Liquid-vapor interface of the Stockmayer fluid in a uniform external field

The effect of a uniform (nonspatially varying) external field on the liquid-vapor interface of the Stockmayer fluid (Lennard-Jones particles embedded with a point dipole) has been investigated by molecular-dynamics simulations. The long-ranged parts of both the dipole and Lennard-Jones interactions are treated using an Ewald summation, which removes the effects of the cutoff. The direction of the field shifts the critical point and interfacial properties in different directions. For an external field parallel to the interface, the critical temperature increases, while for a field applied perpendicular to the interface, it decreases. The effects of the field on surface tension and interfacial width are also investigated. For zero field, dipoles near the liquid-vapor interface show a weak orientation parallel to the interface. For fields parallel to the interface, ordering in the liquid phase is greater than the vapor, while for fields perpendicular to the interface, the opposite is true.

Figure 1

Snapshot of the Stockmayer liquid-vapor interface for (a) ${\mu }^{*}=0.5$, $T^{*}=0.8$, and $E_{\perp }^{*}=10.0$, and for (b) ${\mu }^{*}=0.5$, $T^{*}=1.0$, and $E_{\parallel }^{*}=10.0$. The direction of the external field in relation to the interface is also shown. Dipoles are represented as dual colored spheres, where the dipole points from blue to white.

Figure 2

Conceptual diagram of the polarization that occurs when an external field is applied perpendicular to the interface.

Figure 3

Density profiles of the Stockmayer fluid for ${\mu }^{*}=1.0$, $T^{*}=1.25$ for zero field (black line, middle curve), external field parallel to the interface $E_{\parallel }^{*}=2.0$ (red line, lower curve in liquid phase), and external field perpendicular to the interface $E_{\perp }^{*}=2.0$ (blue line, upper curve in liquid phase). Solid lines represent the data and dashed lines represent a fit of the data using Eq. (4).

Figure 4

Phase coexistence curves of the Stockmayer fluid for (a) $E^{*}=0$ and 2.0 and ${\mu }^{*}=1.0$ and (b) $E^{*}=0$ and 3.2 and ${\mu }^{*}=2.5$.

Figure 5

Shift in critical temperature $\Delta T_{\mathrm{c}}^{*}$ vs field strength $E^{*}$ for Stockmayer fluid at (a) ${\mu }^{*}=0.5$, (b) ${\mu }^{*}=1.0$, and (c) ${\mu }^{*}=2.5$. Black triangles represent simulation results from this work, red squares and diamonds represent simulation and mean-field results, respectively, from Ref. [21], and additional simulation results are also shown as blue circles (Ref. [14]) and green crosses (Ref. [16]). Open triangles, diamonds, and squares represent perpendicular field (i.e., $\Delta T_{\mathrm{c}}^{*}<0)$, while all other symbols represent parallel field.

Figure 6

Relative critical temperature $T_{\mathrm{c}}^E$ vs dimensionless field ${\eta }^E$ for ${\mu }^{*}=0.5$ (circles), ${\mu }^{*}=1.0$ (diamonds), ${\mu }^{*}=2.0$ (squares), and ${\mu }^{*}=2.5$ (triangles). Blue open symbols represent parallel field, and red closed symbols represent perpendicular field. The solid line is a least-squares fit of the data including ${\mu }^{*}\ge 1.0$ with parallel field, ${\mu }^{*}\le 1.0$ with perpendicular field, and the zero-field case. The dashed line is a least-squares fit to the data including ${\mu }^{*}>1.0$ with perpendicular field, ${\mu }^{*}<1.0$ with parallel field, and the zero-field case.

Figure 7

Surface tension vs temperature for ${\mu }^{*}=1.0$ and $E^{*}=0$ and 2.0. Lines are included as a guide for the eye.

Figure 8

Interfacial width ${\Delta }^{*}$ for $A^{*}=100$ vs reduced temperature $T^{*}$ for ${\mu }^{*}=1.0$ and $E^{*}=0$ and 2.0. Lines are included as a guide for the eye.

Figure 9

Average dipole orientation parameter $cos\theta \left(z\right)$ vs position $z$ at $T^{*}=1.0$, for ${\mu }^{*}=1.0$ and $E^{*}=1.0$. Dashed lines are for bulk liquid system and dot-dashed lines are for bulk vapor system. The blue lines (top three lines) are for the parallel field, and the red lines (bottom three lines) are for perpendicular field. For the bulk perpendicular case, the simulation field strength is $E^{*}=1.0/\epsilon$.

Figure 10

Orientation profile $P_2\left(z^{*}\right)$ vs position $z^{*}$ for $E^{*}=0$, ${\mu }^{*}=2.5$, and $T^{*}=2.2$. The dashed line at $P_2\left(z^{*}\right)=0$ is included as a guide for the eye.

Figure 11

Average orientation $cos\theta$ vs external field strength for ${\mu }^{*}=1.0$ and $T^{*}=1.2$ for (a) liquid and (b) vapor phase. The lines are included as a guide for the eye.

Figure 12

Orientation profile of average $cos\theta \left({\rho }^{*}\right)$ vs ${\rho }^{*}$ for $E^{*}=1.0$, ${\mu }^{*}=1.0$, and $T^{*}=1.2$. The lines are included as a guide for the eye.

Figure 13

Liquid orientation for varying size of liquid and vapor regions, with ${\mu }^{*}=1.0$, $T^{*}=1.0$, and $E_{\perp }^{*}=1.0$ with (blue squares) and without (red triangles) the Ewald slab correction. Orientation for a bulk simulation at liquid density with $E^{*}=1.0/\epsilon$ (cf. Fig. 9) is also shown (solid black line).