Universal interrelation between dynamics and thermodynamics and a dynamically driven “c” transition in fluids

Our very wide survey of the supercritical phase diagram and its key properties reveals a universal interrelation between dynamics and thermodynamics and an unambiguous transition between liquidlike and gaslike states. This is seen in the master plot showing a collapse of the data representing the dependence of specific heat on key dynamical parameters in the system for many different paths on the phase diagram. As a result, the observed transition is path independent. We call it a “c” transition due to the c-shaped curve parametrizing the dependence of the specific heat on key dynamical parameters. The c transition has a fixed inversion point and provides a new structure to the phase diagram, operating deep in the supercritical state (up to, at least, 2000 times the critical pressure and 50 times the critical temperature). The data collapse and path independence as well as the existence of a special inversion point on the phase diagram are indicative of either of a sharp crossover or a new phase transition in the deeply supercritical state.

Figure 1

Paths on the phase diagram and pressure and temperature points explored in this paper. Also labeled are the critical point and the state points where the transition at the inversion point at $c_V=1.9$ takes place.

Figure 2

Comparison of (a) viscosities $\eta$ and (b) isochoric specific heat capacities $c_V(k_{\mathrm{B}}=1)$ calculated from simulated trajectories with experimental data from NIST [3]; comparison of viscosities $\eta$ calculated from simulated trajectories along the (c) 10 kbar isobar and (d) 500 K isotherm with experimental data from Abramson [10].

Figure 3

Specific heat $c_v(k_{\mathrm{B}}=1)$ as a function of viscosity $\eta$, calculated along three (a) isobars; (b) isotherms; (c) isochores.

Figure 4

Liquid relaxation time $\tau$ of molecular dynamics trajectories along three (a) isobars; (b) isotherms; (c) isochores.

Figure 5

Specific heat $c_v(k_{\mathrm{B}}=1)$ as a function of relaxation time $\tau$, calculated along three (a) isobars; (b) isotherms; (c) isochores. The solid lines in (c) represent the approach of $c_V$ and $\tau$ to their limiting ideal-gas value $c_V=3/2$ at high temperatures and are meant as guides for the eye.

Figure 6

(a) $c_V$ as a function of the dynamical length, ${\lambda }_d=c\tau$ across nine paths spanning the supercritical state up to $330T_c$ and $8000P_c.k_{\mathrm{B}}=1$. All these paths collapse onto a single curve and undergo a unified dynamic-thermodynamic transition at the path-independent point $c_V=1.88$ and ${\lambda }_d=1\AA$; (b) Divergence in $\frac{d{c}_V}{d{\lambda }_d}$ as a function of $c_V$ at the point $c_V=1.88$. Curves are obtained by fitting $c_V\left({\lambda }_d\right)$ data from all nine supercritical paths.

Figure 7

$c_V$ as a function of $c\tau k_{\mathrm{D}}$ where the curves similarly converge in the liquidlike state at the path-independent point close to $c_V=2$.

Figure 8

Phase diagram showing the inversion points of the c transition corresponding to $c_V\approx 1.9$ in Fig. 6, the FL determined by the VAF criterion [23], the critical point, and the critical isochore.