Percolation in supercritical water: Do the Widom and percolation lines coincide?

Insights into water extraction and aggregation mechanisms of malonamide-alkane mixtures

Structure at the nanoscale in the organic phase of liquid-liquid extraction systems is often tied to separation performance. However, the weak interactions that drive extractant assembly lead to poorly defined structures that are challenging to identify. Here, we investigate the mechanism of water extraction for a malonamide extractant commonly applied to f-element separations. We measure extractant concentration fluctuations in the organic phase with small angle X-ray scattering (SAXS) before and after contact with water at fine increments of extractant concentration, finding no qualitative changes upon water uptake that might suggest significant nanoscopic reorganization of the solution. The critical composition for maximum fluctuation intensity is consistent with small water-extractant adducts. The extractant concentration dependence of water extraction is consistent with a power law close to unity in the low concentration regime, suggesting the formation of 1 : 1 water-extractant adducts as the primary extraction mechanism at low concentration. At higher extractant concentrations, the power law slope increases slightly, which we find is consistent with activity effects modeled using Flory-Huggins theory without introduction of additional extractant-water species. Molecular dynamics simulations are consistent with these findings. The decrease in interfacial tension with increasing extractant concentration shows a narrow plateau region, but it is not correlated with any change in fluctuation or water extraction trends, further suggesting no supramolecular organization such as reverse micellization. This study suggests that water extraction in this system is particularly simple: it relies on a single mechanism at all extractant concentrations, and only slightly enhances the concentration fluctuations characteristic of the dry binary extractant/diluent mixture.

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.

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.

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 pervasive impact of critical fluctuations in liquid-liquid extraction organic phases

Liquid-liquid extraction is an essential chemical separation technique where polar solutes are extracted from an aqueous phase into a nonpolar organic solvent by amphiphilic extractant molecules. A fundamental limitation to the efficiency of this important technology is third phase formation, wherein the organic phase splits upon sufficient loading of polar solutes. The nanoscale drivers of phase splitting are challenging to understand in the complex hierarchically structured organic phases. In this study, we demonstrate that the organic phase structure and phase behavior are fundamentally connected in a way than can be understood with critical phenomena theory. For a series of binary mixtures of trialkyl phosphate extractants with linear alkane diluents, we combine small angle x-ray scattering and molecular dynamics simulations to demonstrate how the organic phase mesostructure over a wide range of compositions is dominated by critical concentration fluctuations associated with the critical point of the third phase formation phase transition. These findings reconcile many longstanding inconsistencies in the literature where small angle scattering features, also consistent with such critical fluctuations, were interpreted as reverse micellar-like particles. Overall, this study shows how the organic phase mesostructure and phase behavior are intrinsically linked, deepening our understanding of both and providing a new framework for using molecular structure and thermodynamic variables to control mesostructure and phase behavior in liquid-liquid extraction.

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.

Mesostructuring in Liquid-Liquid Extraction Organic Phases Originating from Critical Points

Organic phase structure plays an important role in solute extraction energetics and phase behavior of liquid-liquid extraction (LLE) systems. For a binary extractant (amphiphile)/solvent mixture of relevance to LLE, we find that the organic phase mesostructuring is consistent with extractant concentration fluctuations as the compositional isotherm traverses the Widom line above its liquid-liquid critical point. This reveals a different mechanism for the well-documented heterogeneities in LLE organic phases that are typically attributed to micellization.

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.

Breakdown of the Stokes-Einstein Relation in Supercooled Water/Methanol Binary Mixtures: Explanation Using the Translational Jump-Diffusion Approach

A recent experiment has directly checked the validity of the Stokes-Einstein (SE) relation for pure water, pure methanol, and their binary mixtures of three different compositions at different temperatures. The effect of composition on the nature of breakdown of the SE relation is interesting. While in the majority of the systems, an increasing SE breakdown is observed with decreasing temperature, the breakdown is already significant at higher temperatures for the equimolar mixture. Violations of the SE relation in pure supercooled water at different temperatures and pressures have been previously explained using the translational jump-diffusion (TJD) approach, which provides a fundamental molecular basis, by directly connecting the SE breakdown with jump-diffusion of the molecules. We have used the same TJD approach for explaining the SE breakdown for the methanol/water binary mixtures of compositions studied in the experiment over a wide range of temperatures between 220 K and 300 K. We have understood that the jump-diffusion is the key responsible factor for the SE breakdown. The maximum jump-diffusion contribution gives rise to the early SE breakdown observed for the equimolar mixture observed in the experiment. This study, therefore, provides molecular insight into the SE breakdown for the supercooled water/methanol binary mixture, as found in the experiment.

Supercritical Water is not Hydrogen Bonded

Thinking about water is inextricably linked to hydrogen bonds, which are highly directional in character and determine the unique structure of water, in particular its tetrahedral H-bond network. Here, we assess if this common connotation also holds for supercritical water. We employ extensive ab initio molecular dynamics simulations to systematically monitor the evolution of the H-bond network mode of water from room temperature, where it is the hallmark of its fluctuating three-dimensional network structure, to supercritical conditions. Our simulations reveal that the oscillation period required for H-bond vibrations to occur exceeds the lifetime of H-bonds in supercritical water by far. Instead, the corresponding low-frequency intermolecular vibrations of water pairs as seen in supercritical water are found to be well represented by isotropic van-der-Waals interactions only. Based on these findings, we conclude that water in its supercritical phase is not a H-bonded fluid.

Assessing the properties of supercritical water in terms of structural dynamics and electronic polarization effects

Evolution of water's structural dynamics from ambient liquid to supercritical dense liquid-like and dilute gas-like conditions.

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.

Observation of the Chemical Structure of Water up to the Critical Point by Raman Spectroscopic Analysis of Fluid Inclusions

Raman spectra were obtained simultaneously from the liquid and vapor phases of pure water trapped at the critical density (322 kg·m^-3) within synthetic inclusions in quartz. As these inclusions are heated up to the critical temperature (373.946 °C), the liquid phase decreases in density and the maximum of the Raman OH-stretching band increases in wavenumber. Conversely, as the vapor phase increases in density, the maximum of the Raman OH-stretching band decreases in wavenumber. The Raman bands of the liquid and vapor phases converge to a single band at the critical point of water, where the fluid exists as a single phase. A comparison of the band centroids for the vapor and liquid phases of water indicates respective increases and decreases in the amount of hydrogen bonding in these phases as a function of increasing and decreasing density. These effects were further quantified by peak-fitting the Raman OH-stretching peak with five Gaussian components. All the Gaussian components of the liquid phase decrease in amplitude with increasing temperature with the exception of the double donor-single acceptor (H₂O)₄ cluster, which increases in amplitude and becomes the most intense component at temperatures above 300 °C. The Raman spectra of the vapor phase are dominated by the free OH component at temperatures below 300 °C, but, above this temperature, the double donor-single acceptor (H₂O)₄ cluster is again the most intense band. The results indicate that a significant quantity of water clusters is present in both liquid and vapor water at high temperatures and that supercritical water can be considered as a mixture of small water clusters [(H₂O)_n, n = 1-4] dominated by the double donor-single acceptor (H₂O)₄ cluster.