www.nature.com/scientificreports OPEN Locomotion of the ­C60‑based nanomachines on graphene surfaces Seyedeh Mahsa Mofdi1, Hossein Nejat Pishkenari2*, Mohammad Reza Ejtehadi3 & Alexey V. Akimov4 We provide a comprehensive computational characterization of surface motion of two types of nanomachines with four C60 “wheels”: a fexible chassis Nanocar and a rigid chassis Nanotruck. We study the nanocars’ lateral and rotational difusion as well as the wheels’ rolling motion on two kinds of graphene substrates—fexible single‑layer graphene which may form surface ripples and an ideally fat graphene monolayer. We fnd that the graphene surface ripples facilitate the translational difusion of Nanocar and Nanotruck, but have little efect on their surface rotation or the rolling of their wheels. The latter two types of motion are strongly afected by the structure of the nanomachines instead. Surface difusion of both nanomachines occurs preferentially via a sliding mechanism whereas the rolling of the “wheels” contributes little. The axial rotation of all “wheels” is uncorrelated. Natural molecular machines are in the heart of the cellular machinery of living organisms, performing com- plex vital functions, and transferring materials with high efciency 1–3. Tese biomolecular systems inspired the development of artifcial machines that function at the molecular level 4,5. Te widespread function of the controlled molecular motion in fundamental natural processes suggests that notable rewards can be gained by improvements of synthetic molecular machines6,7. Nanocars constitute one example of artifcial molecular machines with chassis, axles, and wheels designed for nanoscale transport on various surfaces8,9. Understand- ing the molecular motion on surfaces is essential for controlling the dynamics and functioning of molecular machines10. In particular, one of the long-standing questions to address is the relationship between the design of nanomachines and their difusion properties11,12. Synthetic chemists suggested a variety of structural designs intended to increase the mobility of nanocars on surfaces13,14. Tour and colleagues synthesized nanocars specifcally for the transportation of other molecules. Tey built a variety of nanocars that consisted of chassis and wheels. Te spherical shape and stability of Buck- minsterfullerene, C60, motivated them to use fullerene moieties as the frst types of wheels for such Nanocars and Nanotrucks15–18. A number of computational studies of nanocars’ motion on a variety of substrates were reported in the past, including C60-based Nanocars and Nanotrucks on metal surfaces using either the rigid- body19–22 or all-atomic23,24 molecular dynamics (MD) methods. Nemati and co-workers investigated the role of 25 26 27 vacancies , impurities , and step-like surface defects to control the difusion of C60 and C60-based nanocars. Lavasani’s group28,29 demonstrated how the chassis structure was afecting the difusive motion of carborane- wheeled nanocars on a gold surface. In the past decade, all-carbon-based materials such as few-layers graphene, graphyne, carbon nanotubes, or graphene nanoribbons have been recognized for their unique electronic and structural properties 30, making them promising materials for a wide range of applications. In particular, graphene can be considered a potential surface for nanocar operation in nanoscale molecular transporting applications. Such potential applications recently stimulated studies of nanocars on such all-carbon based material surfaces. Ejtehadi and co-workers31,32 studied 33 34 the difusive motion of C60 on graphene and on a variety of graphyne structures . Savin et al. characterized 35 the thermally-induced difusion of C60 fullerene on graphene nanoribbons. Jafary-Zadeh et al. created a trans- 36 porting pathway on graphene to confne the difusive motion of C 60. Ganji et al. theoretically investigated the motion of a carborane-wheeled nanocar on graphene and graphyne surfaces using the density functional theory. 1Institute for Nanoscience and Nanotechnology (INST), Sharif University of Technology, 14588-89694 Tehran, Iran. 2Mechanical Engineering Department, Sharif University of Technology, 11155-9567 Tehran, Iran. 3Department of Physics, Sharif University of Technology, 11155-9161 Tehran, Iran. 4Department of Chemistry, University at Bufalo, State University of New York, Bufalo 14260-3000, USA. *email: [email protected] Scientifc Reports | (2021) 11:2576 | https://doi.org/10.1038/s41598-021-82280-7 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1. Atomic structure of Nanocar with Flexible chassis, size of 3 × 4 nm2, and 3 atom types (lef side); and Nanotruck with Rigid chassis, size of 2 × 3 nm2, and 4 atom types (right side). Color codes: tan—sp2 and sp3 carbon, (C); teal—sp carbon (C); purple—hydrogen (H); green—nitrogen (N). Te structures are visualized by VMD44. Figure 2. Representation of the four types of molecule/substrate systems used in the present work. Fixed atoms are demonstrated in gray color. System type 1 (NC/SLG), Nanocar (NC) on the single-layer graphene substrate where long-range ripples of graphene can be observed. System type 2 (NC/FLG), all substrate atoms are kept fxed. System type 3 (NT/SLG), Nanotruck (NT) on the single-layer graphene substrate where long-range ripples of graphene can be observed. System type 4 (NT/FLG), all substrate atoms are kept fxed. Te structures are visualized by VMD44. Monolayers and few-layers of graphene are not fat and exhibit a wavy morphology of the surface, with ripples and out-of-plane deformations 37. As observed by the scanning tunneling microscopy, the thermally- induced ripples in graphene form standing waves that evolve erratically 38 Such ripple waves could in principle afect the motion of nanocars due to occasional variation of the contact level and interlock efects to hinder 39 molecule translation . Although several works reported studies of the motion of a single molecule (e.g. C 60) on graphene32,34,40–42, the dynamics of nanocars on the fexible graphene surface that can form ripples has not been investigated yet. Furthermore, little work has been done to delineate the role of the chassis rigidity in the surface dynamics of nanomachines. To the best of our knowledge, no such studies have been reported for nanomachines moving of graphene surfaces. In this work, we study several efects that can control the dynamics of nanomachines on graphene surfaces: (1) the role of substrate fexibility; (2) the role of the chassis fexibility. We do this by comparing the results of all-atomic molecular dynamics in a variety of atomistic models. To examine the frst efect, we consider the motion of nanocars on single-layer graphene (SLG) and frozen layer graphene (FLG) surfaces. To examine the second efect, we choose two nanocars with four C 60 wheels in each, but diferent in their chassis rigidity: the Nanocar and Nanotruck. Computational methodology 18,43 We study the motion of two types of previously synthesized fullerene-based machines with C60 wheels (Fig. 1): (a) a fexible Nanocar (NC, C310H34), a 3 × 4 nm molecule; and (b) a rigid chassis Nanotruck (NT, C282H18N4) a 2 × 3 nm one. To be able to study graphene fexibility (surface ripples) and elucidate the efects, we defne two types of substrates: Single-layer of graphene (SLG) in which all of graphene’s atoms are allowed to move, which leads to the surface ripple formation. Tis substrate is the best approximation of the SLG that can be fabricated experimentally. Te absence of vertical interactions with other layers (as would be the case for graphite or multi-layer gra- phene), leads to the formation of pronounced ripples (Fig. 2, top panels). Single-layer of graphene with the frozen motion of all atoms (frozen layer graphene, FLG). Tis design cor- responds to a hypothetic case of an ideally fat graphene surface, without ripples and without thermal motions. Scientifc Reports | (2021) 11:2576 | https://doi.org/10.1038/s41598-021-82280-7 2 Vol:.(1234567890) www.nature.com/scientificreports/ Atom pair Ε (meV) σ (Å) C–C 2.41 3.4 H–H 1.449 2.65 N–N 2.597 3.416 C–H 1.337 2.81 N–C 2.501 3.408 N–H 1.973 3.033 Table 1. Lennard–Jones interaction parameters46–49. By considering the motion of Nanocar and Nanotruck on two graphene substrate types, we have four systems to study (Fig. 2). To study the motion of the fullerene-based nanomachines on graphene substrates, we utilize the all-atom classical molecular dynamics (MD) simulations. Te substrates are modeled as 12 × 12 nm2 square sheets containing 5744 carbon atoms. Te graphene sheet is positioned at z 0 plane. Periodic boundary conditions = are applied in x and y directions to allow unlimited difusion of the molecules over the surfaces. For visualizing the initial and output structures we have used VMD 1.9.2 sofware package 44 (http://www. ks.uiuc.edu/Resea rch/vmd/). Molecular interactions are described using classical force felds as implemented in the Largescale Atomic/Molecular Massively Parallel Simulator (LAMMPS 22Aug2018 version) sofware 45. Tersof potential is used to describe covalent bonds in graphene and nanomachines. Lennard–Jones 6–12 (LJ6- 12) potential is used to describe the non-bonded interaction between each atom of graphene with each atom of nano-machine: 12 6 σij σij Uij 4εij rij < rcut , (1) = r − r ij ij Here, σ and ε are the van-der-Waals (vdW) radius and depth of atomic interaction potential for each pair of species, respectively. Te parameters related to each atom pairs are listed in Table 1 based on previous studies 46–49 on non-bonding interactions . Te cut-of radius, rcut of 12 Å is utilized in this work to reduce computational expenses. Tis selection is motivated by the commonly used criterion, rcut > 2.5σ. MD trajectories are integrated for 40 ns for each system in the NVT ensemble. Te velocity Verlet integration scheme with the integration time step of 1 fs is used.