Programmable Transport of C60 by Straining Graphene Substrate.

Controlling the maneuverability of nanocars and molecular machines on the surface is essential for the targeted transportation of materials and energy at the nanoscale. Here, we evaluate the motion of fullerene, as the most popular candidate for use as a nanocar wheel, on the graphene nanoribbons with strain gradients based on molecular dynamics (MD), and theoretical approaches. The strain of the examined substrates linearly decreases by 20%, 16%, 12%, 8%, 4%, and 2%. MD calculations were performed with the open source LAMMPS solver. The essential physics of the interactions is captured by Lennard-Jones and Tersoff potentials. The motion of C60 on the graphene nanoribbon is simulated in canonical ensemble, which is implanted by using a Nose-Hoover thermostat. Since the potential energy of C60 is lower on the unstrained end of nanoribbons, this region is energetically more favorable for the molecule. As the strain gradient of the surface increases, the trajectories of the motion and the C60 velocity indicate more directed movements along the gradient of strain on the substrate. Based on the theoretical relations, it was shown that the driving force and diffusion coefficient of the C60 motion respectively find linear and quadratic growth with the increase of strain gradient, which is confirmed by MD simulations. To understand the effect of temperature, at each strain gradient of substrate, the simulations are repeated at the temperatures of 100, 200, 300, and 400 K. The large ratio of longitudinal speed to the transverse speed of fullerene at 100 and 200 K refers to the rectilinear motion of molecule at low temperatures. Using successive strain gradients on the graphene in perpendicular directions, we steered the motion of C60 to the desired target locations. The programmable transportation of nanomaterials on the surface has a significant role in different processes at the nanoscale, such as bottom-up assembly.

Motion of nanovehicles on pristine and vacancy-defected silicene: implications for controlled surface motion.

Understanding the motion of surface-rolling nanomachines has attracted lots of attention in recent studies, due to their ability in carrying molecular payloads and nanomaterials on the surface. Controlling the surface motion of these nanovehicles is beneficial in the fabrication of nano-transportation systems. In the present study, molecular dynamics (MD) simulations alongside the potential energy analysis have been utilized to investigate the motion of C60 and C60-based nanovehicles on the silicene monolayer. Nano-machine simulations are performed using molecular mechanic forcefield. Compared with graphene and hexagonal boron-nitride, the molecules experience a higher energy barrier on the silicene, which leads to a lower diffusion coefficient and higher activation energy of C60 and nanomachines. Overcoming the maximum energy barrier against sliding motion is more probable at higher temperatures where the nanomachines receive higher thermal energy. After evaluating the motion of molecules around local vacancies, we introduce a nanoroad structure that can restrict surface motion. The motion of C60 and nanovehicles over the surface is limited to the width of nanorods up to a certain temperature. To increase the controllability of the motion, a thermal gradient has been applied to the surface and the molecules move toward the lower temperature regions, where they find lower energy levels. Comparing the results of this study with other investigations regarding the surface motion of molecules on boron-nitride and graphene surfaces brings forth the idea of controlling the motion by silicene-based hybrid substrates, which can be further investigated.

Collective movement and thermal stability of fullerene clusters on the graphene layer.

Understanding the motion characteristics of fullerene clusters on the graphene surface is critical for designing surface manipulation systems. Toward this purpose, using the molecular dynamics method, we evaluated six clusters of fullerenes including 1, 2, 3, 5, 10, and 25 molecules on the graphene surface, in the temperature range of 25 to 500 K. First, the surface motion of clusters is studied at 200 K and lower temperatures, in which fullerenes remain as a single group. The trajectories of the motion as well as the diffusion coefficients indicate the reduction of surface mobility as a response to the increase of the fullerene number. The clusters show normal diffusion at the temperature of 25 K, while they follow the super-diffusion regime at higher temperatures. The separation of fullerenes occurs at 300 K and higher temperatures. Due to the increase of vdW attraction with the increase of the fullerene number, the separation of fullerenes in larger clusters occurs at higher temperatures. The thermal energy at 500 K is sufficient to divide the large C60 clusters into smaller clusters. This energy level is related to the saturation of the interaction energy experienced by individual fullerenes, which can be estimated from the potential energy analysis. The results of simulations reveal that the separation occurs at the edge of clusters. Moreover, we studied the thermal stability of multilayer fullerene clusters on graphene. The simulation results indicate the tendency of multilayer clusters to locate on the surface, which implies the wetting property of C60s on the graphene layer.

Nanocar swarm movement on graphene surfaces.

Investigation of nanomachine swarm motion is useful in the design of molecular transportation systems as well as in understanding the assembly process on the surface. Here, we evaluate the motion of the clusters of nanocars on graphene surfaces, using molecular dynamics (MD) simulations. The mechanism of motion of single nanocars is evaluated by considering the rotation of the wheels, direction of the nanocars' speed and comparing the characteristics of the surface motion of nanocars and similar absorbed molecules. The mentioned analyses reveal that, in the thermally activated surface motion of the nanocars, sliding movements are the dominant mode of motion. A coarse grained (CG) model is proposed for some preliminary studies such as finding the stable orientation of two nanocars. The established model indicates three stable orientations for a pair of nanocars, which are verified by MD simulations and the analysis of potential energy. The radius of gyration and the root mean square deviation (RMSD) are employed to evaluate the configuration of larger nanocar clusters. Nanocar clusters change their configuration at 300 K and higher temperatures; however, there is a threshold temperature (600 K) at which different clusters are broken because at this temperature the thermal fluctuation energy dominates the vdW attraction between a nanocar in the perimeter and the other nanocars of the cluster. The surface motions of the nanocar clusters are investigated at temperatures at which the clusters are thermally stable by computing different motion parameters such as mean square displacements (MSDs), diffusion coefficients and anomaly parameters. As the population of clusters increases from 1 to 10 nanocars, the motion regime changes from long-range to small-range displacements which is attributed to the energy wasted by intermolecular vdW interactions. The anomaly parameters of the motions reveal that the clusters experience almost normal diffusion at low temperatures, while they find a super-diffusive regime at higher temperatures. Ultimately, the preferred arrangement of nanocar assembly can be utilized to fabricate special nanostructures on the surface including molecular rings and chains.

Directional control of surface rolling molecules exploiting non-uniform heat-induced substrates.

Molecular machines, such as nanocars, have shown promising potential for various tasks, including manipulation at the nanoscale. In this paper, we examined the influence of temperature gradients on nanocar and nanotruck motion as well as C60 - as their wheel - on a flat gold surface under various conditions. We also compared the accuracy and computational cost of two different approaches for generating the temperature gradient. The results show that severe vibrations and frequent impacts of gold atoms at high temperatures increase the average distance of C60 from the substrate, reducing its binding energy. Moreover, the temperature field drives C60 to move along the temperature variation; still, the diffusive motion of C60 remained unchanged in the direction perpendicular to the temperature gradient. Increasing the magnitude of the temperature gradient speeds up its motion parallel to the gradient, while raising the average temperature of the substrate increases the diffusion coefficient in all directions. The temperature field influences the nanocar motion in the same manner as C60. However, the nanocars have a substantially shorter motion range compared to C60. The relatively larger, heavier, and more flexible chassis of the nanocar makes it more sluggish than the nanotruck. In general, the motion of large and heavy surface rolling molecules is less affected by the temperature field compared to small and light molecules. The results of the study show that concentrated heat sources can be employed to push surface rolling molecules or break down their large clusters. We can exploit a temperature field as a driving force to push nanocars in a desired direction on prebuilt pathways.

Mechanism of C60 rotation and translation on hexagonal boron-nitride monolayer.

Newly synthesized nanocars have shown great potential to transport molecular payloads. Since wheels of nanocars dominate their motion, the study of the wheels helps us to design a suitable surface for them. We investigated C60 thermal diffusion on the hexagonal boron-nitride (h-BN) monolayer as the wheel of nanocars. We calculated C60 potential energy variation during the translational and rotational motions at different points on the substrate. The study of the energy barriers and diffusion coefficients of the molecule at different temperatures indicated three noticeable changes in the C60 motion regime. C60 starts to slide on the surface at 30 K-40 K, slides freely on the boron-nitride monolayer at 100 K-150 K, and shows rolling motions at temperatures higher than 500 K. The anomaly parameter of the motion reveals that C60 has a diffusive motion on the boron-nitride substrate at low temperatures and experiences superdiffusion with Levy flight motions at higher temperatures. A comparison of the fullerene motion on the boron-nitride and graphene surfaces demonstrated that the analogous structure of the graphene and hexagonal boron-nitride led to similar characteristics such as anomaly parameters and the temperatures at which the motion regime changes. The results of this study empower us to predict that fullerene prefers to move on boron-nitride sections on a hybrid substrate composed of graphene and boron-nitride. This property can be utilized to design pathways or regions on a surface to steer or trap the C60 or other molecular machines, which is a step toward directional transportation at the molecular scale.

Complex self-propelled rings: a minimal model for cell motility.

Collective behavior of active matter is observed for self-propelled particles, such as vibrated disks and active Brownian particles, as well as for cytoskeletal filaments in motile cells. Here, a system of quasi two-dimensional penetrable self-propelled rods inside rigid rings is used to construct a complex self-propelled particle. The rods interact sterically with each other and with a stationary or mobile ring via a separation-shifted Lennard-Jones potential. They either have a sliding attachment to the inside of the ring at one of their ends, or can move freely within the ring confinement. We study the inner structure and dynamics of the mobile self-propelled rings. We find that these complex particles cannot only be characterized as active Brownian particles, but can also exhibit cell-like motility: random walks, persistent motion, circling, and run-and-circle motion.

Directing the diffusive motion of fullerene-based nanocars using nonplanar gold surfaces.

A new method for guiding the motion of fullerene and fullerene-based nanocars is introduced in this paper. The effects of non-flat substrates on the motion of C60, a nanocar and a nanotruck are investigated at different conditions and temperatures. Their behavior is studied using two different approaches: analyzing the variation in potential energy and conducting all-atom classical molecular dynamics simulations. This paper proposes that the use of a stepped substrate will make their motion more predictable and controllable. The results of the simulations show that C60 stays on the top side of the step and cannot jump over the step at temperatures of 400 K and lower. However, at temperatures of 500 K and higher, C60 has sufficient energy to travel to the down side of the step. C60 attaches to the edge and moves just alongside of the edge when it is on the down side of the step. The edge also restricts the motion of C60 alongside the edge and reduces its range of motion. By considering the motion of C60, the general behavior of the nanocar and nanotruck is predictable. The nanocar stays on the top side of the step at temperatures of 400 K and less; at 500 K and higher temperatures, its wheels jump off the edge, and its range of motion is restricted. The relatively rigid chassis of the nanotruck does not allow the free individual motion of the wheels. As a result, the entire nanotruck stays on the top side of the step, even at 600 K. A pathway with the desired route can be fabricated for the motion of C60 and nanocars using the method presented in this paper. This represents a step towards the directional motion of C60 and nanocars.

Self-propelled directed transport of C60 fullerene on the surface of the cone-shaped carbon nanotubes.

Directed transportation of materials at molecular scale is important due to its crucial role in the development of nanoelectromechanical devices, particularly the directional movements along the carbon nanotubes (CNTs), due to the applications of CNTs as nano-manipulators, confined reactors, and drug or other materials delivery systems. In the present investigation, we evaluate the movements of C60 fullerenes on the surface of the cone-shaped CNTs. The fullerene molecules indicate directed motion toward the narrower end of CNTs, which is due to the potential energy gradient along the nanotube length. A continuum model is proposed to evaluate the mechanism of the directed motion and the results of the theoretical model are compared with numerical simulations. Directed movements have been examined at various opening angles of CNTs, considering the trajectories of motions, variation of potential energy, and diffusion coefficients. At smaller opening angles, the driving force on the C60 increases and the molecule experiences more directed transport along the nanotube. The motion of fullerene has also been simulated inside the cone-shaped CNTs, with similar opening angle, and different average radius. At lower average radius of the cone-like nanotubes, the motion of C60 is comparatively more rectilinear. Directional transport of fullerene has been observed in the opposite direction, when the molecule moves on the external surface of the cone-like CNTs, which is due to the stronger interaction of C60 with the parts of the external surface with larger radius. The effect of temperature has been evaluated by performing the simulations at the temperature range of 100 to 400 K. The direction of the velocity reveals that the thermal fluctuations at higher temperatures hinder the directed motion of molecule along the cone-shaped CNTs. The results of the present study propose a new method to obtain directed transport of molecules which can be helpful in different applications such as drug delivery systems.

Toward steering the motion of surface rolling molecular machines by straining graphene substrate.

The surface rolling molecular machines are proposed to perform tasks and carrying molecular payloads on the substrates. As a result, controlling the surface motion of these molecular machines is of interest for the design of nano-transportation systems. In this study, we evaluate the motion of the nanocar on the graphene nanoribbons with strain gradient, through the molecular dynamics (MD) simulations, and theoretical relations. The nanocar indicates directed motion from the maximum strained part of the graphene to the unstrained end of the substrate. The strain gradient induced driving force and diffusion coefficients of nanocars are analyzed from the simulation and theoretical points of view. To obtain the optimum directed motion of nanocar, we consider the effects of temperature, strain average, and magnitude of strain gradient on the directionality of the motion. Moreover, the mechanism of the motion of nanocar is studied by evaluating the direction of the nanocar's chassis and the rotation of wheels around the axles. Ultimately, the programmable motion of nanocar is shown by adjusting the strain gradient of graphene substrate.

Unidirectional motion of C60-based nanovehicles using hybrid substrates with temperature gradient.

With the synthesis of nanocar structures the idea of transporting energy and payloads on the surface became closer to reality. To eliminate the concern of diffusive surface motion of nanocars, in this study, we evaluate the motion of C60 and C60-based nanovehicles on graphene and hexagonal boron-nitride (BN) surfaces using molecular dynamics simulations and potential energy analysis. Utilizing the graphene-hBN hybrid substrate, it has been indicated that C60 is more stable on boron-nitride impurity regions in the hybrid substrate and an energy barrier restricts the motion to the boron-nitride impurity. Increasing the temperature causes the molecule to overcome the energy barrier frequently. A nanoroad of boron-nitride with graphene sideways is designed to confine the surface motion of C60 and nanovehicles at 300 K. As expected, the motion of all surface molecules is limited to the boron-nitride nanoroads. Although the motion is restricted to the boron-nitride nanoroad, the diffusive motion is still noticeable in lateral directions. To obtain the unidirectional motion for C60 and nanocars on the surface, a temperature gradient is applied to the surface. The unidirectional transport to the nanoroad regions with a lower temperature occurs in a short period of time due to the lower energies of molecules on the colder parts.

Locomotion of the C60-based nanomachines on graphene surfaces.

We provide a comprehensive computational characterization of surface motion of two types of nanomachines with four C60 "wheels": a flexible chassis Nanocar and a rigid chassis Nanotruck. We study the nanocars' lateral and rotational diffusion as well as the wheels' rolling motion on two kinds of graphene substrates-flexible single-layer graphene which may form surface ripples and an ideally flat graphene monolayer. We find that the graphene surface ripples facilitate the translational diffusion of Nanocar and Nanotruck, but have little effect on their surface rotation or the rolling of their wheels. The latter two types of motion are strongly affected by the structure of the nanomachines instead. Surface diffusion 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.

Observer Design for Topography Estimation in Atomic Force Microscopy Using Neural and Fuzzy Networks.

In this study, a novel artificial intelligence-based approach is presented to directly estimate the surface topography. To this aim, performance of different artificial intelligence-based techniques, including the multi-layer perceptron neural, radial basis function neural, and adaptive neural fuzzy inference system networks, in estimation of the sample topography is investigated. The results demonstrate that among the designed observers, the multi-layer perceptron method can estimate surface characteristics with higher accuracy than the other methods. In the classical imaging techniques, the scanning speed of atomic force microscope is restricted due to the time required by the oscillating tip to reach the steady state motion while the closed-loop controller tries to maintain the tip vibration amplitude at a set-point value. To address this issue, we have proposed an innovative imaging technique that not only eliminates the need to a closed-loop controller but also estimates the surface topography very quick and accurate compared to the conventional imaging method. Also, the proposed technique is capable of simultaneous estimation of the topography, Hamaker parameter, and the tip-sample interaction force.