Liquidlike behavior of supercritical fluids

Critical Threshold for Bubble-like Nucleation during Pseudoboiling at Supercritical Pressures

Supercritical pseudoboiling was proposed in the 1950s-1960s. Recently, evaporation-like and boiling-like heat transfer have been directly observed in macroscopic scales, and the contribution of pseudoboiling to the total heat transfer rate has been quantitatively characterized experimentally. Here, we explore the critical threshold to generate a bubble-like nucleus at supercritical pressure at the atomic scale, characterized by the total energy (Te = Ke + Pe, where Ke and Pe are kinetic energy and potential energy, respectively). Molecular dynamics simulations are performed, including an argon fluid box heated by a solid wall having its temperature above the fluid temperature. The fluid pressure is controlled by a movable piston wall opposite the heating wall. The effects of pressure, nonuniform heating, and surface wettability on pseudoboiling are investigated. It is found that the criterion Te > 0 should be satisfied for subcritical boiling, matching that reported previously. The criterion for supercritical pseudoboiling was newly obtained such that Te > 0.012 eV at 8 MPa for argon, but the threshold increases as pressure increases. Nonuniform heating and surface wettability do not affect the critical threshold of Te for bubble-like nucleation but affect the location of the initially generated bubble-like nucleus and the stabilized pseudofilm or pseudonucleate heat transfer modes, where the former is similar to (vapor) film boiling and the latter is similar to nucleate boiling at subcritical pressure. Because pseudoboiling occurs without surface tension at supercritical pressure, we observe that the bubble-like structure may not display a perfectly smooth gas-liquid interface but may display an irregular pattern instead. Our work explains pseudoboiling from the viewpoint of the competition between kinetic energy and potential energy and presents a link regarding boiling in the two domains of subcritical pressure and supercritical pressure.

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.

Phase boundaries and the Widom line from the Ruppeiner geometry of fluids

The Ruppeiner geometry has been shown to provide novel ways for constructing the phase boundaries and the Widom line of certain fluids. This paper examines the applicability of these geometric constructions to more general fluids. We develop a general equation-of-state expansion for fluids near a critical point that mainly assumes analyticity with respect to the number density. Based on this general parametrization of fluids, we prove the equivalence of the Ruppeiner geometric construction and the standard Maxwell construction of phase boundaries near the critical point. In contrast, we find that the usual prescription based on the Ruppeiner geometry for the Widom line does not produce the expected Widom line for arbitrary cases of our general fluid equation of state. This usual prescription relies on the Ruppeiner metric induced on a particular hypersurface of the thermodynamic manifold. We show that by choosing a different hypersurface, which we call the Ruppeiner-N surface, and using its associated induced metric, the Ruppeiner construction generates the entire Widom line of the van der Waals fluid exactly, even away from the critical point. Interestingly, this alternative hypersurface yields another benefit. It improves the classification scheme originally proposed by Diósi et al. for partitioning the van der Waals state space into its different phases using geodesics of a thermodynamic metric. We argue that, whereas the original Diósi boundaries did not correspond to any clear thermodynamic lines, the corresponding boundaries based on the Ruppeiner-N metric become sensitive to the presence of the van der Waals Widom line and provide the correct classification of all van der Waals states. These results suggest that the Ruppeiner-N surface may be the more appropriate hypersurface to use when studying phase diagrams with thermodynamic geometry.

Supercritical Relaxor Nanograined Ferroelectrics for Ultrahigh-Energy-Storage Capacitors

Supercritical relaxor nanograined ferroelectrics are demonstrated for high-performance dielectric capacitors, showing record-high overall properties of energy density ≈13.1 J cm^-3 and field-insensitive efficiency ≈90% at ≈74 kV mm^-1 and superior charge-discharge performances of high power density ≈700 MW cm^-3 , high discharge energy density ≈6.67 J cm^-3 , and ultrashort discharge time <40 ns at 55 kV mm^-1 . Ex/in situ transmission electron microscopy, Raman spectroscopy, and synchrotron X-ray diffraction provide clear evidence of the supercritical behavior in (Na,K)(Sb,Nb)O₃ -SrZrO₃ -(Bi_0.5 Na_0.5 )ZrO₃ ceramics, being achieved by engineering the coexistence of multiple local symmetries within the ergodic relaxor zone. The vanished difference between the ground relaxor state and the high-field supercritical state eliminates polarization hysteresis. The supercritical evolution with electric field enables a highly delayed polarization saturation with continuously increased polarization magnitudes. The results demonstrate that such a design strategy of compositionally induced and field-manipulated supercritical behavior can be generalizable for developing desirable energy-storage dielectrics for applications in ceramic/film capacitors.

Gas–liquid crossover in the Lennard-Jones system

It is demonstrated that the crossover between gas- and liquid-like regions on the phase diagram of the Lennard-Jones system occurs at a fixed value of the density divided by its value at the freezing point, ρ/ ρfr ≃ 0.35. This definition is consistent with other definitions proposed recently. As a result, a very simple practical expression for the gas-to-liquid crossover line emerges.

The Anomalous Behavior of Thermodynamic Parameters in the Three Widom Deltas of Carbon Dioxide-Ethanol Mixture

Using molecular dynamics, we demonstrated that in the mixture of carbon dioxide and ethanol (25% molar fraction) there are three pronounced regions on the p-T diagram characterized by not only high-density fluctuations but also anomalous behavior of thermodynamic parameters. The regions are interpreted as Widom deltas. The regions were identified as a result of analyzing the dependences of density, density fluctuations, isobaric thermal conductivity, and clustering of a mixture of carbon dioxide and ethanol in a wide range of pressures and temperatures. Two of the regions correspond to the Widom delta for pure supercritical carbon dioxide and ethanol, while the third region is in the immediate vicinity of the critical point of the binary mixture. The origin of these Widom deltas is a result of the large mixed linear clusters formation.

Quasi-equilibrium phase coexistence in single component supercritical fluids

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout all combinations of pressures and temperatures, although various response functions or transport properties may exhibit anomalous behavior, characterizing a state point as either more gas-like or liquid-like, respectively. While a large body of results has been compiled in the last two decades regarding the details of the supercritical phase in thermodynamic equilibrium, far less studies have been dedicated to out-of-equilibrium situations that nevertheless occur along with the handling of substances such as carbon dioxide or Argon. Here we consider successive compression-expansion cycles of equal amounts of Argon injected into a high-pressure chamber, traversing the critical pressure at two times the critical temperature. Due to expansion cooling, the fluid temporarily becomes sub-critical, and light scattering experiments show the formation of sub-micron-sized droplets and nanometer-scale clusters, both of which are distinct from spontaneous density fluctuations of the supercritical background and persist for a surprisingly long time. A kinetic rate model of the exchange of liquid droplets with the smaller clusters can explain this behavior. Our results indicate non-equilibrium aspects of supercritical fluids that may prove important for their processing in industrial applications.

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout. Lee et al. find that liquid droplets temporarily formed in a supercritical background after sub-critical injection can survive for a surprisingly long time.

Two-Component Dynamics and the Liquidlike to Gaslike Crossover in Supercritical Water

Molecular-scale dynamics in sub- to supercritical water is studied with inelastic x-ray scattering and molecular dynamics simulations. The obtained longitudinal current correlation spectra can be decomposed into two main components: a low-frequency (LF), gaslike component and a high-frequency (HF) component arising from the O-O stretching mode between hydrogen-bonded molecules, reminiscent of the longitudinal acoustic mode in ambient water. With increasing temperature, the hydrogen-bond network diminishes and the spectral weight shifts from HF to LF, leading to a transition from liquid- to gaslike dynamics with rapid changes around the Widom line.

Physical property and gas transport studies of ultrathin polysulfone membrane from 298.15 to 328.15 K and 2 to 50 bar: atomistic molecular simulation and empirical modelling

Elucidation of ultrathin polymeric membrane at the laboratory scale is complicated at different operating conditions due to limitation of instruments to obtain in situ measurement data of membrane physical properties. This is essential since their effects are reversible. In addition, tedious experimental work is required to collect gas transport data at varying operating conditions. Recently, we have proposed a validated Soft Confining Methodology for Ultrathin Films that can be used to simulate ultrathin polysulfone (PSF) membranes upon confinement limited to 308.15 K and 2 bars. In industry application, these ultrathin membranes are operated within 298.15–328.15 K and up to 50 bars. Therefore, our proposed methodology using computational chemistry has been adapted to circumvent limitation in experimental study by simulating ultrathin PSF membranes upon confinement at different operating temperatures (298.15 to 328.15 K) and pressures (2 to 50 bar). The effect of operating parameters towards non-bonded and potential energy, free volume, specific volume and gas transport data (e.g. solubility and diffusivity) for oxygen and nitrogen of the ultrathin films has been simulated and collected using molecular simulation. Our previous empirical equations that have been confined to thickness dependent gas transport properties have been modified to accommodate the effect of operating parameters. The empirical equations are able to provide a good quantitative characterization with R² ≥ 0.99 consistently, and are able to be interpolated to predict gas transport properties within the range of operating conditions. The modified empirical model can be utilized in process optimization studies to determine optimal membrane design for typical membrane specifications and operating parameters used in industrial applications.

Pioneering work to elucidate and model the effect of operating conditions on physical and transport properties of ultrathin membranes.

Polymorphic phase transition in liquid and supercritical carbon dioxide

We present experiments on molecular density fluctuations in liquid and supercritical (SC) CO₂ using small-angle neutron scattering. Thermal density fluctuations in SC-CO₂ determine susceptibility and correlation length identifying the Widom line at their maxima. Droplet formation occurs at the gas–liquid line and between 20 and 60 bar above the Widom line, the corresponding borderline identified as the Frenkel line. The droplets start to form spheres of constant radius of ≈ 45 Å and transform into rods and globules at higher pressure. Droplet formation represents a liquid–liquid (polymorphic) phase transition of the same composition but different density, whose difference defines its order parameter. Polymorphism in CO₂ is a new observation stimulating interesting discussions on the topics of gas-like to liquid-like transition in SC fluids and polymorphism since CO₂ represents a “simple” van der Waals liquid in contrast to water, which is the most widely studied liquid showing polymorphism in its supercooled state.

Investigation concerning the uniqueness of separatrix lines separating liquidlike from gaslike regimes deep in the supercritical phase of water with a focus on Widom line concepts

The supercritical phase of fluids has long been known to feature significantly different liquidlike and gaslike regimes. However, it is textbook knowledge that the supercritical state is a homogeneous fluid phase where properties change continuously. Nevertheless, there has been an increasing amount of evidence published that suggests that there might exist a unique line that rigorously separates different regimes in supercritical phases, particularly in the case of water. Here, we use the quasiexact IAPWS95 equation of state to rigorously assess the macroscopic thermodynamic properties of supercritical water without invoking any water model or related approximations. We focus on how these properties change deep in the supercritical phase, in particular if they allow one to introduce a unique "thermodynamic separatrix." Our rigorous thermodynamic analysis, which relies exclusively on accurate experimental data, makes clear that there is no unique separatrix in real supercritical water-such as the recently much-invoked "Widom line." A comparison to the van der Waals equation of state reproduces qualitatively all our findings for real water, thereby suggesting that our analysis should be transferable to other fluids and critical points. Topological analysis of the H-bond network structure of supercritical water, as obtained from molecular-dynamics simulations using a standard water model, demonstrates that also the percolation line does not provide a meaningful separatrix to rigorously distinguish liquidlike from gaslike regimes.

Viscoelastic anomaly accompanying anti-crossing behaviour in liquid As2Se3

We investigate the dynamic structure factor of the melt of the well known glass former, As₂Se₃, using inelastic x-ray scattering for temperatures, T, [Formula: see text] K and momentum transfers Q from [Formula: see text] nm^-1. An anomaly was observed at Q  =  2.7 nm^-1 ([Formula: see text] K) with, in the context of a simple model, both an abrupt change in frequency and an increased linewidth reminiscent of an anti-crossing in a solid. Comparison with structural information from reverse Monte Carlo modeling of x-ray diffraction data allows us to associate the disappearance of the anomaly at higher temperatures with a drop in the number of mechanical constraints per atom, n _mc, to [Formula: see text] reminiscent of the threshold applicable for glass formation in rigidity theory. It is inferred that the surprising jump in the dispersion in the liquid may be correlated with a stiffness transition in a network glass.

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.

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.

Similarity law for Widom lines and coexistence lines

The coexistence line of a fluid separates liquid and gaseous states at subcritical pressures, ending at the critical point. Only recently, it became clear that the supercritical state space can likewise be divided into regions with liquidlike and gaslike properties, separated by an extension to the coexistence line. This crossover line is commonly referred to as the Widom line, and is characterized by large changes in density or enthalpy, manifesting as maxima in the thermodynamic response functions. Thus, a reliable representation of the coexistence line and the Widom line is important for sub- and supercritical applications that depend on an accurate prediction of fluid properties. While it is known for subcritical pressures that nondimensionalization with the respective species critical pressures p_{cr} and temperatures T_{cr} only collapses coexistence line data for simple fluids, this approach is used for Widom lines of all fluids. However, we show here that the Widom line does not adhere to the corresponding states principle, but instead to the extended corresponding states principle. We resolve this problem in two steps. First, we propose a Widom line functional based on the Clapeyron equation and derive an analytical, species specific expression for the only parameter from the Soave-Redlich-Kwong equation of state. This parameter is a function of the acentric factor ω and compares well with experimental data. Second, we introduce the scaled reduced pressure p_{r}^{*} to replace the previously used reduced pressure p_{r}=p/p_{cr}. We show that p_{r}^{*} is a function of the acentric factor only and can thus be readily determined from fluid property tables. It collapses both subcritical coexistence line and supercritical Widom line data over a wide range of species with acentric factors ranging from -0.38 (helium) to 0.34 (water), including alkanes up to n-hexane. By using p_{r}^{*}, the extended corresponding states principle can be applied within corresponding states principle formalism. Furthermore, p_{r}^{*} provides a theoretical foundation to compare Widom lines of different fluids.

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.

Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures

Unlike phonons in crystals, the collective excitations in liquids cannot be treated as propagation of harmonic displacements of atoms around stable local energy minima. The viscoelasticity of liquids, reflected in transition from the adiabatic to elastic high-frequency speed of sound and in absence of the long-wavelength transverse excitations, results in dispersions of longitudinal (L) and transverse (T) collective excitations essentially different from the typical phonon ones. Practically, nothing is known about the effect of high pressure on the dispersion of collective excitations in liquids, which causes strong changes in liquid structure. Here dispersions of L and T collective excitations in liquid Li in the range of pressures up to 186 GPa were studied by ab initio simulations. Two methodologies for dispersion calculations were used: direct estimation from the peak positions of the L/T current spectral functions and simulation-based calculations of wavenumber-dependent collective eigenmodes. It is found that at ambient pressure, the longitudinal and transverse dynamics are well separated, while at high pressures, the transverse current spectral functions, density of vibrational states, and dispersions of collective excitations yield evidence of two types of propagating modes that contribute strongly to transverse dynamics. Emergence of the unusually high-frequency transverse modes gives evidence of the breakdown of a regular viscoelastic theory of transverse dynamics, which is based on coupling of a single transverse propagating mode with shear relaxation. The explanation of the observed high-frequency shift above the viscoelastic value is given by the presence of another branch of collective excitations. With the pressure increasing, coupling between the two types of collective excitations is rationalized within a proposed extended viscoelastic model of transverse dynamics.

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.

Collective excitations in soft-sphere fluids

Despite that the thermodynamic distinction between a liquid and the corresponding gas ceases to exist at the critical point, it has been recently shown that reminiscence of gaslike and liquidlike behavior can be identified in the supercritical fluid region, encoded in the behavior of hypersonic waves dispersion. By using a combination of molecular dynamics simulations and calculations within the approach of generalized collective modes, we provide an accurate determination of the dispersion of longitudinal and transverse collective excitations in soft-sphere fluids. Specifically, we address the decreasing rigidity upon density reduction along an isothermal line, showing that the positive sound dispersion, an excess of sound velocity over the hydrodynamic limit typical for dense liquids, displays a nonmonotonic density dependence strictly correlated to that of thermal diffusivity and kinematic viscosity. This allows rationalizing recent observation parting the supercritical state based on the Widom line, i.e., the extension of the coexistence line. Remarkably, we show here that the extremals of transport properties such as thermal diffusivity and kinematic viscosity provide a robust definition for the boundary between liquidlike and gaslike regions, even in those systems without a liquid-gas binodal line. Finally, we discuss these findings in comparison with recent results for Lennard-Jones model fluid and with the notion of the "rigid-nonrigid" fluid separation lines.

"Liquid-gas" transition in the supercritical region: fundamental changes in the particle dynamics

Recently, we have proposed a new dynamic line on the phase diagram in the supercritical region, the Frenkel line. Crossing the line corresponds to the radical changes of system properties. Here, we focus on the dynamics of model Lennard-Jones and soft-sphere fluids. We show that the location of the line can be rigorously and quantitatively established on the basis of the velocity autocorrelation function (VAF) and mean-square displacements. VAF is oscillatory below the line at low temperature, and is monotonically decreasing above the line at high temperature. Using this criterion, we show that the crossover of particle dynamics and key liquid properties occur on the same line. We also show that positive sound dispersion disappears in the vicinity of the line in both systems. We further demonstrate that the dynamic line bears no relationship to the existence of the critical point. Finally, we find that the region of existence of liquidlike dynamics narrows with the increase of the exponent of the repulsive part of interatomic potential.

Dynamical crossover at the liquid-liquid transformation of a compressed molten alkali metal

Density-driven phase transformations are a known phenomenon in liquids. Pressure-driven transitions from an open low-density to a higher-density close-packed structure were observed for a number of systems. Here, we show a less intuitive, inverse behavior. We investigated the electronic, atomic, and dynamic structures of liquid Rb along an isothermal line at 573 K, at 1.2-27.4 GPa, by means of ab initio molecular dynamics simulations and inelastic x-ray scattering experiments. The excellent agreement of the simulations with experimental data performed up to 6.6 GPa validates the overall approach. Above 12.5 GPa, the breakdown of the nearly-free-electron model drives a transition of the pure liquid metal towards a less metallic, denser liquid, whose first coordination shell is less compact. Our study unveils the interplay between electronic, structural, and dynamic degrees of freedom along this liquid-liquid phase transition. In view of its electronic nature, we believe that this behavior is general for the first group elements, thus shedding new light into the high-pressure properties of alkali metals.

Dynamics and Thermodynamics beyond the critical point

Sudden changes in the dynamical properties of a supercritical fluid model have been found as a function of pressure and temperature (T/T(c) = 2-5 and P/P(c) = 10-10(3)), striving with the notion of a single phase beyond the critical point established by thermodynamics. The sound propagation in the Terahertz frequency region reveals a sharp dynamic crossover between the gas like and the liquid like regimes along several isotherms, which involves, at sufficiently low densities, the interplay between purely acoustic waves and heat waves. Such a crossover allows one to determine a dynamic line in the phase diagram which exhibits a very tight correlation with a number of thermodynamic observables, showing that the supercritical state is remarkably more complex than thought so far.

Collective dynamics in binary liquids: a molecular dynamics study of the composition dependence of the spectra of collective excitations

The spectra of longitudinal and transverse collective excitations in liquid binary metallic Na(c)K(1-c) alloys are studied for pure components and four different concentrations. A theoretical generalized collective modes approach is used to analyze the concentration dependence of the dispersion of acoustic and optic branches in a wide region of wavenumbers. The dispersion of longitudinal collective excitations in binary alloys is estimated from the eight-variable thermo-viscoelastic dynamic model with full account of thermal fluctuations. It is found that the longitudinal and transverse branches show different dependences on concentration in the short-wavelength region. The issue of 'positive dispersion' of acoustic excitations in liquid binary alloys on the boundary of the hydrodynamic regime is discussed. It is shown that the coupling between longitudinal acoustic and optic modes is responsible for an increase of the 'positive dispersion' close to equimolar composition.

Widom line and noise-power spectral analysis of a supercritical fluid

We have performed extensive molecular dynamics simulations to study noise-power spectra of density and potential energy fluctuations of a Lennard-Jones model of a fluid in the supercritical region. Emanating from the liquid-vapor critical point, there is a locus of isobaric specific heat maxima, called the Widom line, which is often regarded as an extension of the liquid-vapor coexistence line. Our simulation results show that the noise-power spectrum of the density fluctuations on the Widom line of the liquid-vapor transition exhibits three distinct 1/f^{γ} behaviors with exponents γ=0, 1.2, and 2, depending on the frequency f. We find that the intermediate frequency region with an exponent γ∼ 1 appears as the temperature approaches the Widom temperature from above or below. On the other hand, we do not find three distinct regions of 1/f^{γ} in the power spectrum of the potential energy fluctuations on the Widom line. Furthermore, we find that the power spectra of both the density and potential energy fluctuations at low frequency have a maximum on the Widom line, suggesting that the noise power can provide an alternative signature of the Widom line.

Two liquid states of matter: a dynamic line on a phase diagram

It is generally agreed that the supercritical region of a liquid consists of one single state (supercritical fluid). On the other hand, we show here that liquids in this region exist in two qualitatively different states: "rigid" and "nonrigid" liquids. Rigid to nonrigid transition corresponds to the condition τ≈τ(0), where τ is the liquid relaxation time and τ(0) is the minimal period of transverse quasiharmonic waves. This condition defines a new dynamic crossover line on the phase diagram and corresponds to the loss of shear stiffness of a liquid at all available frequencies and, consequently, to the qualitative change in many important liquid properties. We analyze this line theoretically as well as in real and model fluids and show that the transition corresponds to the disappearance of high-frequency sound, to the disappearance of roton minima, qualitative changes in the temperature dependencies of sound velocity, diffusion, viscous flow, and thermal conductivity, an increase in particle thermal speed to half the speed of sound, and a reduction in the constant volume specific heat to 2k(B) per particle. In contrast to the Widom line that exists near the critical point only, the new dynamic line is universal: It separates two liquid states at arbitrarily high pressure and temperature and exists in systems where liquid-gas transition and the critical point are absent altogether. We propose to call the new dynamic line on the phase diagram "Frenkel line".