Gas or Liquid? The Supercritical Behavior of Pure Fluids

Crossover from gas-like to liquid-like molecular diffusion in a simple supercritical fluid

According to textbooks, no physical observable can be discerned allowing to distinguish a liquid from a gas beyond the critical point. Yet, several proposals have been put forward challenging this view and various transition boundaries between a gas-like and a liquid-like behaviour, including the so-called Widom and Frenkel lines, and percolation line, have been suggested to delineate the supercritical state space. Here we report observation of a crossover from gas-like (Gaussian) to liquid-like (Lorentzian) self-dynamic structure factor by incoherent quasi-elastic neutron scattering measurements on supercritical fluid methane as a function of pressure, along the 200 K isotherm. The molecular self-diffusion coefficient was derived from the best Gaussian (at low pressures) or Lorentzian (at high pressures) fits to the neutron spectra. The Gaussian-to-Lorentzian crossover is progressive and takes place at about the Widom line intercept (59 bar). At considerably higher pressures, a liquid-like jump diffusion mechanism properly describes the supercritical fluid on both sides of the Frenkel line. The present observation of a gas-like to liquid-like crossover in the self dynamics of a simple supercritical fluid confirms emerging views on the unexpectedly complex physics of the supercritical state, and could have planet-wide implications and possible industrial applications in green chemistry.

Thermodynamic crossovers in supercritical fluids

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions.

Gas–liquid crossover in the Lennard-Jones system

It is demonstrated that the crossover between gas- and liquid-like regions on the phase diagram of the Lennard-Jones system occurs at a fixed value of the density divided by its value at the freezing point, ρ/ ρfr ≃ 0.35. This definition is consistent with other definitions proposed recently. As a result, a very simple practical expression for the gas-to-liquid crossover line emerges.

Distinct molecular dynamics dividing liquid-like and gas-like supercritical hydrogens

Understanding how a supercritical fluid is related to normal liquid and gas and separating it into liquid-like and gas-like regions are of fundamental and practical importance. Despite the usefulness of hydrogen storage, molecular dynamics images on supercritical hydrogens exhibiting strong nuclear quantum effects are scarce. Taking advantage of the non-empirical ab initio molecular dynamics method for hydrogen molecules, we found that, while radial distribution functions and diffusion show a monotonic change along the density, van Hove time correlation functions and intramolecular properties such as bond length and vibrational frequency exhibit the anomalous order crossing the Widom line. By demonstrating that the anomalous order stemmed from the largest deviations between liquid-like and gas-like solvations formed around the Widom line, we concluded that this supercritical fluid is a mixture of liquid and gas possessing heterogeneity. The obtained physical insights can be an index to monitor the supercriticality and to identify distinct liquid-like and gas-like supercritical fluids.

Quasi-equilibrium phase coexistence in single component supercritical fluids

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout all combinations of pressures and temperatures, although various response functions or transport properties may exhibit anomalous behavior, characterizing a state point as either more gas-like or liquid-like, respectively. While a large body of results has been compiled in the last two decades regarding the details of the supercritical phase in thermodynamic equilibrium, far less studies have been dedicated to out-of-equilibrium situations that nevertheless occur along with the handling of substances such as carbon dioxide or Argon. Here we consider successive compression-expansion cycles of equal amounts of Argon injected into a high-pressure chamber, traversing the critical pressure at two times the critical temperature. Due to expansion cooling, the fluid temporarily becomes sub-critical, and light scattering experiments show the formation of sub-micron-sized droplets and nanometer-scale clusters, both of which are distinct from spontaneous density fluctuations of the supercritical background and persist for a surprisingly long time. A kinetic rate model of the exchange of liquid droplets with the smaller clusters can explain this behavior. Our results indicate non-equilibrium aspects of supercritical fluids that may prove important for their processing in industrial applications.

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout. Lee et al. find that liquid droplets temporarily formed in a supercritical background after sub-critical injection can survive for a surprisingly long time.

Dynamic Crossover in Fluids: From Hard Spheres to Molecules

We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liquid-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to molecules' translation, is exactly equal to a collective property, the contribution to viscosity due to molecular interactions. Such a definition is shown to be consistent with the one based on the minima of the kinematic viscosity. For the hard sphere, this is shown to be an exact solution. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the critical point, and for all studied fluids, it is well captured by the critical excess entropy curve for atomic fluids, emphasizing the link between transport properties and local structure.

Spectroscopic Studies of a Phosphonium Ionic Liquid in Supercritical CO2

Fluorescence spectroscopy was used to study a solution comprised of coumarin 153 (C153)+ trihexyltetradecylphosphonium bis(trifluoromethylsulfonyl)imide ([P6,6,6,14]+ [Tf2N]−)+ supercritical CO2 (scCO2). We compare the spectroscopy of C153 in neat scCO2 to that of C153/scCO2 with the addition of ionic liquid (IL). Excitation and emission peak frequencies of C153 in scCO2 and in IL/scCO2 diverged at reduced densities (ρr = ρ/ρc) below the CO2 critical density. At low fluid density, spectral changes in the IL/scCO2 solutions showed evidence that C153 experiences a very different microenvironment—one that is unlike neat scCO2. The data show that the presence of IL clearly influences the C153 excitation and emission profiles. Excitation was broadened and red shifted by >2000 cm−1 and the presence of an additional low-energy emission component that was red shifted by ~3000 cm−1 was clearly visible and not observed in neat scCO2. The solution heterogeneity was controlled by changing the scCO2 density and at high fluid density, both the excitation and emission spectra were more similar to those in neat scCO2. Steady-state anisotropy also showed that at low fluid density, the C153 emission was significantly polarized. Aggregation of C153 has been reported in the literature and this led us to hypothesize the possibility that C153 dimer (aggregation) formation may be occurring in scCO2. Another possible explanation is that dye–IL aggregates may dissolve into the scCO2 phase due to C153 acting as a “co-solvent” for the IL. Time-resolved intensity decay measurements yielded only slightly non-exponential decays with accompanying time constants of ~3–4 ns that were significantly shorter than the 5–6 ns time constants in neat scCO2, which are suggestive of C153–IL interactions. However, these data did not conclusively support dimer formation. Pre-exponential factors of the time constants showed that almost all of the emission was due to monomeric C153.

Thermodynamics, dynamics, and structure of supercritical water at extreme conditions

Molecular dynamics (MD) simulations to understand the thermodynamic, dynamic, and structural changes in supercritical water across the Frenkel line and the melting line have been performed.

Transition from Gas-like to Liquid-like Behavior in Supercritical N2

We have studied in detail the transition from gas-like to rigid liquid-like behavior in supercritical N₂ at 300 K (2.4 T_C). Our study combines neutron diffraction and Raman spectroscopy with ab initio molecular dynamics simulations. We observe a narrow transition from gas-like to rigid liquid-like behavior at ca. 150 MPa, which we associate with the Frenkel line. Our findings allow us to reliably characterize the Frenkel line using both diffraction and spectroscopy methods, backed up by simulation, for the same substance. We clearly lay out what parameters change, and what parameters do not change, when the Frenkel line is crossed.