Reply to “Comment on ‘Behavior of Supercritical Fluids across the Frenkel Line’”

Substantial breakdown of the hydrogen-bonding network, local density inhomogeneities and fluid-liquid structural transitions in supercritical octanol-1: A molecular dynamics investigation

Molecular dynamics simulations have been employed to explore the hydrogen-bonding structure and dynamics in supercritical octanol-1 at a near-critical temperature and up to high densities and pressures. A substantial breakdown of the hydrogen-bonding network when going from ambient-liquid to supercritical conditions is revealed. The fraction of the non-hydrogen bonded molecules significantly increases in supercritical octanol-1, and a substantial decrease in the intermittent hydrogen-bond lifetime is observed. This behavior is also reflected on the maximum local density augmentation, which is comparable to the values obtained for non-polar and non-hydrogen bonded fluids. The existence of a structural transition from an inhomogeneous fluid phase to a soft-liquid one at densities higher than 2.0 ρc is also revealed. At higher densities, a significant change in the reorientational relaxation process is observed, reflected on the significant increase in the ratio of the Legendre reorientational times τ1R/τ2R. The latter becomes much higher than the value predicted by the Debye model of diffusive reorientation and the corresponding ratio for ambient liquid octanol-1. The non-polar tail of octanol-1 under supercritical conditions reorients more slowly in comparison with the polar tail. Interestingly, the opposite behavior is observed for the ambient liquid, further verifying the strong effect of the breakdown of the hydrogen bonding network on the properties of supercritical octanol-1. In accordance with the above-mentioned findings, the static dielectric constant of supercritical octanol-1 is very low even at high densities and pressures, comparable to the values obtained for non-polar and non-hydrogen bonded fluids.

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.

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.

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.

Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory

We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).

Self-Diffusion in Simple Liquids as a Random Walk Process

It is demonstrated that self-diffusion in dense liquids can be considered a random walk process; its characteristic length and time scales are identified. This represents an alternative to the often assumed hopping mechanism of diffusion in the liquid state. The approach is illustrated using the one-component plasma model.

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.

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.

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.

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.

Comment on "Lagrangian formulation and symmetrical description of liquid dynamics"

Trachenko [Trachenko, Phys. Rev. E 96, 062134 (2017)2470-004510.1103/PhysRevE.96.062134] has argued for creating a Lagrangian formulation of liquid dynamics. This Comment shows that the proposed two-field Lagrangian does not describe dynamics of liquid in a correct way. Other claims on the symmetric description of liquid dynamics and on the similarity of Maxwell and Frenkel characteristic times are discussed.

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.