High pressure physics of liquids and supercritical fluids
The supercritical fluid has since ever (ref 1), until recently, been considered as a unique state with intermediate properties of the liquid and gas phases. The thermodynamical observables show a continuous evolution along any P-T path in supercritical conditions. This fact is supported by the traditional view on liquid and gas as phases of the same symmetry, implying that these phases cannot be distinguished above the critical point where they do not coexist. On the other hand, this view assumes that physics of fluids is entirely determined by their structure. Modern approaches to liquid theory clearly show that this is not always the case. Dynamics plays often a crucial role. Early in 2005 L. Xu and collaborators have pointed out that the diffusion coefficient of water undergoes a non-Arrhenius (‘‘fragile’’) to Arrhenius (‘‘strong’’) crossover accompanying a thermodynamic liquid-liquid transition in the so called ‘‘no-man’s land’’ i.e. not accessible by current experimental technique (ref 2). More recently, it has been discovered that subtle but remarkable changes in supercritical fluids do occur in the positive sound dispersion (PSD) (ref 3–5). These changes posses the potential to part the phase diagram in a gas like anda liquid like region.
We recently studied the evolution of the PSD in Argon, an archetipal simple fluid, along isothermal pressure scans at several temperatures. We discovered two striking features in the density dependence of PSD in supercritical fluids: i) linear behaviour of PSD at sufficiently high densities, that extrapolates right to the density of the isobaric heat capacity, C<sub>P</sub>, thermal diffusivity, D<sub>T</sub> and kinematic shear viscosity, n extrema; ii) a plateau in the density behaviour of PSD at low densities, clearly indicating that this observable is originated by an additional collective process along with structuralrelaxation. The detailed analysis of dynamic eigenmodes and their contributions to S(Q,v)s revealed a novel effect of non-hydrodynamic heat waves on sound dispersion in low-density supercritical fluids. We quantitatively identified the dynamic crossover in a supercritical fluid model, at several temperatures, between the low density gas-like regime and the high density liquid-like regime, based on the analysis of collective modes with mesoscopic/microscopic wavelengths. In this framework, the unique role of heat thermal waves along with their interplay with sound waves have been unveiled. A remarkable outcome of this study is that the dynamic crossover shows a very tight correlation with the extrema of thermodynamic response functions and transport coefficients as C<sub>P</sub>, D<sub>T</sub> and n, defining a narrow region emanating from the critical point, as emphasized in reference (ref 6). This gives a new dimension to a recent work where a crossover in single particle dynamics was identified at the line of maxima of C<sub>P</sub> in a supercritical model fluid (ref 7), in turns anticipated by similar results in the different context of the liquid-liquid transition in water. The deep link between dynamics and thermodynamics beyond a critical point is now rationalized on a very general background (ref 8).
1 Zemanski, M. W. in:Heat and Thermodynamics, (MacGraw-Hill, New York, 1968).
2Xu, L. et al. Relation between the Widom line and dynamic crossover in systems with a liquid-liquid phase transitions. Proc Natl Acad Sci USA 102, 16558–16562 (2005).
3Gorelli, F. A., Santoro, M., Scopigno, T., Krisch, M. & Ruocco, G. Liquidlike behavior of supercritical fluids. Phys Rev Lett 97, 245702 (2006).
4Gorelli, F. A. et al. Inelastic x-ray scattering from high pressure fluids in a diamond anvil cell. Appl. Phys. Lett. 94, 074102 (2009).
5Simeoni, G. G. et al. The Widom’s line as the crossover between liquid-like and gas-like behaviour in supercritical fluids. Nature Physics 6, 503 (2010).
6 Brazhkin, V. V. & Trachenko, K. What separates a liquid from a gas? Phys. Today65, 11, 68 (2012).
7 Han,S.Anomalous change in the dynamics of asupercritical fluid. Phys.Rev.E84,051204 (2011).
8 Gorelli, F, Bryk, T., Krisch, M., Ruocco G., Santoro M, Scopigno T. Scientific Report 3, 1203 (2013)