Widom Line Research Articles

Thermodynamics, phase diagram, structure and anomalies of supercooled aqueous solutions of trehalose: A molecular dynamics study

We perform molecular dynamics simulations of supercooled solutions of trehalose in TIP4P/2005 water, with concentrations of 20 and 40 wt% (weight percentage) in trehalose, a disaccharide often used in cryopreserving solutions. We analyze the thermodynamics and the structure of these solutions. From the isochores we find that in the 20 wt% solution the temperature of maximum density (TMD) line is still present and it is shifted to lower temperatures with respect to that of pure water. We also find that the Widom line and the liquid-liquid critical point (LLCP) are still present for this concentration and we estimate the position of the LLCP to be shifted at lower temperatures and slightly lower pressures with respect to that of pure water. In the 40 wt% solution we find that the TMD line still persists, but the region of density anomaly shrinks. No LLCP is observed down to the lowest temperature investigated, and maxima of the isothermal compressibility, used as proxy for the Widom line, become weaker. The water oxygen - water oxygen radial distribution functions keep on showing the typical distinction between high density and low density liquid found in pure water, but at low temperatures the presence of trehalose appears to favor the high density phase of water more than in pure water. The number of water molecules of the solvation shell confirms this picture.

Experimental study and correlation of critical parameters for three binary mixtures containing R290 and hydrofluoroolefins

The mixtures of R290 (propane) and R1234yf (2,3,3,3-tetrafluoroprop-1-ene), R1243zf (3,3,3-trifluoropropene), or R1234ze(E) (trans-1,3,3,3-tetrafluoropropene) could be potential alternatives for high global warming potential (GWP) refrigerants hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs). Obtaining the critical parameters of mixtures is crucial for establishing thermodynamic models, evaluating the highest operating temperature of refrigerants, determining the phase envelope, and confirming the starting point of the Widom line. However, few studies have been made on their critical properties. In this work, the critical properties of three binary systems containing R290 + R1234yf / R1243zf / R1234ze(E) are obtained experimentally with a metal-bellows volume apparatus. The critical state is judged by direct visual observation of critical opalescence and the recurrence of the vapor-liquid phase interface. The extended total uncertainties for the mole fraction, critical pressure, critical temperature, and critical density were below 0.004, 21 kPa, 50 mK, and 0.6 % (k = 2, 0.95 confidence coefficient), respectively. Experimentally obtained critical data are correlated by the Modified Wilson method and the Redlich–Kister method. The critical parameters of the R290 + R1234yf, R290 + R1243zf, and R290 + R1234ze(E) mixtures are predicted using the Correlated Modified Wilson (CMW) method, He et al.’s method, and the Modified Extended Chueh–Prausnitz (MECP) method. The correlated curve and predicted outcomes are employed for comparison with this work's experimental results. Meanwhile, the critical parameters data obtained experimentally are contrasted with the value of REFPROP 10.0 and other open literature. The fitting and prediction curves somewhat agree with the experimental results.

Characterization of supercritical CO2 heat transfer in microporous media under (T/p)-mutability and integrated random function

The thermophysical properties of supercritical carbon dioxide (sCO2) undergo drastic changes under reservoir conditions, which significantly affects transfer characteristics and the storage efficiency. The present work seeks to identity of the heat transfer response of a mutable sCO2 in porous micromodels with integrated Boolean stochastic models. An upgraded variant of Lattice Boltzmann model is used after a thorough validation with literature experiments. The injection conditions of sCO2 are ranged from 295 to 333 K and 8–10 MPa, with a mass flow rate of 0.05–0.20 kg/min. The thermodynamic instabilities are discussed through the joint bonds between temperature and density, local and overall heat transfer, and pressure drop coefficient, under a series of pore-throats dimension from 7.5 to 401.3 μm. The results showed: (i) the remarkable (T/p)-nature of heat transfer capacity of sCO2 to lead the transfer coefficients with a subordinate impact of thermal conductivity near the Widom line, as long as the convective mode primes with increased temperature and pressure; (ii) The heterogeneity of the microporous media promoted the decrease of the transfer capacity while adjusting the spatiotemporal density and the heat transfer orientations inside the pore bodies; (iii) the growth of the pressure drop under increasing temperature has revealed an equilibrium stage where, neither the mutability of sCO2 properties nor the injection intensity can significantly affect the heat transfer of the integrated microporous.

Introducing the concept of the Widom line in the QCD phase diagram

Introducing the concept of the Widom line in the QCD phase diagram

Semiclassical thermodynamic geometry.

In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength λ_{B} is analyzed for several attractive-potential ranges. A description of the semiclassical R Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.

On a conjecture concerning the Fisher–Widom line and the line of vanishing excess isothermal compressibility in simple fluids

In the statistical mechanics approach to liquid-state theory, understanding the role of the intermolecular potential in determining thermodynamic and structural properties is crucial. The Fisher–Widom (FW) line, which separates regions in the temperature vs density plane where the decay of the total correlation function is monotonic or oscillatory, provides insights into the dominance of the attractive or repulsive part of the interactions. Stopper et al. have recently conjectured [J. Chem. Phys. 151, 014501 (2019)] that the line of vanishing excess isothermal compressibility approximates the FW line in simple fluids. Here, we investigate this conjecture using the Jagla potential and also explore the line of vanishing excess pressure. We employ theoretical approximations and Monte Carlo simulations to study one-dimensional and three-dimensional systems. While exact results for the one-dimensional case do not support the conjecture, our Monte Carlo simulations for the three-dimensional fluid validate it. Our findings not only contribute to the understanding of the relationship between the three transition lines but also provide valuable insights into the thermodynamic and structural behaviour of simple 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.

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.

Thermal Density Fluctuations and Polymorphic Phase Transitions of Ethane (C2D6) in the Gas/Liquid and Supercritical States.

The phase behavior of the liquid C2D6 below and above the critical point was investigated using small-angle neutron scattering (SANS) in temperature and pressure ranges from 10 to 45 °C and 20 to 126 bar, respectively. The scattering of thermal fluctuations of the molecular density was determined and thus the gas-liquid and Widom lines. At the same time, we observed additional scattering of droplets of more densely packed C2D6 molecules above the gas-liquid line and in the supercritical fluid regime from just below the critical point for all temperatures at about ΔP = 10 bar above the Widom line. This line is interpreted as the Frenkel line. These results are consistent with our previous studies on CO2 and thus indicate a universal phase behavior for monomolecular liquids below and above the critical point. The interpretation of the Frenkel line as the lower limit of a polymorphic phase transition is in contrast to the usual interpretation as the limit of a dynamic process. The correlation lengths (ξ) of the thermal density fluctuations at the critical point and at the Widom line are determined between 20 and 35 Å and thus in the range of the droplet radius between 60 and 80 Å. These long-range fluctuations appear to suppress the formation of droplets, which can only form at about 10 bar above the critical point and the Widom line when ξ becomes smaller than 10 Å.

The water bimodal inherent structure and the liquid-liquid transition as proposed by the experimental density data.

The bulk water density data are studied in a very large temperature-pressure range, from stable liquid to glass in the frame of water polymorphism. Because this thermodynamic variable evidences a crossover T*, above which the hydrogen bond (HB) is unable to arrange tetrahedral networks, the T-dependence of their isobars was considered. Such an analysis also shows pressure, P*, around which their thermal behaviors are completely different: concave below P* (with maxima and minima) and convex above (without extremes). Having ρ's measured values of the bimodal structures of the liquid phase, HDL (ρHDL), made of not-bonded monomers (ρNHB) and partially bonded dimers plus trimers (ρNHB), and LDL tetramers (ρLDL) the isobars of the relative distributions [W(P, T)] of the three species (WLDL, WPHB, and WNHB) have been evaluated. The results were studied by means of a logistic function (LF) that details the evolutions of the relative polpulations of the water LDL and HDL phases by decreasing T (for the isobars, in the range of 0.1-400 MPa). The LFs analysis obtained by proposing a full connection between liquid water from its supercooled metastable phase to the stable up to the boiling temperature identifies the Widom line quite satisfactorily and fully supports the presence of the liquid-liquid critical point in the deep supercooled region, located at about 190K and in the range 200 > P > 180 MPa.

A new criterion for vanishing points of Widom lines of CO2/natural gas mixture: Application to pipeline and compressor units in CCUS

The Widom lines of mixture indicate the abnormal response behavior of properties of mixed supercritical fluid near the critical point, determining operating conditions in supercritical region of ground equipment in CCUS. Peng-Robinson equation (PR-EOS) is used to calculate Widom lines of isothermal compressibility coefficient, isobaric expansion coefficient, isobaric specific heat, and density of CO2/natural gas quinary mixture. A new criterion is proposed to calculate the vanishing points of Widom lines using the coefficient of variation (CV) of response function distribution, with a clear statistical meaning and an appropriate range, compared with existing criteria. Based on the new criterion, the effect of CO2 concentration on the thermodynamic fluctuations in the near-critical region of CO2/natural gas mixture is analyzed. It is found that thermodynamic fluctuations of mixture are controlled by CO2 concentration and fluctuations can be considered relatively weak when CO2 concentration is below 60 %. The selection and control of operating conditions of pipeline and compressor unit in CCUS application are discussed to cope with the Widom region movement caused by changes in CO2 concentration.

Effect of operating regimes on the heat transfer and buoyancy characteristics of supercritical CO2 natural circulation loop - A numerical study

At present, 82% of global energy is generated by fossil fuels which produce substantial emissions and have a significant impact on the environment. Heat transfer devices play a vital role in enhancing the efficiency of power generation systems and mitigating environmental impact. Among various heat transfer devices, natural circulation loops (NCLs) assume significance due to their simplicity and safety. In the present study, numerical investigations were conducted on three-dimensional rectangular circular cross-section supercritical CO2-based NCL across three distinct operating regimes. These regions include the average temperature of NCL maintained near the widom line (near pseudo-critical region), away from the widom line (higher buoyancy region) and very far away from the widom line (deeply supercritical region). The results indicate that in all regions, there is an increase in both the mass flow rate and heat transfer rate as pressure increases. At a pressure of 14 MPa, the maximum heat transfer rate across all regions is observed. Although the higher buoyancy region exhibits a superior heat transfer rate, the near pseudo-critical region demonstrates efficient heat transfer capabilities. For example, at 11 MPa, the temperature difference in the higher buoyancy region exceeds that in the near pseudo-critical region by 73%. However, the reduction in heat transfer rate in the near pseudo-critical region is only 37% compared to the higher buoyancy regions. For low-temperature applications, the near pseudo-critical region effectively transfers heat. However, in high-temperature applications, the sink temperature should be kept in the liquid-like region to maximize system buoyancy.

Instability in strongly stratified plane Couette flow, with application to supercritical fluids.

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft's criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831-864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g., miscible fluids) is finally discussed.

Leading elliptic relationship for supercritical fluids in the Widom region

It is well-known that the behaviour of supercritical fluids near the critical point changes considerably in the region around the Widom lines. We have found, for pure fluids, that the relationship between the thermal expansion coefficient and the isothermal compressibility is not only highly nonlinear in this region but in a certain temperature range can also be approximated well at constant pressure by a quadratic relationship, i.e., an ellipse. In this paper, we show this analytically, and demonstrate it for the van der Waals, Berthelot and IAPWS-95 water models numerically. Furthermore, the parameters of the ellipse are discovered to obey power and linear laws. The parameters of these laws are determined for the three aforementioned models.

Complex phase diagram and supercritical matter.

The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquidlike and gaslike, however, suggest "supercritical boundaries." Here we provide a mathematical description of these phenomena by revisiting the Yang-Lee theory and introducing a complex phase diagram, specifically a four-dimensional (4D) one with complex T and p. While the traditional 2D phase diagram with real temperature T and pressure p values (the physical plane) lacks Lee-Yang (LY) zeros beyond the critical point, preventing the occurrence of criticality, the off-plane zeros in this 4D scenario still induce critical anomalies in various physical properties. This relationship is evidenced by the correlation between the Widom line and LY edges in van der Waals, 2D Ising model, and water. The diverged supercritical boundaries manifest the high-dimensional feature of the phase diagram: e.g., when LY zeros of complex T or p are projected onto the physical plane, boundaries defined by isobaric heat capacity C_{p} or isothermal compression coefficient K_{T} emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.

Manifestation of the Widom Line in Microwave Measurements of Sorbents Moistened with Hydrogen Peroxide

Manifestation of the Widom Line in Microwave Measurements of Sorbents Moistened with Hydrogen Peroxide

Recognition of supercritical CO2 liquid-like and gas-like molecules based on deep neural network

So far, it is still controversial about how to divide the liquid-like and gas-like states boundary and Widom delta, since the deviation of boundaries determined by different thermodynamic criteria increases significantly when away from the critical point. For this reason, a superior method that does not rely on thermodynamic criteria to define the boundary line between liquid-like and gas-like states needs to be proposed urgently and the recent extensive use of deep neural networks in molecular dynamics simulation provides a feasible choice. The present work attempts to determine a novel phase state boundary and Widom delta of supercritical CO2 from extracting the microstructure features of subcritical vapor and liquid states in equilibrium by deep neural network coupled with molecular dynamics simulation. In addition, visualization of simulated systems containing distinct liquid-like molecule ratio πLL of supercritical CO2 is also presented as well as the radial distribution function at different states. The results show that the novel boundary is located in the middle of the Widom lines constructed by multiple thermodynamic criteria. The lower boundary T- of the novel Widom delta agrees well with the theoretical boundary constructed by pseudo-boiling theory when it is close to the critical point but starts to deviate when it is far away from the critical point, while the upper boundary T+ of that is opposite. More importantly, the novel boundary and Widom delta constructed have no pressure upper limit compared to those constructed by thermodynamic criteria, only depending on πLL, which means that the novel boundary and Widom delta can extend to the supercritical deep region. Further, the visualization and radial distribution function of simulated systems of supercritical CO2 at different states provide the persistence of a liquid-like and a gas-like transition. The work conducted here can present novel microscopic insight into supercritical phase transition and provide another available alternative to define the Widom line.

Enhanced connectivity and mobility in liquid water: Implications for the high density liquid structure and its onset

In this work, we investigate simulated liquid water at ambient pressure in both stable and metastable supercooled conditions by means of a new order parameter we recently proposed, namely the node total communicability (NTC), based on graph theory concepts. We show that this order parameter is able to identify the two liquid states differing in density, the LDL- and HDL-like states, in simulation conditions at which both states coexist. We also show that NTC is able to capture both the structural and dynamic differences between the two states, being correlated with both the local density and the mobility of water molecules within the network. In addition, we further investigate the high connectivity patches we previously identified as characteristic of the HDL-like state. We show that these extended patches are composed of molecules with an increased local density and mobility, packed in a highly connected network. The formation of these highly connected networks is characterized by a fast dynamics, with mobile molecules entering and exiting the patches. Interestingly, we observe small highly connected patches also at low temperatures, where the prevailing state is LDL-like. We show that the small-to-large patches transition is related to the Widom line crossing and we suggest that the small highly connected patches at low temperatures might function as initial sites for the formation of extended HDL-like regions characteristic of the highest temperatures.

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 ({hbox {CO}}_{2}) 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 {hbox {CO}}_{2} + 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 {hbox {CO}}_{2} with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the p = 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 {hbox {CO}}_{2} 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 {hbox {CO}}_{2} mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical {hbox {CO}}_{2} 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 {hbox {CO}}_{2}. 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.

Global transformation of fluid structure and corresponding phase behavior

The laws governing the fluid structure transformation from a homogeneous state to the special state in the critical region remain intriguing. In addition, there is a drastic change in the supercritical fluid from a liquid-like type to gas-like when crossing the Widom line, which is still highly debatable. Such challenges require new insights to understand the fluid nature in its entirety. The authors have developed a Two-Phase Hierarchical Model (TPHM), which represents the fluid by a system of various size blocks nested in each other. The TPHM shows that supercritical fluids within a certain region of thermodynamic parameters exist in a form of liquid-like and gas-like clusters (supercritical mesophase) and demonstrates the formation of a hierarchical structure, most pronounced near the critical point. Based on the TPHM, a method for correcting the phase behavior in the critical region is presented, applicable both to pure substances and to multi-component mixtures.