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Impeded Mass Transportation Due to Defects in Thermally Driven Nanotube Nanomotor Jige Chen,*,† Yi Gao,† Chunlei Wang,† Renliang Zhang,†,§ Hong Zhao,‡ and Haiping Fang† †

Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, P.O. Box 800-204, Shanghai 201800, China ‡ Department of Physics, Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China § School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China S Supporting Information *

ABSTRACT: A thermally driven nanotube nanomotor provides linear mass transportation controlled by a temperature gradient. However, the underlying mechanism is still unclear, as the mass transportation velocity in experiment is much lower than that resulting from simulations. Considering that defects are common in fabricated nanotubes, we use molecular dynamics simulations to show that the mass transportation would be considerably impeded by defects. The outer tube of a double-walled carbon nanotube transports along the coaxial inner tube subject to a temperature gradient. While encountering the defects in the inner tube, the outer tube might be bounced back or trapped at some specific sites due to the potential barriers or wells induced by the defects. The stagnation phenomenon provides a probable picture to understand the low transportation velocity at the microscopic level. We also show that a similar stagnation phenomenon holds in mass transportation of a fullerene encapsulated in a defective carbon nanotube. Our result is expected to be helpful in designing nanotube nanomotors.

I. INTRODUCTION Controlled mass transportation is the key function of a molecular motor. Nature provides some biological nanomotors,1−3 however, which can only work in specific environmental conditions. In contrast, a nanotube nanomotor4,5 can operate in diverse environments that include various chemical media, as well as electric or magnetic fields.6−13 Such advantage makes it capably evolved into components of versatile nanodevices in applications. Pressure gradient, mechanical force, and electrical bias et al. are the possible driving forces in a nanotube nanomotor.4,5,14,15 Recently, the usage of thermal gradient to actuate mass transportation has been demonstrated to be highly valuable in nanomotor design.8−13 Thermophoresis, also known as the Soret effect, is capable of driving fluids, gases, DNA molecules and many other nano materials that are subjected to a temperature gradient. In 2008, the fabrication of a thermally driven nanotube nanomotor was reported by Barreiro et al.9, in which driven by a temperature gradient, the outer tube of a double-walled carbon nanotube traveled along the coaxial inner tube. Later, mass transportation of other nano materials, such as the carbon nanotube (CNT) capsule, the inner tube instead of the outer tube, the graphene nanoribbon, etc., are experimentally realized or theoretically proposed.8,10,11,13,16−22 Although the underlying mechanism of thermophoresis is still unclear, there is a growing interest in the scientific community to design thermally driven nanotube nanomotor © 2015 American Chemical Society

due to its practical usability and potential applications. We note that in most simulations,11,13,16−22 the average mass transportation velocity is about 1−2 Å/ps (1−2 × 108 um/s), while in experiments9,10,20 it is only 1−2 um/s and it is 7 orders of magnitude lower than the simulation value. Besides the small system dimension and large temperature gradient limited by the calculation capabilities, no other picture is provided to understand the origin of such stagnation at microscopic level. Meanwhile, defects are common in practically fabricated nanotubes according to results from scanning tunneling microscope observations as well as quantum and classical simulations.23−30 They produce changes in the topological structure and consequently affect the electronic, mechanical, and thermal properties of CNTs. Despite the significant impact and inevitable presence of defects, their explicit effect upon the mass transportation of nanotube nanomotors has not been reported. In this paper, we use molecular dynamics (MD) simulations to investigate defective nanotube nanomotors and find out the mass transportation might be considerably impeded by defects, which gives one possible picture to understand the stagnation phenomenon at a microscopic level. Received: March 7, 2015 Revised: June 5, 2015 Published: July 2, 2015 17362

DOI: 10.1021/acs.jpcc.5b02235 J. Phys. Chem. C 2015, 119, 17362−17368

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The Journal of Physical Chemistry C

II. MODEL AND METHODS In our simulation, a nanotube nanomotor consists of a 24 nm long (4, 4) inner tube and a 2 nm long outer tube whose chirality vector ranging from (9, 9) to (14, 14). The diameter of the (4, 4) inner tube is 5.47 Å, and the diameters of outer tubes are 12.17, 13.47, 14.88, 16.19, 17.47, and 18.96 Å, respectively. Defects in carbon nanotubes and similar carbon materials are imperfections of the hexagonal structure, which includes topological (sp2-like) defects, doping or functionalization (sp2- and sp3-like) defects and vacancies/edge type (nonsp2like) defects.30−33 The latter two types relates to structural reconstructions due to chemical doping/functionalization with boron atoms, nitrogen atoms, or other atoms and molecules,34,35 or radiation damage of vacancies36,37 in experiments. A topological defect, on the other hand, does not introduce other elements or change the connectivity of the sp2 lattice,33,38 that is, every carbon atom in the structure has exactly the same three nearest neighbors. To simplify our theoretical analysis, the present study focuses upon topological defects. Two kinds of topological defects induced by formation of pentagon-heptagon (5−7) pairs, namely, the carbon ad-dimer (CD) and the Stone−Wales (SW) defects, are considered. The CD defect is a 7−5−5−7 defect formed by adsorption of a carbon dimer.23−26 The SW defect is a 5−7−7−5 defect formed by the π/2 rotation of a C−C bond.27−30 The scanning-tunneling microscopy (STM) and spectroscopy (STS) images,38−40 and high-resolution transmission electron microscopy (HRTEM) images28,33 reveal their appearance and impact upon the carbon nanotubes. It has also been reported that manipulating the topological defects is possible by using the tip of a STM.41,42 In the present study, the initial geometries are determined using a defect-generating algorithm based on the MM3 Allinger force field.43,44 Two CD defects or two SW defects are symmetrically placed in the middle of the inner tube. Figure 1a shows the initial structure of the nanotube nanomotor. To perform the simulations, an open-source MD package LAMMPS45 is used, and a minimum time step of 1 fs is employed. The Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential46 is adopted to simulate intramolecular and intermolecular interactions between the carbon atoms as E=

1 2

∑ ∑ [EijREBO + EijLJ + ∑ ∑ i

j≠i

k≠i l≠i ,j,k

Figure 1. System and kinetic results. (a) Schematic of the nanotube nanomotor. The fixed atoms are colored silver, and the atoms at the heat source and heat sink are colored red. The carbon ad-dimer (CD) defects (left) or Stone−Wales (SW) defects (right) are placed in the middle of the inner tube. (b,c) The axial trajectory z of the center of mass (COM) of the outer tube as a function of simulation time, t, along the inner tube, with (b) CD defects or (c) SW defects, as determined by independent simulations. The dashed lines indicate the possible bouncing sites and trapping sites.

tube are fixed to prevent atoms from sublimating. This stage is conducted for 100 ps. (2) The second step consists of a nonequilibrium process, which is performed to establish a steady temperature gradient. Two slabs (1 nm long and excluding the fixed atoms), one at each end of the inner tube, are used as the heat source and heat sink. The temperature gradient is established by using the energy and momentum conserving velocity-scaling algorithm developed by Jund and Jullien.53 For the ith atom at the heat bath, the modified velocity is given by v i new = vG + α(v i − vG) i

(2)

i

where v new and v are the new and old velocities of the ith atom, and vG is the average velocity of the atoms at the heat bath. The rescaling factor α is defined by the number of atoms N0 at the heat bath as

EiTORSION ] ,j,k ,l (1)

α=

The REBO term has the same functional form as the hydrocarbon REBO potential47 developed by Brenner with the same coefficients, and it describes the short-ranged C−C covalent bonded interactions. The LJ term adds the longerranged interactions by using a form similar to the standard Lennard-Jones potential. The TORSION term is turned off in simulations since no hydrocarbon configuration is involved in the topological defects. The AIREBO (REBO) potential offers a reasonable description of the shear strength and sliding properties of CNTs,48,49 thus it is used by researchers to study the thermophoretic motion13,21 and defective structure in graphene and carbon nanotubes.50−52 The simulations are performed in three steps: (1) The first step consists of an isothermal equilibration process in which both the inner and outer tubes are thermalized at 300 K. The outmost carbon atoms at the ends of the inner

1±

ΔE ER

(3)

where ΔE is the energy added or removed from the specified atom, and ER is defined as ER =

1 2

N0

∑ mivi2 − i=1

1 2

N0

∑ mivG2 i=1

(4)

By rescaling the atomic velocities at each time step Δt, a specific amount of heat flux J = ΔE/Δt = 4 eV/ps is imposed upon the system. To achieve a steady temperature profile, this stage is performed for 1000 ps (Please see Figure S1 regarding the temperature profiles in the Supporting Information). (3) The third step consists of a mass transportation process of the outer tube. At this stage, the restriction on the outer tube is removed. Driven by the thermophoretic force, the outer tube moves toward the cold end of the inner tube. The final stage is the actual production run, carried out for 1000 ps. 17363


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Figure 2. van der Waals energy change Eg induced by defects. (a) Schematics of the axial coordinate z and the deviation distance δr. (b, c) Eg as a function of z around the (b) CD defects and (c) SW defects. The chirality vector of the outer tube ranges from (9, 9) to (14, 14). The possible bouncing and trapping sites are indicated by dashed cyan and orange lines, respectively. (d,e) Eg as a function of both z and δr around the (d) CD defects and (e) SW defects in the (4, 4)/(11, 11) nanotube nanomotor. The possible bouncing and trapping sites are indicated by arrows. N

III. RESULTS AND DISCUSSION Figure 1 shows the typical axial trajectories of the center of mass (COM) of the outer tube. When encountering CD defects, the outer tube may exhibit three typical kinetic behaviors: (1) it passes through the defects, (2) it bounces back at some specific sites, and (3) it is trapped at some specific sites. While upon encountering the SW defects, the outer tube exhibits (1) and (2) phenomena. For example, the blue line in the upper panel of Figure 1(b) exhibits the first phenomena by encountering CD defects. The outer tube first easily passes through the defects and reaches the cold end of the inner tube. After reaching the end, it bounces back. To this point, the mass transportation is quite the same as the process that occurs in a perfect nanotube nanomotor. When encountering the defects again in another bounce-back motion, the tube fails to pass through the defects and bounce back (Please see movie 1 in the Supporting Information). The red line in the upper panel of Figure 1b illustrates the second phenomenon, and the three lines in the lower panel of Figure 1b illustrate the third phenomenon (Please see movies 2−5 in the Supporting Information). Similarly, lines in Figure 1c illustrate the first and second phenomena by encountering SW defects. To understand the microscopic mechanism of the stagnation, it is helpful to analyze the energy change brought by the defects when the outer tube encounters them. Since the influence of the defective inner tube upon the outer tube is dependent upon the intermolecular interaction between the carbon atoms, the energy change is actually evaluated by the LJ term in the AIREBO potential. The intermolecular interaction describes the van der Waals energy between the carbon atoms in the inner tube and the outer tube. Therefore, we define the van der Waals energy change induced by the defects as

Eg =

∑i = 1 (E Di − Ei) N

(5)

EiD

where is the van der Waals energy between the ith atom in the outer tube and the other atoms in the defective inner tube, and Ei is the corresponding one by removing the defects in the inner tube, and N is the total number of atoms in the outer tube. As shown in Figure 2a, EiD and Ei vary with respect to the configuration between the inner tube and the outer tube. For simplicity, two main factors are considered to evaluate the value of Eg: (1) z, the axial coordinate of the COM of the outer tube, and (2) δr, the deviation distance between the two tubes. To compute Eg, the position of the inner tube is kept invariant, and the outer tube is varied according to different values of z and δr. Therefore, Eg describes the van der Waals energy change when the outer tube is at a different position relative to the inner tube. If the inner tube is a defect-free carbon nanotube, then Eg = 0 is obtained under any configuration. We first keep δr = 0 and vary the position of the outer tube according to z. Figure 2b,c shows that Eg varies as a function of z. It shows that Eg reveals possible potential barriers and potential wells around the position of the CD defects in Figure 2b, and SW defects in Figure 2c. The position of the potential barriers and potential wells correspond to the bouncing sites and trapping sites observed in the thermophoretic mass transportation in Figure 1b,c. Figure 2d,e shows that Eg varies as a function of z and δr. The potential barriers and wells, which represent the van der Waals energy change around the defects, are observed under different configurations between the inner tube and the outer tube. The above observation indicates that at microscopic level, defects ruin the perfect crystal structure of the inner tube and may impede the mass transportation of the outer tube. It leads to a possible relationship between the stagnation phenomenon 17364


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the possibility that both defect simultaneously exist, we suggest that a proper diameter difference (about 10 Å which is neither too small nor too large) is most helpful for an optimal passing through ratio. Figure 3 also shows that ηB and ηT vary with ΔR. For the nanotube nanomotor with the CD defect, when its diameter difference is larger than 6.7 Å, ηB increases and ηT decreases with ΔR. It means that the failure of passing through the CD defects is more due to the potential barriers rather than the potential wells. For the nanotube nanomotor with the SW defects, ηT is always 0% since only potential barriers are observed. Now we tend to understand the trend of the passing ratio through the defects. Driven by the thermophoretic force, the outer tube gathers a specific transportation velocity, vz. Only if the actuated kinetic energy, Ek = mvz2/2, is greater than the potential barriers and potential wells, the outer tube is able to pass through the defects. In Figure 4a, we show the actuated

and surface roughness at microscopic level. The characteristic of the defects are represented by the van der Waals energy change Eg, which exhibits potential barriers and potential wells around the defects. Once away from the defects, Eg drops to zero quickly and thus the stagnation (bouncing back or trapping) occurs near the edge of the defects. Since Eg represents the van der Waals energy change rather than the absolute value of the potential energy, similar stagnation is observed in a large nanotube nanomotor with enlarged tube diameter and tube length (please see Figure S2 in the Supporting Information). We attempt to determine the optimal structure to minimize the stagnation by varying the outer tube diameter. Therefore, we define the ratio of passing through, bouncing back and trapping as ηP = NP/(NP + NB + NP)

(6)

ηB = NB/(NP + NB + NP)

(7)

ηT = NT/(NP + NB + NP)

(8)

where NP is the number of times that the outer tube passes through the defects in less than 30 ps, and NB and NT are the number of times that the outer tube bounces back and trapped, respectively. Here 50 (50 × 6 × 2 = 600 in total) independent simulations are carried out to obtain one ratio. In each simulation, the initial positions of the outer tube and the inner tube are the same, and a random value of initial velocity is given at the beginning. The kinetic behavior is dependent upon the configuration between the outer tube and the inner tube when the outer tube encounters the defects. Since the transportation of the inner tube is proportional to the heat flux, or the temperature gradient,10,13,16,21 the heat flux value is maintained at 4 eV/ps in each simulation. In Figure 3a,b we show that ηP varies with the diameter difference ΔR between the two tubes. A large ηP means the stagnation of the defects is comparatively small. The optimal diameter difference is 10.7 Å to pass through the CD defects, and 6.7 and 9.4 Å to pass through the SW defects. Considering

Figure 4. (a) The average actuated kinetic energy Ek of the outer tube as the function of the diameter difference ΔR. (b) The cyan areas represent the possible value of δr, which is able to pass through the potential potential barriers and potential wells of the CD defects in the (4, 4)/(11, 11) nanotube nanomotor. The value span of the possible δr is denoted as δh. The dashed lines represent the value of Ek and −Ek. To pass through the defects, Ek > Eg, Eg > 0 or −Ek < −Eg, Eg < 0 are required. (c) The value of δh/ΔR as a function of the diameter difference ΔR. It represents the ratio of the possible configurations of the outer tube, which is able to pass through the defects.

kinetic energy as a function of ΔR. It exhibits a smaller value with respect to a large ΔR. Here the (4, 4)/(9, 9) system exhibits a much larger value than any other nanotube nanomotor system. It is due to the fact that the diameter difference is ΔR = 6.7 Å, which means the closest distance between the outer tube and the inner tube is about 3.4 Å. It is similar to the interlayer distance of graphite and leads to a much stronger intermolecular interaction and thus a large actuated kinetic energy. Since Eg varies according to δr, to pass through the potential barriers at the bouncing sites, a requirement of Ek > Eg, Eg > 0 is needed with a given value of Ek. Similarly, a requirement of −Ek < −Eg, Eg < 0 is needed with a given value of Ek to pass through the potential wells at the trapping sites. Therefore, δr has to be restricted in a specific value span, which is denoted as δh, to fulfill those requirements. In Figure 4b, we show the value span δh in the (4, 4)/(11, 11) nanotube nanomotor with CD defects. The value span of δr, covered by the cyan boxes as δh, corresponds to the possible configurations of passing through. In Figure 4c, we show the

Figure 3. (a,b) ηP as the ratio of passing through, ηB as the ratio of bouncing back, and ηT as the ratio of trapping, vary as a function of the diameter difference ΔR when the outer tube meets (a) CD defects and (b) SW defects. 17365


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The Journal of Physical Chemistry C average value of ⟨δh⟩/ΔR as a function of ΔR, by considering both the potential barriers and potential wells. If ⟨δh⟩/ΔR = 0, it means no matter how the δr varies with the given value of Ek, it is impossible for the outer tube to pass through the defects. Therefore, it explains why ηP = 0 is observed in Figure 3a when ΔR = 6.7 Å. Although a considerable large value of Ek = 0.005 eV is actuated, the CD defects provide an even larger potential barrier, Eg ≈ 0.05 eV at the bouncing sites, as shown in Figure 2b. Therefore, it is derived that ⟨δh⟩/ΔR = 0, and it prohibits the change of passing through. Similarly, it also explains why ηP = 0 is observed in Figure 3b when ΔR = 8.0 Å. It is due to the fact that in the system with SW defects, Ek = 0.00015 eV and Eg ≈ 0.00019 eV at the bouncing sites, and it leads to ⟨δh⟩/ΔR = 0. And for ηP = 100% in Figure 3b when ΔR = 6.7 Å. Ek = 0.005 eV and Eg ≈ 0.0006 eV at the bouncing sites, and it leads to ⟨δh⟩/ΔR = 0.16, which enables the 100% passing through. The variance of δh/ΔR provides a comprehensive picture to understand the increasing ratio of passing through. It explains the zero value of passing through in Figure 3. However, further increasing ΔR, a decrease of ηP is observed, which is insufficient to be explained by δh/ΔR. We surmise that the decrease is due to other possible configuration parameters not included in our simplified theoretical analysis. For example, the deviation angle, δα, as shown in Figure 5, contributes a lot to the potential

molecules, and other nano particles inside CNT being driven by thermophoretic actuation.11,21,54−57 Therefore, we perform MD simulations of a fullerene (C60) encapsulated in a defective (10, 10) CNT as a typical example to investigate the stagnation phenomenon induced by defects. Two SW defects are symmetrically placed in the middle of the inner tube. The C60 particle is actuated by the thermal gradient, and transports from the hot to the cold part of the outer tube. When encountering the defect, the encapsulated C60 particle exhibits three similar typical kinetic behaviors as shown in Figure 6a:

Figure 6. Schematic of a C60 particle encapsulated in a defective CNT. Two SW defects are symmetrically placed in the middle of the tube (indicated by a blue circle). (a) Three axial trajectories z of the C60 particle as a function of simulation time, t, along the inner tube, as determined by independent simulations. The dark dashed line indicates the possible bouncing and trapping sites, which are approximately at the same place. (b) van der Waals energy change Eg around the SW defects as a function of z and δr.

Figure 5. (a) The deviation angle δα as the function of time, t, in the (4, 4)/(9, 9) and (4, 4)/(14, 14) nanotube nanomotors. (b) van der Waals energy change Eg is modified by considering the contribution of δα in the (4, 4)/(11, 11) nanotube nanomotor. (c) The average value of δα as a function of ΔR.

(1) it passes through the defects, (2) it bounces back at one specific site, and (3) it is trapped at one specific site. The bouncing site and trapping site are approximately at the same position. In Figure 6b, we investigate the van der Waals energy change Eg of the C60 particle. Interestingly, it reveals one potential barrier and two potential wells, which correspond to the possible bouncing and trapping sites. The kinetic behavior of the C60 particle encapsulated in CNT implies that defects would also impede the mass transportation in similar nanotube nanomotor design.

barriers when ΔR further increases. Figure 5(a) shows δα as the function of time in the (4, 4)/(9, 9) and (4, 4)/(14, 14) nanotube nanomotors, and Figure 5b shows the average value of δα as a function of ΔR. The results imply the necessity to consider δα if the diameter of the outer tube is large. A large value of δα enhances the potential barriers at the bouncing sites. For example, as shown in Figure 5(c), Eg increases at the bouncing sites with respect to δα in the (4, 4)/(11, 11) system with CD defects. It provides a possible picture to understand the decrease of ηP by further increasing ΔR. Thus, a more comprehensive theoretical analysis would be helpful in future studies, which includes other configuration parameters, such as the deviation angle, diameter change in the inner tube subject to the temperature gradient,13 the angular rotation of the outer tube,16 etc. Technically speaking, the mass transportation subjects could be objects inside the CNT as well. In theoretical studies, researchers have proposed fullerene (C60) particles, water

IV. CONCLUSIONS In summary, we have performed MD simulations on defective nanotube nanomotors to study the impact of defects upon the mass transportation driven by thermophoretic actuation. The simulation results have demonstrated that defect may considerably impede the thermophoretic mass transportation due to the potential barriers and potential wells, which bounce back or trap the outer tube/encapsulated fullerene. The stagnation phenomena may provide a possible picture to understand the low transportation velocity in experiments, which is 7 orders of magnitude lower than that obtained from a perfect nanotube nanomotor in simulations. Since defects are very common in fabricated nanotubes, we propose that a proper choose of diameter difference is helpful to achieve the optimal robustness against defects. On the theoretical side, our result presents a scenario of stagnation due to defects/ roughness at microscopic/macroscopic level; and on the experimental side, it suggests a way to minimize the negative 17366


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effect and provides a positive application of defects in nanoengineering.

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ASSOCIATED CONTENT

* Supporting Information S

Simulation movies of various kinetic behaviors when encountering the CD defects, and discussions about the temperature profiles in the inner tube and simulation results in a large nanotube nanomotor. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b02235.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: 86-21-39523458. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (#11405245, #11290164, #21273268, #11204341), and Shanghai Natural Science Research Funding (#14ZR1448100), and the Key Research Program of Chinese Academy of Sciences (#KJZD-EW-M03). The authors also thank the Knowledge Innovation Program of the Chinese Academy of Sciences, Shanghai Supercomputer Center of China, the Deepcomp7000 and ScGrid of the Supercomputing Center, Computer Network Information Center of the Chinese Academy of Sciences.

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