Effect of an external field on capillary waves in a dipolar fluid

The role of an external field on capillary waves at the liquid-vapor interface of a dipolar fluid is investigated using molecular dynamics simulations. For fields parallel to the interface, the interfacial width squared increases linearly with respect to the logarithm of the size of the interface across all field strengths tested. The value of the slope decreases with increasing field strength, indicating that the field dampens the capillary waves. With the inclusion of the parallel field, the surface stiffness increases with increasing field strength faster than the surface tension. For fields perpendicular to the interface, the interfacial width squared is linear with respect to the logarithm of the size of the interface for small field strengths, and the surface stiffness is less than the surface tension. Above a critical field strength that decreases as the size of the interface increases, the interface becomes unstable due to the increased amplitude of the capillary waves.

Figure 1

(a) Snapshot of the Stockmayer liquid-vapor system with $E^{*}=0$. Zoomed-in snapshots of the liquid-vapor interface with (b) $E_{\parallel }^{*}=2.2$, (c) $E^{*}=0$, and (d) $E_{\perp }^{*}=2.2$. $L^{*}=20$ in all snapshots.

Figure 2

(a) Interfacial width squared ${\mathrm{\Delta }}^2$ as a function $ln\left(L^{*}\right)$ for varying external field strengths applied parallel to the interface, $E_{\parallel }^{*}$, for $E_{\parallel }^{*}$ values where $E_{\parallel }^{*}=0$ (black circles), $E_{\parallel }^{*}=0.5$ (red squares), $E_{\parallel }^{*}=1$ (blue diamonds), $E_{\parallel }^{*}=2$ (green upward triangles), $E_{\parallel }^{*}=4$ (orange downward triangles), and $E_{\parallel }^{*}=10$ (violet sideways triangles). The lines are linear fits of the data. (b) Slope of ${\mathrm{\Delta }}^2$ vs $ln\left(L^{*}\right)$ as a function of $E_{\parallel }^{*}$. The inset emphasizes the plateau of the slope at very high $E_{\parallel }$ values. (c) ${\gamma }^{*}$ (black circles) and ${\kappa }^{*}$ (red squares) as a function of $E_{\parallel }^{*}$.

Figure 3

Interfacial width squared as a function of $ln\left(L^{*}\right)$ for varying $E_{\perp }^{*}$ for $E_{\perp }^{*}=0$ (black circles), $E_{\perp }^{*}$ = 0.5 (red squares), $E_{\perp }^{*}$ = 1 (blue diamonds). The lines are linear fits to the data. For $E_{\perp }^{*}=1$, the solid line is a linear fit for $L^{*}\le 40$.

Figure 4

Visualization of dipolar liquid-vapor system for varying $E_{\perp }^{*}$ and $L^{*}$ values. Each snapshot is at $t=10000\tau$. Every atom is colored red or blue if $cos\theta$ is below or above 0.3, respectively, where $\theta$ is the angle between the dipole moment and the $z$ axis. $cos\theta =1$ means the dipole is aligned parallel with the field, while $cos\theta =0$ means the dipole is aligned perpendicular to the field.

Figure 5

Stability map of liquid-vapor phase for external electric field applied perpendicular to the interface, $E_{\perp }^{*}$, as a function of the interface length, $L^{*}$. The red $\times$'s and blue circles denote unstable and stable state points, respectively. The black line is an approximate phase boundary of the critical value of $E_{\perp }^{*}$ as a function of $L^{*}$.