Curvature effect on the surface diffusion of silver adatoms on carbon nanotubes: Deposition experiments and numerical simulations

The cluster formation of silver adatoms on carbon nanotubes (CNTs) is investigated to infer the curvature effect on surface diffusion. By analyzing the cluster density as a function of the deposition time $t$ for different diameters $d_c$ of CNTs, we obtain the scaling form for describing the curvature effect on surface diffusion in the first-order approximation. We find that the curvature effect on the surface diffusion can well be described by using the relation between the deposition time $t$ and the scaled deposition time $\tau$ in the form of $\tau \sim t{d}_c^{-z}$, with $z$ being the exponent characterizing geometric properties of CNTs and the nanotube helicity. The value of $z$ for the armchair-type CNT is larger than those for the zig-zag type and the chiral-type CNTs. The scaling form is further demonstrated and verified by numerical simulations, and is explained by the two-dimensional random walk model. Our study may provide a potential application of determining the armchair-type single-wall CNT from measuring the value of $z$.

Figure 1

Sequential TEM images of the formation of Ag clusters on the CNTs at two different temperatures. Images in the top row were taken at room temperature $296\mathrm{K}$ (heating current $I_h=0$) and those in the bottom at $503\mathrm{K}$ $(I_h=0.17\mathrm{A})$. From the left frame to right, the images were taken with time at about 5, 15, 35, and $55\min$ after Ag deposition. The scale bars are $5\mathrm{nm}$ in length.

Figure 2

(Color online) Cluster density $\eta$ as a function of $t$ for (a) different $d_c$ and $I_h=0$, and (b) different $d_c$ and $I_h\ne 0$. The curve of graphite shown in (a) is for comparison.

Figure 3

(Color online) Schematic drawing for typical honeycomb structures of (a) the zig-zag type ($a$ connects to $b$), (b) the armchair-type ($a$ connects to $b$), and (c) the chiral-type ($a^{\prime }$ connects to $b$) CNTs. (d) The relation between components of the diffusion rate and the orientation of the CNT.

Figure 4

(Color online) The normalized cluster density $\overline{\eta }$ as (a) a function of $\tau$ and $d_c$, and (b) a function of $\tau$, $d_c$, and $I_h$.

Figure 5

(Color online) Simulations for (a) $I_h=0$ and (b) $I_h\ne 0$. The same specifications of the CNTs as those in experiments (see Table ) and $z=0.5$ have been used in these simulations.

Figure 6

(Color online) Simulations for different ${\rho }^{\prime }={\rho }_{\Vert }∕{\rho }_{\perp }$ ratios, and $\tau$ is rescaled with (a) $z=0.5$ for all ${\rho }^{\prime }$, and (b) $z=0.75$ for ${\rho }^{\prime }=0$, $z=0.7$ for ${\rho }^{\prime }=0.1$, $z=0.5$ for ${\rho }^{\prime }=0.45$, and $z=0.5$ for ${\rho }^{\prime }=1.0$.