Capillary condensation and orientational ordering of confined polar fluids

The phase behavior and the orientational structure of polar model fluids confined to slit pores is investigated by means of density functional theory in a modified mean-field approximation. We focus on fluid states and further assume a uniform number density throughout the pore. Our results for spherical dipolar particles with additional van der Waals–like interactions (Stockmayer fluids) reveal complex fluid-fluid phase behavior involving condensation and first- and second-order isotropic-to-ferroelectric phase transitions, where the ferroelectric ordering occurs parallel to the confining walls. The relative importance of these phase transitions depends on two “tuning” parameters, that is the strength of the dipolar interactions (relative to the isotropic attractive ones) between fluid particles, and on the pore width. In particular, in narrow pores the condensation transition seen in bulk Stockmayer fluids is entirely suppressed. For dipolar hard spheres, on the other hand, the impact of confinement consists in a decrease of the isotropic-to-ferroelectric transition temperatures. We also demonstrate that the local orientational structure is inhomogeneous and anisotropic even in globally isotropic systems, in agreement with computer simulation results.

Figure 1

Phase diagram of a bulk Stockmayer fluid at $m^{*}=1.5$ in the density-temperature plane. Gray regions indicate two- or three-phase coexistence regions, and the dashed line stands for a line of critical points. For further explanation of the lines and symbols, see main text.

Figure 2

Density-temperature phase diagrams of confined Stockmayer fluids $(m^{*}=1.5)$ at $L_z^{*}=10$ (solid/dashed lines) and $L_z^{*}=4$ (dotted lines). The crosses indicate the critical and tricritical temperatures of the corresponding bulk system (see Fig. 1).

Figure 3

Phase diagrams for bulk and confined Stockmayer fluids at $m^{*}=1.5$ in the chemical potential-temperature plane. The solid lines, crosses, and squares indicate first-order transition lines corresponding to the bulk fluid $L_z^{*}=10$ and $L_z^{*}=4$. Dashed lines denote the lines of IF-FF critical points.

Figure 4

Phase diagram of a bulk Stockmayer fluid at $m^{*}=1.65$ in the density-temperature plane. Symbols as in Fig. 1.

Figure 5

Density-temperature phase diagrams of confined Stockmayer fluids at $m^{*}=1.65$ and $L_z^{*}=10$ (a), $L_z^{*}=4$ (b). Crosses indicate the critical and tricritical temperatures of the corresponding bulk system (see Fig. 4).

Figure 6

Same as Fig. 3 but for $m^{*}=1.65$.

Figure 7

Phase diagram of the bulk DHS fluid (solid lines) and a corresponding confined system at $L_z^{*}=4$ (dotted lines) in the density-temperature plane.

Figure 8

Phase diagrams of bulk and confined DHS fluids in the chemical potential-temperature plane. The solid, dot-dashed, and dotted lines indicate the IF-FF first-order transition line corresponding to the bulk fluid, $L_z^{*}=10$ and $L_z^{*}=4$. Dashed lines denote the lines of IF-FF critical points.

Figure 9

Components of the local polarization in the $x$ direction (solid line) and $y$ direction (dotted) within the ferroelectric phase of a confined Stockmayer fluid at $m^{*}=1.5$ and $L_z^{*}=10$ ($\tau =1.68$, ${\rho }^{*}=0.879$).

Figure 10

Local order parameter $Q_{zz}\left(z\right)$ within the ferroelectric phase of a confined Stockmayer fluid (same parameters as in Fig. 9).

Figure 11

Local order parameter $Q_{zz}\left(z\right)$ within the isotropic gas phase (solid line, ${\rho }^{*}=0.042$) and the isotropic liquid phase (dotted line, ${\rho }^{*}=0.44$) of a confined Stockmayer fluid at $m^{*}=1.5$, $L_z^{*}=10$, and $\tau =1.68$.

Figure 12

Local order parameter $Q_{zz}\left(z\right)$ within the isotropic liquid phase $({\rho }^{*}=0.477)$ of a confined Stockmayer fluid at $m^{*}=1.5$, $L_z^{*}=10$, and $\tau =1.55$.