Phase diagrams in the lattice restricted primitive model: From order-disorder to gas-liquid phase transition

The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range nearest neighbor (NN) repulsive interactions has been studied by grand canonical Monte Carlo simulations. We obtain a rich phase behavior as the NN strength is varied. In particular, the phase diagram is very similar to that of the continuum RPM for high NN strength. Specifically, we have found both gas-liquid phase separation, with associated Ising critical point, and a first-order liquid-solid transition. We discuss how the line of continuous order-disorder transitions present for the low NN strength changes into continuum-space behavior as one increases the NN strength and compare our findings with recent theoretical results by Ciach and Stell [Phys. Rev. Lett. 91, 060601 (2003)].

Figure 1

Two-dimensional projection of the three-dimensional lattice structure used in our simulations. In addition to the electrostatic potential, a charged particle in site 0 will be affected by a repulsion with the other particles on the first nearest neighbor sites (1, 2, 3, and 4, plus two more off the plane). For the second nearest neighbor sites (5, 6, 7, and 8, and the corresponding off-plane positions) just the electrostatic potential is considered.

Figure 2

Isotherms calculated in grand canonical simulations $(L^{*}=12)$ for different repulsive strength $J^{*}=$ (a) 0.01, (b) 0.03, (c) 0.05, and (d) 0.06. The dashed line marks the approximated location of the order-disorder phase transition. The solid lines are just guides to the eye. Statistical uncertainties are smaller than the symbol size.

Figure 3

(Color online) Coexisting phases generated for $J^{*}=0.01$. The temperature is $T^{*}=0.11$ and the densities are ${\rho }^{*}=$ (a) 0.19 and (b) 0.93.

Figure 4

Phase diagram as a function of the repulsive strength $J^{*}$. Open circles from top to bottom are for $J^{*}=0.01$, 0.03, 0.05, 0.06, and 0.3, respectively. The $\zeta =1$ lattice RPM results of Panagiotopoulos and Kumar [17] $(J^{*}=0)$ are shown as filled circles. Tricritical points $(\times )$ were obtained using a linear extrapolation (dotted lines) of coexistence lines, as expected for $d=3$ tricriticality. The critical point $(+)$ for $J^{*}=0.3$ was estimated from finite-size scaling using $L^{*}=15$. Statistical uncertainties are smaller than the symbol size.

Figure 5

(Color online) Isotherms calculated in grand canonical simulations $(L^{*}=12)$ for different repulsive strength $J^{*}=$ (a) 0.065, (b) 0.07, and (c) 0.1. Statistical uncertainties are smaller than the symbol size.

Figure 6

(Color online) Configurations generated in the intermediate density region for (a) $J^{*}=0.07$, $T^{*}=0.04016$, and ${\rho }^{*}=0.17$ and (b) $J^{*}=0.1$, $T^{*}=0.06$, and ${\rho }^{*}=0.5$. Both boxes have edge length $L^{*}=12$.

Figure 7

(Color online) Density versus chemical potential for $J^{*}=0.3$. Statistical uncertainties are smaller than the symbol size.

Figure 8

(Color online) Ordering operator distribution for $\zeta =1$ and $J^{*}=0.3$, for $L^{*}=12$ (triangles), 15 (squares), and 18 (circles). The $L^{*}=15$ and 18 curves have been displaced vertically for visual clarity. Lines are for the three-dimensional Ising universality class (data courtesy of N. B. Wilding).

Figure 9

(Color online) Gas-liquid coexistence curves for the lattice RPM supplemented by a nearest neighbor repulsive strength $J^{*}=0.3$, for $L^{*}=12$ (squares), 15 (triangles), and 18 (diamonds). The continuum RPM curves (circles) were taken from the finely discretized simulations from Panagiotopoulos and Kumar [17]. Statistical uncertainties smaller than the symbol size have been omitted.

Figure 10

(Color online) Typical configuration observed in the high-density region for $J^{*}=0.3$, $T^{*}=0.07$, and ${\rho }^{*}=0.75$. Simulation box edge length is $L^{*}=12$.