Fluctuotaxis: Nanoscale directional motion away from regions of fluctuation

Abstract

Regulating the motion of nanoscale objects on a solid surface is vital for a broad range of technologies such as nanotechnology, biotechnology, and mechanotechnology. In spite of impressive advances achieved in the field, there is still a lack of a robust mechanism which can operate under a wide range of situations and in a controllable manner. Here, we report a mechanism capable of controllably driving directed motion of any nanoobjects (e.g., nanoparticles, biomolecules, etc.) in both solid and liquid forms. We show via molecular dynamics simulations that a nanoobject would move preferentially away from the fluctuating region of an underlying substrate, a phenomenon termed fluctuotaxis-for which the driving force originates from the difference in atomic fluctuations of the substrate behind and ahead of the object. In particular, we find that the driving force can depend quadratically on both the amplitude and frequency of the substrate and can thus be tuned flexibly. The proposed driving mechanism provides a robust and controllable way for nanoscale mass delivery and has potential in various applications including nanomotors, molecular machines, etc.

Keywords: atomic fluctuation; mechanical vibration; molecular dynamics; regulating motion; robust driving mechanism.

Fig. 1.

Fluctuotaxis of a sericin molecule within a water droplet on a graphene substrate. (A) Simulation model for molecular dynamics. The sericin molecule is immersed in a water droplet containing 6,800 water molecules. The graphene substrate is 7.4-nm wide and 520-nm long. The imposed transverse vibration has an amplitude of 1.5 Å and a frequency of 0.2 THz. The system temperature is maintained at 300 K. (B) Snapshots of fluctuotaxis. The sericin molecule together with the water droplet is propelled along the wave-propagating direction. (C) Fluctuotaxis displacements of the sericin molecule on graphene substrates with contact angles (θ₀) ranging from 40° to 114°. (The corresponding LJ interaction strengths are 1.1, 1.0, 0.75, and 0.5 times of the original ɛ_CO and ɛ_CH.). (D) Advancing (solid symbols) and receding (open symbols) contact angles of the water droplet during simulations. The data are collected by averaging instantaneous atomic trajectory in every 0.2 ns. (E) Profiles of water droplet during fluctuotaxis on substrates with various wettability.

Fig. 2.

Fluctuotaxis in different systems. (A) Displacements of a sericin molecule (lines) and a graphene flake (Flake I) containing 2,080 atoms (symbols) on a graphene substrate. For comparison, the displacements of the same graphene flake on different substrates of mono- (1L) and multilayered (nL) graphene, h-BN and MoS₂ are depicted in (B1–B3). A lower frequency (0.125 THz) is used in the MoS₂ substrate to avoid fracture due to its lower strength compared to graphene and h-BN. (C) RMSD for the sericin molecule in the sericin–substrate (SS) and SWS at room temperature. RMSD for typical biomolecules [including α-chymotrypsin (ChT), villin headpiece (HP35), and α-helical peptide (Heli-P)] on a graphene substrate are also shown for comparison. The time duration of the sericin molecule and the graphene flake I-III (with configuration parameters shown in Table 1) versus (D) the amplitude and (E) the frequency of the imposed vibration.

Fig. 3.

Mechanism of fluctuotaxis. (A) Schematic diagram of an 8-nm-long graphene flake (blue) on a 520-nm-long substrate (gray) for force analysis. The rigid flake is immobilized on the fully relaxed substrate with an equilibrium distance of ~0.34 nm in the out-of-plane direction. The transverse vibration with an amplitude of 2.5 Å and a frequency of 0.25 THz is imposed on the substrate. The y and d are the distances from a position to the wave source and the center of mass of the flake, respectively. (B) The interlayer vdW energy and the total driving force that experienced by the graphene flake at various positions of substrate. (C) The interlayer vdW energy and forces (a positive value indicates that the force points toward the wave-propagating direction) exerted on the different regions of the flake. (D) Comparison of the total driving force with the difference in edge barriers per unit area. (E) RMSA (solid symbols) and the vibrating frequencies (solid lines) of the graphene substrate. All data are averaged more than 100 vibrating periods after the wave reaches to the flake.

Fig. 4.

Effects of the amplitude and frequency. The system same as that appeared in Fig. 3 is used. The flake is immobilized at a position of y = 50 nm from the source of vibration on the substrate. (A) RMSA of the graphene substrate, (B) Interlayer vdW energy on the rear and front edges of the flake, (C) Distribution of the interlayer vdW energy of the flake, and (D) Total driving force on the flake for the imposed vibration with different amplitudes A₀ and a constant frequency f₀ = 0.25 THz. (E–H) Similar to (A–D) but for the imposed vibration with a constant amplitude A₀ = 2.5 Å and different frequencies f₀.

Fig. 5.

Continuous motion along a loop track via fluctuotaxis. (A) Schematic diagram of the simulation model. A square loop track composed of four stripes of graphene (in yellow), laid on a copper basement (in gray), is used to guide the motion of nanoparticles. Each stripe has a dimension of 6 × 40 nm, and the size of copper basement is 48 × 48 nm. The mechanical vibrations are imposed on the stripes simultaneously to generate the waves along the red arrows. The thermostat is applied on the copper basement to maintain the system at room temperature. (B) The displacements of the graphene flake and sericin molecule versus time under the vibration with a frequency of 0.5 THz and an amplitude of 2.5 Å. The snapshots for the (C1) flake and (C2) sericin motion during the first cycle, with lines indicating the motion trajectories.