Simple estimation of thermodynamic properties of Yukawa systems

A simple analytical approach to estimate thermodynamic properties of model Yukawa systems is presented. The approach extends the traditional Debye-Hückel theory into the regime of moderate coupling and is able to qualitatively reproduce thermodynamics of Yukawa systems up to the fluid-solid phase transition. The simplistic equation of state (pressure equation) is derived and applied to the hydrodynamic description of the longitudinal waves in Yukawa fluids. The relevance of this study to the topic of complex (dusty) plasmas is discussed.

Figure 1

Reduced excess energy (in units of $-\Gamma$) as a function of the reduced coupling parameter $\Gamma /{\Gamma }_{\mathrm{melt}}$ in the regime $\kappa \le 1$. Solid curves correspond to our calculation using Eqs. (18) and (19); symbols are the results from MD simulations [11]. Data for $\kappa =0.0$, $0.6$, and $1.0$ are shown. The dashed curve corresponds to the DH approximation in the OCP ($\kappa =0$) limit. The dotted curve is the fit by Eq. (22).

Figure 2

Reduced excess energy (in units of $-\Gamma \kappa /2$) as a function of the reduced coupling parameter $\Gamma /{\Gamma }_{\mathrm{melt}}$ in the regime $\kappa >1$. Curves correspond to our calculation using Eqs. (18) and (19); symbols are the results from MD simulations [11]. Data for $\kappa =2.0$, $3.0$, and $5.0$ are shown.

Figure 3

Reduced excess pressure $p_{\mathrm{ex}}$ as a function of the coupling parameter $\Gamma$ in the DHH approximation. Data for various $\kappa$ are shown. $p_{\mathrm{ex}}$ increases with $\kappa$.

Figure 4

Sketch of the phase diagram of Yukawa systems in the ($\kappa$, $\Gamma$) plane. The curve marks the fluid-solid phase transition as obtained in Ref. [11]. The symbols correspond to the phase states for which the numerical simulations of density waves have been performed. The dispersion relations for the longitudinal waves at these state points are shown in Fig. 5.

Figure 5

Dispersion of the longitudinal waves in Yukawa fluids near freezing. Symbols correspond to the results from numerical experiment [29]. Solid lines are calculated using Eqs. (26, 27, 28). Dashed curves correspond to the dispersion relation (29) with the OCP expression (22) for $u_{\mathrm{ex}}$. The values of $\kappa$ and $\Gamma$ are given in the upper left corner of each figure. For further details see the text.