Vapor-liquid phase behavior of a size-asymmetric model of ionic fluids confined in a disordered matrix: The collective-variables-based approach

We develop a theory based on the method of collective variables to study the vapor-liquid equilibrium of asymmetric ionic fluids confined in a disordered porous matrix. The approach allows us to formulate the perturbation theory using an extension of the scaled particle theory for a description of a reference system presented as a two-component hard-sphere fluid confined in a hard-sphere matrix. Treating an ionic fluid as a size- and charge-asymmetric primitive model (PM) we derive an explicit expression for the relevant chemical potential of a confined ionic system which takes into account the third-order correlations between ions. Using this expression, the phase diagrams for a size-asymmetric PM are calculated for different matrix porosities as well as for different sizes of matrix and fluid particles. It is observed that general trends of the coexistence curves with the matrix porosity are similar to those of simple fluids under disordered confinement, i.e., the coexistence region gets narrower with a decrease of porosity and, simultaneously, the reduced critical temperature $T_c^{*}$ and the critical density ${\rho }_{i,c}^{*}$ become lower. At the same time, our results suggest that an increase in size asymmetry of oppositely charged ions considerably affects the vapor-liquid diagrams leading to a faster decrease of $T_c^{*}$ and ${\rho }_{i,c}^{*}$ and even to a disappearance of the phase transition, especially for the case of small matrix particles.

Figure 1

Vapor-liquid phase diagrams at the fixed size ratios (a) ${\lambda }_0=1.5$, (b) ${\lambda }_0=2.0$, and (c) ${\lambda }_0=3.0$ [see Eq. (15)]. In each case, data are shown for different ratios of ion size asymmetry $\lambda$ as indicated in the legends and for different matrix porosities ${\varphi }_0$. At the fixed $\lambda$, ${\varphi }_0=1$, 0.95, 0.9, and 0.85 (from top to bottom). The bulk case (${\varphi }_0=1$) is presented for comparison. Temperature $T^{*}$ and the ion density ${\rho }_i^{*}$ are in dimensional reduced units defined in Eqs. (32).

Figure 2

Dependence of the critical temperature $T_c^{*}$ on the size of matrix particles ${\lambda }_0$ [see Eq. (15)] for different matrix porosities: (a) ${\varphi }_0=0.85$, (b) ${\varphi }_0=0.9$, and (c) ${\varphi }_0=0.95$. In each case, data are shown for different values of the ion size ratio $\lambda$.

Figure 3

Dependence of the critical temperature $T_c^{*}$ on the ion size ratio $\lambda$ at the fixed size ratios (a) ${\lambda }_0=1.5$, (b) ${\lambda }_0=2.0$, and (c) ${\lambda }_0=3.0$ [see Eq. (15)]. In each case, data are for different values of the matrix porosity as indicated in the legends. Open symbols denote the results obtained in this study using the CV approach, filled triangles are MSA results [20], and filled circles denote simulation results [14].

Figure 4

Dependence of the critical density ${\rho }_{i,c}^{*}$ on the ion size ratio $\lambda$ at the fixed size ratios (a) ${\lambda }_0=1.5$, (b) ${\lambda }_0=2.0$, and (c) ${\lambda }_0=3.0$ [see Eq. (15)]. In each case, data are for different values of the matrix porosity as indicated in the legends. Open symbols denote the results obtained in this study using the CV approach and filled triangles are MSA results [20].