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

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.

Freezing density scaling of transport coefficients in the Weeks-Chandler-Andersen fluid

It is shown that the transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of the Weeks-Chandler-Andersen (WCA) fluid along isotherms exhibit a freezing density scaling (FDS). The functional form of this FDS is essentially the same or closely related to those in the Lennard-Jones fluid, hard-sphere fluid, and some liquefied noble gases. This proves that this FDS represents a quasi-universal corresponding state principle for simple classical fluids with steep interactions. Some related aspects, such as a Stokes-Einstein relation without a hydrodynamic diameter and gas-to-liquid dynamical crossover, are briefly discussed. Simple fitting formulas for the transport coefficients of the dense WCA fluid are suggested.

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Liquid-Liquid Crossover in Water Model: Local Structure vs Kinetics of Hydrogen Bonds

In equilibrium and supercooled liquids, polymorphism is manifested by thermodynamic regions defined in the phase diagram, which are predominantly of different short- and medium-range order (local structure). It is found that on the phase diagram of the water model, the thermodynamic region corresponding to the equilibrium liquid phase is divided by a line of the smooth liquid-liquid crossover. In the case of the water model TIP4P/2005, this crossover is revealed by various local order parameters and corresponds to pressures on the order of 3150 ± 350 atm at ambient temperature. In the vicinity of the crossover, the dynamics of water molecules change significantly, which is reflected, in particular, in the fact that the self-diffusion coefficient reaches its maximum values. In addition, changes in the structure also manifest themselves in changes in the kinetics of hydrogen bonding, which are captured by values of such quantities as the average lifetime of hydrogen bonding, the average lifetimes of different local coordination numbers, and the frequencies of changes in different local coordination numbers. An interpretation of the hydrogen bond kinetics in terms of the free energy landscape concept in the space of possible coordination numbers is proposed.

Collective ion dynamics in Coulomb one-component plasmas within the self-consistent relaxation theory

In this paper, we present the theoretical formalism describing the collective ion dynamics of the nonideal Coulomb classical one-component plasmas on the basis of the self-consistent relaxation theory. The theory is adapted to account for correlations between the frequency relaxation parameters that characterize the three- and four-particle dynamics and the parameters associated with the two-particle dynamics. The dynamic structure factor spectra and dispersion characteristics calculated for a wide range of wave numbers are in agreement with the molecular dynamics simulation data and the results obtained with the theory of the frequency moments. The proposed formalism reproduces all the features inherent to the Coulomb one-component plasmas and requires only knowledge of the coupling parameter and the information about the structure.

Observation of fast sound in two-dimensional dusty plasma liquids

Equilibrium molecular dynamics simulations are performed to study two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal motion of simulated particles, the longitudinal and transverse phonon spectra are calculated, and used to determine the corresponding dispersion relations. From there, the longitudinal and transverse sound speeds of 2D dusty plasma liquids are obtained. It is discovered that, for wavenumbers beyond the hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon appears at roughly the same length scale of the cutoff wavenumber for transverse waves, confirming its relation to the emergent solidity of liquids in the nonhydrodynamic regime. Using the thermodynamic and transport coefficients extracted from the previous studies, and relying on the Frenkel theory, the ratio of the longitudinal to the adiabatic sound speeds is derived analytically, providing the optimal conditions for fast sound, which are in quantitative agreement with the current simulation results.

From Atoms to Colloids: Does the Frenkel Line Exist in Discontinuous Potentials?

The Frenkel line has been proposed as a crossover in the fluid region of phase diagrams between a "nonrigid" and a "rigid" fluid. It is generally described as a crossover in the dynamical properties of a material and as such has been described theoretically using a very different set of markers from those with which is it investigated experimentally. In this study, we have performed extensive calculations using two simple yet fundamentally different model systems: hard spheres and square-well potentials. The former has only hardcore repulsion, while the latter also includes a simple model of attraction. We computed and analyzed a series of physical properties used previously in simulations and experimental measurements and discuss critically their correlations and validity as to being able to uniquely and coherently locate the Frenkel line in discontinuous potentials.

Krypton and the Fundamental Flaw of the Lennard-Jones Potential

We have performed a series of neutron scattering experiments on supercritical krypton. Our data and analysis allow us to characterize the Frenkel line crossover in this model monatomic fluid. The data from our measurements was analyzed using Empirical Potential Structure Refinement to determine the short- and medium-range structure of the fluids. We find evidence for several shells of neighbors which form approximately concentric rings of density about each atom. The ratio of second to first shell radius is significantly larger than in any crystal structure. Modeling krypton using a Lennard-Jones potential is shown to give significant errors, notably that the liquid is overstructured. The true potential appears to be longer ranged and with a softer core than the 6-12 powerlaws permit.

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.

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.

Frenkel Line in Nitrogen Terminates at the Triple Point

Recent studies on supercritical nitrogen revealed clear changes in structural markers and dynamical properties when the coordination number approaches its maximum value. The line in P and T space where these changes occur is referred to as the Frenkel line. Here, we qualitatively reproduce such changes in the supercritical regime using the popular "optimized potential for liquid simulation" (OPLS) classical force field for molecular dynamics. Unfortunately, at 160 K, OPLS nitrogen predicts sublimation rather than producing a liquid phase; therefore, we developed our own force field to achieve quantitative agreement with experimental data. We confirm the asymptotic behavior of the coordination number on crossing the Frenkel line and note an associated change in the diffusion constant, consistent with the non-rigid to rigid liquid-like character of the "transition". The simulations allow us to track the Frenkel line to subcritical temperatures and demonstrate that it terminates at the triple point. This establishes the experimentally measurable changes, which could unequivocally determine the Frenkel line in other systems.

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.

Universal interrelation between dynamics and thermodynamics and a dynamically driven "c" transition in fluids

Our very wide survey of the supercritical phase diagram and its key properties reveals a universal interrelation between dynamics and thermodynamics and an unambiguous transition between liquidlike and gaslike states. This is seen in the master plot showing a collapse of the data representing the dependence of specific heat on key dynamical parameters in the system for many different paths on the phase diagram. As a result, the observed transition is path independent. We call it a "c" transition due to the c-shaped curve parametrizing the dependence of the specific heat on key dynamical parameters. The c transition has a fixed inversion point and provides a new structure to the phase diagram, operating deep in the supercritical state (up to, at least, 2000 times the critical pressure and 50 times the critical temperature). The data collapse and path independence as well as the existence of a special inversion point on the phase diagram are indicative of either of a sharp crossover or a new phase transition in the deeply supercritical state.

Structural Markers of the Frenkel Line in the Proximity of Widom Lines

We have performed a neutron scattering experiment on supercritical fluid nitrogen at 160 K (1.27 T_C) over a wide pressure range (7.8 MPa/0.260 g/mL-125 MPa/0.805 g/mL). This has enabled us to study the process by which nitrogen changes from a fluid that exhibits gaslike behavior to one that exhibits rigid liquidlike behavior at a temperature close to, but above, the critical temperature by crossing the Widom lines followed by the Frenkel line on pressure (density) increase. We find that the Frenkel line transition is indicated by a transition to a regime of rigid liquidlike behavior in which the coordination number remains constant within error, in agreement with our previous work at 300 K. The Frenkel line transition takes place at approximately the same density at 160 and 300 K. The data do not conclusively show an additional transition at the location of the known Widom lines. We find that behavior remains gaslike until the Frenkel line is crossed and our data support the hypothesis that Widom line transitions are density increase-driven.

Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO₂ in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. The first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO₂ is the C-C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO₂ model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

Crossover of dynamical instability and chaos in the supercritical state

We calculate the maximal Lyapunov exponent for a bulk system of 256 Lennard-Jones particles in constant energy molecular dynamics simulations deep into the supercritical state. We find that the maximal Lyapunov exponent undergoes a crossover and that this crossover coincides with the dynamical crossover at the Frenkel line from liquid physics. We explain this crossover in terms of two different contributions to dynamical instability: diffusion in the liquidlike state below the Frenkel line and collisions in the gaslike state above. These results provide insight into the phase-space dynamics far from the melting line and densities where rare-gas approximation are inapplicable.

Speed of sound from fundamental physical constants

Two dimensionless fundamental physical constants, the fine structure constant α and the proton-to-electron mass ratio [Formula: see text], are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant that provides the upper bound for the speed of sound in condensed phases, v_u We find that [Formula: see text], where c is the speed of light in vacuum. We support this result by a large set of experimental data and first-principles computations for atomic hydrogen. Our result expands the current understanding of how fundamental constants can impose new bounds on important physical properties.

Dispersion of acoustic excitations in tetrahedral liquids

Investigation of the longitudinal and transverse excitations in liquids is of great importance for understanding the fundamentals of the liquid state of matter. One of the important questions is the temperature and density dependence of the frequency of the excitations. In our recent works it was shown that while in simple liquids the frequency of longitudinal excitations increases when the temperature is increased isochorically, in water the frequency can anomalously decrease with the temperature increase. In the present manuscript we study the dispersion curves of longitudinal and transverse excitations of water and liquid silicon modelled by Stillinger-Weber (SW) potential. We show that both in liquid silicon and SW model of water the frequencies of longitudinal excitations slightly increase with temperature which is in contrast to the results for SPC/E model of water.

Pronounced structural crossover in water at supercritical pressures

There have been ample studies of the many phases of H2O in both its solid and low pressure liquid states, and the transitions between them. Using molecular dynamics simulations we address the hitherto unexplored deeply supercritical pressures, where no qualitative transitions are thought to take place and where all properties are expected to vary smoothly. On the basis of these simulations we predict that water at supercritical pressures undergoes a structural crossover across the Frenkel line at pressures as high as 45 times the critical pressure. This provides a new insight into the water phase diagram and establishes a link between the structural and dynamical properties of supercritical water. Specifically, the crossover is demonstrated by a sharp and pronounced at low pressures, and smooth at high pressures, signified by changes in the pair distribution functions and local coordination which coincide with the dynamical transition (the loss of all oscillatory molecular motion) at the Frenkel line on the phase diagram.

An entropy scaling demarcation of gas- and liquid-like fluid behaviors

In this work, we propose a generic and simple definition of a line separating gas-like and liquid-like fluid behaviors from the standpoint of shear viscosity. This definition is valid even for fluids such as the hard sphere and the inverse power law that exhibit a unique fluid phase. We argue that this line is defined by the location of the minimum of the macroscopically scaled viscosity when plotted as a function of the excess entropy, which differs from the popular Widom lines. For hard sphere, Lennard-Jones, and inverse-power-law fluids, such a line is located at an excess entropy approximately equal to -2/3 times Boltzmann's constant and corresponds to points in the thermodynamic phase diagram for which the kinetic contribution to viscosity is approximately half of the total viscosity. For flexible Lennard-Jones chains, the excess entropy at the minimum is a linear function of the chain length. This definition opens a straightforward route to classify the dynamical behavior of fluids from a single thermodynamic quantity obtainable from high-accuracy thermodynamic models.

Experimental and modeling evidence for structural crossover in supercritical CO_{2}

The physics of supercritical states is understood to a much lesser degree compared to subcritical liquids. Carbon dioxide, in particular, has been intensely studied, yet little is known about the supercritical part of its phase diagram. Here, we combine neutron scattering experiments and molecular dynamics simulations and demonstrate the structural crossover at the Frenkel line. The crossover is seen at pressures as high as 14 times the critical pressure and is evidenced by changes of the main features of the structure factor and pair distribution functions.

Minimal quantum viscosity from fundamental physical constants

Viscosity of fluids is strongly system dependent, varies across many orders of magnitude, and depends on molecular interactions and structure in a complex way not amenable to first-principles theories. Despite the variations and theoretical difficulties, we find a new quantity setting the minimal kinematic viscosity of fluids: ν m = 1 4 π ℏ m e m , where m_e and m are electron and molecule masses. We subsequently introduce a new property, the "elementary" viscosity ι with the lower bound set by fundamental physical constants and notably involving the proton-to-electron mass ratio: ι m = ℏ 4 π ( m p m e ) 1 2 , where m_p is the proton mass. We discuss the connection of our result to the bound found by Kovtun, Son, and Starinets in strongly interacting field theories.

Thermodynamics, dynamics, and structure of supercritical water at extreme conditions

Molecular dynamics (MD) simulations to understand the thermodynamic, dynamic, and structural changes in supercritical water across the Frenkel line and the melting line have been performed.

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.

Supercritical water anomalies in the vicinity of the Widom line

Supercritical water is used in a variety of chemical and industrial applications. As a consequence, a detailed knowledge of the structure-properties correlations is of uttermost importance. Although supercritical water was considered as a homogeneous fluid, recent studies revealed an anomalous behaviour due to nanoscale density fluctuations (inhomogeneity). The inhomogeneity is clearly demarked through the Widom line (maxima in response factions) and drastically affect the properties. In the current study the physical properties of supercritical water have been determined by classical molecular dynamics simulations using a variety of polarized and polarizable interatomic potentials. Their validity which was not available at supercritical conditions has been assessed based on the ability to reproduce experimental data. Overall, the polarized TIP4P/2005 model accurately predicted the properties of water in both liquid-like and gas-like regions. All interatomic potentials captured the anomalous behaviour providing a direct evidence of molecular-scale inhomogeneity.

Frenkel line crossover of confined supercritical fluids

We investigate the temperature evolution of dynamics and structure of partially confined Lennard Jones (LJ) fluids in supercritical phase along an isobaric line in the P-T phase diagram using molecular dynamics simulations. We compare the Frenkel line (FL) crossover features of partially confined LJ fluids to that of the bulk LJ fluids in supercritical phase. Five different spacings have been chosen in this study and the FL crossover characteristics have been monitored for each of these spacings for temperatures ranging from 240 K to 1500 K keeping the pressure fixed at 5000 bar. We characterize the FL crossover using density of states (DoS) function and find that partially confined supercritical fluids (SCF) exhibit a progressive shift of FL crossover point to higher temperatures for smaller spacings. While the DoS perpendicular to the walls shows persistent oscillatory modes, the parallel component exhibits a smooth crossover from an oscillatory to non-oscillatory characteristics representative of FL crossover. We find that the vanishing of peaks in DoS parallel to the walls indicates that the SCF no longer supports shear mode excitations and could serve as an identifier of the FL crossover for confined systems just as is done for the bulk. Layer heights of density profiles, self-diffusivity and the peak heights of radial distribution function parallel to the walls also feature the FL crossover consistent with the DoS criteria. Surprisingly, self-diffusivity undergoes an Arrhenius to super-Arrhenius crossover at low temperatures for smaller spacings as a result of enhanced structural order evidenced via pair-excess entropy. This feature, typical of glass-forming liquids and binary supercooled liquids, is found to develop from the glass-like characteristic slowdown and strong caging in confined supercritical fluid, evidenced via mean squared displacement and velocity autocorrelation function respectively, over intermediate timescales.

Two-dimensional infrared spectroscopy from the gas to liquid phase: density dependent J-scrambling, vibrational relaxation, and the onset of liquid character

Ultrafast 2DIR spectra and pump-probe responses of the N₂O ν₃ asymmetric stretch in SF₆ as a function of density from the gas to supercritical phase and liquid are reported. 2DIR spectra unequivocally reveal free rotor character at all densities studied in the gas and supercritical region. Analysis of the 2DIR spectra determines that J-scrambling or rotational relaxation in N₂O is highly efficient, occurring in ∼1.5 to ∼2 collisions with SF₆ at all non-liquid densities. In contrast, N₂O ν₃ vibrational energy relaxation requires ∼15 collisions, and complete vibrational equilibrium occurs on the ∼ns scale at all densities. An independent binary collision model is sufficient to describe these supercritical state point dynamics. The N₂O ν₃ in liquid SF₆ 2DIR spectrum shows no evidence of free rotor character or spectral diffusion. Using these 2DIR results, hindered rotor or liquid-like character is found in gas and all supercritical solutions for SF₆ densities ≥ρ* = 0.3, and increases with SF₆ density. 2DIR spectral analysis offers direct time domain evidence of critical slowing for SF₆ solutions closest to the critical point density. Applications of 2DIR to other high density and supercritical solution dynamics and descriptions are discussed.

Anticrossing of Longitudinal and Transverse Modes in Simple Fluids

If interacting modes of the same symmetry cross, they repel from each other and become hybridized. This phenomenon is called anticrossing and is well-known for mechanical oscillations, electromagnetic circuits, waveguides, metamaterials, polaritons, and phonons in crystals, but it still remains poorly understood in simple fluids. Here, we show that structural disorder and anharmonicity, governing properties of fluids, lead to the anticrossing of longitudinal and transverse modes, which is accompanied by their hybridization and strong redistribution of excitation spectra. We combined theory and simulations for noble gases to prove the reliability of mode anticrossing in simple fluids, studied here for the first time. Our results open novel prospects in understanding collective dynamics, thermodynamics, and transport phenomena in various fluids, spanning from noble gas fluids and metallic melts to strongly coupled plasmas and molecular and complex fluids.

Excitation spectra in fluids: How to analyze them properly

Although the understanding of excitation spectra in fluids is of great importance, it is still unclear how different methods of spectral analysis agree with each other and which of them is suitable in a wide range of parameters. Here, we show that the problem can be solved using a two-oscillator model to analyze total velocity current spectra, while other considered methods, including analysis of the spectral maxima and single mode analysis, yield rough results and become unsuitable at high temperatures and wavenumbers. To prove this, we perform molecular dynamics (MD) simulations and calculate excitation spectra in Lennard-Jones and inverse-power-law fluids at different temperatures, both in 3D and 2D cases. Then, we analyze relations between thermodynamic and dynamic features of fluids at (Frenkel) crossover from a liquid- to gas-like state and find that they agree with each other in the 3D case and strongly disagree in 2D systems due to enhanced anharmonicity effects. The results provide a significant advance in methods for detail analysis of collective fluid dynamics spanning fields from soft condensed matter to strongly coupled plasmas.

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.

Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids

A fluid particle changes its dynamics from diffusive to oscillatory as the system density increases up to the melting density. Hence the notion of the Frenkel line was introduced to demarcate the fluid region into rigid and nonrigid liquid subregions based on the collective particle dynamics. In this work, we apply a topological framework to locate the Frenkel lines of the soft-sphere and the hard-sphere models relying on the system configurations. The topological characteristics of the ideal gas and the maximally random jammed state are first analyzed, then the classification scheme designed in our earlier work is applied to soft-sphere and hard-sphere fluids. The dependence of the classification result on the bulk density is understood based on the theory of fluid polyamorphism. The percolation behavior of solid-like clusters is described based on the fraction of solid-like molecules in an integrated manner. The crossover densities are obtained by examining the percolation of solid-like clusters. The resultant crossover densities of soft-sphere fluids converge to that of hard-sphere fluid. Hence the topological method successfully highlights the generality of the Frenkel line.

Soft-wall induced structure and dynamics of partially confined supercritical fluids

The interplay between the structure and dynamics of partially confined Lennard Jones (LJ) fluids, deep into the supercritical phase, is studied over a wide range of densities in the context of the Frenkel line (FL), which separates rigid liquidlike and non-rigid gaslike regimes in the phase diagram of the supercritical fluids. Extensive molecular dynamics simulations carried out at the two ends of the FL (P = 5000 bars, T = 300 K, and T = 1500 K) reveal intriguing features in supercritical fluids as a function of stiffness of the partially confining atomistic walls. The liquidlike regime of a LJ fluid (P = 5000 bars, T = 300 K), mimicking argon, partially confined between walls separated by 10 Å along the z-axis, and otherwise unconstrained, reveals amorphous and liquidlike structural signatures in the radial distribution function parallel to the walls and enhanced self-diffusion as the wall stiffness is decreased. In sharp contrast, in the gas-like regime (P = 5000 bars, T = 1500 K), soft walls lead to increasing structural order hindering self-diffusion. Furthermore, the correlations between the structure and self-diffusion are found to be well captured by excess entropy. The rich behaviour shown by supercritical fluids under partial confinement, even with simple interatomic potentials, is found to be fairly independent of hydrophilicity and hydrophobicity. The study identifies persisting sub-diffusive features over intermediate time scales, emerging from the strong interplay between density and confinement, to dictate the evolution and stabilization of structures. It is anticipated that these results may help gain a better understanding of the behaviour of partially confined complex fluids found in nature.

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.

Dissipative phase transitions in systems with nonreciprocal effective interactions

The reciprocity of effective interparticle forces can be violated in various open and nonequilibrium systems, in particular, in colloidal suspensions and complex (dusty) plasmas. Here, we obtain a criterion under which a nonreciprocal system can be strictly reduced to a pseudo-Hamiltonian system with a detailed dynamic equilibrium. In particular, the criterion is satisfied for catalytically active colloids interacting via nonreciprocal diffusiophoretic forces. However, in the general case, when this criterion is not satisfied, the steady state is determined by the interplay between dissipation and the energy source due to the nonreciprocity of interactions. The results indicate the realization of bistability and dissipative spinodal decomposition in a broad class of systems with nonreciprocal effective interactions.

Topological Characterization of Rigid-Nonrigid Transition across the Frenkel Line

The dynamics of supercritical fluids, a state of matter beyond the gas-liquid critical point, changes from diffusive to oscillatory motions at high pressure. This transition is believed to occur across a locus of thermodynamic states called the Frenkel line. The Frenkel line has been extensively investigated from the viewpoint of the dynamics, but its structural meaning is still not well-understood. This Letter interprets the mesoscopic picture of the Frenkel line entirely based on a topological and geometrical framework. This discovery makes it possible to understand the mechanism of rigid-nonrigid transition based not on the dynamics of individual atoms but on their instantaneous configurations. The topological classification method reveals that the percolation of solid-like structures occurs above the rigid-nonrigid crossover densities.

"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.