According to textbook definitions, each fluid substance is characterised by a peculiar critical pressure (Pc) and temperature (Tc), whose values define an upper thermodynamic limit. Above this limit, any classical distinction between liquid and gas phases loses its validity, and the system enters the supercritical fluid state. In the P-T phase diagram, (Pc,Tc) represents the so-called critical point. Despite intensive research efforts on fluids throughout the past century, knowledge about properties of fluids in the supercritical regime is limited, mainly due to technical difficulties encountered in dealing with the required complex sample environment.

Important new insights were recently gained through an inelastic X-ray scattering experiment on dense hot supercritical argon (at T=4•Tc and P>102•Pc), conducted at beamline ID28, in conjunction with molecular dynamics simulations. We identified two distinct dynamical regimes (liquid-like and gas-like), contradicting the notion of a homogeneous supercritical phase. Specifically, our investigation revealed the sound propagation to be strongly dependent on the wavelength of the acoustic waves as well as on the thermodynamic conditions of the medium. As already observed in the subcritical region for most liquids, the measured hypersound velocity exceeds its adiabatic value (a dynamical feature known as positive sound dispersion). This implies the presence, even deep inside the supercritical regime, of at least one relaxation process such as the visco-elastic relaxation, reflecting the interaction of local structural changes (on nm length- and picosecond time scales) with acoustic sound waves, and considered to be a clear fingerprint of the liquid behaviour [1].

Fig. 6: Positive sound dispersion of argon as a function of pressure at 573 K. Full and open circles indicate the positive sound dispersion as obtained from IXS experimental data and from molecular dynamics simulations, respectively. The dotted line marks the point on the extrapolated Widom line at 573 K.

Figure 6 reports the amount of positive sound dispersion, as a function of pressure, derived from experiment and molecular dynamics simulations. A sharp decrease from about 13% to 4% is observed on pressure decrease with a cross-over located at 0.4 GPa. This distinct decrease is due to the progressive disappearance of the structural relaxation process, and thus marks the transition from a collective liquid-like to a single particle gas-like behaviour. This clearly provides a connection between dynamics and thermodynamics, contradicting the widespread belief of a homogeneous supercritical phase. Furthermore, we speculate that the positive sound dispersion plays the role of an order parameter, sensitive to the local structure and able to amplify the degree of correlation between thermal heterogeneities and mechanical density fluctuations on a macroscopic scale.

Fig. 7: Sketch of the (P/Pc, T/Tc) plane. Red line: Widom line of argon obtained from the NIST database (continuous) and its extrapolation (dotted). Black line: best fit of the liquid-vapour coexistence lines for argon, neon, nitrogen and oxygen using the Plank-Riedel equation. Dots with different colours correspond to different investigated systems (this study, and also ref. [2] and references therein). Isothermal, experimental and MD simulation data on argon are reported in pink inside the black rectangle. Open circles: weak positive sound dispersion, full circles: large positive dispersion.

Most remarkably, the crossover value of 0.4 GPa corresponds to the extrapolation of the so-called Widom line (Figure 7) into the supercritical phase. This ascribes a much more general role to the Widom line, since the partition between liquid-like and gas-like regimes survives even above the theoretical definition of the Widom line itself. In analogy with the subcritical behaviour, the Widom line embodies the extrapolation of the liquid-vapour coexistence line into the supercritical region, thus supplying the first fundamental insight into the correspondence between subcritical and supercritical fluid behaviour. This newly discovered relationship between thermodynamics and the viscoelastic behaviour of hot dense fluids is expected to allow major breakthroughs in areas such as the physics of planetary systems, solvation techniques for nanotechnologies, and in geophysics for the validation of seismological models based on the thermophysical properties of materials.


Principal publication and authors

G.G. Simeoni (a), T. Bryk (b,c), F.A. Gorelli (d,e), M. Krisch (f), G. Ruocco (e,g), M. Santoro (d,e) and T. Scopigno (e,g), Nature Physics 6, 503 (2010).
(a) FRM II, Technische Universität München, Garching (Germany)
(b) Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv (Ukraine)
(c) National Polytechnic University of Lviv (Ukraine)
(d) LENS, European Laboratory for Non Linear Spectroscopy, Firenze (Italy)
(e) IPCF-CNR, UOS Roma (Italy) (f) ESRF (g) Università di Roma ‘La Sapienza’ (Italy)


[1] T. Scopigno, G. Ruocco and F. Sette, Rev. Mod. Phys. 77, 881 (2005).
[2] F.A. Gorelli et al, Phys. Rev. Lett. 97, 245702 (2006).