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graphyne surfaces: van der Waals corrected density functional theory study
Materials Chemistry and Physics xxx (2014) 1e9
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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study M. Darvish Ganji a, M. Ghorbanzadeh Ahangari b, *, S.M. Emami c a
Nanotechnology Research Institute, Faculty of Chemical Engineering, Babol Noshirvani University of Technology, Babol, Iran Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran c Center of Nano-Science, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran b
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
First-principles vdW-DF calculations were used to investigate the nanocar motion on graphene/graphyne substrate. Two different types of nanocar wheel movement (slipping and slithering) is considered. The accuracy of this method is validated by experimental results and the MP2 level of theory. First-principles molecular dynamics simulation is also used to consider the type of nanocar movement on the substrate.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 June 2014 Received in revised form 3 August 2014 Accepted 6 August 2014 Available online xxx
Investigations of nanocar motion on one-dimensional substrate surfaces provide an important contribution to the practical goal of designing nanoscale transporters. As a preliminary step toward modeling the dynamics of these species, first-principles vdW-DF calculations were performed to investigate the interaction between the nanocar and the graphene/graphyne surface. The accuracy of this method is validated by experimental results and the MP2 level of theory. The results obtained reveal that the nanocar would require at least 71.39 and 18.33 kJ mol1 to activate its movement on the graphene and graphyne surfaces, respectively. First-principles molecular dynamics simulations show that the nanocar moved on the substrate without additional external factors under ambient conditions. The nanocar displays a tendency toward slipping on the graphyne surface within 2 ps of simulation time movement. These findings provide insights that will facilitate the coherent design and control of surfaceoperational molecular machines and a realistic benchmark for the nanocar's movement mechanism. © 2014 Elsevier B.V. All rights reserved.
Keywords: A. Nanostructures A. Surfaces C. Ab initio calculations C. Computer modeling and simulation
1. Introduction Recent efforts have been devoted to the synthesis of nanocars that can perform specific tasks at the molecular level and,
* Corresponding author. Tel./fax: þ98 1135302903. E-mail address: [email protected] (M. Ghorbanzadeh Ahangari).
ultimately, construct molecular assemblies using a bottomeup approach [1e6]. Nanocars, including molecular motors, are nanostructures that convert electromagnetic energy into mechanical motion [7]. The electromagnetic energy may take various forms, including light, thermal, and electron beams, e.g., nanocars that move simply by heating the substrate. The first nanocar was synthesized by Tour's research group at Rice University in 2005 [8] and consisted of a chassis, four freely rotating axles made of well-
http://dx.doi.org/10.1016/j.matchemphys.2014.08.011 0254-0584/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: M. Darvish Ganji, et al., Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study, Materials Chemistry and Physics (2014), http://dx.doi.org/10.1016/j.matchemphys.2014.08.011
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Fig. 1. Schematic representation of (a) a single carborane wheel on the surface of the graphene cluster (coronene), (b) a benzene molecule adsorbed on the graphene surface.
Fig. 2. Optimized structures and geometric parameters, including length (L), width (W), and CeC bond length (LCeC) of (a) graphene and (b) graphyne.
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nanocar on a substrate has not been studied using high-level quantum mechanics methods. Akimov et al. [7] used classical MD simulations to calculate the adsorption energy and amount of charge transfer between a fullerene-wheeled nanocar and two different types of gold specific crystal planes at a series of temperatures in the range of 100e1000 K. They found that the
Fig. 3. The optimized structure and geometric parameters of the nanocar.
defined, rodlike acetylenic structures with a pivoting suspension, and wheels made of fullerene molecules that can turn independently because the bond between wheel and axle is freely rotatable (fullerene-wheeled nanocar). Based on scanning tunneling microscopy (STM) measurements and experimental evidence, this nanocar spontaneously rolls on a surface [9] but requires a special surface to move. Movement of this nanocar across a gold (Au) surface has been demonstrated [10]. STM imaging studies confirmed that as the temperature of the surface was raised to approximately 170 C, the nanocar remained almost stable and stationary, but at higher temperatures, the molecules started to move on the underlying surface [11]. This stability has been attributed to relatively strong binding between the fullerene wheels and the gold surface. However, due to the substantial interaction energy between fullerene and the gold surface, the nanocar moves relatively slowly [12]. Furthermore, these fullerene wheels produce photoactive nanocars with low solubility, which is crucial for light-powered nanocars. To overcome their impediments, a new class of faster single-molecule transporters, namely, motorized nanocars, have been designed to move along different surfaces. This nanocar bears a light-activated unidirectional molecular motor and an oligo(phenylene ethynylene) chassis and axle system with four carboranes as the wheels [3,9]. The molecular motor is set in the central portion of the carborane-wheeled nanocar for an eventual paddlewheel-like propulsion action along a substrate surface for motion. Of the various molecular motors, Feringa's motor is mostly commonly used because it uses light and mild heating (35e65 C) as the power input, can perform repetitive rotary movement, and precisely performs unidirectional rotation [13]. The direct observation of nanocar motion on a substrate via STM inspired the development of various theoretical methods for understanding the mechanisms and dynamics of nanocar movement [7,14,15]. The most challenging aspect of such studies is the proper description of the interactions between the nanocar and the substrate. Current theoretical investigations are mostly based on the interactions of the molecular motors, rotors and wheels with a metal or glassy substrate, and they rely on molecular dynamics (MD) and molecular mechanics (MM) computer simulations and quantum mechanical studies. The molecular mechanism of a
Fig. 4. Two different possible adsorption configurations of the nanocar on the surface of the substrate (R1 and R2).
Please cite this article in press as: M. Darvish Ganji, et al., Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study, Materials Chemistry and Physics (2014), http://dx.doi.org/10.1016/j.matchemphys.2014.08.011
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Fig. 5. The optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) of the car/graph complex in the favorable configuration.
interaction energy and the charge transfer amounts between the nanocar and the Au(111) surface at room temperature (300 K) were approximately 45 kcal mol1 and 0.78 electrons, respectively. First-principles calculations play an essential role in attempting to understand many of the electronic properties of a material, and density functional theory (DFT) is a common approach to calculating material properties. The field of nanomaterials continues to expand, with new materials and new structures of existing materials continually being reported. First-principles DFT methods have low computational cost, and they are the most popular methods for calculating the electronic structure of many-atom systems. DFT calculations can often provide predictions that can be tested experimentally, which in turn inform and refine the calculations. Here, we report the interactions of a carborane-wheeled nanocar with a graphene or graphyne surface, as studied for the first time using the DFT method. These systems were used to study the adsorption energy, geometrical parameters, and charge transfer between the carborane-wheeled nanocar and the substrate. We also examined the effect on the binding properties of the complexes of the two different types of nanocar wheel movement (slipping and slithering) as well as the effect of temperature. Finally, we evaluated the effect of the environment on the nanocar's situation on the surface at room temperature, using DFT-based molecular dynamics (DFT-MD) simulations. 2. Computational methods Our calculations based on the adsorption and motion of the carborane-wheeled nanocar on the graphene or graphyne substrate were performed within the framework of first-principles DFT
Fig. 6. The geometry of the (a) graphene and (b) nanocar in the car/graph complex.
implemented using the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) code [16]. We adopted the generalized gradient approximation (GGA) to treat the electronic exchange and correlation effects, as described by PerdeweBurkeeErnzerhof [17]. All calculations were performed using a double-x plus polarization (DZP) basis set. A 4 4 1 MonkhorstePack [18] grid for k-point sampling of the Brillouin zone was set, and the atomic positions were relaxed until the residual forces on each atom were lower than 0.02 eV Å 1. The mesh cutoff, an energy that corresponds to the grid spacing, was selected as 125 Ry. The supercells of graphene and graphyne consisted of 80 and 100C atoms, respectively, and a periodic boundary condition was applied to the supercells. A vacuum width of 30 Å was constructed to eliminate interaction between adjacent images of the supercell. Unfortunately, conventional DFT methods do not adequately describe the van der Waals (vdW) forces, i.e., the dispersion interactions, which play an important role in weakly interacting systems [19e24]. Hence, the standard DFT in the GGA approximation was supplemented in this study by an ab initio vdW approach proposed by Grimme known as the vdW-DFT method, which incorporates dispersive vdW interactions into DFT [25,26].
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ensemble (constant number of particles, volume, and temperature) using the NoseeHoover thermostat [27]. The temperature effects on the structures were calculated at a temperature of 300 K. The simulation time t duration of the molecular dynamics simulation was 5 ps, and the time step was 1 fs. MD simulations were based on the Verlet-type algorithm [28] for integrating Newton's equations of motion. 3. Results and discussion 3.1. Adsorption of a single carborane wheel on graphene The validity of our method was first evaluated by considering the adsorption of a single carborane wheel on the surface of the graphene cluster using the MøllerePlesset perturbation (MP2) level of theory. We considered a molecular model of coronene (six benzene rings capped with hydrogen atoms (C24H12)) as a substrate for the adsorption process. Fig. 1 represents the model for the interacting systems under consideration. The interaction between a single carborane wheel and the selected graphene substrate was calculated using both the MP2 and the current vdW-DF methods. In the MP2 calculations, the basis sets used for all atoms for the individual entities as well as the adsorbates were 3-21 þ G**.
Fig. 7. Nanocar movement on the graphene surface during (a) slipping and (b) slithering.
The binding energy, Eb, was computed by subtracting the energies of the nanocar molecule and the substrate from the energy of the adsorption system, as shown in the following equation:
Eb ¼ Enanocarþsubstrate ðEnanocar þ Esubstrate Þ
(1)
where Enanocarþsubstrate is the energy of the final optimized configuration of the adsorption system, Enanocar is the energy of the carborane-wheeled nanocar, and Esubstrate is the energy of the graphene or graphyne substrate. Using this definition, a negative Eb value corresponds to stable adsorption on the surface. We have also performed DFT-based MD simulations for the system under study. The systems were simulated in the NVT
Fig. 8. The optimized structure and geometric parameters of the car/graph complex after slipping of the nanocar on the graphene surface from the R2 configuration to the slip-2 position.
Fig. 9. The geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) after optimization for the (a) slith-1 and (b) slith-2 positions.
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Fig. 10. Various possible configurations of the nanocar molecule adsorbed on the graphyne surface: (a) Brig, (b) Hex, and (c) Vac.
During the optimization steps, the molecular structures were fully optimized, i.e., all atoms were free to move. The optimization was performed using the quasi-Newton method to achieve a gradient convergence factor of less than 105 hartree/bohr. All of the structural optimizations and total energy calculations at the MP2 level were performed using the software PC_GAMESS/Firefly [29,30]. After full structural optimization, we determined that the binding energy of the carborane on the graphene substrate is equal to 0.60 eV and 0.58 eV with the MP2 method and the vdW-DF calculation, respectively, indicating the accuracy of our vdW-DF calculations for the systems under consideration. The binding energies obtained are typical for the physisorption [31,32]. Because the benzene rings in the nanocar play an important role in the adsorption process, we tested our technical settings by performing calculations for a benzene molecule interacting with the graphene surface. We calculated a binding energy of approximately Eb ¼ 0.59 eV for the most energetically favorable configuration, which is in good agreement with the experimental value [33] as well as with previous theoretical work utilizing the DFT-D2 method (Eb ¼ 0.58 eV) [34]. The calculated equilibrium distance between the benzene and the graphene surface is also in reasonable agreement with the reported experimental value of 3.40 Å. The optimized structure of the benzene molecule adsorbed on the graphene layer is represented in Fig. 1(b).
including the graphene and graphyne sheets. The optimized structures and geometric parameters, including length (L), width (W), and CeC bond length (LCeC), of the substrates, are shown in Fig. 2. Our calculation predicted that the CeC bond length is approximately 1.41 Å. In addition, according to Fig. 2, graphyne has three CeC bond lengths, 1.44, 1.43, and 1.24 Å (L1, L2, and L3, respectively). The optimized nanocar structure and the geometric parameters are also presented in Fig. 3. The distances between BeB and BeH in the wheel of the nanocar are equal to 1.77 and 1.19 Å, respectively. The above results are similar to the previous experimental results and theoretical calculations. The calculated lengths of the chassis
3.2. Optimization We began the procedure with the creation and full structural optimization of the carborane-wheeled nanocar and the substrate,
Fig. 11. Optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsubof the car/graphyne complex in the most stable configuration.
chas)
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Fig. 13. The optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) of the car/graphyne complex after slithering of the nanocar on the graphyne surface.
Fig. 12. The optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) of the car/graphyne complex after slipping of the nanocar on the graphene surface from the R2 configuration to the (a) slip-1 and (b) slip-2 positions.
(Lchassis) and axle (Laxle) are approximately 10.90 and 10.98 Å, respectively. In addition, based on the Mulliken population charge analysis, a considerable amount of electron charge transfer (1.96 e) is transferred from the chassis and axle to the carborane wheel. 3.3. Adsorption of the nanocar on graphene To examine the movement of the nanocar on the graphene surface (car/graph complex), we investigated the binding energy of the complex for different possible configurations of the nanocar on the substrate. Two different possible adsorbing configurations were investigated by rotating the nanocar by 90 in the z-axis direction on the surface of the substrate. These two possible configurations, named R1 and R2, are illustrated in Fig. 4. After fully optimizing these configurations, we determined that the binding energy at R1 and R2 was equal to 0.74 and 0.65 eV, respectively. These results demonstrated that the nanocar in the R2 configuration can move more simply on the graphene surface than in the R1 configuration due to the lower binding energy of the R2 configuration. Furthermore, to investigate the change in the electronic structure of graphene caused by the adsorption of the nanocar, the electron charge transfer between the substrate and the nanocar was calculated using Mulliken analysis. An analysis of the Mulliken charges revealed effective charge transfer (0.21 e) from the adsorbed nanocar to the graphene. The optimized structure and geometric parameters of the complex for the energetically favorable configuration R2 are shown in Fig. 5. The binding distances between the chassis, axle, and carborane wheel and graphene are presented in Fig. 5(a); the binding distance is defined as the
distance between the closest atoms in the nanocar component to the substrate surface. The calculated binding distances between the substrate and the chassis (dsub-chas), axle (dsub-axle), and carborane wheel (dsub-wheel) were approximately 2.71, 3.87 and 2.57 Å, respectively. In addition, the value of the deflection angle at the center of the graphene plate from the straight position (a) after the adsorption of the nanocar is depicted in Fig. 5(b). After adsorption, the graphene was deflected by approximately 5.83 compared to pristine graphene. The length (l) and width (w) of the graphene after adsorption of the nanocar were calculated to be approximately 23.19 and 24.68 Å, respectively. Therefore, despite the deflection of graphene, the length and width of the substrate remained almost unchanged (Fig. 6(a)). In addition, we found that the CeC bond length of the graphene in the car/graph complex was increased slightly compared to pristine graphene. The CeC bond length of graphene in the complex was calculated in the range 1.413e1.420 Å, as shown in Fig. 6(a). Moreover, we calculated the geometry of the nanocar after adsorption on graphene and determined that the geometry of the nanocar was almost invariable (Fig. 6(b)). In this section, we focus our study on the nanocar movement on the surface of graphene. Two types of nanocar movement on the surface are considered: slipping and slithering. In the slipping movement, the nanocar slips on the surface with a displacement (d) of 1.60 Å at each step of the movement. In the slithering movement, the wheels of the nanocar slither on the surface with a slithering degree (q) of 13.3 at each step of the movement. Two steps for each movement were performed for this investigation (slip-1 and slip-2 for the slipping movement and slith-1 and slith-2 for the slithering movement). The nanocar movement types on the graphene surface are shown schematically in Fig. 7. The binding energies produced by the slipping of the nanocar on the graphene surface at the slip-1 and slip-2 positions were 0.65 and 0.61 eV, respectively. These results demonstrate that the binding energy is approximately constant during slipping, and thus the nanocar can slip easily on the graphene surface. In comparison with slipping, the slithering movement of the nanocar on the graphene surface at the slith-2 position (Eb ¼ 0.79 eV) was stronger than at the slith-1 position (Eb ¼ 0.61 eV). Thus, the slithering of the nanocar on the graphene surface at the slith-2 position is more difficult than at the other positions. After full optimization of the complex due to the slipping and slithering movement of the nanocar on the graphene at different positions, we did not observe any significant structural changes in the graphene and nanocar compared with the situation prior to the movement of the nanocar. However, with slipping of the nanocar on the graphene surface from the base configuration (R2) to the slip-2 position, we observed
Please cite this article in press as: M. Darvish Ganji, et al., Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study, Materials Chemistry and Physics (2014), http://dx.doi.org/10.1016/j.matchemphys.2014.08.011
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that the values of dsub-axle and dsub-wheel decreased by approximately 0.17 and 0.24 Å, respectively, but the value dsub-chas was almost constant (as presented in Fig. 8). Furthermore, with slithering movement of the nanocar on the graphene of approximately 13.3 , geometrical analysis after optimization revealed that the values of dsub-axle, and dsub-wheel decreased from 3.87 to 2.57 Å for the R2 configuration to 3.71 and 2.45 Å for the slith-1 position, respectively (Fig. 9(a)). In addition, the value of dsub-chas in the slith-1 position increased by approximately 0.16 Å compared to the R2 configuration. As is apparent in Fig. 9(b), with slithering movement of the nanocar from the slith-1 to slith-2 position, the values of dsub-axle and dsub-wheel increased to 2.57 and 3.81 Å, respectively, but the value of dsub-chas decreased to 2.82 Å. 3.4. Adsorption of the nanocar on graphyne To identify the most favorable configurations for beginning the nanocar movement on the graphyne surface, the nanocar molecule was initially placed at different positions above the graphyne surface (car/graphyne). As shown in Fig. 10, various configurations of the nanocar molecule adsorbed onto the graphyne surface have been investigated; these configurations are known as the Brig, Hex, and Vac configurations. The smallest binding energy was selected as the best configuration for starting of the nanocar movement on the graphyne. After full structural optimization, the Hex configuration exhibited a smaller binding energy (Eb ¼ 0.19 eV) than the Brig (Eb ¼ 0.26 eV) and Vac (Eb ¼ 0.20 eV) configurations, and thus the movement of nanocar in this configuration is easier than the other configurations. Our results also revealed that a charge transfer of 0.46 e occurs from the nanocar to the graphyne in the Hex configuration. Fig. 11 represents the structure and geometrical parameters of the car/ graphyne complex at the Hex configuration. The geometrical properties consist of the binding distance between the substrate and the chassis (dsub-chas), axle (dsub-axle), and carborane wheel (dsub-wheel) for the car/graphyne complex. The values of dsub-chas, dsub-axle, and dsub-wheel increased significantly from 2.71, 3.87, and 2.57 Å in the car/graph complex to 3.14, 4.61, and 2.63 Å in the car/ graphyne complex, respectively. Based on the above results, we can conclude that graphyne is a better substrate than graphene for the movement of the carborane-wheeled nanocar. Moreover, the changes in the geometric parameters for each part of the complex (nanocar and graphyne) are nearly negligible.
The effect of nanocar slipping on the binding properties of the complex was considered by dislocating the nanocar by approximately 1.6 and 3.2 Å (slip-1 and slip-2) from the origin position, as shown in Fig. 6(a). The calculated binding energies for the car/ graphyne complexes in both slipping movements changed slightly and were equal to 0.20 and 0.18 eV for the slip-1 and slip-2 positions, respectively. Therefore, the movement of the nanocar on the graphene surface from the slip-1 position is more difficult than from the slip-2 position. In addition, we determined that the binding distance between the nanocar and graphyne decreased slightly upon slipping of the nanocar on the graphyne. For example, the values of dsub-chas, dsub-axle, and dsub-wheel decreased from 3.14, 4.61, and 2.63 Å for the origin position to 3.04, 4.50, and 2.58 Å for the slip-2 position, respectively. The optimized structures and their geometrical parameters for both slipping movements (slip-1 and slip-2 positions) are illustrated in Fig. 12. In this section, we consider the effect of slithering the nanocar's wheels on the binding properties of the car/graphyne complex. The obtained results revealed that the slithering movement of the nanocar on graphyne had no effect on the binding energy of the car/ graphyne complex, which was equal to 0.48 eV. As shown in Fig. 13, the geometric parameters of the car/graphyne complex are almost constant upon slithering of the nanocar on the substrate. Finally, we performed ab initio vdW-DFT MD simulations at room temperature to examine the nanocar position on the surface of graphyne at the most favorable configuration. After ps, we observed that the complex was quite stable and that the nanocar was clearly moving on the surface of the graphyne sheet. This finding indicates that the nanocar prefers to be slipped on the graphyne surface in the narrow time window considered. A schematic representation of the nanocar movement on the surface of the substrate is presented in Fig. 14. As the time increased, the distance between the nanocar and the substrate increased, thereby facilitating the movement of the nanocar on the graphyne surface. The binding distance between the substrate and chassis after 2 ps is shown in Fig. 14. 4. Conclusion In this work, we used ab initio vdW-DF calculations with the SIESTA code to describe the adsorption properties of a carborane wheel-like nanocar adsorbed on graphene/graphyne surfaces. Based on our calculations, energy of at least 0.74 or 0.19 eV is required to activate the movement of a nanocar with four carborane wheels along a graphene or graphyne surface, respectively. Our
Fig. 14. Snapshots of ab initio MD simulation of the nanocar movement on the surface of the substrate at 300 K after (a) 100 fs and (b) 2000 fs.
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results suggest that the movement of the nanocar on the surface of graphyne is easier than on graphene due to the lower binding energy of the nanocar on graphyne. Furthermore, our models for the favorable configurations were applied to analyze the dynamics of the nanocar on the graphene and graphyne surfaces. We analyzed two different mechanisms of the motion of the nanocar's wheels: slipping and slithering. We determined that both sliding and slithering can occur in the movement of the nanocar on the selected substrates, but the slithering mechanism was preferred. Furthermore, our results imply that the movement of the nanocars is affected by the strength of the interactions between the nanocar wheels and the considered surface. These first-principles findings yield complementary reference data and provide constructive insights regarding the nanometer-scale motion of the nanocar on the substrate at the atomic scale. Using the ab initio vdW-DF-based MD simulations, we observed the movement of the carborane nanocar on a graphyne surface at room temperature. The nanocar slipped on the graphyne surface during the simulation time movement. Changing the surface might therefore have a large impact on nanocar mobility.
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Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study M. Darvish Ganji a, M. Ghorbanzadeh Ahangari b, *, S.M. Emami c a
Nanotechnology Research Institute, Faculty of Chemical Engineering, Babol Noshirvani University of Technology, Babol, Iran Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran c Center of Nano-Science, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran b
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
First-principles vdW-DF calculations were used to investigate the nanocar motion on graphene/graphyne substrate. Two different types of nanocar wheel movement (slipping and slithering) is considered. The accuracy of this method is validated by experimental results and the MP2 level of theory. First-principles molecular dynamics simulation is also used to consider the type of nanocar movement on the substrate.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 June 2014 Received in revised form 3 August 2014 Accepted 6 August 2014 Available online xxx
Investigations of nanocar motion on one-dimensional substrate surfaces provide an important contribution to the practical goal of designing nanoscale transporters. As a preliminary step toward modeling the dynamics of these species, first-principles vdW-DF calculations were performed to investigate the interaction between the nanocar and the graphene/graphyne surface. The accuracy of this method is validated by experimental results and the MP2 level of theory. The results obtained reveal that the nanocar would require at least 71.39 and 18.33 kJ mol1 to activate its movement on the graphene and graphyne surfaces, respectively. First-principles molecular dynamics simulations show that the nanocar moved on the substrate without additional external factors under ambient conditions. The nanocar displays a tendency toward slipping on the graphyne surface within 2 ps of simulation time movement. These findings provide insights that will facilitate the coherent design and control of surfaceoperational molecular machines and a realistic benchmark for the nanocar's movement mechanism. © 2014 Elsevier B.V. All rights reserved.
Keywords: A. Nanostructures A. Surfaces C. Ab initio calculations C. Computer modeling and simulation
1. Introduction Recent efforts have been devoted to the synthesis of nanocars that can perform specific tasks at the molecular level and,
* Corresponding author. Tel./fax: þ98 1135302903. E-mail address: [email protected] (M. Ghorbanzadeh Ahangari).
ultimately, construct molecular assemblies using a bottomeup approach [1e6]. Nanocars, including molecular motors, are nanostructures that convert electromagnetic energy into mechanical motion [7]. The electromagnetic energy may take various forms, including light, thermal, and electron beams, e.g., nanocars that move simply by heating the substrate. The first nanocar was synthesized by Tour's research group at Rice University in 2005 [8] and consisted of a chassis, four freely rotating axles made of well-
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Fig. 1. Schematic representation of (a) a single carborane wheel on the surface of the graphene cluster (coronene), (b) a benzene molecule adsorbed on the graphene surface.
Fig. 2. Optimized structures and geometric parameters, including length (L), width (W), and CeC bond length (LCeC) of (a) graphene and (b) graphyne.
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nanocar on a substrate has not been studied using high-level quantum mechanics methods. Akimov et al. [7] used classical MD simulations to calculate the adsorption energy and amount of charge transfer between a fullerene-wheeled nanocar and two different types of gold specific crystal planes at a series of temperatures in the range of 100e1000 K. They found that the
Fig. 3. The optimized structure and geometric parameters of the nanocar.
defined, rodlike acetylenic structures with a pivoting suspension, and wheels made of fullerene molecules that can turn independently because the bond between wheel and axle is freely rotatable (fullerene-wheeled nanocar). Based on scanning tunneling microscopy (STM) measurements and experimental evidence, this nanocar spontaneously rolls on a surface [9] but requires a special surface to move. Movement of this nanocar across a gold (Au) surface has been demonstrated [10]. STM imaging studies confirmed that as the temperature of the surface was raised to approximately 170 C, the nanocar remained almost stable and stationary, but at higher temperatures, the molecules started to move on the underlying surface [11]. This stability has been attributed to relatively strong binding between the fullerene wheels and the gold surface. However, due to the substantial interaction energy between fullerene and the gold surface, the nanocar moves relatively slowly [12]. Furthermore, these fullerene wheels produce photoactive nanocars with low solubility, which is crucial for light-powered nanocars. To overcome their impediments, a new class of faster single-molecule transporters, namely, motorized nanocars, have been designed to move along different surfaces. This nanocar bears a light-activated unidirectional molecular motor and an oligo(phenylene ethynylene) chassis and axle system with four carboranes as the wheels [3,9]. The molecular motor is set in the central portion of the carborane-wheeled nanocar for an eventual paddlewheel-like propulsion action along a substrate surface for motion. Of the various molecular motors, Feringa's motor is mostly commonly used because it uses light and mild heating (35e65 C) as the power input, can perform repetitive rotary movement, and precisely performs unidirectional rotation [13]. The direct observation of nanocar motion on a substrate via STM inspired the development of various theoretical methods for understanding the mechanisms and dynamics of nanocar movement [7,14,15]. The most challenging aspect of such studies is the proper description of the interactions between the nanocar and the substrate. Current theoretical investigations are mostly based on the interactions of the molecular motors, rotors and wheels with a metal or glassy substrate, and they rely on molecular dynamics (MD) and molecular mechanics (MM) computer simulations and quantum mechanical studies. The molecular mechanism of a
Fig. 4. Two different possible adsorption configurations of the nanocar on the surface of the substrate (R1 and R2).
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Fig. 5. The optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) of the car/graph complex in the favorable configuration.
interaction energy and the charge transfer amounts between the nanocar and the Au(111) surface at room temperature (300 K) were approximately 45 kcal mol1 and 0.78 electrons, respectively. First-principles calculations play an essential role in attempting to understand many of the electronic properties of a material, and density functional theory (DFT) is a common approach to calculating material properties. The field of nanomaterials continues to expand, with new materials and new structures of existing materials continually being reported. First-principles DFT methods have low computational cost, and they are the most popular methods for calculating the electronic structure of many-atom systems. DFT calculations can often provide predictions that can be tested experimentally, which in turn inform and refine the calculations. Here, we report the interactions of a carborane-wheeled nanocar with a graphene or graphyne surface, as studied for the first time using the DFT method. These systems were used to study the adsorption energy, geometrical parameters, and charge transfer between the carborane-wheeled nanocar and the substrate. We also examined the effect on the binding properties of the complexes of the two different types of nanocar wheel movement (slipping and slithering) as well as the effect of temperature. Finally, we evaluated the effect of the environment on the nanocar's situation on the surface at room temperature, using DFT-based molecular dynamics (DFT-MD) simulations. 2. Computational methods Our calculations based on the adsorption and motion of the carborane-wheeled nanocar on the graphene or graphyne substrate were performed within the framework of first-principles DFT
Fig. 6. The geometry of the (a) graphene and (b) nanocar in the car/graph complex.
implemented using the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) code [16]. We adopted the generalized gradient approximation (GGA) to treat the electronic exchange and correlation effects, as described by PerdeweBurkeeErnzerhof [17]. All calculations were performed using a double-x plus polarization (DZP) basis set. A 4 4 1 MonkhorstePack [18] grid for k-point sampling of the Brillouin zone was set, and the atomic positions were relaxed until the residual forces on each atom were lower than 0.02 eV Å 1. The mesh cutoff, an energy that corresponds to the grid spacing, was selected as 125 Ry. The supercells of graphene and graphyne consisted of 80 and 100C atoms, respectively, and a periodic boundary condition was applied to the supercells. A vacuum width of 30 Å was constructed to eliminate interaction between adjacent images of the supercell. Unfortunately, conventional DFT methods do not adequately describe the van der Waals (vdW) forces, i.e., the dispersion interactions, which play an important role in weakly interacting systems [19e24]. Hence, the standard DFT in the GGA approximation was supplemented in this study by an ab initio vdW approach proposed by Grimme known as the vdW-DFT method, which incorporates dispersive vdW interactions into DFT [25,26].
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ensemble (constant number of particles, volume, and temperature) using the NoseeHoover thermostat [27]. The temperature effects on the structures were calculated at a temperature of 300 K. The simulation time t duration of the molecular dynamics simulation was 5 ps, and the time step was 1 fs. MD simulations were based on the Verlet-type algorithm [28] for integrating Newton's equations of motion. 3. Results and discussion 3.1. Adsorption of a single carborane wheel on graphene The validity of our method was first evaluated by considering the adsorption of a single carborane wheel on the surface of the graphene cluster using the MøllerePlesset perturbation (MP2) level of theory. We considered a molecular model of coronene (six benzene rings capped with hydrogen atoms (C24H12)) as a substrate for the adsorption process. Fig. 1 represents the model for the interacting systems under consideration. The interaction between a single carborane wheel and the selected graphene substrate was calculated using both the MP2 and the current vdW-DF methods. In the MP2 calculations, the basis sets used for all atoms for the individual entities as well as the adsorbates were 3-21 þ G**.
Fig. 7. Nanocar movement on the graphene surface during (a) slipping and (b) slithering.
The binding energy, Eb, was computed by subtracting the energies of the nanocar molecule and the substrate from the energy of the adsorption system, as shown in the following equation:
Eb ¼ Enanocarþsubstrate ðEnanocar þ Esubstrate Þ
(1)
where Enanocarþsubstrate is the energy of the final optimized configuration of the adsorption system, Enanocar is the energy of the carborane-wheeled nanocar, and Esubstrate is the energy of the graphene or graphyne substrate. Using this definition, a negative Eb value corresponds to stable adsorption on the surface. We have also performed DFT-based MD simulations for the system under study. The systems were simulated in the NVT
Fig. 8. The optimized structure and geometric parameters of the car/graph complex after slipping of the nanocar on the graphene surface from the R2 configuration to the slip-2 position.
Fig. 9. The geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) after optimization for the (a) slith-1 and (b) slith-2 positions.
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Fig. 10. Various possible configurations of the nanocar molecule adsorbed on the graphyne surface: (a) Brig, (b) Hex, and (c) Vac.
During the optimization steps, the molecular structures were fully optimized, i.e., all atoms were free to move. The optimization was performed using the quasi-Newton method to achieve a gradient convergence factor of less than 105 hartree/bohr. All of the structural optimizations and total energy calculations at the MP2 level were performed using the software PC_GAMESS/Firefly [29,30]. After full structural optimization, we determined that the binding energy of the carborane on the graphene substrate is equal to 0.60 eV and 0.58 eV with the MP2 method and the vdW-DF calculation, respectively, indicating the accuracy of our vdW-DF calculations for the systems under consideration. The binding energies obtained are typical for the physisorption [31,32]. Because the benzene rings in the nanocar play an important role in the adsorption process, we tested our technical settings by performing calculations for a benzene molecule interacting with the graphene surface. We calculated a binding energy of approximately Eb ¼ 0.59 eV for the most energetically favorable configuration, which is in good agreement with the experimental value [33] as well as with previous theoretical work utilizing the DFT-D2 method (Eb ¼ 0.58 eV) [34]. The calculated equilibrium distance between the benzene and the graphene surface is also in reasonable agreement with the reported experimental value of 3.40 Å. The optimized structure of the benzene molecule adsorbed on the graphene layer is represented in Fig. 1(b).
including the graphene and graphyne sheets. The optimized structures and geometric parameters, including length (L), width (W), and CeC bond length (LCeC), of the substrates, are shown in Fig. 2. Our calculation predicted that the CeC bond length is approximately 1.41 Å. In addition, according to Fig. 2, graphyne has three CeC bond lengths, 1.44, 1.43, and 1.24 Å (L1, L2, and L3, respectively). The optimized nanocar structure and the geometric parameters are also presented in Fig. 3. The distances between BeB and BeH in the wheel of the nanocar are equal to 1.77 and 1.19 Å, respectively. The above results are similar to the previous experimental results and theoretical calculations. The calculated lengths of the chassis
3.2. Optimization We began the procedure with the creation and full structural optimization of the carborane-wheeled nanocar and the substrate,
Fig. 11. Optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsubof the car/graphyne complex in the most stable configuration.
chas)
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Fig. 13. The optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) of the car/graphyne complex after slithering of the nanocar on the graphyne surface.
Fig. 12. The optimized structure and geometric parameters (dsub-axle, dsub-wheel, and dsub-chas) of the car/graphyne complex after slipping of the nanocar on the graphene surface from the R2 configuration to the (a) slip-1 and (b) slip-2 positions.
(Lchassis) and axle (Laxle) are approximately 10.90 and 10.98 Å, respectively. In addition, based on the Mulliken population charge analysis, a considerable amount of electron charge transfer (1.96 e) is transferred from the chassis and axle to the carborane wheel. 3.3. Adsorption of the nanocar on graphene To examine the movement of the nanocar on the graphene surface (car/graph complex), we investigated the binding energy of the complex for different possible configurations of the nanocar on the substrate. Two different possible adsorbing configurations were investigated by rotating the nanocar by 90 in the z-axis direction on the surface of the substrate. These two possible configurations, named R1 and R2, are illustrated in Fig. 4. After fully optimizing these configurations, we determined that the binding energy at R1 and R2 was equal to 0.74 and 0.65 eV, respectively. These results demonstrated that the nanocar in the R2 configuration can move more simply on the graphene surface than in the R1 configuration due to the lower binding energy of the R2 configuration. Furthermore, to investigate the change in the electronic structure of graphene caused by the adsorption of the nanocar, the electron charge transfer between the substrate and the nanocar was calculated using Mulliken analysis. An analysis of the Mulliken charges revealed effective charge transfer (0.21 e) from the adsorbed nanocar to the graphene. The optimized structure and geometric parameters of the complex for the energetically favorable configuration R2 are shown in Fig. 5. The binding distances between the chassis, axle, and carborane wheel and graphene are presented in Fig. 5(a); the binding distance is defined as the
distance between the closest atoms in the nanocar component to the substrate surface. The calculated binding distances between the substrate and the chassis (dsub-chas), axle (dsub-axle), and carborane wheel (dsub-wheel) were approximately 2.71, 3.87 and 2.57 Å, respectively. In addition, the value of the deflection angle at the center of the graphene plate from the straight position (a) after the adsorption of the nanocar is depicted in Fig. 5(b). After adsorption, the graphene was deflected by approximately 5.83 compared to pristine graphene. The length (l) and width (w) of the graphene after adsorption of the nanocar were calculated to be approximately 23.19 and 24.68 Å, respectively. Therefore, despite the deflection of graphene, the length and width of the substrate remained almost unchanged (Fig. 6(a)). In addition, we found that the CeC bond length of the graphene in the car/graph complex was increased slightly compared to pristine graphene. The CeC bond length of graphene in the complex was calculated in the range 1.413e1.420 Å, as shown in Fig. 6(a). Moreover, we calculated the geometry of the nanocar after adsorption on graphene and determined that the geometry of the nanocar was almost invariable (Fig. 6(b)). In this section, we focus our study on the nanocar movement on the surface of graphene. Two types of nanocar movement on the surface are considered: slipping and slithering. In the slipping movement, the nanocar slips on the surface with a displacement (d) of 1.60 Å at each step of the movement. In the slithering movement, the wheels of the nanocar slither on the surface with a slithering degree (q) of 13.3 at each step of the movement. Two steps for each movement were performed for this investigation (slip-1 and slip-2 for the slipping movement and slith-1 and slith-2 for the slithering movement). The nanocar movement types on the graphene surface are shown schematically in Fig. 7. The binding energies produced by the slipping of the nanocar on the graphene surface at the slip-1 and slip-2 positions were 0.65 and 0.61 eV, respectively. These results demonstrate that the binding energy is approximately constant during slipping, and thus the nanocar can slip easily on the graphene surface. In comparison with slipping, the slithering movement of the nanocar on the graphene surface at the slith-2 position (Eb ¼ 0.79 eV) was stronger than at the slith-1 position (Eb ¼ 0.61 eV). Thus, the slithering of the nanocar on the graphene surface at the slith-2 position is more difficult than at the other positions. After full optimization of the complex due to the slipping and slithering movement of the nanocar on the graphene at different positions, we did not observe any significant structural changes in the graphene and nanocar compared with the situation prior to the movement of the nanocar. However, with slipping of the nanocar on the graphene surface from the base configuration (R2) to the slip-2 position, we observed
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that the values of dsub-axle and dsub-wheel decreased by approximately 0.17 and 0.24 Å, respectively, but the value dsub-chas was almost constant (as presented in Fig. 8). Furthermore, with slithering movement of the nanocar on the graphene of approximately 13.3 , geometrical analysis after optimization revealed that the values of dsub-axle, and dsub-wheel decreased from 3.87 to 2.57 Å for the R2 configuration to 3.71 and 2.45 Å for the slith-1 position, respectively (Fig. 9(a)). In addition, the value of dsub-chas in the slith-1 position increased by approximately 0.16 Å compared to the R2 configuration. As is apparent in Fig. 9(b), with slithering movement of the nanocar from the slith-1 to slith-2 position, the values of dsub-axle and dsub-wheel increased to 2.57 and 3.81 Å, respectively, but the value of dsub-chas decreased to 2.82 Å. 3.4. Adsorption of the nanocar on graphyne To identify the most favorable configurations for beginning the nanocar movement on the graphyne surface, the nanocar molecule was initially placed at different positions above the graphyne surface (car/graphyne). As shown in Fig. 10, various configurations of the nanocar molecule adsorbed onto the graphyne surface have been investigated; these configurations are known as the Brig, Hex, and Vac configurations. The smallest binding energy was selected as the best configuration for starting of the nanocar movement on the graphyne. After full structural optimization, the Hex configuration exhibited a smaller binding energy (Eb ¼ 0.19 eV) than the Brig (Eb ¼ 0.26 eV) and Vac (Eb ¼ 0.20 eV) configurations, and thus the movement of nanocar in this configuration is easier than the other configurations. Our results also revealed that a charge transfer of 0.46 e occurs from the nanocar to the graphyne in the Hex configuration. Fig. 11 represents the structure and geometrical parameters of the car/ graphyne complex at the Hex configuration. The geometrical properties consist of the binding distance between the substrate and the chassis (dsub-chas), axle (dsub-axle), and carborane wheel (dsub-wheel) for the car/graphyne complex. The values of dsub-chas, dsub-axle, and dsub-wheel increased significantly from 2.71, 3.87, and 2.57 Å in the car/graph complex to 3.14, 4.61, and 2.63 Å in the car/ graphyne complex, respectively. Based on the above results, we can conclude that graphyne is a better substrate than graphene for the movement of the carborane-wheeled nanocar. Moreover, the changes in the geometric parameters for each part of the complex (nanocar and graphyne) are nearly negligible.
The effect of nanocar slipping on the binding properties of the complex was considered by dislocating the nanocar by approximately 1.6 and 3.2 Å (slip-1 and slip-2) from the origin position, as shown in Fig. 6(a). The calculated binding energies for the car/ graphyne complexes in both slipping movements changed slightly and were equal to 0.20 and 0.18 eV for the slip-1 and slip-2 positions, respectively. Therefore, the movement of the nanocar on the graphene surface from the slip-1 position is more difficult than from the slip-2 position. In addition, we determined that the binding distance between the nanocar and graphyne decreased slightly upon slipping of the nanocar on the graphyne. For example, the values of dsub-chas, dsub-axle, and dsub-wheel decreased from 3.14, 4.61, and 2.63 Å for the origin position to 3.04, 4.50, and 2.58 Å for the slip-2 position, respectively. The optimized structures and their geometrical parameters for both slipping movements (slip-1 and slip-2 positions) are illustrated in Fig. 12. In this section, we consider the effect of slithering the nanocar's wheels on the binding properties of the car/graphyne complex. The obtained results revealed that the slithering movement of the nanocar on graphyne had no effect on the binding energy of the car/ graphyne complex, which was equal to 0.48 eV. As shown in Fig. 13, the geometric parameters of the car/graphyne complex are almost constant upon slithering of the nanocar on the substrate. Finally, we performed ab initio vdW-DFT MD simulations at room temperature to examine the nanocar position on the surface of graphyne at the most favorable configuration. After ps, we observed that the complex was quite stable and that the nanocar was clearly moving on the surface of the graphyne sheet. This finding indicates that the nanocar prefers to be slipped on the graphyne surface in the narrow time window considered. A schematic representation of the nanocar movement on the surface of the substrate is presented in Fig. 14. As the time increased, the distance between the nanocar and the substrate increased, thereby facilitating the movement of the nanocar on the graphyne surface. The binding distance between the substrate and chassis after 2 ps is shown in Fig. 14. 4. Conclusion In this work, we used ab initio vdW-DF calculations with the SIESTA code to describe the adsorption properties of a carborane wheel-like nanocar adsorbed on graphene/graphyne surfaces. Based on our calculations, energy of at least 0.74 or 0.19 eV is required to activate the movement of a nanocar with four carborane wheels along a graphene or graphyne surface, respectively. Our
Fig. 14. Snapshots of ab initio MD simulation of the nanocar movement on the surface of the substrate at 300 K after (a) 100 fs and (b) 2000 fs.
Please cite this article in press as: M. Darvish Ganji, et al., Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study, Materials Chemistry and Physics (2014), http://dx.doi.org/10.1016/j.matchemphys.2014.08.011
M. Darvish Ganji et al. / Materials Chemistry and Physics xxx (2014) 1e9
results suggest that the movement of the nanocar on the surface of graphyne is easier than on graphene due to the lower binding energy of the nanocar on graphyne. Furthermore, our models for the favorable configurations were applied to analyze the dynamics of the nanocar on the graphene and graphyne surfaces. We analyzed two different mechanisms of the motion of the nanocar's wheels: slipping and slithering. We determined that both sliding and slithering can occur in the movement of the nanocar on the selected substrates, but the slithering mechanism was preferred. Furthermore, our results imply that the movement of the nanocars is affected by the strength of the interactions between the nanocar wheels and the considered surface. These first-principles findings yield complementary reference data and provide constructive insights regarding the nanometer-scale motion of the nanocar on the substrate at the atomic scale. Using the ab initio vdW-DF-based MD simulations, we observed the movement of the carborane nanocar on a graphyne surface at room temperature. The nanocar slipped on the graphyne surface during the simulation time movement. Changing the surface might therefore have a large impact on nanocar mobility.
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Please cite this article in press as: M. Darvish Ganji, et al., Carborane-wheeled nanocar moving on graphene/graphyne surfaces: van der Waals corrected density functional theory study, Materials Chemistry and Physics (2014), http://dx.doi.org/10.1016/j.matchemphys.2014.08.011