Repulsive forces between neutral surfaces induced by adatoms

Charge neutral objects usually attract each other in the nanoscale and it is actually not favorable for nanoscale manipulation as attractive forces tend to make objects stick together. It would be highly desirable if the sign of the force between charge neutral objects could be controlled by surface chemical modification. In this work, we show that the static electric field generated by a submonolayer of chemisorbed adatoms can be used to control the sign of the forces between neutral surfaces. The local density functional method combined with an electrostatic stress tensor approach is used to study the forces between tungsten surfaces with stripes of noble metal atoms adsorbed on top. When the metal substrate is partially covered by the adatom stripes, the electric field generated by the local variation of the work function can extend into the vacuum, which in turn can attract or repel other surfaces in close vicinity. Chemisorption may hence offer a good strategy to manipulate nanoscale objects.

Figure 1

Schematic picture of Au/W slab structure. The solid red circles denote Au atoms and black open circles represent W atoms. The black dashed lines mark the primitive supercell boundaries in the calculation. The distance between these slabs is $\mathrm{\Delta }d$. The numbers of surface W atoms and Au adatoms along the $x$ direction are represented by $N_{\mathrm{W}}=12$ and $N_{\mathrm{Au}}=6$, respectively. The $N_{\mathrm{shift}}=0$, 2, 4, and 6 cases are shown in panels (a–d), respectively. (e) The electrostatic forces per unit area calculated by the surface integral of the electrostatic stress tensor for Au/W slab structure with $N_{\mathrm{W}}=12,N_{\mathrm{Au}}=6$, and $\mathrm{\Delta }d=13\AA$ as a function of $N_{\mathrm{shift}}$ are shown by open black circles. The negative (positive) number means repulsive (attractive) forces between these slabs. The dotted line is a guide to the eye.

Figure 2

The left panels show the electrostatic potential in units of eV (color map) and the corresponding electric field (vector field) for $N_{\mathrm{shift}}=0$, 1, 2, 3, 4, 5, and 6 are shown in the left panel of (a–g), respectively. The zero of the $z$ axis is chosen to be at the middle of the vacuum. The units in the $x$ axis and $z$ axis are in angstroms. The right panels show the direction and the relative magnitude of the electrostatic force density calculated at the center of the vacuum gap $\left(z=0\right)$. The system parameters are $N_{\mathrm{W}}=12,N_{\mathrm{Au}}=6$, and $\mathrm{\Delta }d=13\AA$. If the force density vector points up (down), the force between the slabs is attractive (repulsive). Panel (a) shows that for the symmetric $N_{\mathrm{shift}}=0$ configuration, the repulsive force is mainly localized at the edge of the Au stripe. Panel (g) shows that for the asymmetric $N_{\mathrm{shift}}=6$ configuration, the attractive force is strongest in the middle of the stripe.

Figure 3

The electrostatic repulsive forces per unit area for the $N_{\mathrm{Au}}=3,N_{\mathrm{Au}}=5$, and $N_{\mathrm{Au}}=7$ slab structures as a function of $\mathrm{\Delta }d$ are shown by black, red, and green lines, respectively, for $N_{\mathrm{shift}}=0$. We fix $N_{\mathrm{W}}=2N_{\mathrm{Au}}$ (i.e., half the W surface is covered by Au). The atomic structure in (a) is chosen at the ideal position and the atomic structures are fully relaxed in (b). The line between the points is a guide to the eye.

Figure 4

(a) The electrostatic repulsive forces per unit area for Au/W and Ag/W slab structures as a function of $N_{\mathrm{Au}\left(\mathrm{Ag}\right)}$ for the fixed ratio $N_{\mathrm{W}}=2N_{\mathrm{Au}\left(\mathrm{Ag}\right)}$ are shown by black and red dots, respectively. (b) The electrostatic forces for the Au/W slab structure for $N_{\mathrm{w}}=12$ as a function of $N_{\mathrm{Au}}$ are shown by black dots. The filled and open circles in both figures denote unrelaxed and relaxed results, respectively. The used parameters are $\mathrm{\Delta }d=13\AA$ and $N_{\mathrm{shift}}=0$. The line between the points is a guide to the eye.

Figure 5

Plot of the electrostatic potential in units of eV (color map) and the corresponding electric field (vector field) for $N_{\mathrm{Au}}=2$, 4, 6, and 8 are shown in the left panel of (a–d), respectively. The zero of the $z$ axis is chosen to be at the middle of the vacuum. The units in the $x$ axis and $z$ axis are in angstroms. The right panels show the direction and the relative magnitude of the electrostatic force density calculated at the center of the vacuum region. The system parameters are $N_{\mathrm{W}}=12,N_{\mathrm{shift}}=0$, and $\mathrm{\Delta }d=13\AA$.

Figure 6

The relative total energy (using $\mathrm{\Delta }d=20\AA$ as a reference), relative exchange-correlation energy, relative Coulomb energy, the force calculated by the gradient of the Coulomb energy, and the force calculated by the surface integral of the electrostatic stress tensor as a function of interslab distance for $N_{\mathrm{shift}}=5$ and $N_{\mathrm{shift}}=0$. The system parameters are $N_{\mathrm{Au}}=5$ and $N_{\mathrm{W}}=2N_{\mathrm{Au}}$.

Figure 7

Picture of (a) side view and (b) top view of relaxed Au/W slab structure with $N_{\mathrm{W}}=12,N_{\mathrm{Au}}=6,N_{\mathrm{shift}}=0$, and $\mathrm{\Delta }d=9\AA$. The solid red circles denote Au atoms and black solid gray circles represent W atoms. The black lines mark the primitive supercell boundaries in the calculation.