Nanoscale Directional Motion towards Regions of Stiffness

How to induce nanoscale directional motion via some intrinsic mechanisms pertaining to a nanosystem remains a challenge in nanotechnology. Here we show via molecular dynamics simulations that there exists a fundamental driving force for a nanoscale object to move from a region of lower stiffness toward one of higher stiffness on a substrate. Such nanoscale directional motion is induced by the difference in effective van der Waals potential energy due to the variation in stiffness of the substrate; i.e., all other conditions being equal, a nanoscale object on a stiffer substrate has lower van der Waals potential energy. This fundamental law of nanoscale directional motion could lead to promising routes for nanoscale actuation and energy conversion.

Figure 1

A model slider-substrate system. (a) Configuration of a short graphene slider on a long graphene substrate for molecular dynamics simulations. (b) Atoms of the substrate are anchored on an array of springs with linearly graded stiffness along the length direction of the substrate. (c) Stiffness guided nanoscale directional motion, i.e., nanodurotaxis, of an object from the soft side to the hard side of the substrate. (d) A macroscopic object slides down on a curved ramp guided by gravity.

Figure 2

Nanodurotaxis of a 10 nm long slider on a 97 nm long substrate with a linear stiffness gradient. (a) Snapshots of a typical system in which the stiffness gradient $\gamma$ is $0.288\mathrm{nN}/{\mathrm{nm}}^2$ and the stiffness at the midpoint of the substrate $k_{\mathrm{m}}$ is $14.4\mathrm{nN}/\mathrm{nm}$. The displacements and velocities of the slider on different substrates are shown in (b) and (c), respectively.

Figure 3

Nanodurotaxis of a 19 nm long slider on a 48 nm long substrate with stiffness jumps across piecewise homogeneous regions. The displacements (solid lines) and velocities (dot lines) of the slider on substrates with different stiffness jumps are shown in (a). The shuttle behavior of the slider on a substrate with alternate soft or hard ($0.801/2.403$) regions are shown in (b), where the displacement is measured from the center of the hard region.

Figure 4

Interlayer interactions between the slider and the substrate. (a) The interlayer vdW potential and the standard deviations of the vibration magnitudes of substrate atoms outside (diamond) and within (square) the contact area against the spring stiffness. (b) The interlayer vdW forces (a positive value indicates that the force points towards the hard side) exerted on different regions of the sliders for the system of a 19 nm long slider on a 48 nm long substrate with a stiffness jump ($0.801/4.005$) across piecewise homogeneous regions and for the system of a 10 nm long slider on a 97 nm long substrate with a stiffness gradient $0.096\mathrm{nN}/{\mathrm{nm}}^2$ and a midpoint spring stiffness of $4.8\mathrm{nN}/\mathrm{nm}$. In both cases, the average velocity of the slider is about $8.8\mathrm{nm}/\mathrm{ns}$.