Impact of Friedel oscillations on vapor-liquid equilibria and supercritical properties in two and three dimensions

We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions ($2\text{D}$)] and bulk phases [three dimensions ($3\text{D}$)]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter $X$ ($0<X<1$). Varying $X$ allows us to control the height of the first Friedel oscillation and to provide a complete characterization of the effect of the metal-like character in the potential on the thermodynamic properties over a wide range of conditions. For $3\text{D}$ systems, we are able to show that the critical parameters exhibit a linear dependence on $X$ and that the loci for the thermodynamic state points, for which the system shows the same compressibility factor or enthalpy as an ideal gas, are two straight lines spanning the subcritical and supercritical regions of the phase diagram for all $X$ values. Reducing the dimensionality to $2\text{D}$ results in a loss of impact of the Friedel oscillation on the critical properties, as evidenced by the virtually constant critical density across the range of $X$ values. Furthermore, our results establish that the straightness of the two ideality lines is retained in $2\text{D}$ and is independent from the height of the first Friedel oscillation in the potential.

Figure 1

Mixed pair potential used in this work for $X=1, X=0.9, X=0.8$, and $X=0.7$.

Figure 2

Logarithm of the grand-canonical partition function $\mathrm{\Theta }(\mu ,V,T)$ and of $Q(N,V,T)$ for $3\text{D}$ systems: (a) Subcritical fluids ($T=0.85$) and (b) Supercritical fluids ($T=2$). Same legend as in Fig. 1.

Figure 3

Examples of number distribution for $X=1$. (Left) Subcritical fluid ($T=1.1$): vapor and liquid peaks at coexistence and peak for the Zeno line. (Right) Supercritical fluid ($T=2.5$): Peak corresponding to the $S_0$ contour, Zeno line, $H_{\text{min}}$ contour, and $H$ line.

Figure 4

(a) Thermodynamic contours in $3\text{D}$ for $X=1$ (same legend as in Fig. 2), with the critical point shown as a filled circle. The same qualitative behavior is observed for all $X$ values. (b) Coexistence curves and critical points (filled circles) for increasing $X$ values in $3\text{D}$ (same legend as in Fig. 1). The critical temperature and the critical density exhibit a linear dependence on $X$.

Figure 5

Zeno lines (a) and $H$ lines (b) for different $X$ values in $3\text{D}$ (same legend as in Fig. 1).

Figure 6

Logarithm of the partition function $\mathrm{\Theta }(\mu ,V,T)$ and of the $Q(N,V,T)$ functions for $2\text{D}$ systems: (a) subcritical fluids ($T=0.41$) and (b) supercritical fluids ($T=1.5$). Same legend as in Fig. 1.

Figure 7

(a) Thermodynamic contours for $X=1$ in $2\text{D}$ (same legend as in Fig. 2), with the critical point shown as a filled circle. The same qualitative behavior is observed for all $X$ values. (b) Coexistence curves and critical points (filled circles) for increasing $X$ values in $2\text{D}$ (same legend as in Fig. 1). The critical temperature exhibit a linear dependence on $X$, while the critical density remains essentially constant.

Figure 8

Zeno lines (a) and $H$ lines (b) for different $X$ values in $2\text{D}$ (same legend as in Fig. 1).