How Chassis Structure and Substrate Crystalline Direction Affect the

Article pubs.acs.org/JPCC

Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

How Chassis Structure and Substrate Crystalline Direction Affect the Mobility of Thermally Driven p‑Carborane-Wheeled Nanocars Seyed Mohammad Hosseini Lavasani, Hossein Nejat Pishkenari,* and Ali Meghdari Nanorobotics Laboratory, Center of Excellence in Design, Robotics, and Automation (CEDRA), Mechanical Engineering Department, Sharif University of Technology, Tehran 11365-11155, Iran

J. Phys. Chem. C Downloaded from pubs.acs.org by UNIV OF TEXAS AT DALLAS on 02/21/19. For personal use only.

S Supporting Information *

ABSTRACT: In recent years, various nanocars have been synthesized in order to provide controlled mechanical function, transport other nanoparticles, or enable bottom-up assembly capability. There have even been racing competitions among well-known nanocars in which the wheels play an influential role. In this paper, the motion of thermally driven nanocars equipped with p-carborane wheels on Au(111) and Au(001) substrates is investigated. For the sake of comparison, classical all-atom molecular dynamics (MD) and rigid-body MD (RBMD) have been used to study the motion threshold as well as to analyze the effect of temperature, substrate crystalline direction, and chassis shape on the diffusive motion of a nanocooper, trimer, nanocaterpillar, and angled nanocar. It was observed that the motion regime of the nanocars on a gold substrate is a function of temperature and translational diffusion as well as the rotational diffusion coefficient, which shows non-Arrhenius behavior. Nanocar motion has three main regimes, trapped in the crystal structure, short-range fluctuations, and continuous motion for different temperatures from 50 to 600 K. Nanocar structure and crystalline direction may have a significant influence on the translational or rotational diffusion as well as on the surface temperatures in which the motion regime switch occurs. Fluctuations of the nanocars at temperatures below 450 K do not lead to considerable displacement; in this regard, there is a suitable consistency with experimental observations. The simulation results indicate that RBMD overestimates the diffusion coefficient by at least 10 times more than classic MD and predict less adsorption energy on gold, both of which have been reported in previous studies. Rotational motion of nanocars around an axis perpendicular to the gold surface initiates at higher temperatures relative to their pure translational motion; as a result, carborane-wheeled nanocars have less tendency to rotate and rather perform translational motion. In addition, p-carborane wheels have the tendency to slide toward an adjacent adsorption site rather than to roll, and their rotations occur completely independent from each other. These findings can be used to predict the behavior of other variants of carborane-based nanocars, such as motorized or nonmotorized, and to assist designers to increase their nanocar structure-based controllability on the substrate.

1. INTRODUCTION The idea of building molecular machines was first propounded by Nobel laureate Feynman in 1960,1 and since then, significant efforts have been made to synthesize molecularlevel mechanisms. Stochastic thermal fluctuations of atoms of nanoscale machines dominate their desirable mechanical behavior, and these machines are often propelled by their internal molecular motor or are manipulated by sharp tools, external fields, or by harnessing the energy of Brownian motion of nanoparticles.2,3 Inspired by current surrounding macroscopic machine counterparts, several molecular machines, such as nanoscale elevators, switches, brakes, shuttles, and nanocars to name but a few, have been synthesized.4 Moreover, a closer look at nature reveals that the concept of molecular machines is not a new idea and a number of artificial molecular machines have been created by nano-biomimicry. Awarding the 2016 Nobel Prize in Chemistry for the design and synthesis of molecular machines raised a new wave of interest in this area despite the lack of the introduction of any new nanocars in the © XXXX American Chemical Society

past few years. Nowadays, there are several different methods for the manipulation of materials on a variety of surfaces and environments and each has their own exclusive merits and demerits.5 Most of the recent methods have limited capabilities in simultaneously carrying numerous particles or in their manipulation speed; thus, new approaches must be employed. In the “bottom-up” approach, researchers use nanoscale building blocks with self-assembly capabilities to construct microscopic structures, where the cooperation among small and feeble molecules may lead to efficient and powerful nanomachines.6 In recent years, a research group under the supervision of Tour introduced a couple of molecular-level vehicles for moving or transporting a nanoscale payload on substrates.7−9 Because these nanomachines are equipped with a chassis, axles, Received: November 5, 2018 Revised: January 20, 2019

A

DOI: 10.1021/acs.jpcc.8b10779 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 1. Competitors in the first international nanocar race held at the CEMES-CNRS center at the University of Toulouse, France, April 2017. Hydrogen, carbon, oxygen, and nitrogen atoms are colored in white, gray, red, and blue, respectively.

and several wheels, they bear a strong resemblance with ordinary cars and hence are called nanocars. The first wheel utilized in a molecular vehicle was a triptycene chemical group with D3h symmetry. It was mounted on a molecular wheelbarrow and guided by a scanning tunneling microscopy (STM) system tip apex stimulating its rear legs. However, in early generations, the wheels had no rolling motion on a Cu(100) substrate and instead just hopped.10 The vigorous efforts of Tour’s group produced various designs of nanocars first based on fullerene wheels,7 then p-carborane wheels on gold substrate, 8 , 1 1 − 1 4 followed by trans-alkynyl(dppe)2ruthenium-based wheels,15 and finally hydrophobic adamantane on glass surfaces were made and tested.16−19 Different nanocars with bowl-shaped subphthalocyanine wheels were also tested on gold by Joachim and Rapenne.20 In April, 2017 the first international nanocar competition among well-known nanocar manufacturers from all over the world was held at the CEMES-CNRS center at the University of Toulouse, France. The nanocars, shown in Figure 1, raced under an ultrahigh vacuum on a shared or dedicated gold and silver surface at the temperature of 4 K, where the newly developed 4-tips STM was used for scanning.21 The teams were not allowed to mechanically push or pull the nanocars with the STM tip.22 Rice and Graz University’s nanocar, Dipolar Racer, navigated a 150 nm Ag(111) track in 1 h and 33 min, while the University of Basel’s nanocar, Swiss Nano Dragster, finished the 133 nm course on shared Au(111) in 6.5 h to share the first place.23,24 Ohio’s team with their Bobcat Nano-wagon car achieved third place. In the fourth place, Dresden University’s Windmill nanocar became stuck on the reconstruction edge of the gold surface, where excessively accumulated STM pulses destroyed it.25 Although Toulouse’s Green Buggy on shared Au(111) was kept out of ranking for not following the competition rules, it was awarded the prize of elegance for its high quality and smart STM imaging.26 The Tsukuba team attended the competition with the MANANIMS nanocar (bisbinaph-thyldurene molecule), a flat conformer that laterally jumped on an Au(111) substrate with STM inelastic excitation. This group was also removed from the competition for two software failures.27 In this paper, we studied the motion of some p-carboranebased nanocars. These nanocars, developed by Morin et al.,11 are presented in Figure 2 and are called the nanocooper, trimer, nanocaterpillar, and angled nanocar. These nanocars are equipped with aryleneethynylene derivative bearings with 4, 3, 6, and 4 p-carborane wheels mounted on them, respectively. Dicarba-closo-dodecaboranes C2B10H12, an icosahedral molecule, is one of the notable boron cluster compounds synthesized in 1963.28,29 Wheels made of this molecule afford advantages over other options utilized in nanocars due to their spherical shape, high resistance to

Figure 2. Top view of Corey−Pauling−Koltun model of optimized pcarborane-wheeled nanocars in the gaseous phase. (a) Nanocooper. (b) Simplified timer. (c) Nanocaterpillar. (d) Simplified angled nanocar. Hydrogen, boron, carbon, oxygen, and nitrogen atoms are colored in white, pink, gray, red, and blue, respectively.

thermal degradation, and aromatic nature.30 In addition, it easily takes part in substitution reactions.31 Contrary to fullerene, carboranes are easily dissolved in organic solvents; thus, reducing the number of synthetic steps which makes more compact nanocars feasible. Thermal stability analysis done by Morin and co-workers demonstrated that the weakest bond, that is alkyne−carborane, is stable up to 390 °C, while the alkyne−fullerene bond decomposes at 300 °C.11 Therefore, in this study, the maximum substrate temperature was set to 600 K during the simulation in order to be sure there is no bond breaking. Other variants of p-carborane-based nanocars with the ability to transport a nanocargo12 across a surface or selfassembly32−34 were also proposed. Propulsion of thermally driven nanocars was mainly provided by temperature-induced vibrations of substrate atoms and it is evident that this motion may be diffusive in every direction. Therefore, in order to enhance directional motion, nanocar manufacturers introduced the chassis-like nanocooper or the better-designed nanocaterpillar and predicted that these structures would reduce the lateral motion compared to the other compositions. With regard to this idea, it was expected that an angled nanocar would have the ability to travel in circular pathways and the trimer would have mostly rotational movement around its pivot.6,11 The next generation of nanocars were introduced B


Article


substrates. Among these studies, experimental studies about adsorption of carborane isomers and their different compound on various substrates should be mentioned, some of which performed ab initio calculations as well. These analyses include atomic beam scattering, X-ray photoelectron spectroscopy, STM, electron spectroscopy, photoemission, reflection− absorption infrared spectroscopy, and DFT or force field calculations, in which carborane physisorption or chemisorption on transition metals was studied.52−57 Furthermore, Lavasani et al. analyzed the motion regimes of isolated pcarborane on Au(100) using the two different approaches of MD simulation and potential energy surfaces (PES).58 In this regard, we intend to comprehensively study the effect of chassis shape, nanocar rigidity, and the number of wheels on nanocars mobility, which has never been studied before. Also, the effect of temperature and substrate crystalline direction on the motion will also be scrutinized. In the following, detailed modeling of carborane-based nanocar on gold and essential setup parameters are explained in Section 2. In Section 3, the outcomes of the MD and rigidbody MD (RBMD) simulations are analyzed and compared. By comparing the motion of the nanocars and the isolated wheel, we have tried to discover the similarity between their motion regimes on gold substrate. In Section 4, the results of previous experimental observation are compared with current theoretical results. In the last section, a summary of our findings and main conclusions are presented.

with internal motor to overcome the diffusive motion. Motorized nanocar35 and the three-wheeled nanoroadster36 actuated with a light-induced rotary motor were built by the Feringa group37 and the nanoworm38 with an azobenzene molecular motor which mimics worm motion are examples of this trend. Considering the advances in nanocars capabilities, it is hoped that in the future they will be used in transporting other molecules and materials in a fully controlled motion. The first step in analyzing the capabilities of nanocars is to study their motion on applicable substrates. After constructing the first fullerene-wheeled nanocar and trimer, their mobility was investigated by means of the STM technique.7,39 It was shown that the nanocar tends to travel in a longitudinal direction and also occasionally rotates around itself, rotation motion was more likely to occur in the fullerene-wheeled trimer. Shortly afterward, the carborane-wheeled nanocar motion threshold on metallic surfaces39 was examined by STM as well as the movement on nonmetallic substrates40,41 by fluorescence imaging. Translational diffusion of a singlemolecule on nonmetallic substrates is measured by chasing of a fluorescent marker attached to the chassis. The STM technique has a limited scanning speed7 and scanning is only possible on conductive substrates. It is often performed on gold substrates due to their excellent stability. As the fluorescent motion tracking system does not have direct contact with the system, it imposes the lowest perturbation to the temperature-induced dynamics of nanocar relative to the STM technique. However, the dynamics of a nanocar even with a proper marker is different from the dynamics of the nanocar without it, and the achievable resolution is far less than the STM technique. Considering the fact that some of the motion details, for example wheel hopping or rolling motion, happen in a timescale less than a nanosecond, neither of these two techniques meet our needs. There have been only limited theoretical studies and simulations conducted on nanocars so far, which include a thermally driven fullerene-wheeled rigid nanotruck and trimer motion analysis on gold42,43 by Akimov et al., rigid fullerenewheeled 5-fragment nanotruck simulation under STM-induced electrical field44 by Akimov and Kolomeisky, and thermally driven fullerene-wheeled rigid z-car (Z-shaped nanocar) and nanotruck by Konyukhov et al.45,46 Nemati et al. have also investigated the thermal-induced motion regime of a fullerene molecule47 as well as a flexible nanocar and nanotruck equipped with fullerene wheels on a flat48 and stepped49 Au(100) substrate using molecular dynamics (MD) simulations. Ahangari et al. estimated the binding energy by −9.43 eV for the adsorption of a fullerene-wheeled nanotruck on an Au(111) substrate using the first-principles density functional theory (DFT) by combining the interaction energies between its fragment and the surface. It was found that 9.56 electrons transferred from the nanotruck to the substrate.50 Ganji et al. investigated the adsorption of a carborane-wheeled nanocooper to graphene and graphyne.51 The calculations were based on first-principle van der Waals (vdW)-corrected DFT and some parts of it were validated by MP2 level of theory. They reported the activation energies of −0.74 and −0.19 eV for the nanocooper on graphene and graphyne monolayer, respectively. There has been no research done to date for detailed motion analysis of the p-carborane-based nanocars presented in Figure 2 on a gold surface; although there might be some studies about nanocars components such as the wheels with different

2. THEORETICAL MODEL AND SETUP DETAILS In this section, the details and steps for implementation of the MD model are discussed. In order to simulate the carboranebased nanocars, the equilibrium geometries and distribution of partial charges are calculated. Comprehensive ab initio calculation using the open-source quantum chemistry package of NWChem59 has been carried out to reach the equilibrium state. Nanocar structure in the gaseous phase is optimized. First, a series of conformation analysis of the nanocars chassis is accomplished to identify the most stable one. Regarding the fact that the structure of nanocars on the substrate maintain their near flat shape and in most of the cases this conformer has the minimum energy, a planar chassis is considered for further optimizations. Afterward, each nanocar fragments, that is, the chassis and wheels are optimized separately at the restricted Hartree−Fock (HF) level using a Pople’s 6-31+G* basis set with polarization and diffuse functions for heavy atoms. Subsequently, the fragments are joined together to form a completed nanocar, and the optimization is repeated at the same level of theory. Also, the analytic Hessian of the optimized geometry is calculated. Frequency analysis verifies the geometry to be the minimum state. Finally, DFT calculations utilizing the Becke 3-parameter hybrid functional combined with the Lee−Yang−Parr correlation functional (B3LYP) were performed to further optimize the nanocar geometry. At this step, a split-valence double-zeta basis set of 6-31++G(d,p) that contains polarization and diffuse functions over all atoms was employed. Optimizations are accomplished using the quasi-Newton scheme until the norm of the exerted force on each atom became smaller than 1 × 10−5 hartree/ bohr. The final optimized structures of the nanocooper, trimer, nanocaterpillar, and angled nanocar belonging to the C2h, C3h, C2, and C2v symmetry point groups, respectively, are shown in Figure 2. The p-carborane wheel itself also has perfect five-fold C


Article

The Journal of Physical Chemistry C Table 1. Point Group, Absolute Energy, HOMO and LUMO Energies, Molecular Weight, Chemical Formula, vdW Dimensions, and Dipole Moment of the p-Carborane and Nanocars at the B3LYP/6-31++G(d,p) Level nanocar variant

point group

absolute energy (hartree)

HOMO energy (eV)

LUMO energy (eV)

molecular weight (g·mol−1)

chemical formula

vdW L × W × H or Ø (Å)

dipole moment (debye)

p-carborane nanocooper trimer nanocaterpillara angled nanocar

D5d C2h C3h C2 C2v

−332.1537 −2704.1858 −2375.2627 −3289.3280 −2760.3070

−8.874 −5.570 −6.160 −5.841 −5.678

−0.548 −2.494 −2.353 −2.566 −2.238

144.227 1003.327 877.161 1275.739 1032.370

C2H12B10 C40H58B40O2 C42H48B30 C46H74B60 C44H57B40N

Ø8 21.8 × 22.1 × 8 Ø 35.6 × 8 21.8 × 22.6 × 8 20.6 × 25.8 × 8

0 0 0 0 3.5

a B3LYP/6-31G(d,p) level is performed to achieve optimized geometry of the nanocaterpillar due to weak convergence of diffuse functions over steric repulsion of the wheels.

D5d symmetry. A portion of the results from the ab initio calculations, including absolute energy, point group, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, molecular weight, chemical formula, vdW dimensions, and dipole moment of the nanocars and the wheel, are presented in Table 1. More information consisting of atomic Cartesian coordinates, Mulliken and restrained electrostatic potential (RESP) charges, and illustration of HOMO and LUMO molecular orbitals are presented in Supporting Information Tables S1−S4 and Figures S1−S4. The RESP-fitting algorithm60 is performed utilizing the Antechamber package,61 and geometry visualization and orbitals illustration are depicted using VMD software,62 and the Avogadro molecular editor and visualization tool,63 respectively. Mulliken charges, in general, may lead to inaccurate results, especially in aqueous and solvents environments. Here, the nanocar is only interacting with the gold substrate in which our simulation tests revealed that the intramolecular electrostatic potential has a small influence on the nanocars dynamics. However, if a colony of nanocars is deposited on the surface, the choices of electrostatic potential approach will be of great importance in the way the nanocars move. Contrary to numerous ab initio calculations which consider optimized structure,64 vibrational frequencies,65 stability,66 acidity,67 and cage substitution68 of borane and carborane derivatives, few force fields are introduced to describe their bonding interactions. Among these resources, the substantial effort of Allinger and co-workers in developing the highaccuracy MM3 force field for 12-vertex carboranes should be noted.69−71 Herein, the intramolecular interactions of the wheels and chassis were calculated using the frameworks of an MM3 force field as described in refs 71−74, respectively. The Coulomb interactions between the fragments were calculated using the point charges derived from the Mulliken population analysis of the DFT level. Furthermore, nonbond interactions between the wheels were the same as parameters proposed by Gamba and Powell.75 The conventional 12-6 Lennard-Jones (LJ) potential has been used in order to describe the nonbond interaction of the adsorbed nanocars on gold, as shown in eq 1. E LJ =

Ag substrates interacting with water molecules or organic compounds. The Lorentz−Berthelot combining rule77,78 is implemented to estimate nonbond parameters between different atom types within the system of nanocar and gold substrate, which is presented in Table 2. Although this rule is a Table 2. 12-6 LJ Parameters of Nonbond Interaction between the Carborane-Wheeled Nanocars and Gold Substrate atom type

ϵ (meV)

σ (Å)

a

Au C B H C (alkane) C (alkyne) H (nonpolar) O (ether) H (amine) N (pyrrole) C (benzene)

229.4 4.104 1.847 0.4249 1.311 2.719 0.9709 2.864 0.8738 2.087 2.719

2.63 3.45 4.31 2.97 3.63 3.46 2.89 3.24 2.85 3.44 3.49

substrate p-carborane wheelb

nanocars chassisc

a c

Parameters are taken from ref 76. bParameters are taken from ref 75. Parameters are taken from refs 72,74.

rough estimation, a comparison between the simulation results and experimental observation confirms the accuracy of the calculated coefficients. The global cutoff and neighbor radii for the pairwise interaction are set to 15 and 18 Å, respectively. A supercell of gold with an approximate length and width of 100 Å × 100 Å in the x- and y-directions and a thickness of 16 Å in the z-direction is created for the MD simulation. The normal vector to the gold surface-where the nanocar is in contact-is in the z-direction, and its crystalline direction is considered as two different surfaces of (001) and (111) in order to be compared with each other. Boundary conditions in the x- and y-directions are periodic. The lattice constant of the gold at 300 K is set to 4.087 Å;79 however, its temperatureadjusted value80,81 is used at different simulation temperatures to avoid undesired stress. The lowermost layer of the gold is fixed. The embedded atom method82,83 is employed for calculating the interactions among gold atoms. Classical MD simulations have been carried out using a velocity Verlet integrator of the LAMMPS package.84 First, the total potential energy is minimized through a conjugate gradient algorithm; then, the system relaxes for 200 ps till thermal and potential stability is achieved. Afterward, MD simulation in isothermal condition is accomplished for 10 ns and the integration time step is set to 1 fs in order to accommodate the rapid vibration of the light atoms with suitable accuracy. Canonical ensemble

∑ 4ϵij[(σij/rij)12 − (σij/rij)6 ] i,j

section

(1)

where ϵij is the depth of the potential well in equilibrium distance between atoms i and j, σij is the distance between atoms where the nonbond energy becomes zero, and rij denotes the distance between atoms i and j. These parameters, that is ϵ and σ, are provided for several face-centered cubic metals by Heinz et al. as well.76 They proposed the parameters of the 12-6- and 9-6, LJ form of Pt, Pd, Pb, Ni, Cu, Au, Al, and D


Article


Figure 3. Trajectory of first simulation of nanocooper on the Au(111) substrate at different temperatures. (a) The nanocooper is immobile at temperatures below 200 K. (b) At 200 K the nanocooper jumps to adjacent cells a few times. The jumps size will increase with heating and the motion regime consists mostly of occasional hopping to the next adsorption site at temperatures between 200 and 400 K, which do not have a considerable displacement. (c) The nanocooper has a continuous motion at temperatures above 450 K.

Figure 4. Trajectory of first simulation of nanocooper on the Au(001) substrate at different temperatures. (a) The nanocooper motion for temperatures below 200 K is limited to a gold unit cell. (b) In the range of 200−400 K, the nanocooper motion consists of short-range fluctuations. By increasing the temperature, the translational motion will increase. (c) At 450 K, the nanocooper motion regime changes and it can continuously travel long distances at high temperatures.

employing two Nosé−Hoover thermostats85,86 has been used to equally adjust the temperature of the flexible nanocar and the substrate during the simulation. In calculating nanocars temperature, the velocity of the center of mass (COM) is excluded. On the other hand, a chain thermostat approach87,88 is employed to control the rigid nanocars temperature during RBMD simulations. Each of the rigid nanocars consists of a rigid chassis and a couple of rigid wheels which can freely rotate. The optimized geometries derived from the DFT level are used for RBMD simulations of nanocars. The rigid nanocooper consists of five rigid parts including a chassis and four p-carborane wheels; the rigid trimer consists of four rigid parts including a chassis and three wheels; the rigid nanocaterpillar consists of seven rigid parts including a chassis and six wheels; and finally, the rigid angled nanocar is made of five rigid parts including a chassis and four wheels.

times with different initial conditions for 10 ns. In this regard, a large portion of the system phase space is explored during 30 ns and the effect of the initial condition can be ignored. Our series of simulation tests revealed that simulation times longer than 1 × 30 or 3 × 10 ns do not provide further information about the dynamics of the nanocars. The motion of the isolated p-carborane molecule on the gold substrate in the range 10−600 K is also studied in order to be compared with nanocar behavior. Global thermodynamics parameters, such as temperature, potential, and kinetic energies, as well as the states of the cars, for example position, linear and angular velocities of the nanocars and their fragments, are recorded every 100 fs. Therefore, every parameter is saved by 300 000 data points after excluding the relaxation steps. 3.1. Comparison of the Nanocars Trajectories on Different Substrates. In the following, the motion regime of the nanocars and trajectory of their COM on Au(111) and Au(001) are presented. The first set of simulations is presented here and the second and third sets are presented in the Supporting Information. The motion regime of the carboranewheeled nanocars on gold is a temperature-dependent characteristic of the system, and the three main regimes of trapped in a crystal structure, short-range fluctuations, and continuous motion can be observed. The translational motion of the nanocooper on Au(111) substrate is depicted in Figure 3 and also in the Supporting

3. SIMULATION RESULTS AND DISCUSSION Herein, the results of the MD simulations of the flexible and rigid carborane-wheeled nanocars on gold substrate are presented. In the following, trajectory, rotational motion, and wheels rotation of the nanocars at several temperatures are analyzed qualitatively and quantitatively. The motion regimes of the nanocars were investigated at several temperatures ranging from 50 to 600 K. Each simulation is repeated three E


Article


Figure 5. Trajectory of first simulation of trimer on the Au(111) substrate at different temperatures. (a) The trimer does not have sufficient energy to leave the gold crystal at temperatures below 250 K. (b) At 250 K, the trimer jumps to adjacent cells twice. The jump size increases as the temperature rises, but the dominant motion regime is short-range fluctuations up to 400 K. (c) Above 450 K the trimer has a significant displacement and experiences continuous motion.

Figure 6. Trajectory of first simulation of trimer on the Au(001) substrate at different temperatures. (a) The trimer is stationary below 100 K. (b) At 100 K, the trimer gains the required energy and jump to the next gold cell. By increasing the temperature from 100 to 400 K, the jump size increases; however, this traveling length is short and the motion consists mostly of short-range fluctuations. (c) Above 450 K, the trimer has a free and smooth movement on gold.

motion regime happens gradually at temperatures between 400 and 450 K. Diffusive motion of the nanocooper on the Au(001) surface at different temperatures in three sets of simulations is illustrated in Figure 4 and Supporting Information Figures S7 and S8. As can be observed in Figure 4a, the nanocooper motion on Au(001) for temperatures below 200 K is also limited to a unit cell. In the range of 200−350 K, the nanocooper is no longer stationary; however, its motion consists of short-range fluctuations and it occasionally hops to an adjacent cell. By increasing the temperature, the nanocooper translational motion will also increase, but its overall displacements are still negligible (Figure 4b); however, at this temperature range, the traveling distance is slightly longer on Au(001) compared to the motion on Au(111). At 450 K, the nanocooper motion regime gradually changes to a smooth motion as demonstrated in Figure 4c and it can continuously travel long distances. In Figure 5 and also Supporting Information Figures S9 and S10, the motion of the trimer on the Au(111) substrate in three sets of simulations is presented. As shown in Figure 5a, the trimer does not have any translational movement at temperatures below 250 K and does not have sufficient energy to leave the gold crystal. After increasing the temperature to 250 K, the trimer jumped to adjacent cells twice. As can be observed in Figure 5b, the overall displacement of the trimer at

Information Figures S5 and S6. As shown in Figure 3a, the nanocooper is immobile on Au(111) at temperatures below 200 K and hence gets trapped in a gold crystal. In this situation, one or more of the wheels are stuck in potential wells of the substrate preventing the nanocooper from moving. Increasing the temperature to 200 K causes the first sign of motion to appear and the nanocooper jumps to adjacent cells a few times. The rate of occurrence and the range of the jumps will increase with heating so much so that the jump can increase to a cell located two or more cells apart. As depicted in Figure 3b, the overall displacement of the nanocooper at 300 K during the entire simulation time does not reach 20 Å, which is smaller than the length of the nanocooper (see Table 1). Moreover, the motion regime consists mostly of occasional hopping to the next adsorption site, which is not a considerable displacement. Thus, the motion regime can be considered as short-range fluctuations in the range of 200−400 K. By increasing the temperature, the motion will become more continuous and smoother. As it can be observed in Figure 3c, the nanocooper has a continuous and considerable motion range at temperatures between 450 and 600 K and travels distances a couple of times bigger than its length. At a temperature of 600 K, the nanocooper will be very agile and travel for long distances. It should be noted that there is no distinct border where the motion regime changes from shortrange fluctuations to continuous motion. This change in the F


Article


Figure 7. Trajectory of first simulation of nanocaterpillar on the Au(111) substrate at different temperatures. (a) The nanocaterpillar is immobile at temperatures below 100 K. (b) Upon heating to 100 K, the nanocaterpillar jumps to the adjacent adsorption site a few times during the simulation time. In the range of 100−350 K, the dominant motion regime is short-range fluctuations without considerable movement. (c) At 400 K, the nanocaterpillar motion regime switches and turns into a smooth motion.

Figure 8. Trajectory of first simulation of nanocaterpillar on the Au(001) substrate at different temperatures. (a) The nanocaterpillar motion below 100 K is limited to a gold unit cell. (b) Above 100 K, the nanocaterpillar motion turns into a regime of short-range back and forth fluctuations along the diagonal line, which its range will increase more than the other three nanocars as the temperature rises. (c) At 450 K, the motion regime of the nanocaterpillar turns into a continuous motion.

300 K in a period of 10 ns is less than 15 Å, about half of the diameter of the trimer. The range of the trimer jump increases as the temperature rises, but the dominant motion regime is still short-range fluctuations up to 400 K. Figure 5c demonstrates that at temperatures above 450 K the trimer has a significant displacement and experiences continuous motion due to regime switching similar to the nanocooper at temperatures between 400 and 450 K. Considering these three sets of simulation, it is revealed that although the trimer has a higher motion threshold relative to the nanocooper, in a temperature range of 450−600 K, where their motion is continuous, the trimer has 40% more mobility than the nanocooper. The trajectory of the trimer on Au(001) substrate is depicted in Figure 6 and Supporting Information Figures S11 and S12. As can be observed from Figure 6a, the trimer is stationary below 100 K, when the temperature reaches 100 K it gains the required energy and finds an opportunity to jump to the next cell. By increasing the temperature from 100 to 400 K, the range and frequency of the jumps will gradually increase as shown in Figure 6b; however, this traveling length is still small relative to the trimer size. Similar to the nanocooper, in this temperature range the motion consists mostly of a series of short-range fluctuations, and the trimer’s overall displacement on Au(001) is longer than its motion on Au(111). At temperatures above 450 K, as depicted in Figure 6c, the trimer

has a free and smooth movement on Au(001) and its motion range on Au(111) surpasses the motion on Au(001). It should also be noted that the translational mobility of the trimer at these temperatures is slightly more than that of the nanocooper. In Figure 7 and also Supporting Information Figures S13 and S14, the trajectory of the nanocaterpillar COM on Au(111) is illustrated at several temperatures. The motion patterns of this nanocar are also diffusive and become more diffusive as the temperature increases. As shown in Figure 7a, the nanocaterpillar is immobile at temperatures below 100 K. Upon heating to 100 K and thus increasing the kinetic energy, the nanocaterpillar jumped to the adjacent adsorption site 2 or 3 times during the simulation time. Figure 7b confirms that overall traveling at 200 K during the simulation time is less than its length, which is 22 Å as shown in Table 1. In the range of 200−350 K, these trajectories mainly consist of hexagonally close-packed pathways with a minimum potential barrier. Moreover, at these temperatures, the dominant motion regime is short-range fluctuations without considerable movement. Finally, as depicted in Figure 7c, the motion regime gradually switches and turns into a completely smooth motion at temperatures above 400 K. Three sets of simulations of the nanocaterpillar trajectories on Au(001) at several temperatures are represented in Figure 8 and Supporting Information Figures S15 and S16. As shown in G


Article


Figure 9. Trajectory of first simulation of angled nanocar on the Au(111) substrate at different temperatures. (a) The angled nanocar does not have a translational displacement on gold below 200 K. (b) At 200 K, the angled nanocar jumps to the next adsorption site but the dominant motion regime is still short-range fluctuations up to 400 K. (c) At 450 K, angled nanocar has a considerable continuous motion.

Figure 10. Trajectory of first simulation of angled nanocar on the Au(001) substrate at different temperatures. (a) Below 200 K, the angled nanocar is almost immobile on gold. (b) At 200 K, the angled nanocar is no longer stationary and jumps to the adjacent cell. By increasing the temperature from 200 to 400 K the range of the motion increases but the motion regime consists mostly of short-range fluctuations. (c) At 450 K, the motion regime switches to continuous and traveling longer distances occurs at high temperatures.

Figure 8a, the nanocaterpillar motion below 100 K is limited to a gold unit cell. At temperatures above 100 K which is shown in Figure 8b, the nanocaterpillar is no longer stationary and its motion turns into a regime of short-range back and forth fluctuations along a straight diagonal line. This figure indicates that if the longitudinal axis of the nanocaterpillar is oriented along a [1 ±1 0] direction relative to the global xyz axes, an enhanced directional sliding motion will be achievable. It is worthy to note that the nanocaterpillar motion range will increase more than the other three nanocars as the temperature rises. So that in suitable conditions, the path length traveled during the simulation time will be longer than the length of the nanocar even at a low temperature of 200 K. Also, because of its unique design and having more wheels, the nanocaterpillar does not experience undesired rotations, and this nanocar has the least rotation on Au(001) compared to the others. A notable event can be observed in Figure 8b, where the nanocaterpillar movement is reduced at 300 K and greater translational motion occurs at lower temperatures. This may be due to the initial orientation of the nanocar not being aligned with the diagonal direction. Also, the required kinetic energy for rotation is not available at this temperature (refer to Section 3.5 for the rotation threshold). This is one of the reasons exploring various initial conditions is needed; therefore, every simulation was repeated three times. According to the mentioned points, the nanocaterpillar on Au(100) in the range of 200−400 K is a smart setup to enhance directional

motion. Furthermore, if the substrate has a controlled temperature gradient, unidirectional movement from the hot side to the cold side is likely to occur. Finally, at temperatures above 450 K, the motion regime of the nanocaterpillar turns into a continuous motion. The trajectory of angled nanocar on the Au(111) substrate with three sets of various initial velocities and at different temperatures is presented in Figure 9 and Supporting Information Figures S17 and S18. As shown in Figure 9a, the angled nanocar does not have a translational motion on Au(111) until the temperature reaches 200 K when the nanocar jumped to the next adsorption site a few times. At temperatures between 200 and 350 K, as depicted in Figure 9b, the dominant motion regime is short-range fluctuations to the adjacent unit cells. The angled nanocar at 450 K depicted in Figure 9c has a considerable motion range and at almost the same temperature as the nanocooper starts to switch to a continuous motion. Furthermore, the angled nanocar mobility is close to that of the nanocooper on the Au(111) substrate. The trajectory of the angled nanocar on Au(001) substrate is depicted in Figure 10 and also Supporting Information Figures S19 and S20. As can be observed in Figure 10a, the angled nanocar is almost immobile on Au(001) at temperatures below 200 K. At 200 K and higher temperatures the angled nanocar is no longer stationary and for some moments there is a possibility for it to jump to the adjacent cell. As depicted in Figure 10b, by increasing the temperature from 200 to 400 K H


Article


Figure 11. (a) Translational diffusion coefficients of the flexible carborane-wheeled nanocars on gold as a function of temperature, (b) Arrhenius plot of the translational motion of the flexible nanocars on gold substrates.

the range and frequency of the hopping motion gradually increases but the displacements are still negligible. At 450 K and higher temperatures as shown in Figure 10c, the motion regime gradually switches to continuous and traveling longer distances occurs. Unlike the nanocooper, the angled nanocar mobility on the Au(001) substrate is less than its motion on Au(111) in the whole studied temperature range, and it should be mentioned that the translational motion of the angled nanocar is noticeably smaller than nanocooper. 3.2. Investigating Nanocar Mobility through Diffusion Coefficient. The trajectory of the nanocooper, trimer, nanocaterpillar, and angled nanocar was qualitatively discussed in Section 3.1. It can be observed that the regime and range of the motion as well as the motion threshold are slightly similar among the nanocars. Therefore, a quantitative comparison is made to find differences among the nanocars on surfaces Au(111) and Au(001). Here, the conventional diffusion coefficient is employed to describe the nanocars mobility on a surface utilizing mean square displacement (MSD). The MSD is usually applied to a system of many particles exhibiting a random/Brownian motion, representing the average distance particles travel over time. Herein, an innovative yet accurate method proposed by Ernst and Köhler is employed to calculate the MSD of a single particle.89 They exposed a 2 pM solution of fluorescent beads in a mixture of water and glycerol to a rotating laser beam while the 2-dimensional (2D) trajectory of a single selected bead is recorded by collecting the emissions. They decomposed the long trajectory containing NT = 1.52 × 105 pairs of data points into shorter segments of the same length of Nseg. Each data segment was assumed to belong to an independent imaginary particle, and thus it forms an ensemble consisting of NT/Nseg particles. Now, by standard definition presented in eq 2, the MSD can be calculated as a function of time MSD(t ) = ⟨|r(t ) − r0|2 ⟩

We found that there is a linear relationship between the variation of the MSD of carborane-wheeled nanocar and time. Therefore, in this study the anomalous exponent α is equal to 1, indicating a normal diffusion. In this paper, each of the three simulation parameters contains 1 × 105 data points, thus NT = 3 × 105. After a series of tests, each segment length is set to 1000. Thus, an ensemble of NT/Nseg = 300 imaginary nanocars is used to determine the diffusion coefficient. To analyze the influence of temperature on nanocars motion, the diffusion coefficient is fitted to the Arrhenius equation90 as follows. D = D0 e−Ea / kBT

The Arrhenius model shows the variation of the reaction rate for thermodynamic temperature and also provides an estimation of the activation energy Ea of the process, where prefactor D0 indicates the diffusion coefficient when there is no interaction between the nanocar and the substrate. The translational diffusion coefficients of the flexible nanocooper, trimer, nanocaterpillar, and angled nanocar on the gold surface of (111) and (001) are depicted in Figure 11a. In order to find the activation energy or distinguish between the motion regimes of the nanocars, the logarithm of the diffusion coefficients is also drawn versus the reciprocal of the system temperature in Figure 11b. This revealed that the slopes of the Arrhenius plot in the studied temperature range do not remain constant; consequently, it is not possible to have a unique value for the activation energy over the whole temperature range. In other words, translational motion of carborane-wheeled nanocars on a gold surface exhibits a nonArrhenius behavior. As the temperature rises, the slope of the curves significantly changes, corresponding to a switch in the motion regimes from trapped in the crystal structure to shortrange fluctuations. By further increasing the temperature, the slopes become much steeper, suggesting a new change in the regimes. However, the border of the continuous motion regime cannot be accurately observed. The Arrhenius plot as shown in Figure 11b revealed that the nanocooper motion regime on either Au(111) or Au(001) change from trapped in the crystal structure to short-range fluctuations takes place at about 200 K. Nanocooper mobility on Au(001) is more compared to Au(111), but increasing the temperature will cause the diffusion on Au(111) to surpass it. Regarding the Arrhenius plot, it is evident that the second regime change occurs gradually from 400 to 450 K, and at higher temperatures the nanocooper shows continuous motion. At this temperature range, the slope for Au(111) is

(2)

where r(t) = [x,y]T is the position vectors of the nanocar on a gold surface at time t, r0 = r(0), and the ⟨⟩ symbol denotes averaging over all the segments. Finally, the 2D anomalous diffusion coefficient (D) of translational motion is calculated as follows. D = lim

t →∞

MSD(t ) 4t α

(4)

(3) I


Article


Figure 12. (a) Translational diffusion coefficients of the rigid carborane-wheeled nanocars on gold as a function of temperature, (b) Arrhenius plot of the translational motion of the rigid nanocars on gold substrates.

chassis and a number of rigid wheels rotating freely around their axle. RBMD may drastically overestimate or in some cases underestimate the mobility of the nanocars. For example, it can be observed that the rigid nanocooper shows much more mobility for all temperatures in comparison with the flexible nanocooper modeled by the more accurate MD method. Not only is the motion threshold shifted by the rigid-body constraint, but also the motion regimes may completely change. For example, as depicted in Supporting Information Figure S22, the rigid nanocooper on Au(001) shows a completely different regime of back and forth linear movement at a low temperature of 100 K compared to the flexible nanocooper. On the other hand, the rigid trimer, nanocaterpillar, and angled nanocar have less diffusive motion on Au(001) compared to the flexible ones. Motion analysis of different variants of nanocars using RBMD has already been done by Akimov et al.42,44 and Konyukhov et al.45,46 They have simulated the dynamics of fullerene-wheeled nanocars using their innovative method derived from the symplectic quaternion scheme combined with a Nosé−Poincaré thermostat. They considered the chassis of the z-car, trimer, and nanotruck to be rigid with a number of rigid fullerene wheels mounted on their axles. In this case, the z-car and nanotruck were made of five rigid fragments while the trimer included four rigid fragments. They also compared these results with a z-car or nanotruck composed of 1, 2, 3, and 4 rigid fragments, by merging some wheels with the rigid chassis.43,46 It should be noted that the rigid body technique has limitations, and some details about the nanocars motion will not be accurately represented. Konyukhov et al. reported that the translational diffusion of the nanotruck and z-car on Au(110) at 300 K is equal to 20 and 11 Å2/ps, respectively,45 while the diffusion of the z-car on Au(111) is calculated as 15 Å2/ps.46 They have shown that by changing the number of rigid fragments from 1 to 5, the activation energy increases considerably. Also, Konyukhov et al. indicated that the calculated diffusion coefficient using RBMD can be overestimated 10−100 times compared to the MD results.46 The RBMD results demonstrate that the nanotruck and z-car are agile and have a long-range of motion at 300 K; therefore, there is not a valid conformity with experimental observations. In order to enhance the accuracy, Akimov et al. included a charge transfer between the vehicle and substrate as well, because the charge transfer between C60 and gold surface is large. They reported that the nanotruck diffusion on the

steeper than Au(001). This illustrates the fact that the nanocooper activation energy on Au(111) is larger than that on Au(001). As depicted in Figure 11b, the first regime switch for the trimer from trapped in the crystal structure to short-range fluctuations occurs at 100 and 250 K on Au(001) and Au(111), respectively. Similar to the nanocooper, there is more mobility on Au(001) at low temperatures, but increasing the temperature causes the motion on Au(111) to exceed it. Arrhenius analysis shows that trimer activation energy on Au(111) substrate is also higher than Au(001) in the continuous motion region. Furthermore, it has to be mentioned that the translational motion of the trimer is not less than that of the nanocooper, and the observed motion is contrary to the initially desired rotational motion about its center. According to the Arrhenius analysis of the nanocaterpillar motion, it is evident that the regime change from trapped in the crystal structure to short-range fluctuations on both Au(111) and Au(001) surfaces happened at 100 K. Also, the nanocaterpillar has superior mobility on Au(001) relative to Au(111) for all temperatures. This nanocar is more agile and has more directional motion compared to any of the other studied carborane-wheeled nanocars. According to the gradient of Arrhenius curves at high temperatures, the nanocaterpillar activation energy on Au(111) is larger than that on Au(001). It can be seen that on both Au(111) and Au(001) surfaces, the motion regime of the angled nanocar changes from trapped in the crystal structure to short-range fluctuations at around 200 K. The angled nanocar has a smoother motion on Au(111) because every temperature diffusion coefficient on Au(111) substrate is larger than that on Au(001). Regarding the slopes of the Arrhenius curves in the region of continuous motion, the activation energy on both crystalline directions is the same. Although the angled nanocar on Au(001) has the least mobility at most of the temperatures, Figure 11a revealed that its translational mobility is only about 30% less than the nanocooper. As illustrated in Figure 12, utilizing RBMD, the translational diffusion coefficient, and Arrhenius analysis of the rigid carborane-wheeled nanocars motion on gold are illustrated for the sake of comparison with the flexible nanocars. Also in Supporting Information Figures S21−S28 the trajectories of the rigid nanocooper, trimer, nanocaterpillar and angled nanocar COM on Au(111) and Au(001) are illustrated at several temperatures. The rigid nanocars consist of a rigid J


Article


Table 3. Binding Energy of the Nanocars to the Gold Substrate, Center of Mass Height of the Nanocars on the Gold Corresponding to the Binding Energy, and Transition State and Activation Energy for Hopping Motion toward the Adjacent Cell substrate

Au(111)

nanocar variant nanocooper trimer nanocaterpillar angled nanocar

flexible rigid flexible rigid flexible rigid flexible rigid

Au(001)

binding energy (eV)

COM height (Å)

transition state energy (eV)

activation energy (eV)

binding energy (eV)

COM height (Å)

transition state energy (eV)

activation energy (eV)

−10.93 −7.25 −10.36 −6.27 −12.79 −9.52 −11.30 −7.36

3.88 4.45 3.71 4.35 4.08 4.53 3.85 4.44

−10.74 −7.19 −10.08 −6.19 −12.69 −9.43 −11.12 −7.24

0.19 0.05 0.20 0.06 0.10 0.09 0.15 0.09

−10.51 −7.53 −9.85 −6.77 −12.51 −9.58 −10.97 −7.57

3.78 4.27 3.64 4.11 3.96 4.39 3.75 4.28

−10.29 −7.28 −9.60 −6.17 −12.48 −8.52 −10.76 −7.28

0.12 0.05 0.11 0.16 0.03 0.16 0.16 0.15

Au(111) substrate at 300 K is equal to 0.006 Å2/ps, which is very accurate and close to experimental results.43 As it can be observed in Figure 11, translational diffusion of the flexible nanocooper on Au(111) at 300 K is also 0.0063 Å2/ps. Translational diffusion of a rigid nanocooper is on average 10 times larger than that of a flexible one. The chassis of the nanocooper has three phenylene ethynylene moieties less than the z-car, and thus it has a shorter chassis and axles with fewer adsorption sites. The p-carborane wheels are also lighter than fullerene and therefore the nanocooper rigidity is intrinsically higher than the z-car. Thus, the difference between the diffusion coefficients in the rigid nanocooper and the flexible nanocooper is considerably less than that between the rigid and flexible z-car. Three main reasons can be mentioned for the different diffusion of rigid nanocars in comparison with flexible ones. First, the different distance between the COM and therefore different adhesion between the flexible and rigid nanocars relative to the substrate, as depicted in Supporting Information Figures S29−S36 as a function of temperature. Also in Table 3, the most stable COM heights for the nanocars corresponding to the lowest energy on Au(111) and Au(001) are reported. According to this table, it is observed that the rigid nanocooper, trimer, nanocaterpillar, and angled nanocar on Au(111) substrate are equilibrated at a vertical position averaging 0.57, 0.64, 0.45, and 0.59 Å higher than their flexible counterparts, respectively. The vertical equilibrium positions of these rigid nanocars on Au(001) substrate are also 0.49, 0.47, 0.43, and 0.53 Å higher than the flexible ones, respectively. As illustrated in Figure 13, the rather small diameter of the wheels as well as the flexibility of the nanocooper causes its chassis to stick to the substrate,23 preventing the flexible nanocooper from freely moving. Second, the nanocar flexibility allows its fragments, for example the wheels, to move more freely and may allow them to fall simultaneously in potential wells, reducing the mobility. There is less possibility for this issue to occur in the rigid one due to the fixed distance between the wheels and it is observed that the rigid nanocooper mobility on Au(001) is much greater than the flexible nanocooper. However, in the three other nanocars, that is the trimer, nanocaterpillar, and angled nanocar on Au(001), a different situation is observed. The specific rigid arrangement of their wheels could lead to a situation where most of the wheels fall in the potential minima of the Au(001) substrate at the same time. As a consequence, the mobility of these three rigid nanocars on Au(001) is less than that of the flexible type. This behavior is not observed on

Figure 13. (left) Rigid nanocooper and (right) the flexible nanocooper on Au(111) surface. The small diameter of wheels and the flexibility causes the chassis to stick to the substrate and reduces the nanocar mobility.

Au(111), and all the rigid carborane-wheeled nanocars are considerably more agile on Au(111) compared to flexible ones. The third reason for the different diffusion of rigid nanocars is the deformation of the nanocar axles at high temperatures, which causes the wheels or other fragments to collide or attach to each other. As a result, a portion of the kinetic energy will be dissipated or transferred to the next wheels; consequently, the dynamics of the flexible nanocar differs from the rigid one. 3.3. Comparison of the Nanocar Mobility with Their Wheels. In this section, the analogy between the translational motion of the nanocars and the isolated p-carborane molecule on gold substrate is compared. In other words, we intend to investigate if is it possible to predict nanocar mobility based on its wheels motion? Nemati et al. demonstrated that there are some kinds of quantitative similarities between the translational movement of a fullerene-based nanocar on Au(001) and the motion of a system consisting of only four wheels.48 Contrary to fullerene with Ih symmetry, p-carborane is not perfectly spherical instead it is an icosahedron with the symmetry group of D5d. It is worth mentioning that the nanocar axle or the five-fold symmetry axis of the p-carborane wheel remains approximately parallel to the gold surface during the nanocar movements. It was already reported that in this orientation, called C-axle, the p-carborane molecule has the highest translational motion energy barrier on the gold. While the lowest barrier occurs when one carbon with two adjacent boron atoms are in the closest position relative to the gold, called as C−B−B-down orientation.58 Comparison of the translational motion of nanocars and p-carborane, as shown in K


Article

The Journal of Physical Chemistry C Supporting Information Figures S37−S40, revealed that this Caxle configuration greatly influences the diffusion coefficient of the nanocar and restricts it. A gold substrate with (111) crystalline direction has higher surface-packing density. Accordingly, it is smoother and has shallower potential wells relative to Au(001). This fact may support the idea that every molecule diffuses faster on Au(111) than on Au(001).43 Using the PES analyzing approach, Lavasani et al. predicted that the translational motion of pcarborane on Au(111) is much more than that on Au(001).58 Here, the translational diffusion coefficient of p-carborane as shown in Supporting Information Figure S37, and its trajectories on Au(111) and Au(001) in Figures S41−S46 also confirm this idea. Unlike this finding for the small pcarborane molecule, in Figure 11 it can be observed that these conditions are not valid for the nanocooper and trimer for temperatures below 500 K or the nanocaterpillar at any studied temperatures. The main reason for this dissimilarity comes from the number of potential wells. Gold’s higher density in (111) crystalline direction leads to more potential wells per surface unit; thus, shallower but closer potential wells will be created, while Au(001) has fewer, deeper and farther wells. Thus, regarding the chassis structure, the possibility for most of the wheels to be in Au(111) wells simultaneously may be more than in Au(001). In this regard, some of the nanocar fragments will stand on high energy zones of Au(001) substrate and this makes the nanocar move faster. 3.4. Binding Energy and Motion Barrier of Nanocars. Herein, the potential energy caused by vdW interactions between the nanocars and the gold substrate is presented and discussed. By increasing the temperature, the impulses to the nanocars from the substrate will be stronger and the height of their COM will increase (refer to Supporting Information Figures S29−S32). Consequently, the adsorption force acting on the nanocar diminishes and eventually reduces to zero at high temperatures, indicating desorption of the nanocar from the substrate. Supporting Information Figures S33−S36 show the LJ potential energy between the nanocars and the gold surface as a function of temperature. It should be noted that at high temperatures the nanocar is no longer stable and undergoes dissociative desorption. Morin et al. performed a thermogravimetric analysis to investigate the nanocars thermal stability. They heated samples of a nanocooper under a nitrogen atmosphere at the rate of 20 °C per minute and observed that the alkyne−carborane bonds, corresponding to the coupling of the wheel to the axle, start to decompose when the temperature reached 390 °C (663 K).11 On the other hand, above 1170 K, the Au(001) topmost layer experiences irreversible disorders,91,92 while the two top layers of Au(111) do not melt until the temperature reaches the bulk melting point of 1337 K.93 Hence, such a high temperature must be avoided during the MD simulations. In this section, a series of simulated annealing calculations is done in order to find the binding energy of the nanocars to the gold substrate. The position of the nanocars is sustained at the fixed point of the gold substrate by attaching a weak, in comparison with the LJ potential, harmonic spring to their COM. The system is heated up to 1000 K, then quenched to around 0 K in a period of 200 ps, and finally maintained at this temperature for 1 ns. This procedure was repeated several times until the minimum binding energy was achieved. According to Table 3, the binding energy of the nanocooper on Au(111) is on average 0.42 eV larger than on Au(001). The

trimer, nanocaterpillar, and angled nanocar are also more adsorbed to Au(111) relative to the Au(001) substrate with the amount of 0.51, 0.28, and 0.33 eV, respectively. This is due to a higher surface-packing density of gold in the (111) crystalline direction. Table 3 also revealed that the nanocooper binding energy to Au(111) and Au(001) equals −10.93 and −10.51 eV, respectively, which is in the typical range of chemisorption. The rigid nanocooper also adsorbs on Au(111) and Au(001) substrates with binding energies of −7.25 and −7.53 eV, respectively. To have a comparison, Ahangari et al. calculated the binding energy of fullerene wheels and nanotruck chassis to the gold using the DFT method.50 They roughly estimated the overall binding energy of the nanotruck as −9.43 eV by summing each fragment, for example the wheels and the chassis binding energy. Each of the fragments on its own is prone to be in a different potential well, but the equilibrium positions of the nanotruck wheels are strongly influenced by the chassis shape. Therefore, the equilibrium state and the binding energy of the nanocar as a unit is different from the summation of the binding energies of different parts. One of the common quantitative approaches for calculating the motion barrier of molecules is analyzing their PES on a substrate and finding transition states.47,94−97 In small molecules which are intrinsically more stiff, for example the wheels, it can be assumed that the molecule has 3 translational and 3 rotational degrees of freedom (DOF) on the substrate, and then the 6-dimensional hypersurface of PES is searched for transition states as reported in refs 47, 49, and58. For the diffusion of a larger molecule like the nanocooper which is flexible, the DOF is equal to 3 × Natom = 420, where Natom = 140 is the number of atoms forming the nanocooper. It is obvious that searching for the transition state of a 420dimensional PES is an arduous task. For this reason, a heuristic technique for detection of transition states must be provided. For this goal, after annealing the system, an induced translation of the nanocar is implemented using constant-velocity steered MD (SMD) around 0 K to successively pull the nanocar toward the adjacent cell while the interaction energy between the nanocar and substrate is monitored. At first, the nanocar is pulled with a constant speed of 0.002 Å/ps along the x-axis, then along the y-axis, and finally in the diagonal direction by means of a weak tether attached to the COM. The pulling speed is 100 times slower than the root mean square (RMS) speed of the nanocar. According to this technique, the lowest transition state energies for the translational motion of the nanocooper on Au(111) and Au(001) substrates can be estimated as −10.74 and −10.29 eV, respectively. The transition state and activation energies of the trimer, nanocaterpillar, and angled nanocar are also presented in Table 3. 3.5. Rotational Mobility of Nanocars around the zAxis. The rotation of the flexible nanocooper, trimer, nanocaterpillar, and angled nanocar around the normal vector to the gold surface (z-axis) is presented in Supporting Information Figures S47−S50, respectively. The nanocooper rotation first appears when the temperature reaches 350 K. The range of this rotation is limited to 0.5 rad during the simulation time of 10 ns. Regarding its first translational motion, which occurs at 200 K, it can be concluded that the nanocooper’s tendency to rotate around the z-axis is less than its translational motion. By increasing the temperature, the rotation range of nanocooper will increase and its motion L


Article


Figure 14. (a) Rotational diffusion coefficients of the flexible nanocars on gold as a function of temperature, (b) Arrhenius plot of the rotational motion of the flexible nanocars on gold substrates.

The mentioned figure shows that the rotational diffusion of the nanocooper on Au(111) substrate for temperatures below 450 K is less than Au(001), but increasing the temperature to 500 K causes its rotation mobility on Au(111) to surpass it. The trimer has a different behavior, and for all studied temperatures it experiences more rotation on Au(001). It should be noted that the trimer has more rotational mobility relative to the nanocooper on Au(001), while their rotational mobility on Au(111) is approximately equal. Also, the rotational diffusion of the nanocaterpillar and the angled nanocar on Au(001) is smaller than that on Au(111) at any given temperature. Similar to the trimer, nanocaterpillar and nanocooper rotational mobility on Au(111) in the range 50− 600 K are approximately equal, while the rotational mobility of the angled nanocar on Au(001) is equal to the nanocooper. It can be concluded that the angled nanocar has the most rotational mobility on Au(111), while the three other nanocars have approximately equal rotational mobility. On the Au(001) surface, the trimer has the highest rotational mobility and the nanocaterpillar has the lowest. Therefore, the nanocaterpillar looks like a convincing option for producing directional motion on Au(001) substrate. 3.6. Evaluation of Directional Motion. Nanocar manufacturers designed the nanocooper and nanocaterpillar to reduce any lateral diffusive motion and enhance their directional motion. They have anticipated that the parallel axles of the nanocooper would lead the nanocar to move in a straight pathway; hence, appending one more axle, like the 3axle structure of the nanocaterpillar, will totally diminish the transverse sliding motion. Herein, regarding the flexibility of chassis, longitudinal and transverse directions of these nanocars are estimated through the position of the wheels. Then, the position vector of the nanocars COM is expressed in terms of the nanocar-fixed frames of êL and êT, where êL and êT are the unit longitudinal and unit transverse vectors, respectively. The longitudinal and transverse MSD are defined as follows.

regime turns into a back and forth rotation; eventually, the nanocooper showed three complete rotation at 600 K during the simulation. It was observed that the nanocooper’s first rotation on Au(001) occurs at 250 K. This means that similar to the (111) surface, translation on Au(001) also takes place easier than rotation. Rotation of the nanocooper on Au(001) starts at a lower temperature than that on Au(111); however, when the temperature is increased the rotation on Au(111) surpasses it. The flexible trimer does not have a considerable rotational motion on Au(111) until 350 K, rotating only 2 rad during the entire simulation time, while it has a translational motion at 250 K. On Au(001) its first rotation occurs at 200 K, which is higher than the temperature where translational motion begins. Therefore, similar to the nanocooper, the trimer tends to translate rather than rotate. Motion analysis of the nanocaterpillar revealed that it does not have any notable rotation below 350 K on either the Au(111) or Au(001) surface, while it has translational motion at the even low temperature of 100 K. Accordingly, it can be stated that the nanocaterpillar has the least rotation relative to the three other nanocars and its trajectory on gold is more directional. The angled nanocar showed its first rotational motion on both Au(111) and Au(001) substrates at 250 K with the range of 1 rad during the simulation time. This temperature is very close to the translational motion thresholds which are 200 K on both Au(111) and Au(001). Similar to Section 3.2 which employed an ensemble consisting of NT/Nseg = 300 nanocars, rotational MSD is calculated as a function of temperature using eq 5 while its slope is divided by 2, this represents 1D rotational diffusion coefficient (Drot) of the nanocar around the z-axis as follows. MSDrot (t ) = ⟨|ϕ(t ) − ϕ0|2 ⟩,

Drot = lim

t →∞

MSDrot (t ) 2t (5)

where ϕ(t) is the (yaw) angle of the nanocar around the z-axis at time t and ϕ0 = ϕ(0). The rotational diffusion coefficients of the flexible nanocooper, trimer, nanocaterpillar, and angled nanocar on gold as a function of temperature and their Arrhenius plot are presented in Figure 14. The figure reveals that the slopes of the Arrhenius plot are not constant and thus it is not reasonable to define a unique activation energy for the entire range 50−600 K. Similar to translational motion analysis, nanocars rotation on the gold substrate exhibits a non-Arrhenius behavior.

MSDL (t ) = ⟨|[ e L̂ ·x ̂ e L̂ ·y ̂][r(t ) − r0]|2 ⟩ MSDT(t ) = ⟨|[ e T̂ ·x ̂ e T̂ ·y ̂][r(t ) − r0]|2 ⟩

(6)

where · denotes the scalar product of two vectors. The longitudinal diffusion (DL) and transverse diffusion (DT) of the nanocars on the surface are calculated by eq 7. M


Article

The Journal of Physical Chemistry C DL = lim

t →∞

MSDL (t ) , 2t

DT = lim

t →∞

MSDT(t ) 2t

the wheel of an isolated nanocar around the alkyne group is presumably unrestrained. While Lavasani et al. proved that gold substrate resists against the wheel rotation, especially in C-axle configurations, where the five-fold symmetry axis of the p-carborane is parallel to the gold surface.58 Similar to Section 3.2, in order to calculate rotational MSD of the nanocars wheels, an ensemble consisting of NWNT/Nseg wheels is created for each nanocar, where NW is the number of its wheels. The rotational diffusion of p-carborane wheels of the flexible nanocars around their axles (DW,rot) and the rotational diffusion of an isolated p-carborane molecule on gold are presented in Figure 16. It can be observed that the rotational mobility of different nanocars wheels is slightly similar in the studied temperatures. Furthermore, they are equal to the rotational diffusion of p-carborane molecule around x- and y-axes on the gold substrate. While rotational diffusion of p-carborane around only the z-axis is 1 order of magnitude larger than that of the nanocar wheels. This difference in rotational mobility arises from different configurations of p-carborane on the surface. A p-carborane wheel mounted on the chassis coercively remains in the C-axle configuration and shows less tendency to rotate. While a single p-carborane on the gold is oriented in a more stable C-down configuration. In this configuration, one of the two carbon atoms is in the closest position to the substrate, and even at low temperatures it tends to rotate rapidly around the z-axis.58 Therefore, it can be concluded that estimating the rotational behavior of the nanocar wheel based on the rotation of an isolated p-carborane molecule on a substrate is not precise; this is due to its shape and several atom types, and because in various orientations it can be adsorbed. Furthermore, Lavasani et al. demonstrated that the energy barrier for a complete turn of p-carborane on the gold surface is higher than that of a hopping or sliding motion.58 Thus, a complete turn of the wheels will be rarely seen, and they will instead oscillate back and forth while traveling to adjacent cells. Wheels show pure rotation when their translational velocity is close to ωW × rW, where ωW denotes the angular velocity of the wheel and |rW| = 4 Å is the p-carborane wheel radius. Comparing Figures 11a and 16a, it is found that the translational diffusion coefficient of the wheel (rW2DW,rot) is much larger than the translational diffusion of the nanocars COM (D). Considering that nanocars have slight rotational mobility (Drot) around the z-axis as depicted in Figure 14a, this

(7)

In Figure 15, the ratio of DL/DT is presented for the nanocooper and nanocaterpillar on Au(111) and Au(001) as a

Figure 15. Ratio of the longitudinal to the transverse diffusion coefficient of the flexible nanocooper and nanocaterpillar on Au(111) and Au(001) as a function of temperature.

function of temperature. An increase of this ratio does not necessarily show rectilinear motion, but its decrease indicates more lateral sliding. It was observed that in accordance with the designers’ expectation, the ratio of DL/DT was greater than 1 in the whole studied temperature range. Generally, by increasing the temperature of the nanocars on Au(111), the ratio DL/DT will decrease and converges to 1. In other words, the nanocooper and the nanocaterpillar will have more lateral sliding motions on Au(111) at higher temperatures, indicating more diffusive motion. The nanocooper and nanocaterpillar have different behaviors on the Au(001) substrate. The nanocaterpillar experienced more longitudinal motion on Au(001) upon heating. The nanocooper had its most longitudinal motion at 300 K and its lateral sliding increased and exhibited more diffusive motion during the increase in the temperature. 3.7. Discussion on Wheels Rotation. In this section, a comparison between the rotation of wheels around the nanocar axle and isolated p-carborane molecule on the gold surface is made. Timofeeva et al. showed that the torsional barrier for different substituents attached to the carborane cage is negligible.71 Therefore, one can conclude that the rotation of

Figure 16. (a) Rotational diffusion coefficient of the p-carborane wheels of the flexible nanocars around their axles on Au(111) and Au(001) as a function of temperature. (b) Rotational diffusion of an isolated p-carborane molecule around x- and y-axes and z-axis on Au(111) and Au(001) as a function of temperature. N


Article


and 1.99 i and j are the wheel numbers and k is representative of the x-, y-, and z-component of the angular velocity vector. When indicator CW approaches 1 there is a perfect linear (positive or negative) relationship, and when it approaches 0 there is no linear relationship among the angular velocities of the wheels. As depicted in Figure 18, indicator CW is negligible in the whole studied temperature range; consequently, all combina-

confirms that the wheels tend to slide rather than roll while traveling to the next cell. In order to provide a measure for the sliding-rolling ratio of the nanocar wheel, we use the same approach proposed by the society of automotive engineers98 for an ordinary tire, as shown in eq 8. Slip ratio =

ωW × rW − VW ̅ VW ̅

(8)

where V̅ W denotes for the velocity vector of the COM of nanocars wheel. When the slip ratio approaches 0, it means that the wheels are undergoing pure rolling motion. As shown in Figure 17, the slip ratios of different nanocars wheels are

Figure 18. Correlation of angular velocity of nanocars wheels vs temperature.

tion of ρ(ωW,ki,ωW,kj) must be negligible as well. It should be noted that all angular velocities have a normal distribution. Furthermore, considering the scatter diagram of ωW,kj versus ωW,ki reveals that there is no even nonlinear relationship among them. Thus, it can be summarized that the rotation of the wheels occurs completely independently. Additionally, parameters such as chassis shape, substrate crystalline direction, and temperature do not have any effect on these correlation values.

Figure 17. RMS slip ratio of the flexible nanocars wheels on gold as a function of temperature.

exactly the same in the whole studied temperatures and are much larger than 0. This confirms that most of the times the wheels tend to slide rather than roll. Additionally, the slip ratio is not a function of temperature. Our investigations indicate that in SMD simulation, the slip ratio of the wheels is still much greater than 0, but slightly lower than that of non-SMD. It is observed that the average slip ratios of the wheels of the nanocooper, trimer, nanocaterpillar, and angled nanocar on Au(111) substrate are 3.5, 3.4, 3.8, and 3.4, respectively, and their slip ratios on Au(001) substrate are 3.6, 3.4, 4.2, and 3.7, respectively. Although the nanocars are guided by some springs, the wheels tend to slip. 3.8. Correlations in the Rotation of Nanocar Wheels. Herein, it will be investigated whether the rotation of one nanocar wheel has an influence on the others or not. Konyukhov et al. proposed some techniques for calculating corresponding effects of wheels. They demonstrated that the correlation in the rotation of the wheels of the fullerene-based z-car is almost identical to the correlation in a system made of only four interacting fullerene molecules on gold substrate and these correlation values are both small.46 In order to analyze the correlation in the motion of the carborane-based nanocar wheels, we introduced indicator CW, which provides a measure for the correlation in any possible combination of two wheels angular velocity and is defined as follows. N

CW =

4. RECENT EXPERIMENTAL OBSERVATIONS Most of the past research studies mentioned in Section 1 are limited to the synthesis and scanning of nanocars movement, and quite a few works focus on the simulation of nanocars performance. Nanocar variants are diverse but the wheel composition and chassis structure, generally used to categorize nanocars, are two of the main parameters specifying motion behavior. Therefore, it is expected that analyzing one or a couple nanocars from one family should efficiently reveal the general aspects about the whole family. As it was thoroughly discussed in the results section and despite a few differences among nanocars in the same family, the same qualitative behaviors could be expected for the whole nanocar family. One of the main difficulties in experimentally analyzing carboranebased nanocars is the small size of their wheels. Unlike fullerene wheels, detection and tracing of carborane wheels at high temperatures is an arduous task. Most of the time only the p-carborane wheels and in some cases both the wheels and chassis are observable in STM imaging of p-carborane-based nanocars, generating some interference; while only the wheels are observed in fullerene-based nanocars. It is worthy to note that the nanocooper has a nearly square shape which makes it hard to detect its orientation on the surface. In this regard, the rectangular nanocaterpillar has an advantage over it.11 Considering these equipment limitations, there is little experimental observation available for carborane-based nanocars. Consequently, validating theoretical studies is limited to some qualitative experimental observations.

N

2∑i =W1 ∑ j >Wi ∑k = x , y , z |ρ(ωW, ki , ωW, kj )| 3NW (NW − 1)

(9)

where ρ denotes a linear correlation between two variables, ρ(ωW, ki , ωW, kj ) =

cov(ωW, ki , ωW, kj ) σω W, kiσω W, kj

, and its range lies between −1 O


Article


5. SUMMARY AND CONCLUSIONS In this research, the motion of p-carborane-wheeled nanocars on Au(111) and Au(001) surfaces in the range of 50−600 K has been investigated utilizing the classical MD method. The nanocars studied are the nanocooper, trimer, nanocaterpillar, and angled nanocar equipped with 4, 3, 6, and 4 wheels, respectively. The motion regimes of these nanocars on gold substrate have not been previously meticulously studied. We discovered that the motion regime of the nanocars on gold is a function of temperature, and the three main regimes that are trapped in the crystal structure, short-range fluctuations, and continuous motion are observed upon heating. Also, the chassis structure and gold crystalline direction influence the regime switching temperatures and the diffusion on the gold surface. It should be noted that most of the time a distinct border between the two motion regimes of short-range fluctuations and continuous motion cannot be observed. The nanocooper is immobile on Au(111) and Au(001) for temperatures below 200 K and is trapped in the potential wells on the gold surface. By increasing the temperature to 200−400 K, the dominant regime switches to short-range fluctuations but the nanocooper does not experience a significant overall displacement. The motion regime changes to continuous when the temperature reaches 450 K, and this nanocar can travel long distances freely. At low temperatures, the nanocooper mobility on the Au(001) substrate is more than that on Au(111), but increasing the temperature will cause its translation on Au(111) to surpass it. At 100 K, the trimer has sufficient energy to start a hopping motion to an adjacent cell on Au(001), while on Au(111) the hopping motion occurs at 250 K. These short-range fluctuations do not lead to a notable displacement until 450 K. At this temperature range, the trimer has more mobility on Au(001). However, at 500 K and higher temperatures, the trimer shows more translational motion on Au(111). Contrary to the designers’ expectation, the translational motion of the trimer is not less than the nanocooper, and it has no pure rotation about its pivot. The nanocaterpillar motion regime on both Au(111) and Au(001) at 100 K changes from trapped in the crystal structure to shortrange fluctuations. The nanocaterpillar does not tend to rotate on Au(001) until the temperature reaches 350 K. In that case, its longitudinal axis aligned parallel to the diagonal direction on Au(001) substrate and a back and forth directional motion can be achieved. Thus, the nanocaterpillar shows the most directed mobility relative to the three other nanocars. The angled nanocar on Au(111) and A(001) also has the required energy to hop to an adjacent cell at 200 K. Flexible and rigid p-carborane-wheeled nanocar diffusion on gold has been analyzed and it was observed that these motions exhibit non-Arrhenius behavior. In this research, the results of classical MD and RBMD methods have been compared. The results demonstrate that the RBMD simulation may overestimate the diffusion coefficient up to 10 times more than the one predicted by MD method as previously reported in ref 46, and the results of the MD simulation are in a good agreement with available experimental observations. The mechanism of motion of nanocars depends on how well the essential physics of interactions with the substrate or the other nanoparticles is captured by the potential in use. In general, vdW and electrostatic forces adsorb nanocars on the substrate. The LJ interaction as a commonly used potential for modeling interactions of nanoparticles and surfaces, and it

One of the rare experimental observations has been done by nanocar manufacturers themselves. Zhang et al. analyzed the motion of p-carborane- and fullerene-wheeled nanocars by STM; however, they did not publish the diffusion coefficient data.39 Although they have not reported the capturing frame rate, the acquisition time for each STM image in a similar situation and by a similar team was reported to be 1 min.9 For that reason, when the temperature reaches 300 °C and the nanocar accelerates, nanocar tracking by a tip apex is no longer possible. Zhang et al. deposited many fullerene- and carboranewheeled nanocars on a gold substrate and gradually heated the system in ultrahigh vacuum conditions to investigate the motion threshold. Specifically, the fullerene-wheeled nanocar at 200 °C (473 K) and carborane-wheeled nanocar after 2 min of annealing at the approximate temperature of 150 °C (423 K) started a translational motion. Motion regime and translational diffusion analysis of carborane-based nanocars presented in Sections 3.1 and 3.2 show that the nanocars do not have noticeable motion for temperatures below 400 K, but significant translational motions can be observed by increasing the temperature to 450 K. Therefore, there is a qualitative agreement between the simulation results and experimental observations. Zhang et al. also demonstrated that a nanocaterpillar colony preferred to align themselves with the orientation of the substrate herringbone structures formed during the surface reconstruction. A similar behavior was observed in MD simulations of the nanocaterpillar on gold and the nanocaterpillar tends to have rectilinear motion without rotation. The MD results of Section 3.7 indicate that the nanocars wheels mostly tend to hop toward the adjacent cell rather than to roll. Also, this hopping motion happens in a few picoseconds order of magnitude. In this regard, the manufacturers stated that their microscopy or spectroscopy tools did not have the capability to detect the rotation at that time period and the need for further development is quite obvious.8 Rolling has more advantages than a hopping motion and this determines the nanocar efficiency. That is because hopping to the adjacent sites can occur in every direction even on flat surfaces, while a rolling motion is more directional. Because carborane-wheeled nanocars were introduced no research on the rotation of the wheels of the nanocooper, trimer, nanocaterpillar, and angled nanocar on the gold substrate were accomplished till now, although the wheels rotation of different carborane-based vehicle on hydrated silica,100 glass,101 and Cu(111) substrate34 have been investigated. Villagómez et al. studied the assembly of carborane-wheeled molecular wagons on Au(111) and Ag(110) surfaces as well as Cu(111), though deposition of these wagons onto gold and silver substrates did not form a train.34 They reported that a series of lateral manipulation of a single wagon by an STM tip only led a few wagons to slide on the surface. Therefore, they concluded that strong trainsubstrate adsorption resists against wheels rotation, and consequently collective movement of the whole wagons is prevented. Considering the above-mentioned discussions, it can be asserted that there is a proper qualitative agreement between MD results and the available experimental observations. These simulations revealed more details for nanocars motion than can be observed by the currently available equipment in all situations. P


Article


motorized nanocars with higher controllability and maneuverability.

enables simulation of large systems over a long period of time with a low computational cost. The proper agreement between our simulation results and experimental observations, such as predicting the nanocar motion threshold, diffusion coefficient, and the hopping motion of the wheels, indicates that the LJ parameters are well-chosen. It should be added that considering electrostatic interactions due to charge transfer between nanocar and the surface may increase the nanocars motion activation energy and restrict their mobility. Although including electrostatic interactions improves the simulation accuracy, due to the high computational cost of these new calculations, our current calculations are not feasible. Nanocars binding energy to the substrate was studied using a simulated annealing technique and it was indicated that the binding energy to Au(111) is greater than Au(001). Rigid nanocars have less binding energy due to the larger gap between their COM and the surface and consequently show greater yet more imprecise diffusion on gold. In addition, the nanocars motion activation energy between two local minima on gold substrate was reported. Nanocar manufacturers designed the nanocooper and especially the nanocaterpillar to diminish the lateral sliding motion and improve a directional motion. It was observed that in accordance with the designers’ expectation, the longitudinal motion is larger than the transverse in the studied temperature range. However, increasing the temperature reduced the longitudinal motion of these nanocars on Au(111) and they show more diffusive motion. On the other hand, the nanocaterpillar on Au(001) experienced more longitudinal motion at higher temperatures, while the nanocooper’s longitudinal to transverse motion ratio increased until 300 K and then decreased afterward. Comparing the translational and rotational motion thresholds of the nanocars showed that the nanocar translation occurs at lower temperatures. In this regard, the nanocar tendency toward translational motion is more than its tendency to rotate around the z-axis. Rotational diffusion shows that the nanocooper, trimer, and nanocaterpillar have the same rotational mobility on Au(111) for all studied temperatures and these rotations are smaller than that of the angled nanocar. There is a different situation on Au(001), where the trimer has the most rotational mobility and the nanocaterpillar has the lowest. Therefore, a nanocaterpillar on Au(001) is an excellent choice for performing directional motion. It can be predicted that if the nanocaterpillar on Au(001) is subjected to a diagonal temperature gradient, its motion will be unidirectional. The wheel rotational behavior of the carborane-based nanocars around their axles was analyzed and it was observed that the different nanocars have the same wheel rotational mobility. Nanocar wheels have only a slight tendency to perform complete rotations and they often hop to an adjacent cell rather than roll; this behavior is consistent with the experimental observations. It was proven that the rotation of the wheels is completely independent of each other, and temperature variation, substrate crystalline direction, and chassis shape have no influence on this issue. The results from this research give a more detailed knowledge of diffusive rotational and translational motion of the p-carborane-wheeled nanocars, which can be utilized to predict overall behavior of other similar structured nanocars. Furthermore, these results can be used to design and analyze

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b10779. Geometry, charge, HOMO, and LUMO of nanocars; trajectory of second and third simulations; trajectory of rigid nanocars, nanocars height, vdW interaction between nanocars and substrate, and diffusion coefficient of nanocars versus p-carborane; trajectory of pcarborane; and rotational motion of nanocars (PDF) Trajectory of the nanocooper on Au(111) and Au(001) at different temperatures (AVI) Trajectory of the trimer on Au(111) and Au(001) at different temperatures (AVI) Trajectory of the nanocaterpillar on Au(111) and Au(001) at different temperatures (AVI) Trajectory of the angled nanocar on Au(111) and Au(001) at different temperatures (AVI)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +98 21 6616 5543 (H.N.P.). ORCID

Hossein Nejat Pishkenari: 0000-0002-3487-3198 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This study was partly supported by the Iran Nanotechnology Innovation Council (grant 57085). The authors would also like to gratefully acknowledge the facilities of high-performance computing at the Information and Communication Technology Center of Sharif University of Technology. The authors also appreciate Shari Lin Holderread for English editing of the manuscript.

■

REFERENCES

(1) Feynman, R. P. There’s Plenty of Room at the Bottom. Eng. Sci. 1960, 23, 22−36. (2) Kay, E. R.; Leigh, D. A.; Zerbetto, F. Synthetic Molecular Motors and Mechanical Machines. Angew. Chem., Int. Ed. 2007, 46, 72−191. (3) Shirai, Y.; Minami, K.; Nakanishi, W.; Yonamine, Y.; Joachim, C.; Ariga, K. Driving Nanocars and Nanomachines at Interfaces: From Concept of Nanoarchitectonics to Actual Use in World Wide Race and Hand Operation. Jpn. J. Appl. Phys. 2016, 55, 1102a2. (4) Kassem, S.; van Leeuwen, T.; Lubbe, A. S.; Wilson, M. R.; Feringa, B. L.; Leigh, D. A. Artificial Molecular Motors. Chem. Soc. Rev. 2017, 46, 2592−2621. (5) Samorì, P. Scanning Probe Microscopies Beyond Imaging: Manipulation of Molecules and Nanostructures; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2006. (6) Vives, G.; Tour, J. M. Synthesis of Single-Molecule Nanocars. Acc. Chem. Res. 2009, 42, 473−487. (7) Shirai, Y.; Osgood, A. J.; Zhao, Y.; Kelly, K. F.; Tour, J. M. Directional Control in Thermally Driven Single-Molecule Nanocars. Nano Lett. 2005, 5, 2330−2334. (8) Shirai, Y.; Morin, J.-F.; Sasaki, T.; Guerrero, J. M.; Tour, J. M. Recent Progress on Nanovehicles. Chem. Soc. Rev. 2006, 35, 1043− 1055. Q


Article

The Journal of Physical Chemistry C (9) Shirai, Y.; et al. Surface-Rolling Molecules. J. Am. Chem. Soc. 2006, 128, 4854−4864. (10) Joachim, C.; Tang, H.; Moresco, F.; Rapenne, G.; Meyer, G. The Design of a Nanoscale Molecular Barrow. Nanotechnology 2002, 13, 330−335. (11) Morin, J.-F.; Sasaki, T.; Shirai, Y.; Guerrero, J. M.; Tour, J. M. Synthetic Routes toward Carborane-Wheeled Nanocars. J. Org. Chem. 2007, 72, 9481−9490. (12) Sasaki, T.; Morin, J.-F.; Lu, M.; Tour, J. M. Synthesis of a Single-Molecule Nanotruck. Tetrahedron Lett. 2007, 48, 5817−5820. (13) Sasaki, T.; Tour, J. M. Synthesis of a Dipolar Nanocar. Tetrahedron Lett. 2007, 48, 5821−5824. (14) Vives, G.; Kang, J.; Kelly, K. F.; Tour, J. M. Molecular Machinery: Synthesis of a ″Nanodragster″. Org. Lett. 2009, 11, 5602− 5605. (15) Vives, G.; Tour, J. M. Synthesis of a Nanocar with Organometallic Wheels. Tetrahedron Lett. 2009, 50, 1427−1430. (16) Chu, P.-L. E.; Wang, L.-Y.; Khatua, S.; Kolomeisky, A. B.; Link, S.; Tour, J. M. Synthesis and Single-Molecule Imaging of Highly Mobile Adamantane-Wheeled Nanocars. ACS Nano 2012, 7, 35−41. (17) Chen, F.; García-López, V.; Jin, T.; Neupane, B.; Chu, P.-L. E.; Tour, J.; Wang, G. Moving Kinetics of Nanocars with Hydrophobic Wheels on Solid Surfaces at Ambient Conditions. J. Phys. Chem. C 2016, 120, 10887−10894. (18) García-López, V.; Alemany, L. B.; Chiang, P.-T.; Sun, J.; Chu, P.-L.; Martí, A. A.; Tour, J. M. Synthesis of Light-Driven Motorized Nanocars for Linear Trajectories and Their Detailed NMR Structural Determination. Tetrahedron 2017, 73, 4864−4873. (19) Jin, T.; García-López, V.; Kuwahara, S.; Chiang, P.-T.; Tour, J. M.; Wang, G. Diffusion of Nanocars on an Air-Glass Interface. J. Phys. Chem. C 2018, 122, 19025−19036. (20) Joachim, C.; Rapenne, G. Molecule Concept Nanocars: Chassis, Wheels, and Motors? ACS Nano 2013, 7, 11−14. (21) Ariga, K.; Mori, T.; Nakanishi, W. Nano Trek Beyond: Driving Nanocars/Molecular Machines at Interfaces. Chem.Asian J. 2018, 13, 1266−1278. (22) Rapenne, G.; Joachim, C. The First Nanocar Race. Nat. Rev. Mater. 2017, 2, 17040. (23) Simpson, G. J.; García-López, V.; Petermeier, P.; Grill, L.; Tour, J. M. How to Build and Race a Fast Nanocar. Nat. Nanotechnol. 2017, 12, 604−606. (24) Pawlak, R.; et al. Design and Characterization of an Electrically Powered Single Molecule on Gold. ACS Nano 2017, 11, 9930−9940. (25) Eisenhut, F.; Durand, C.; Moresco, F.; Launay, J.-P.; Joachim, C., Training for the 1st International Nano-Car Race: The Dresden Molecule-Vehicle. EPJ Appl. Phys. 2016, 76, No. 10001. DOI: 10.1051/epjap/2016160259 (26) de Rouville, H.-P. J.; Kammerer, C.; Rapenne, G., From the Synthesis of Nanovehicles to Participation in the First Nanocar Race View from the French Team. Molecules 2018, 23, No. 612. DOI: 10.3390/molecules23030612 (27) Soe, W.-H.; Shirai, Y.; Durand, C.; Yonamine, Y.; Minami, K.; Bouju, X.; Kolmer, M.; Ariga, K.; Joachim, C.; Nakanishi, W. Conformation Manipulation and Motion of a Double Paddle Molecule on an Au(111) Surface. ACS Nano 2017, 11, 10357−10365. (28) Fein, M. M.; Bobinski, J.; Mayes, N.; Schwartz, N.; Cohen, M. S.; Carboranes, I. Carboranes. I. The Preparation and Chemistry of 1Isopropenylcarborane and its Derivatives (a New Family of Stable Clovoboranes). Inorg. Chem. 1963, 2, 1111−1115. (29) Heying, T. L.; Ager, J. W.; Clark, S. L.; Mangold, D. J.; Goldstein, H. L.; Hillman, M.; Polak, R. J.; Szymanski, J. W. A New Series of Organoboranes. I. Carboranes from the Reaction of Decaborane with Acetylenic Compounds. Inorg. Chem. 1963, 2, 1089−1092. (30) Chen, Z.; King, R. B. Spherical Aromaticity: Recent Work on Fullerenes, Polyhedral Boranes, and Related Structures†. Chem. Rev. 2005, 105, 3613−3642.

(31) Valliant, J. F.; Guenther, K. J.; King, A. S.; Morel, P.; Schaffer, P.; Sogbein, O. O.; Stephenson, K. A. The Medicinal Chemistry of Carboranes. Coord. Chem. Rev. 2002, 232, 173−230. (32) Sasaki, T.; Guerrero, J. M.; Leonard, A. D.; Tour, J. M. Nanotrains and Self-Assembled Two-Dimensional Arrays Built from Carboranes Linked by Hydrogen Bonding of Dipyridones. Nano Res. 2008, 1, 412−419. (33) Sasaki, T.; Guerrero, J. M.; Tour, J. M. The Assembly Line: Self-Assembling Nanocars. Tetrahedron 2008, 64, 8522−8529. (34) Villagómez, C. J.; Sasaki, T.; Tour, J. M.; Grill, L. Bottom-up Assembly of Molecular Wagons on a Surface. J. Am. Chem. Soc. 2010, 132, 16848−16854. (35) Morin, J.-F.; Shirai, Y.; Tour, J. M. En Route to a Motorized Nanocar. Org. Lett. 2006, 8, 1713−1716. (36) Saywell, A.; Bakker, A.; Mielke, J.; Kumagai, T.; Wolf, M.; García-López, V.; Chiang, P.-T.; Tour, J. M.; Grill, L. Light-Induced Translation of Motorized Molecules on a Surface. ACS Nano 2016, 10, 10945−10952. (37) van Delden, R. A.; ter Wiel, M. K. J.; Pollard, M. M.; Vicario, J.; Koumura, N.; Feringa, B. L. Unidirectional Molecular Motor on a Gold Surface. Nature 2005, 437, 1337−1340. (38) Sasaki, T.; Tour, J. M. Synthesis of a New Photoactive Nanovehicle: A Nanoworm. Org. Lett. 2008, 10, 897−900. (39) Zhang, J.; Osgood, A.; Shirai, Y.; Morin, J.-F.; Sasaki, T.; Tour, J. M.; Kelly, K. F. In Investigating the Motion of Molecular Machines on Surfaces by STM: The Nanocar and Beyond. 2007 7th IEEE Conference on Nanotechnology (IEEE NANO), Hong Kong, Aug 2−5, 2007; pp 243−246. (40) Claytor, K.; Khatua, S.; Guerrero, J. M.; Tcherniak, A.; Tour, J. M.; Link, S. Accurately Determining Single Molecule Trajectories of Molecular Motion on Surfaces. J. Chem. Phys. 2009, 130, 164710− 164718. (41) Khatua, S.; Guerrero, J. M.; Claytor, K.; Vives, G.; Kolomeisky, A. B.; Tour, J. M.; Link, S. Micrometer-Scale Translation and Monitoring of Individual Nanocars on Glass. ACS Nano 2009, 3, 351−356. (42) Akimov, A. V.; Nemukhin, A. V.; Moskovsky, A. A.; Kolomeisky, A. B.; Tour, J. M. Molecular Dynamics of SurfaceMoving Thermally Driven Nanocars. J. Chem. Theory Comput. 2008, 4, 652−656. (43) Akimov, A. V.; Williams, C.; Kolomeisky, A. B. Charge Transfer and Chemisorption of Fullerene Molecules on Metal Surfaces: Application to Dynamics of Nanocars. J. Phys. Chem. C 2012, 116, 13816−13826. (44) Akimov, A. V.; Kolomeisky, A. B. Unidirectional Rolling Motion of Nanocars Induced by Electric Field. J. Phys. Chem. C 2012, 116, 22595−22601. (45) Konyukhov, S. S.; Artemov, N. N.; Kaliman, I. A.; Kupchenko, I. V.; Nemukhin, A. V.; Moskovskii, A. A. Diffusion of FullereneBased Nanocars on the Surface of a Gold Crystal. Moscow Univ. Chem. Bull. 2010, 65, 219−220. (46) Konyukhov, S. S.; Kupchenko, I. V.; Moskovsky, A. A.; Nemukhin, A. V.; Akimov, A. V.; Kolomeisky, A. B. Rigid-Body Molecular Dynamics of Fullerene-Based Nanocars on Metallic Surfaces. J. Chem. Theory Comput. 2010, 6, 2581−2590. (47) Nejat Pishkenari, H.; Nemati, A.; Meghdari, A.; Sohrabpour, S. A Close Look at the Motion of C60 on Gold. Curr. Appl. Phys. 2015, 15, 1402−1411. (48) Nemati, A.; Meghdari, A.; Nejat Pishkenari, H.; Sohrabpour, S. Investigation into Thermally Activated Migration of Fullerene-Based Nanocars. Sci. Iran. 2018, 25, 1835−1848. (49) Nemati, A.; Nejat Pishkenari, H.; Meghdari, A.; Sohrabpour, S. Directing the diffusive motion of fullerene-based nanocars using nonplanar gold surfaces. Phys. Chem. Chem. Phys. 2018, 20, 332−344. (50) Ahangari, M. G.; Ganji, M. D.; Jalali, A. Interaction between Fullerene-Wheeled Nanocar and Gold Substrate: A DFT Study. Phys. E 2016, 83, 174−179. (51) Ganji, M. D.; Ahangari, M. G.; Emami, S. M. CarboraneWheeled Nanocar Moving on Graphene/Graphyne Surfaces: Van Der R


Article

The Journal of Physical Chemistry C Waals Corrected Density Functional Theory Study. Mater. Chem. Phys. 2014, 148, 435−443. (52) Zeng, H.; Byun, D.; Zhang, J.; Vidali, G.; Onellion, M.; Dowben, P. A. Adsorption and Bonding of Molecular Icosahedra on Cu(100). Surf. Sci. 1994, 313, 239−250. (53) Caruso, A. N.; Bernard, L.; Xu, B.; Dowben, P. A. Comparison of Adsorbed Orthocarborane and Metacarborane on Metal Surfaces. J. Phys. Chem. B 2003, 107, 9620−9623. (54) Tillekaratne, A.; Siap, D.; Trenary, M. Adsorption and Dehydrogenation of Ortho-Carborane on the Pt(111) Surface. J. Phys. Chem. C 2008, 112, 8682−8689. (55) von Wrochem, F.; Scholz, F.; Gao, D.; Nothofer, H.-G.; Yasuda, A.; Wessels, J. M.; Roy, S.; Chen, X.; Michl, J. High-Band-Gap Polycrystalline Monolayers of a 12-Vertex p-Carborane on Au(111). J. Phys. Chem. Lett. 2010, 1, 3471−3477. (56) Scholz, F.; Nothofer, H.-G.; Wessels, J. M.; Nelles, G.; von Wrochem, F.; Roy, S.; Chen, X.; Michl, J. Permethylated 12-Vertex PCarborane Self-Assembled Monolayers. J. Phys. Chem. C 2011, 115, 22998−23007. (57) Thomas, J. C.; Boldog, I.; Auluck, H. S.; Bereciartua, P. J.; Dušek, M.; Machácě k, J.; Bastl, Z.; Weiss, P. S.; Baše, T. SelfAssembled p-Carborane Analogue of p-Mercaptobenzoic Acid on Au{111}. Chem. Mater. 2015, 27, 5425−5435. (58) Lavasani, S. M. H.; Pishkenari, H. N.; Meghdari, A. Mechanism of 1,12-Dicarba-Closo-Dodecaborane Mobility on Gold Substrate as a Nanocar Wheel. J. Phys. Chem. C 2016, 120, 14048−14058. (59) Valiev, M.; et al. Nwchem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477−1489. (60) Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A WellBehaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The Resp Model. J. Phys. Chem. 1993, 97, 10269−10280. (61) Case, D. A.; et al. AMBER 2018; University of California: San Francisco, 2018. (62) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graph. 1996, 14, 33−38. (63) Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeerschd, T.; Zurek, E.; Hutchison, G. R., Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. J. Cheminf. 2012, 4, No. 17. DOI: 10.1186/1758-2946-4-17 (64) Turner, A. R.; Robertson, H. E.; Borisenko, K. B.; Rankin, D. W. H.; Fox, M. A. Gas-Phase Electron Diffraction Studies of the Icosahedral Carbaboranes, Ortho-, Meta- and Para-C2B10H12. Dalton Trans. 2005, 1310−1318. (65) Salam, A.; Deleuze, M. S.; François, J.-P. Computational Study of the Structural and Vibrational Properties of Ten and Twelve Vertex Closo-Carboranes. Chem. Phys. 2003, 286, 45−61. (66) Hnyk, D.; Holub, J.; Hofmann, M.; von Ragué Schleyer, P.; Robertson, H. E.; Rankin, D. W. H. Synthesis and Molecular Structure of 1,12-Dicarba-Closo-Dodecaborane(12)-1,12-Dithiol, 1,12-(SH)21,12-C2B10H10, in the Gaseous Phase, Determined by Electron Diffraction and Ab Initio Calculations; Geometrical Consequences of Three-Dimensional Aromaticity in Carbaboranes 1,12-X2-1,12C2B10H10. J. Chem. Soc., Dalton Trans. 2000, 4617−4622. (67) Hermansson, K.; Wójcik, M.; Sjö berg, S. o-,m-, andpCarboranes and Their Anions: Ab Initio Calculations of Structures, Electron Affinities, and Acidities†. Inorg. Chem. 1999, 38, 6039−6048. (68) Oliva, J. M.; Klein, D. J.; Schleyer, P. v. R.; Serrano-Andrés, L. Design of Carborane Molecular Architectures with Electronic Structure Computations: From Endohedral and Polyradical Systems to Multidimensional Networks. Pure Appl. Chem. 2009, 81, 719−729. (69) Timofeeva, T. V.; Allinger, N. L.; Buehl, M.; Mazurek, U. Application of Molecular Mechanics for Calculations of Metallocarborane Molecules. Russ. Chem. Bull. 1994, 43, 1795−1801. (70) Timofeeva, T. V.; Mazurek, U.; Allinger, N. L. Molecular Mechanics Calculations on Carboranes and Metallocarboranes. J. Mol. Struct.: THEOCHEM 1996, 363, 35−42.

(71) Timofeeva, T. V.; Suponitsky, K. Y.; Yanovsky, A. I.; Allinger, N. L. The MM3 Force Field for 12-Vertex Boranes and Carboranes. J. Organomet. Chem. 1997, 536−537, 481−488. (72) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. Molecular Mechanics. The MM3 Force Field for Hydrocarbons. 1. J. Am. Chem. Soc. 1989, 111, 8551−8566. (73) Lii, J. H.; Allinger, N. L. Molecular Mechanics. The MM3 Force Field for Hydrocarbons. 2. Vibrational Frequencies and Thermodynamics. J. Am. Chem. Soc. 1989, 111, 8566−8575. (74) Lii, J. H.; Allinger, N. L. Molecular mechanics. The MM3 force field for hydrocarbons. 3. The van der Waals’ potentials and crystal data for aliphatic and aromatic hydrocarbons. J. Am. Chem. Soc. 1989, 111, 8576−8582. (75) Gamba, Z.; Powell, B. M. The Condensed Phases of Carboranes. J. Chem. Phys. 1996, 105, 2436−2440. (76) Heinz, H.; Vaia, R. A.; Farmer, B. L.; Naik, R. R. Accurate Simulation of Surfaces and Interfaces of Face-Centered Cubic Metals Using 12−6 and 9−6 Lennard-Jones Potentials. J. Phys. Chem. C 2008, 112, 17281−17290. (77) Lorentz, H. A. Ueber Die Anwendung Des Satzes Vom Virial in Der Kinetischen Theorie Der Gase. Ann. Phys. 1881, 248, 127−136. (78) Berthelot, D. Sur Le Mélange Des Gaz. C. R. Hebd. Seances Acad. Sci. 1898, 126, 1703−1857. (79) Touloukian, Y. S.; Kirby, R. K.; Taylor, R. E.; Desai, P. D. Thermal Expansion Metallic Elements and Alloys. Thermophysical Properties of Matter; IFI/Plenum: New York, 1975; Vol. 12, p 127. (80) Dutta, B. N.; Dayal, B. Lattice Constants and Thermal Expansion of Gold up to 878 °C by X-Ray Method. Phys. Status Solidi B 1963, 3, 473−477. (81) Sheng, H. W.; Kramer, M. J.; Cadien, A.; Fujita, T.; Chen, M. W. Highly Optimized Embedded-Atom-Method Potentials for Fourteen Fcc Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 134118. (82) Daw, M. S.; Baskes, M. I. Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1984, 29, 6443−6453. (83) Grochola, G.; Russo, S. P.; Snook, I. K. On Fitting a Gold Embedded Atom Method Potential Using the Force Matching Method. J. Chem. Phys. 2005, 123, 204719. (84) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (85) Nosé, S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods. J. Chem. Phys. 1984, 81, 511−519. (86) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695−1697. (87) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 1992, 97, 2635−2643. (88) Kamberaj, H.; Low, R. J.; Neal, M. P. Time Reversible and Symplectic Integrators for Molecular Dynamics Simulations of Rigid Molecules. J. Chem. Phys. 2005, 122, 224114. (89) Ernst, D.; Köhler, J. Measuring a Diffusion Coefficient by Single-Particle Tracking: Statistical Analysis of Experimental Mean Squared Displacement Curves. Phys. Chem. Chem. Phys. 2013, 15, 845−849. (90) Arrhenius, S. Ü ber Die Reaktionsgeschwindigkeit Bei Der Inversion Von Rohrzucker Durch Säuren. Z. Phys. Chem. 1889, 4, 226−248. (91) Bilalbegović, G.; Tosatti, E. Incomplete Melting of the Au(100) Surface. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48, 11240− 11248. (92) Mochrie, S. G. J.; Zehner, D. M.; Ocko, B. M.; Gibbs, D. Structure and Phases of the Au(001) Surface: X-Ray Scattering Measurements. Phys. Rev. Lett. 1990, 64, 2925−2928. (93) Carnevali, P.; Ercolessi, F.; Tosatti, E. Melting and Nonmelting Behavior of the Au(111) Surface. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 36, 6701−6704. S


Article

The Journal of Physical Chemistry C (94) Jafary-Zadeh, M.; Reddy, C.; Sorkin, V.; Zhang, Y.-W. Kinetic Nanofriction: A Mechanism Transition from Quasi-Continuous to Ballistic-Like Brownian Regime. Nanoscale Res. Lett. 2012, 7, 148. (95) Savin, A. V.; Kivshar, Y. S. Transport of Fullerene Molecules Along Graphene Nanoribbons. Sci. Rep. 2012, 2, 1012. (96) Jafary-Zadeh, M.; Reddy, C. D.; Zhang, Y.-W. Effect of Rotational Degrees of Freedom on Molecular Mobility. J. Phys. Chem. C 2013, 117, 6800−6806. (97) Ozmaian, M.; Fathizadeh, A.; Jalalvand, M.; Ejtehadi, M. R.; Allaei, S. M. V. Diffusion and Self-Assembly of C60 Molecules on Monolayer Graphyne Sheets. Sci. Rep. 2016, 6, 21910. (98) Vehicle Dynamics Terminology; Standard No. J670_200801; SAE International, 2008. (99) Kendall, M. G. The Advanced Theory of Statistics, 2nd ed.; Charles Griffin & Company Limited: London, 1945; Vol. 1, p 331. (100) Kupchenko, I. V.; Moskovsky, A. A.; Nemukhin, A. V.; Kolomeisky, A. B. On the Mechanism of Carborane Diffusion on a Hydrated Silica Surface. J. Phys. Chem. C 2010, 115, 108−111. (101) Khatua, S.; Godoy, J.; Tour, J. M.; Link, S. Influence of the Substrate on the Mobility of Individual Nanocars. J. Phys. Chem. Lett. 2010, 1, 3288−3291.

T


How Chassis Structure and Substrate Crystalline Direction Affect the

Recommend Documents