Widom Line Research Articles

A statistical mechanical model of supercooled water based on minimal clusters of correlated molecules.

In this paper, we apply a theoretical model for fluid state thermodynamics to investigate simulated water in supercooled conditions. This model, which we recently proposed and applied to sub- and super-critical fluid water [Zanetti-Polzi et al., J. Chem. Phys. 156(4), 44506 (2022)], is based on a combination of the moment-generating functions of the enthalpy and volume fluctuations as provided by two gamma distributions and provides the free energy of the system as well as other relevant thermodynamic quantities. The application we make here provides a thermodynamic description of supercooled water fully consistent with that expected by crossing the liquid-liquid Widom line, indicating the presence of two distinct liquid states. In particular, the present model accurately reproduces the Widom line temperatures estimated with other two-state models and well describes the heat capacity anomalies. Differently from previous models, according to our description, a cluster of molecules that extends beyond the first hydration shell is necessary to discriminate between the statistical fluctuation regimes typical of the two liquid states.

Molecular dynamics investigation on Widom line of binary mixtures of supercritical carbon dioxide containing noble gases

This work focuses on the effects of the addition of noble gases (Xe and Kr) at different concentrations on the thermodynamic properties and Widom line (WL) of supercritical carbon dioxide (S-CO2), as well as the microstructures of the binary mixture at different thermodynamic state points. Three thermodynamic properties (volume expansivity αp, isothermal compressibility κT, and isobaric heat capacity Cp) of CO2 + Xe and CO2 + Kr binary mixtures are investigated in the near-critical region (280–370 K, 8–14 MPa), and both of them significantly reduce the peaks of the three thermodynamic properties compared to pure CO2, and this effect enhances as the concentration of noble gases increases. The WL constructed by the maxima of the three thermodynamic properties of the CO2 + Xe binary mixture rotates clockwise around the critical point on the P-T plane as the concentration of Xe increases, while the same WL of the CO2 + Kr binary mixture shifts in the direction of temperature decrease on the P-T plane as the concentration of Xe increases. The Radial distribution function (RDF) of Xe and Kr in CO2 binary mixtures both exhibit significant first and blurry second peaks of RDF in the near-critical region consistent with pure CO2, which suggests the miscibility and homogeneity between CO2 and the two noble gases combined with visualization of the simulated mixture system.

Thermodynamic Quantities of Morse Fluids in the Supercritical Region

The critical point parameters for liquid alkali metals (sodium and potassium) are calculated accounting for the non-Gaussian order parameter fluctuations and the Morse interaction potential. The behavior of the isothermal compressibility, density fluctuations, and thermal expansion for sodium is studied in the supercritical temperature region. A significant increase in the isothermal compressibility and the density fluctuations near the critical point indicates a substantial density sensitivity to tiny pressure fluctuations. The thermal expansion coefficient for various fixed pressure values shows a typical gas decrease with increasing supercritical temperature. The Widom line separating the gaseous and liquid structures of the fluid at temperatures above the critical one is represented. Note that our calculations are valid in a small neighborhood of the critical point, which is problematic for theoretical and experimental studies.

Holding water in a sieve—stable droplets without surface tension

Our understanding of supercritical fluids has seen exciting advances over the last decades, often in direct contradiction to established textbook knowledge. Rather than being structureless, we now know that distinct supercritical liquid and gaseous states can be distinguished and that a higher order phase transition - pseudo boiling - occurs between supercritical liquid and gaseous states across the Widom line. Observed droplets and sharp interfaces at supercritical pressures are interpreted as evidence of surface tension due to phase equilibria in mixtures, given the lack of a supercritical liquid-vapor phase equilibrium in pure fluids. However, here we introduce an alternative physical mechanism that unexpectedly causes a sharpening of interfacial density gradients in absence of surface tension: thermal gradient induced interfaces (TGIIF). We show from first principles and simulations that, unlike in gases or liquids, stable droplets, bubbles, and planar interfaces can exist without surface tension. These results challenge and generalize our understanding of what droplets and phase interfaces are, and uncover yet another unexpected behavior of supercritical fluids. TGIIF provide a new physical mechanism that could be used to tailor and optimize fuel injection or heat transfer processes in high-pressure power systems.

Analysis of Structural Change across the Liquid-Liquid Transition and the Widom Line in Supercooled Stillinger-Weber Silicon.

We consider the changes in the structure of supercooled Stillinger-Weber silicon at pressures at which the studied range of temperatures traverses the liquid-liquid transition or the "Widom line" (at which the isothermal compressibility or the specific heat exhibits a maximum). In addition to the conventional characterizations in terms of the pair-correlation function and bond orientational order, we analyze the statistics of rings in the bond network as well as the statistics of clusters of low density liquid (LDL)- and high density liquid (HDL)-like atoms. We investigate the nature of the change in these structural characterizations when the liquid-liquid transition line or the Widom line is crossed. We find that the isobaric temperature variation of these structural features reveals clear indications of maximal structural heterogeneity or frustration upon crossing the liquid-liquid transition or the Widom line, as in the case of water, but with some differences in detail, which we discuss.

Density fluctuations and transport properties of supercritical carbon dioxide calculated by molecular dynamics simulation near the Widom line

The phenomenon of supercritical pseudo-boiling reveals the anomalous behavior of various physical and chemical properties of supercritical fluids near the Widom line (WL). To explore the regularity of this anomalous behavior, density fluctuations and transport properties of supercritical carbon dioxide are calculated by molecular dynamics (MD) simulation near the WL. The results show that the loci of density fluctuations extremes form ridge lines near the WL with the same trends. The average errors of the ridge lines are only 1.92% for spatial density fluctuation and 2.61% for temporal density fluctuation compared with the WL, respectively. The viscosity and self-diffusion coefficient have inflection points but no extremes near the WL. By comparing the ridge lines formed by the density fluctuations and the inflection points from the transport properties on the phase diagram, it can be found that the ridge lines and inflection points close to the critical point bunch into a straight line along the WL, and gradually diverge away from the critical point, which is similar to the loci of a series of thermodynamic response functions extremes.

Demixing of homogeneous binary lipid membranes induced by protein inclusions.

We study a model of a lipid bilayer membrane described by two order parameters: the chemical composition described using the Gaussian model and the spatial configuration described with the elastic deformation model of a membrane with a finite thickness or, equivalently, for an adherent membrane. We assume and explain on physical grounds the linear coupling between the two order parameters. Using the exact solution, we calculate the correlation functions and order parameter profiles. We also study the domains that form around inclusions on the membrane. We propose and compare six distinct ways to quantify the size of such domains. Despite its simplicity, the model has many interesting features like the Fisher-Widom line and two distinct critical regions.

Theoretical profiles of two-phase transcritical laminar boundary layer near the Widom line

Boundary layers can be defined as sub-, trans-, and supercritical regime according to whether their temperature profiles cross the Widom line. The transcritical boundary layers which contain liquid and supercritical phases are hard to solve. In this paper, adiabatic flat plate laminar boundary layers of supercritical carbon dioxide (SCO2) are preliminarily explored by the self-similar solution. We analyze the difference of boundary layer profiles at 8 MPa - inflow pressure by varying inflow temperature Te and Mach number Ma. The influence of Te and Ma on the velocity profiles exhibits complex diversity at three boundary layer regimes. Compared with subcritical and supercritical boundary layers, transcritical boundary layers with smaller skin friction coefficients are the most special, and they include the “sub-layer”. Notably, there is no transcritical boundary layer when Te increases to pseudo-critical temperature Tpc at small Ma. The wall temperature Tw of transcritical boundary layers may be greater than inflow total temperature T0 at larger Ma.

A revisit of the vapor–liquid interface of the Lennard-Jones fluid

In this work a mean-field crossover generated by the Maxwell construction is defined as the dividing interface for the vapor–liquid interface area. An accurate and physically preferable density-profile equation is used to correlate the local density and to predict various interfacial properties. By using the density gradient theory and a mean-field equation of state for the Lennard-Jones fluid, we are able to extensively explore the interface system in terms of the Gibbs free energy, the Helmholtz free energy and heat capacity. The peak of the intrinsic free energy at the interface reveals the most unstable state and suggests that the interface area is thus divided into vapor- enriched and liquid- enriched sub-regions. The local maxima of the intrinsic isobaric heat capacity echo such a dividing, which is in accordance with the Widom line in the supercritical region. Consequently the mean-field dividing interface is the natural extension of the Widom line into the coexistence region. Hence the entire phase space is coherently divided into liquid-like and gas-like regions in all three (temperature–pressure-volume) planes. Finally, the modeling of adsorption on the interface is briefly discussed.

Mott transition, Widom line, and pseudogap in the half-filled triangular lattice Hubbard model

The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half-filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous time auxiliary field quantum Monte Carlo to solve this model for 1, 4, 6, 12, and 16 site clusters with detailed analysis performed for the 6 site cluster. We show that a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; c) the loss of spectral weight in the metal to Mott insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.

Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study.

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water at negative pressure conditions. Our results suggest a peculiar nonmonotonic temperature dependence of vapor-liquid surface tension at temperatures where vapor-liquid coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a nonmonotonic temperature dependence. We further report that, for low density isochores, the temperature of the minimum vapor nucleation barrier does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The difference between the and the TMD, however, decreases with increasing the density of the isochore. The vapor nucleation barrier along isobars shows an interesting crossover behavior in the vicinity of the Widom line on lowering the temperature. Our results on the ice nucleation suggest an anomalous retracing behavior of the nucleation barrier along isotherms at negative pressures and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence line can induce a drastic change in the kinetics of ice nucleation. Thus, this study establishes a direct connection between the metastable water's thermodynamic anomalies and the (vapor and ice) nucleation kinetics. In addition, this study provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

Synchronization transitions on connectome graphs with external force

We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of external excitation. By numerical solution we determine the crackling noise durations with and without thermal noise and show extended non-universal scaling tails characterized by the exponent 2 < τt < 2.8, in contrast with the Hopf transition of the Kuramoto model, without the force τt = 3.1(1). Comparing the phase and frequency order parameters we find different synchronization transition points and fluctuation peaks as in case of the Kuramoto model, related to a crossover at Widom lines. Using the local order parameter values we also determine the Hurst (phase) and β (frequency) exponents and compare them with recent experimental results obtained by fMRI. We show that these exponents, characterizing the auto-correlations are smaller in the excited system than in the resting state and exhibit module dependence.

Pressure-dependent dielectric response of the frustrated Mott insulator κ−(BEDT−TTF)2Ag2(CN)3

We explore the dielectric properties of the molecular quantum-spin-liquid candidate $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{Ag}}_{2}{(\mathrm{CN})}_{3}$ as a function of frequency, pressure, and temperature. The transition from the incoherent semiconducting to the Mott-insulating state at the quantum Widom line yields a drop of the low-frequency dielectric constant to small positive values ${\ensuremath{\varepsilon}}_{1}\ensuremath{\approx}10$. The characteristic relaxor-type peak around $T=50$ K moves to lower temperatures when pressurized. An additional feature appears and quickly grows as the percolative first-order transition is approached with rising pressure. Above 4 kbar, it dominates the dielectric response and rapidly shifts to $T\ensuremath{\rightarrow}0$. Overall, the pressure-dependent dielectric response is remarkably similar to the less-correlated sister compound $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}$. At the Mott transition, we identify a reentrant insulating behavior at ${T}^{★}=11$ K which might indicate a low-entropy ground state --- possibly with a spin gap.

From the vapour–liquid coexistence region to the supercritical fluid: the van der Waals fluid

ABSTRACT In this work the interface system of the van der Waals fluid is investigated by using the density gradient theory incorporated with the mean-field theory. Based on the mean-field dividing interface generated by the Maxwell construction, we propose a highly accurate density profile model for the density gradient theory to facilitate reliable predictions of various properties for the interface region. It is found that the local intrinsic Helmholtz free energy peaks at the interface and that the maximum difference of the normal and tangential components of the pressure tensor corresponds to the maximum of the intrinsic Gibbs free energy. It is also found that the entire phase space is divided into gas-like and liquid-like regions by the single line composed of the mean-field interface and the Widom line. The two-fluid feature of the supercritical fluid is hence inherited from the coexistence region. Phase diagrams extended into the coexistence region in all the temperature-pressure-volume planes are thus completed with the solutions to the vapor–liquid equilibrium problem by the van der Waals equation of state.

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.

On the Capabilities of Optical Diagnostics Methods to Monitor the State of Supercritical Fluids near the Widom Line

On the Capabilities of Optical Diagnostics Methods to Monitor the State of Supercritical Fluids near the Widom Line

Phase boundaries and the Widom line from the Ruppeiner geometry of fluids.

The Ruppeiner geometry has been shown to provide novel ways for constructing the phase boundaries and the Widom line of certain fluids. This paper examines the applicability of these geometric constructions to more general fluids. We develop a general equation-of-state expansion for fluids near a critical point that mainly assumes analyticity with respect to the number density. Based on this general parametrization of fluids, we prove the equivalence of the Ruppeiner geometric construction and the standard Maxwell construction of phase boundaries near the critical point. In contrast, we find that the usual prescription based on the Ruppeiner geometry for the Widom line does not produce the expected Widom line for arbitrary cases of our general fluid equationof state. This usual prescription relies on the Ruppeiner metric induced on a particular hypersurface of the thermodynamic manifold. We show that by choosing a different hypersurface, which we call the Ruppeiner-N surface, and using its associated induced metric, the Ruppeiner construction generates the entire Widom line of the van der Waals fluid exactly, even away from the critical point. Interestingly, this alternative hypersurface yields another benefit. It improves the classification scheme originally proposed by Diósi etal. for partitioning the van der Waals state space into its different phases using geodesics of a thermodynamic metric. We argue that, whereas the original Diósi boundaries did not correspond to any clear thermodynamic lines, the corresponding boundaries based on the Ruppeiner-N metric become sensitive to the presence of the van der Waals Widom line and provide the correct classification of all van der Waals states. These results suggest that the Ruppeiner-N surface may be the more appropriate hypersurface to use when studying phase diagrams with thermodynamic geometry.

Dynamic charge Kondo effect and a slave fermion approach to the Mott transition

Mott transition plays a key role in strongly correlated physics but its nature is not yet fully understood. Motivated by recent development of Schwinger boson approach for the Kondo lattice, we propose in this work a novel slave fermion algorithm to study the Mott transition. Upon local approximation, our method yields a phase diagram with a zero-temperature continuous (Mott) metal-insulator transition at finite Coulomb interaction $U$ for the half-filled one-band Hubbard model on a square lattice, and the resistivity exhibits a critical scaling around the quantum Widom line. We argue that the Mott transition may be associated with a dynamic charge Kondo effect of local degenerate doublon and holon states, causing sharp resonances on the doublon/holon and electron spectra. The transition is pushed to $U=0$ once intersite antiferromagnetic correlations are included, in agreement with exact numerical calculations. Our approach captures some essential features of the Mott transition and offers an alternative angle to view this important problem. It can be extended to study other correlated electron models with more complicated local interactions.

Manifestations of the structural origin of supercooled water's anomalies in the heterogeneous relaxation on the potential energy landscape.

Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models-based on the assumption of the existence of two types of competing local states (or, structures) in liquid water-have been extremely successful in describing water's thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a predefined structural order parameter-free approach to unambiguously identify two types of competing local states-entropically and energetically favored-with significantly different structural and energetic features in the TIP4P/2005 liquid water. This identification is based on the heterogeneous structural relaxation of the system in the potential energy landscape (PEL) during the steepest-descent energy minimization. This heterogeneous relaxation is characterized using order parameters inspired by the spin-glass transition in frustrated magnetic systems. We have further established a direct relationship between the population fluctuation of the two states and the anomalous behavior of the heat capacity in supercooled water. The composition-dependent spatial distribution of the entropically favored local states shows an interesting crossover from a spanning network-like single cluster to the spatially delocalized clusters in the close vicinity of the Widom line. Additionally, this study establishes a direct relationship between the topographic features of the PEL and the water's thermodynamic anomalies in the supercooled state and provides alternate markers (in addition to the locus of maxima of thermodynamic response functions) for the Widom line in the phase plane.

Instabilities in three-dimensional boundary-layer flows with a highly non-ideal fluid

The present work investigates the linear instability of three-dimensional boundary layers in thermodynamically non-ideal regimes. As a representative fluid, we consider carbon dioxide at supercritical pressure (80 bar). The flow set-up is matched to the redesigned DLR (German Aerospace Center) experiment on cross-flow instability, with identical pressure-coefficient distribution (accelerating the flow), sweep angle and Reynolds number, at a low Mach number. The flow temperature relative to the Widom line – also known as the pseudocritical line – thus characterises the non-ideality of the flow. We consider supercritical (gas-like), subcritical (liquid-like) and transcritical (pseudoboiling) regimes, where the flow temperature remains above, below or crosses the Widom line. The stability analyses of the parabolised Navier–Stokes baseflows indicate that wall heating destabilises the flow in the supercritical regime while wall cooling stabilises both effects similar to the ideal-fluid situation but being stronger. On the contrary, wall heating/cooling exhibits reversed effects in the subcritical regime, like for an ideal liquid. In the transcritical regime, with its sharp gradients of the thermodynamic and transport properties, wall heating stabilises the flow. Most substantially, however, wall cooling provokes a changeover of the leading instability mechanism: the accelerated streamwise flow attains inflectional wall-normal profiles, and the invoked inviscid Tollmien–Schlichting instability prevails with growth rates up to one order of magnitude larger than those of the cross-flow mode. We establish a two-fold mathematical relation from the momentum equation that explains the consequence of non-ideality and wall heating/cooling. The streamwise perturbation patterns of the flows in their linear instability regime are shown by mimicking wave trains emanating from virtual point-disturbance sources. From the viewpoint of keeping laminar flows, the transcritical thermodynamic state with a cooling wall must be avoided.