Revealing the supercritical dynamics of dusty plasmas and their liquidlike to gaslike dynamical crossover

Dusty plasmas represent a powerful platform to study the collective dynamics of strongly coupled systems with important interdisciplinary connections to condensed matter physics. Due to the pure Yukawa repulsive interaction between dust particles, dusty plasmas do not display a traditional liquid-vapor phase transition, perfectly matching the definition of a supercritical fluid. Using molecular dynamics simulations, we verify the supercritical nature of dusty plasmas and reveal the existence of a dynamical liquidlike to gaslike crossover which perfectly matches the salient features of the Frenkel line in classical supercritical fluids. We present several diagnostics to locate this dynamical crossover spanning from local atomic connectivity, shear relaxation dynamics, velocity autocorrelation function, heat capacity, and various transport properties. All these different criteria well agree with each other and are able to successfully locate the Frenkel line in both 2D and 3D dusty plasmas. In addition, we propose the unity ratio of the instantaneous transverse sound speed $C_T$ to the average particle speed ${\overline{v}}_p$, i.e., $C_T/{\overline{v}}_p=1$, as a diagnostic to identify this dynamical crossover. Finally, we observe an emergent degree of universality in the collective dynamics and transport properties of dusty plasmas as a function of the screening parameter and dimensionality of the system. Intriguingly, the temperature of the dynamical transition is independent of the dimensionality and it is found to always be 20 times of the corresponding melting point. Our results open a path for the study of single particle and collective dynamics in plasmas and their interrelation with supercritical fluids in general.

Figure 1

A putative phase diagram for dusty plasmas as a function of the coupling parameter $\mathrm{\Gamma }$ and the screening parameter $\kappa$. The solid blue line indicates the first-order solid-liquid phase transition. The dashed red line refers to a possible dynamical crossover in the supercritical regime which is the subject of this work.

Figure 2

Specific heat $c_V$ for 2D and 3D dusty plasmas as a function of the reduced coupling strength $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m$ for different values of the screening parameter $\kappa$. Following the arguments in [8, 9] on the disappearance of propagating shear waves, the liquidlike and gaslike transition occurs when $c_V^{2\mathrm{D}}=1.5$ and $c_V^{3\mathrm{D}}=2$ for 2D and 3D dusty plasmas, respectively. Independently of the number of dimensions, this occurs at $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.05$, which is indicated by the vertical dashed line. The horizontal dotted line corresponds to the value 0.5.

Figure 3

Calculated normalized velocity autocorrelation function (VACF) $C_v\left(t\right)$ for 2D (a) and 3D (b) fluid dusty plasmas with $\kappa =1$ and different values of the reduced coupling strength $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m$. The black lines correspond to the critical value ${\gamma }_c=0.05$.

Figure 4

Local atomic connectivity time ${\tau }_{LC}$ and shear stress relaxation time ${\tau }_M^{\mathrm{ex}}$ multiplied with the Einstein frequency ${\omega }_E$ for various conditions of 2D (a) and 3D dusty plasmas (b).

Figure 5

The ratio of the instantaneous transverse sound speed $C_T$ to the average particle speed ${\overline{v}}_p$ for various conditions in 2D and 3D dusty plasmas. The vertical dashed line indicates the location of the Frenkel line as derived from the specific heat and the other diagnostics above.

Figure 6

Obtained phase diagrams for 2D (a) and 3D (b) dusty plasmas. For both 2D and 3D dusty plasmas, the melting point ${\mathrm{\Gamma }}_m$ for the solid-liquid phase transition (solid blue curves) is obtained from [59, 60]. The dashed line indicates the location of the dynamical Frenkel crossover, which is universally given by $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.05$.

Figure 7

Obtained normalized self-diffusion coefficient $D$ (a) and the corresponding logarithmic derivative $d\left[ln(D/\left(n^{-\frac{1}{3}}{\overline{v}}_p\right))\right]/d\left[ln(\mathrm{\Gamma }/{\mathrm{\Gamma }}_m)\right]$ (b) for our 3D dusty plasma simulations, as well as those performed in [68]. The dashed line indicates the critical line, $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.05$, as probed by other diagnostics.

Figure 8

The normalized shear viscosity $\eta$ for 2D and 3D dusty plasmas as a function of the coupling parameter $\mathrm{\Gamma }$ varies from our MD simulations. The original viscosity results for 3D Yukawa fluids and one component plasmas reported in [69, 70] are also plotted here for comparison. The minimum of the normalized shear viscosity always occurs at $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.05$, as shown by the dashed line.

Figure 9

The normalized thermal conductivity for 3D Yukawa fluids and 3D one-component plasmas as the coupling parameter $\mathrm{\Gamma }$ varies. The corresponding original data are reported in [71, 72]. The minimum of the normalized thermal conductivity always occurs at $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.05$, as indicated by the dashed line.