference for the further theoretical and molecular simulation investigations of systems involving SCW.

Mysterious long-living ultrahigh-pressure or secondary impact crisis

High-pressure glass has attracted interest in terms of both its fundamental state under extreme conditions and its possible applications as an advanced material. In this context, natural impact glasses are of considerable interest because they are formed under ultrahigh-pressure and high-temperature (UHPHT) conditions in larger volumes than laboratory fabrication can produce. Studying the UHPHT glasses of the unique giant Kara astrobleme (Russia), we found that the specific geological position of the UHPHT melt glass veins points to an origin from a secondary ultrahigh-pressure (UHP) melt according to the characteristics of the host suevites, which suggest later bottom flow. Here, we propose a fundamentally novel model involving an upward-injected UHP melt complex with complicated multi-level and multi-process differentiation based on observations of the UHP silica glass, single-crystal coesite and related UHP smectite that crystallized from an impact-generated hydrous melt. This model proposes a secondary UHP crisis during the modification stage of the Kara crater formation. The results are very important for addressing fundamental problems in fields as diverse as condensed matter states under extreme pressure and temperature (PT) conditions, material and geological reconstructions of impact structures, water conditions in mineral substances under UHP conditions in the deep Earth, and the duration and magnitude of the catastrophic effects of large asteroid impacts.

Universality, Scaling, and Collapse in Supercritical Fluids

Supercritical fluid (SCF) is known to exhibit salient dynamic and thermodynamic crossovers and an inhomogeneous molecular distribution. However, the question as to what basic physics underlies these microscopic and macroscopic anomalies remains open. Here, using an order parameter extracted by machine learning, the fraction of gas-like (or liquid-like) molecules, we find simplicity and universality in SCF: First, all isotherms of a given fluid collapse onto a single master curve described by a scaling relation. The observed power law holds from the high-temperature and -pressure regime down to the critical point where it diverges. Second, phase diagrams of different compounds collapse onto their master curves by the same scaling exponent, thereby demonstrating a putative law of corresponding supercritical states in simple fluids. The reported results support a model of the SCF as a mixture of two interchangeable microstates, whose spatiotemporal dynamics gives rise to unique macroscopic properties.

Structural behavior of fluids from the vapor and liquid region to the supercritical phase

A metric (χ) is introduced to quantify the relative proportion of particles having a specified number of near neighbors that are characteristic of liquid-phase properties. It can be used as a simple alternative to other methods for the investigation of some aspects of percolation behavior. Values of χ are obtained from molecular-dynamics simulations spanning the heterogeneous vapor and liquid region and the supercritical phase of the Lennard-Jones fluid. The supercritical phase can be delineated into regions of different structural properties. At different isochoric subcritical conditions, the temperature versus χ behavior shows evidence of inflections, which are associated with the onset of transitions from the vapor and liquid region to the supercritical phase. The analysis suggests a phenomenological requirement for the critical point in terms of a near-equal proportion of near neighbors with gaslike and liquidlike characteristics.

Deciphering Melatonin-Stabilized Phase Separation in Phospholipid Bilayers

Lipid bilayers are fundamental building blocks of cell membranes, which contain the machinery needed to perform a range of biological functions, including cell-cell recognition, signal transduction, receptor trafficking, viral budding, and cell fusion. Importantly, many of these functions are thought to take place in the laterally phase-separated regions of the membrane, commonly known as lipid rafts. Here, we provide experimental evidence for the "stabilizing" effect of melatonin, a naturally occurring hormone produced by the brain's pineal gland, on phase-separated model membranes mimicking the outer leaflet of plasma membranes. Specifically, we show that melatonin stabilizes the liquid-ordered/liquid-disordered phase coexistence over an extended range of temperatures. The melatonin-mediated stabilization effect is observed in both nanometer- and micrometer-sized liposomes using small angle neutron scattering (SANS), confocal fluorescence microscopy, and differential scanning calorimetry. To experimentally detect nanoscopic domains in 50 nm diameter phospholipid vesicles, we developed a model using the Landau-Brazovskii approach that may serve as a platform for detecting the existence of nanoscopic lateral heterogeneities in soft matter and biological materials with spherical and planar geometries.

Thermodynamic heterogeneity and crossover in the supercritical state of matter

A hallmark of a thermodynamic phase transition is the qualitative change of system thermodynamic properties such as energy and heat capacity. On the other hand, no phase transition is thought to operate in the supercritical state of matter and, for this reason, it was believed that supercritical thermodynamic properties vary smoothly and without any qualitative changes. Here, we perform extensive molecular dynamics simulations in a wide temperature range and find that a deeply supercritical state is thermodynamically heterogeneous, as witnessed by different temperature dependence of energy, heat capacity and its derivatives at low and high temperature. The evidence comes from three different methods of analysis, two of which are model-independent. We propose a new definition of the relative width of the thermodynamic crossover and calculate it to be in the fairly narrow relative range of 13%-20%. On the basis of our results, we relate the crossover to the supercritical Frenkel line.

The nature of collective excitations and their crossover at extreme supercritical conditions

Physical properties of an interacting system are governed by collective excitations, but their nature at extreme supercritical conditions is unknown. Here, we present direct evidence for propagating solid-like longitudinal phonon-like excitations with wavelengths extending to interatomic separations deep in the supercritical state at temperatures up to 3,300 times the critical temperature. We observe that the crossover of dispersion curves develops at k points reducing with temperature. We interpret this effect as the crossover from the collective phonon to the collisional mean-free path regime of particle dynamics and find that the crossover points are close to both the inverse of the shortest available wavelength in the system and to the particle mean free path inferred from experiments and theory. Notably, both the shortest wavelength and mean free path scale with temperature with the same power law, lending further support to our findings.

"Two-Phase" Thermodynamics of the Frenkel Line

The Frenkel line, a crossover line between rigid and nonrigid dynamics of fluid particles, has recently been the subject of intense debate regarding its relevance as a partitioning line of the supercritical phase, where the main criticism comes from the theoretical treatment of collective particle dynamics. From an independent point of view, this Letter suggests that the two-phase thermodynamics model may alleviate this contentious situation. The model offers new criteria for defining the Frenkel line in the supercritical region and builds a robust connection among the preexisting, seemingly inconsistent definitions. In addition, one of the dynamic criteria locates the rigid-nonrigid transition of the soft-sphere and the hard-sphere models. Hence, we suggest the Frenkel line be considered as a dynamic rigid-nonrigid fluid boundary, without any relation to gas-liquid transition. These findings provide an integrative viewpoint combining fragmentized definitions of the Frenkel line, allowing future studies to be carried out in a more reliable manner.

A Simple Two Dimensional Model of Methanol

Methanol is the simplest alcohol and possible energy carrier because it is easier to store than hydrogen and burns cleaner than fossil fuels. It is a colorless liquid, completely miscible with water and organic solvents and is very hygroscopic. Here, simple two-dimensional models of methanol, based on Mercedes-Benz (MB) model of water, are examined by Monte Carlo simulations. Methanol particles are modeled as dimers formed by an apolar Lennard-Jones disk, mimicking the methyl group, and a sphere with two hydrogen bonding arms for the hydroxyl group. The used models are the one proposed by Hribar-Lee and Dill (Acta Chimica Slovenica, 53:257, 2006.) with the overlapping discs and a new model with tangentially fused dimers. The comparison was done between the models, in connection to the MB water, as well as with experimental results and with new simulations done for 3D models of methanol. Both 2D models show similar trends in structuring and thermodynamics. The difference is the most pronounced at lower temperatures, where the smaller model exhibits spontaneous crystallization, while the larger model shows metastable states. The 2D structural organization represents well the clustering tendency observed in 3D models, as well as in experiments. The models qualitatively agree with the bulk methanol thermodynamic properties like density and isothermal compressibility, however, heat capacity at the constant pressure shows trend more similar to the water behavior. This work on the smallest amphiphilic organic solute provides a simple testing ground to study the competition between polar and non-polar effects within the molecule and physical properties.

High-veracity functional imaging in scanning probe microscopy via Graph-Bootstrapping

The key objective of scanning probe microscopy (SPM) techniques is the optimal representation of the nanoscale surface structure and functionality inferred from the dynamics of the cantilever. This is particularly pertinent today, as the SPM community has seen a rapidly growing trend towards simultaneous capture of multiple imaging channels and complex modes of operation involving high-dimensional information-rich datasets, bringing forward the challenges of visualization and analysis, particularly for cases where the underlying dynamic model is poorly understood. To meet this challenge, we present a data-driven approach, Graph-Bootstrapping, based on low-dimensional manifold learning of the full SPM spectra and demonstrate its successes for high-veracity mechanical mapping on a mixed polymer thin film and resolving irregular hydration structure of calcite at atomic resolution. Using the proposed methodology, we can efficiently reveal and hierarchically represent salient material features with rich local details, further enabling denoising, classification, and high-resolution functional imaging.

Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry

Aspects of isomorph theory, Rosenfeld-Tarazona temperature scaling, and thermodynamic geometry are comparatively discussed on the basis of the Lennard-Jones potential. The first two approaches approximate the high-density fluid state well when the repulsive interparticle interactions become dominant, which is typically the case close to the freezing line. However, previous studies of Rosenfeld-Tarazona scaling for the isochoric heat capacity and its relation to isomorph theory reveal deviations for the temperature dependence. It turns out that a definition of a state region in which repulsive interactions dominate is required for achieving consistent results. The Riemannian thermodynamic scalar curvature R allows for such a classification, indicating predominantly repulsive interactions by R>0. An analysis of the isomorphic character of the freezing line and the validity of Rosenfeld-Tarazona temperature scaling show that these approaches are consistent only in a small state region.

Structural behavior of supercritical fluids under confinement

The existence of the Frenkel line in the supercritical regime of a Lennard-Jones (LJ) fluid shown through molecular dynamics (MD) simulations initially and later corroborated by experiments on argon opens up possibilities of understanding the structure and dynamics of supercritical fluids in general and of the Frenkel line in particular. The location of the Frenkel line, which demarcates two distinct physical states, liquidlike and gaslike within the supercritical regime, has been established through MD simulations of the velocity autocorrelation (VACF) and radial distribution function (RDF). We, in this article, explore the changes in the structural features of supercritical LJ fluid under partial confinement using atomistic walls. The study is carried out across the Frenkel line through a series of MD simulations considering a set of thermodynamics states in the supercritical regime (P=5000 bar, 240K≤T≤1500K) of argon well above the critical point. Confinement is partial, with atomistic walls located normal to z and extending to "infinity" along the x and y directions. In the "liquidlike" regime of the supercritical phase, particles are found to be distributed in distinct layers along the z axis with layer spacing less than one atomic diameter and the lateral RDF showing amorphous-like structure for specific spacings (packing frustration) and non-amorphous-like structure for other spacings. Increasing the rigidity of the atomistic walls is found to lead to stronger layering and increased structural order. For confinement with reflective walls, layers are found to form with one atomic diameter spacing and the lateral RDF showing close-packed structure for the smaller confinements. Translational order parameter and excess entropy assessment confirms the ordering taking place for atomistic wall and reflective wall confinements. In the "gaslike" regime of the supercritical phase, particle distribution along the spacing and the lateral RDF exhibit features not significantly different from that due to normal gas regime. The heterogeneity across the Frenkel line, found to be present both in bulk and confined systems, might cause the breakdown of the universal scaling between structure and dynamics of fluids necessitating the determination of a unique relationship between them.

Crossover between liquidlike and gaslike behavior in CH_{4} at 400 K

We report experimental evidence for a crossover between a liquidlike state and a gaslike state in fluid methane (CH_{4}). This crossover is observed in all of our experiments, up to a temperature of 397 K, 2.1 times the critical temperature of methane. The crossover has been characterized with both Raman spectroscopy and x-ray diffraction in a number of separate experiments, and confirmed to be reversible. We associate this crossover with the Frenkel line-a recently hypothesized crossover in dynamic properties of fluids extending to arbitrarily high pressure and temperature, dividing the phase diagram into separate regions where the fluid possesses liquidlike and gaslike properties. On the liquidlike side the Raman-active vibration increases in frequency linearly as pressure is increased, as expected due to the repulsive interaction between adjacent molecules. On the gaslike side this competes with the attractive van der Waals potential leading the vibration frequency to decrease as pressure is increased.

Behavior of Supercritical Fluids across the "Frenkel Line"

The "Frenkel line" (FL), the thermodynamic locus where the time for a particle to move by its size equals the shortest transverse oscillation period, has been proposed as a boundary between recently discovered liquid-like and gas-like regions in supercritical fluids. We report a simulation study of isothermal supercritical neon in a range of densities intersecting the FL. Specifically, structural properties and single-particle and collective dynamics are scrutinized to unveil the onset of any anomalous behavior at the FL. We find that (i) the pair distribution function smoothly evolves across the FL displaying medium-range order, (ii) low-frequency transverse excitations are observed below the "Frenkel frequency", and (iii) the high-frequency shear modulus does not vanish even for low-density fluids, indicating that positive sound dispersion characterizing the liquid-like region of the supercritical state is unrelated to transverse dynamics. These facts critically undermine the definition of the FL and its significance for any relevant partition of the supercritical phase.

Widom Lines in Binary Mixtures of Supercritical Fluids

Recent experiments on pure fluids have identified distinct liquid-like and gas-like regimes even under supercritical conditions. The supercritical liquid-gas transition is marked by maxima in response functions that define a line emanating from the critical point, referred to as Widom line. However, the structure of analogous state transitions in mixtures of supercritical fluids has not been determined, and it is not clear whether a Widom line can be identified for binary mixtures. Here, we present first evidence for the existence of multiple Widom lines in binary mixtures from molecular dynamics simulations. By considering mixtures of noble gases, we show that, depending on the phase behavior, mixtures transition from a liquid-like to a gas-like regime via distinctly different pathways, leading to phase relationships of surprising complexity and variety. Specifically, we show that miscible binary mixtures have behavior analogous to a pure fluid and the supercritical state space is characterized by a single liquid-gas transition. In contrast, immiscible binary mixture undergo a phase separation in which the clusters transition separately at different temperatures, resulting in multiple distinct Widom lines. The presence of this unique transition behavior emphasizes the complexity of the supercritical state to be expected in high-order mixtures of practical relevance.

Crossover of collective modes and positive sound dispersion in supercritical state

Supercritical state has been viewed as an intermediate state between gases and liquids with largely unknown physical properties. Here, we address the important ability of supercritical fluids to sustain collective excitations. We directly study propagating modes on the basis of correlation functions calculated in molecular dynamics simulations and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line but not above where there is one longitudinal mode only. Important thermodynamic implications of this finding are discussed. We directly detect positive sound dispersion (PSD) below the Frenkel line where transverse modes are operative and quantitatively explain its magnitude on the basis of transverse and longitudinal velocities. PSD disappears above the Frenkel line which therefore demarcates the supercritical phase diagram into two areas where PSD does and does not operate.

Correlated Particle Motion and THz Spectral Response of Supercritical Water

Molecular dynamics simulations of supercritical water reveal distinctly different distance-dependent modulations of dipolar response and correlations in particle motion compared to ambient conditions. The strongly perturbed H-bond network of water at supercritical conditions allows for considerable translational and rotational freedom of individual molecules. These changes give rise to substantially different infrared spectra and vibrational density of states at THz frequencies for densities above and below the Widom line that separates percolating liquidlike and clustered gaslike supercritical water.

Thermally triggered phononic gaps in liquids at THz scale

In this paper we present inelastic X-ray scattering experiments in a diamond anvil cell and molecular dynamic simulations to investigate the behavior of phononic excitations in liquid Ar. The spectra calculated using molecular dynamics were found to be in a good agreement with the experimental data. Furthermore, we observe that, upon temperature increases, a low-frequency transverse phononic gap emerges while high-frequency propagating modes become evanescent at the THz scale. The effect of strong localization of a longitudinal phononic mode in the supercritical phase is observed for the first time. The evidence for the high-frequency transverse phononic gap due to the transition from an oscillatory to a ballistic dynamic regimes of motion is presented and supported by molecular dynamics simulations. This transition takes place across the Frenkel line thermodynamic limit which demarcates compressed liquid and non-compressed fluid domains on the phase diagram and is supported by calculations within the Green-Kubo phenomenological formalism. These results are crucial to advance the development of novel terahertz thermal devices, phononic lenses, mirrors, and other THz metamaterials.

Collective modes and thermodynamics of the liquid state

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.

The Frenkel Line: a direct experimental evidence for the new thermodynamic boundary

Supercritical fluids play a significant role in elucidating fundamental aspects of liquid matter under extreme conditions. They have been extensively studied at pressures and temperatures relevant to various industrial applications. However, much less is known about the structural behaviour of supercritical fluids and no structural crossovers have been observed in static compression experiments in any temperature and pressure ranges beyond the critical point. The structure of supercritical state is currently perceived to be uniform everywhere on the pressure-temperature phase diagram, and to change only in a monotonic way even moving around the critical point, not only along isotherms or isobars. Conversely, we observe structural crossovers for the first time in a deeply supercritical sample through diffraction measurements in a diamond anvil cell and discover a new thermodynamic boundary on the pressure-temperature diagram. We explain the existence of these crossovers in the framework of the phonon theory of liquids using molecular dynamics simulations. The obtained results are of prime importance since they imply a global reconsideration of the mere essence of the supercritical phase. Furthermore, this discovery may pave the way to new unexpected applications and to the exploration of exotic behaviour of confined fluids relevant to geo- and planetary sciences.

Nonlinear dielectric effect in supercritical diethyl ether

Nonlinear dielectric effect (NDE) describes changes of dielectric permittivity induced by a strong electric field in a liquid dielectric. The most classical finding related to this magnitude is the negative sign of NDE in liquid diethyl ether (DEE), recalled by Peter Debye in his Nobel Prize lecture. This article shows that the positive sign of NDE in DEE is also possible, in the supercritical domain. Moreover, NDE on approaching the gas-liquid critical point exhibits a unique critical effect described by the critical exponent ψ ≈ 0.4 close to critical temperature (T(C)) and ψ ≈ 0.6 remote from T(C). This can be linked to the emergence of the mean-field behavior in the immediate vicinity of T(C), contrary to the typical pattern observed for critical phenomena. The multi-frequency mode of NDE measurements made it possible to estimate the evolution of lifetime of critical fluctuations. The new way of data analysis made it possible to describe the critical effect without a knowledge of the non-critical background contribution in prior.

Revealing the Mechanism of the Viscous-to-Elastic Crossover in Liquids

In this work, we report on inelastic X-ray scattering experiments combined with the molecular dynamics simulations on deeply supercritical Ar. The presented results unveil the mechanism and regimes of sound propagation in the liquid matter and provide compelling evidence for the adiabatic-to-isothermal longitudinal sound propagation transition. We introduce a Hamiltonian predicting low-frequency transverse sound propagation gaps, which is confirmed by experimental findings and molecular dynamics calculations. As a result, a universal link is established between the positive sound dispersion (PSD) phenomenon and the origin of transverse sound propagation revealing the viscous-to-elastic crossover in liquids. The PSD and transverse phononic excitations evolve consistently with theoretical predictions. Both can be considered as a universal fingerprint of the dynamic response of a liquid, which is also observable in a subdomain of supercritical phase. The simultaneous disappearance of both these effects at elevated temperatures is a manifestation of the Frenkel line. We expect that these findings will advance the current understanding of fluids under extreme thermodynamic conditions.

Reply to "Comment on 'Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants' "

We have recently proposed the dynamic transition of molecular hydrogen in gas giants around 10 GPa based on the recent understanding of a supercritical state related to the Frenkel line. In the preceding Comment, Bryk makes several remarks with regard to the Frenkel line and its relationship to the speed of sound. We disagree with this discussion and respond to it in this Reply.

Frenkel line and solubility maximum in supercritical fluids

A new dynamic line, the Frenkel line, has recently been proposed to separate the supercritical state into rigid-liquid and nonrigid gaslike fluid. The location of the Frenkel line on the phase diagram is unknown for real fluids. Here we map the Frenkel line for three important systems: CO(2), H(2)O, and CH(4). This provides an important demarcation on the phase diagram of these systems, the demarcation that separates two distinct physical states with liquidlike and gaslike properties. We find that the Frenkel line can have a similar trend as the melting line above the critical pressure. Moreover, we discuss the relationship between unexplained solubility maxima and Frenkel line, and we propose that the Frenkel line corresponds to the optimal conditions for solubility.

Dynamic transition in supercritical iron

Recent advance in understanding the supercritical state posits the existence of a new line above the critical point separating two physically distinct states of matter: rigid liquid and non-rigid gas-like fluid. The location of this line, the Frenkel line, remains unknown for important real systems. Here, we map the Frenkel line on the phase diagram of supercritical iron using molecular dynamics simulations. On the basis of our data, we propose a general recipe to locate the Frenkel line for any system, the recipe that importantly does not involve system-specific detailed calculations and relies on the knowledge of the melting line only. We further discuss the relationship between the Frenkel line and the metal-insulator transition in supercritical liquid metals. Our results enable predicting the state of supercritical iron in several conditions of interest. In particular, we predict that liquid iron in the Jupiter core is in the "rigid liquid" state and is highly conducting. We finally analyse the evolution of iron conductivity in the core of smaller planets such as Earth and Venus as well as exoplanets: as planets cool off, the supercritical core undergoes the transition to the rigid-liquid conducting state at the Frenkel line.