Trajectory fluctuations accompanying the manipulation of spherical nanoparticles

We relate the frictional forces acting on spherical nanoparticles pushed by a scanning probe tip on a flat surface to the trajectories of the particles. Based on a simple collisional model, we predict that the average direction of motion of the nanoparticles is almost independent of the friction force, whereas the fluctuations of the particle directions are inversely proportional to friction. The model is applied to interpret the trajectory fluctuations and the apparent discontinuities observed when spherical gold particles are manipulated on a silicon-oxide surface by atomic force microscopy.

Figure 1

Simulated trajectories of a nanosphere pushed by an AFM tip in tapping mode. The center of the tip follows the horizontal lines, which are separated by a distance $b=15\text{nm}$. The sum of the radii of the sections of tip and particle (at their contact point) is $R=35\text{nm}$ and the displacement of the particle after collision is (a) $d=2\text{nm}$ and (b) 20 nm. The black dots represent the particle position at the end of each scan line.

Figure 2

(a) Average angle of deflection and (b) fluctuations of the trajectories of spherical particles plotted as a function of the “mean path” $d$ of the nanoparticles. The parameters $R$ and $b$ have the same values as in Fig. 1.

Figure 3

(a) Forward and (b) backward topography images showing the trajectories of gold nanospheres pushed by an AFM tip on a silicon surface in tapping mode (frames size: $3.85\times 2.65\mu {\text{m}}^2$). The particles have a radius of 25 nm and the distance between consecutive scan lines is $b=7.8\text{nm}$.

Figure 4

Statistic distribution of the discontinuities in the trajectories of the three particles enhanced in Fig. 4a. The average value of the discontinuities is 20.6 nm.