Widom Lines in Binary Mixtures of Supercritical Fluids

Widom Line in Supercritical Water in Terms of Changes in Local Structure: Theoretical Perspective

Performing molecular dynamics simulations with the TIP4P/2005 water model along 9 isobars (from 175 to 375 bar) in the temperature range between 300 and 1100 K, we have found that the loci of the extrema in the rate of change of specific structural properties can be used to define purely structure-based Widom lines. We have examined several parameters that describe the local structure of water, such as the tetrahedral arrangement, nearest neighbor distance, local density around the molecules, and the size of the largest dense domain. The last two parameters were determined using the Voronoi polyhedral and density-based spatial clustering of applications with noise methods, respectively. By analyzing the moments of the associated distributions, we show that along a given isobar, the temperature at which we observe a maximum in the fluctuation, the rate of change of the average values, or in the skewness values unambiguously determines the Widom line that is in agreement with the experimentally detected, thermodynamic response function-based ones.

Diffusion of hydrocarbons diluted in supercritical carbon dioxide

Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide ([Formula: see text]) is studied by molecular dynamics simulation near the Widom line, i.e., in the temperature range from 290 to 345 K along the isobar 9 MPa. The [Formula: see text] + aromatics mixtures are additionally sampled at 10 and 12 MPa and an experimental database with Fick diffusion coefficient data for those systems is provided. Taylor dispersion experiments of [Formula: see text] with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the [Formula: see text] 10 MPa isobar. Maxwell-Stefan and Fick diffusion coefficients are analyzed, together with the thermodynamic factor that relates them. It is found that the peculiar behavior of the Fick diffusion coefficient of some [Formula: see text] mixtures in the extended critical region is a consequence of the thermodynamic factor minimum due to pronounced clustering on the molecular scale. Further, the strong dependence of the Fick diffusion coefficient on the molecular mass of the solute as well as the breakdown of the Stokes-Einstein relation near the Widom line are confirmed. Eleven correlations for the prediction of the Fick diffusion coefficient of [Formula: see text] mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical [Formula: see text] mixtures is proposed. It requires only the state point in terms of temperature and pressure (or density) as well as the molecular solute mass as input parameters. First, entropy scaling is applied to estimate the self-diffusion coefficient of [Formula: see text]. Subsequently, this coefficient is used to determine the infinite dilution Fick diffusion coefficient of the mixture, based on the finding that these two diffusion coefficients exhibit a linear relationship, where the slope depends only on the molecular solute mass.

Boiling line and near-critical maxima of propane-nitrogen mixtures

It is well known that some thermodynamic quantities demonstrate maxima in the vicinity of a critical point. The lines of these maxima in the density-temperature or pressure-temperature planes are called "Widom lines." The behavior of Widom lines of one-component fluids has already been well studied in a number of papers by different authors. However, up to now the understanding of Widom lines in binary mixtures is still lacking. In this paper we study the boiling curve and the near-critical maxima of mixtures of nitrogen and propane by means of molecular dynamics simulation. We calculate the boiling curves and estimate the critical temperatures in a set of concentrations from pure nitrogen to pure propane. The influence of the composition of the mixture on the Widom lines of the system is evaluated. We find that the mixture of propane and nitrogen behaves as a type I mixture in the van Konynenburg-Scott classification, i.e., when the concentration is changed, the critical point and the corresponding Widom lines continuously shift in the density-temperature plane.

New insight into 3-picoline-deuterium oxide (D2O) mixtures of limited miscibility with the lower critical consolute temperature

Coexistence curves in mixtures of limited miscibility with the lower critical consolute temperature (LCT), of 3-picoline with deuterium oxide (D₂O), and D₂O/H₂O have been determined. They were tested with respect to the order parameter, the diameter of the binodal, and coordinates of the critical consolute point (critical temperature [Formula: see text] and critical concentration [Formula: see text]). Studies were carried out using the innovative method based on the analysis of relative volumes occupied by coexisting phases, yielding high-resolution data. The clear violation of the Cailletet-Mathew law of rectilinear diameter for the LCT mixtures of limited miscibility is evidenced. For the order parameter, the new distortion-sensitive analysis method yielded the evidence for the model-value of the order parameter critical exponent [Formula: see text], up to ca. 1 K from [Formula: see text]. Finally, the simple & easy method for determining the critical concentration by testing relative volumes of coexisting phases (or alternatively fractional meniscus heights, h) is presented. The significance of the invariant value [Formula: see text] is highlighted. The appearance of the milky & bluish critical opalescence is also shown.

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.

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.

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.

Cluster Identification Using Modularity Optimization to Uncover Chemical Heterogeneity in Complex Solutions

Structural heterogeneity is commonly manifested in solutions and liquids that feature competition of different interparticle forces. Identifying and characterizing heterogeneity across different length scales requires multimodal experimental measurement and/or the application of new techniques for the interrogation of atomistic simulation data. Within the latter, the parsing of networks of interparticle interactions (chemical networks) has been demonstrated to be a valuable tool for identifying subensembles of chemical environments. However, chemical networks can adopt a wide variety of topologies that challenge generalizable methods for identifying heterogeneous behavior, and few network analysis algorithms have been proposed for multiscale resolution. In this study, we apply a method of partitioning using the graph theoretic concept of clusters and communities. Using a modularity optimization algorithm, the cluster partition creates subgraphs based on their relative internal and external connectivities. The methodology is tested on two soft matter systems that have significantly different network topologies so as to probe its ability to identify multiple scale features and its generalizability. A binary Lennard-Jones fluid is first examined, where one component causes subgraphs that have high internal network connectivity yet are still connected to the rest of the interparticle network of interactions. The impact of connectivity and edge weighting on the cluster partition is investigated. In the second system, hierarchically organized molecular structures comprised of hydrogen bonded water molecules are identified at a liquid/liquid interface. These structures have a much more sparse network with significantly varied internal connectivity that is a challenge to differentiate from the background hydrogen bonding network of water molecules at the instantaneous interface. The organized macrostructures are effectively isolated from the background network using the cluster partition, and a time-dependent implementation allows us to reveal their reactivity. These studies indicate that cluster partitioning based upon intermolecular network connectivity patterns is broadly generalizable, depending only on user-defined intermolecular connectivity, is operable across different length scales, and is extensible to the study of dynamic phenomena.

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.

Optimization of process parameters for preparation of polystyrene PM2.5 particles by supercritical antisolvent method using BBD-RSM

The objective of this study is to optimize the process parameters for preparing polystyrene (PS) PM2.5 particles by supercritical antisolvent (SAS) method. Toluene was selected as the solvent and supercritical carbon dioxide (SC-CO₂) was used as the antisolvent. The Box–Behnken design-response surface method was applied to investigate the effect of crystallizer pressure, PS massic concentration, flow ratio of CO₂/solution and crystallizer temperature on the size and the distribution of PS particles, systematically. It is found that crystallizer temperature is the most significant variable on the size and the distribution of PS particles, followed by flow ratio of CO₂/solution and PS massic concentration, and crystallizer pressure is the slightest significant factor. The particle size increases with the increase of crystallizer temperature. The optimum conditions are obtained as crystallizer pressure 9.8 MPa, PS massic concentration 1.6 wt%, flow ratio of CO₂/solution 140 g/g and crystallizer temperature 309 K. Under these conditions, the PS particle with the size of 2.78 μm and a narrow size distribution has been prepared, meeting PM2.5 standard aerosols. The results suggest that it is feasible to produce PM2.5 standard aerosols by SAS.

Utilization of CO2 as Cushion Gas for Depleted Gas Reservoir Transformed Gas Storage Reservoir

Underground gas storage reservoirs (UGSRs) are used to keep the natural gas supply smooth. Native natural gas is commonly used as cushion gas to maintain the reservoir pressure and cannot be extracted in the depleted gas reservoir transformed UGSR, which leads to wasting huge amounts of this natural energy resource. CO2 is an alternative gas to avoid this particular issue. However, the mixing of CO2 and CH4 in the UGSR challenges the application of CO2 as cushion gas. In this work, the Donghae gas reservoir is used to investigate the suitability of using CO2 as cushion gas in depleted gas reservoir transformed UGSR. The impact of the geological and engineering parameters, including the CO2 fraction for cushion gas, reservoir temperature, reservoir permeability, residual water and production rate, on the reservoir pressure, gas mixing behavior, and CO2 production are analyzed detailly based on the 15 years cyclic gas injection and production. The results showed that the maximum accepted CO2 concentration for cushion gas is 9% under the condition of production and injection for 120 d and 180 d in a production cycle at a rate of 4.05 kg/s and 2.7 kg/s, respectively. The typical curve of the mixing zone thickness can be divided into four stages, which include the increasing stage, the smooth stage, the suddenly increasing stage, and the periodic change stage. In the periodic change stage, the mixed zone increases with the increasing of CO2 fraction, temperature, production rate, and the decreasing of permeability and water saturation. The CO2 fraction in cushion gas, reservoir permeability, and production rate have a significant effect on the breakthrough of CO2 in the production well, while the effect of water saturation and temperature is limited.

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.

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.

Diffusion of methane in supercritical carbon dioxide across the Widom line

Diffusion of methane diluted in supercritical carbon dioxide is studied by experiment and molecular simulation in the temperature range from 292.55 to 332.85 K along the isobars 9.0, 12.5 and 14.7 MPa. Measurements of the Fick diffusion coefficient are carried out with the Taylor dispersion technique. Molecular dynamics simulation and the Green-Kubo formalism are employed to obtain Fick, Maxwell-Stefan and intradiffusion coefficients as well as shear viscosity. The obtained diffusion coefficients are on the order of 10-8 m2/s. The composition, temperature and density dependence of diffusion is analyzed. The Fick diffusion coefficient of methane in carbon dioxide shows an anomaly in the near-critical region. This behavior can be attributed to the crossing of the so-called Widom line, where the supercritical fluid goes through a transition between liquid-like and gas-like states. Further, several classical equations are tested on their ability to predict this behavior and it is found that equations that explicitly include the density are better suited to predict the sharp variation of the diffusion coefficient near the critical region predicted by molecular simulation.

Structural properties of the Jagla fluid

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.

Behavior of Supercritical Fluids across the "Frenkel Line"

The "Frenkel line" (FL), the thermodynamic locus where the time for a particle to move by its size equals the shortest transverse oscillation period, has been proposed as a boundary between recently discovered liquid-like and gas-like regions in supercritical fluids. We report a simulation study of isothermal supercritical neon in a range of densities intersecting the FL. Specifically, structural properties and single-particle and collective dynamics are scrutinized to unveil the onset of any anomalous behavior at the FL. We find that (i) the pair distribution function smoothly evolves across the FL displaying medium-range order, (ii) low-frequency transverse excitations are observed below the "Frenkel frequency", and (iii) the high-frequency shear modulus does not vanish even for low-density fluids, indicating that positive sound dispersion characterizing the liquid-like region of the supercritical state is unrelated to transverse dynamics. These facts critically undermine the definition of the FL and its significance for any relevant partition of the supercritical phase.