Widom Delta of Supercritical Gas-Liquid Coexistence

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.

Self-assembly prediction of architecture-controlled bottlebrush copolymers in solution using graph convolutional networks

The investigation of bottlebrush copolymer self-assembly in solution involves a comprehensive approach integrating simulation and experimental research, due to their unique physical characteristics. However, the intricate architecture of bottlebrush copolymers and the diverse solvent conditions introduce a wide range of parameter spaces. In this study, we investigated the solution self-assembly behavior of bottlebrush copolymers by combining dissipative particle dynamics (DPD) simulation results and machine learning (ML) including graph convolutional networks (GCNs). The architecture of bottlebrush copolymers is encoded by graphs including connectivity, side chain length, bead types, and interaction parameters of DPD simulation. Using GCN, we accurately predicted the single chain properties of bottlebrush copolymers with over 95% accuracy. Furthermore, phase behavior was precisely predicted using these single chain properties. Shapley additive explanations (SHAP) values of single chain properties to the various self-assembly morphologies were calculated to investigate the correlation between single chain properties and morphologies. In addition, we analyzed single chain properties and phase behavior as a function of DPD interaction parameters, extracting relevant physical properties for vesicle morphology formation. This work paves the way for tailored design in solution of self-assembled nanostructures of bottlebrush copolymers, offering a GCN framework for precise prediction of self-assembly morphologies under various chain architectures and solvent conditions.

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.

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.

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

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

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

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

Universal Two-Component Dynamics in Supercritical Fluids

Despite the technological importance of supercritical fluids, controversy remains about the details of their microscopic dynamics. In this work, we study four supercritical fluid systems—water, Si, Te, and Lennard-Jones fluid—via classical molecular dynamics simulations. A universal two-component behavior is observed in the intermolecular dynamics of these systems, and the changing ratio between the two components leads to a crossover from liquidlike to gaslike dynamics, most rapidly around the Widom line. We find evidence to connect the liquidlike component dominating at lower temperatures with intermolecular bonding and the component prominent at higher temperatures with free-particle, gaslike dynamics. The ratio between the components can be used to describe important properties of the fluid, such as its self-diffusion coefficient, in the transition region. Our results provide an insight into the fundamental mechanism controlling the dynamics of supercritical fluids and highlight the role of spatiotemporally inhomogeneous dynamics even in thermodynamic states where no large-scale fluctuations exist in the fluid.

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.

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.

Phase distribution including a bubblelike region in supercritical fluid

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

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.

Machine learning for phase behavior in active matter systems

We demonstrate that deep learning techniques can be used to predict motility-induced phase separation (MIPS) in suspensions of active Brownian particles (ABPs) by creating a notion of phase at the particle level. Using a fully connected network in conjunction with a graph neural network we use individual particle features to predict to which phase a particle belongs. From this, we are able to compute the fraction of dilute particles to determine if the system is in the homogeneous dilute, dense, or coexistence region. Our predictions are compared against the MIPS binodal computed from simulation. The strong agreement between the two suggests that machine learning provides an effective way to determine the phase behavior of ABPs and could prove useful for determining more complex phase diagrams.

Diffusion of the carbon dioxide-ethanol mixture in the extended critical region

The effect of traces of ethanol in supercritical carbon dioxide on the mixture's thermodynamic properties is studied by molecular simulations and Taylor dispersion measurements. This mixture is investigated along the isobar p = 10 MPa in the temperature range between T = 304 and 343 K. Along this path, the mixture undergoes two transitions: First, the Widom line is crossed, marking the transition from liquid-like to gas-like conditions. A second transition occurs from the supercritical gas-like domain to a subcritical gas. The Widom line crossover entails inflection points for most of the studied properties, i.e. density, enthalpy, shear viscosity, Maxwell-Stefan and intradiffusion coefficients. On the other hand, the transition between the super- and subcritical regions is found to be generally smooth, an observation that is qualitatively confirmed by experimental Taylor dispersion measurements. Dedicated atomistic simulations show the presence of microheterogeneities due to ethanol self-association along the investigated path, which lead to the mixture's anomalous behavior in its extended critical region.

Optical Diagnostics of Supercritical CO2 and CO2-Ethanol Mixture in the Widom Delta

The supercritical CO₂ (scCO₂) is widely used as solvent and transport media in different technologies. The technological aspects of scCO₂ fluid applications strongly depend on spatial–temporal fluctuations of its thermodynamic parameters. The region of these parameters’ maximal fluctuations on the p-T (pressure-temperature) diagram is called Widom delta. It has significant practical and fundamental interest. We offer an approach that combines optical measurements and molecular dynamics simulation in a wide range of pressures and temperatures. We studied the microstructure of supercritical CO₂ fluid and its binary mixture with ethanol in a wide range of temperatures and pressures using molecular dynamics (MD) simulation. MD is used to retrieve a set of optical characteristics such as Raman spectra, refractive indexes and molecular refraction and was verified by appropriate experimental measurements. We demonstrated that in the Widom delta the monotonic dependence of the optical properties on the CO₂ density is violated. It is caused by the rapid increase of density fluctuations and medium-sized (20–30 molecules) cluster formation. We identified the correlation between cluster parameters and optical properties of the media; in particular, it is established that the clusters in the Widom delta acts as a seed for clustering in molecular jets. MD demonstrates that the cluster formation is stronger in the supercritical CO₂-ethanol mixture, where the extended binary clusters are formed; that is, the nonlinear refractive index significantly increased. The influence of the supercritical state in the cell on the formation of supersonic cluster jets is studied using the Mie scattering technique.

Universality, Scaling, and Collapse in Supercritical Fluids

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

The use of process simulation in supercritical fluids applications

Modelling and simulation from micro- to macro-scale are needed to attain a broader commercialization of supercritical technologies.

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.

Visualization of supercritical water pseudo-boiling at Widom line crossover

Supercritical water is a green solvent used in many technological applications including materials synthesis, nuclear engineering, bioenergy, or waste treatment and it occurs in nature. Despite its relevance in natural systems and technical applications, the supercritical state of water is still not well understood. Recent theories predict that liquid-like (LL) and gas-like (GL) supercritical water are metastable phases, and that the so-called Widom line zone is marking the crossover between LL and GL behavior of water. With neutron imaging techniques, we succeed to monitor density fluctuations of supercritical water while the system evolves rapidly from LL to GL as the Widom line is crossed during isobaric heating. Our observations show that the Widom line of water can be identified experimentally and they are in agreement with the current theory of supercritical fluid pseudo-boiling. This fundamental understanding allows optimizing and developing new technologies using supercritical water as a solvent.

Supercritical water exists in gas- and liquid-like forms, but these have not been distinguished yet at the macroscale. Here the authors investigate supercritical water interacting with microporous carbon by neutron imaging, and observe the coexistence of gas- and liquid-like states upon crossing the Widom 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.

Deep neural network learning of complex binary sorption equilibria from molecular simulation data

We employed deep neural networks (NNs) as an efficient and intelligent surrogate of molecular simulations for complex sorption equilibria using probabilistic modeling. Canonical (N ₁ N ₂ VT) Gibbs ensemble Monte Carlo simulations were performed to model a single-stage equilibrium desorptive drying process for (1,4-butanediol or 1,5-pentanediol)/water and 1,5-pentanediol/ethanol from all-silica MFI zeolite and 1,5-pentanediol/water from all-silica LTA zeolite. A multi-task deep NN was trained on the simulation data to predict equilibrium loadings as a function of thermodynamic state variables. The NN accurately reproduces simulation results and is able to obtain a continuous isotherm function. Its predictions can be therefore utilized to facilitate optimization of desorption conditions, which requires a laborious iterative search if undertaken by simulation alone. Furthermore, it learns information about the binary sorption equilibria as hidden layer representations. This allows for application of transfer learning with limited data by fine-tuning a pretrained NN for a different alkanediol/solvent/zeolite system.

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.