Dynamic Behavior of Rotation Transmission Nano-System in Helium Environment: a Molecular Dynamics Study

molecules

Article Dynamic Behavior of Rotation Transmission Nano-System in Helium Environment: A Molecular Dynamics Study

Pan Zheng 1, Wugui Jiang 1,* , Qinghua Qin 2 and Duosheng Li 3

1 School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China; [email protected] 2 Department of Engineering, Shenzhen MSU-BIT University, Shenzhen 518172, China; [email protected] 3 School of Material Science and Engineering, Nanchang Hangkong University, Nanchang 330063, China; [email protected] * Correspondence: [email protected]

Abstract: The molecular dynamics (MD) method is used to investigate the inﬂuence of the shielding gas on the dynamic behavior of the heterogeneous rotation transmission nano-system (RTS) built on carbon nanotubes (CNTs) and boron nitride nanotube (BNNT) in a helium environment. In the heterogeneous RTS, the inner CNT acts as a rotor, the middle BNNT serves as a motor, and the outer CNT functions as a stator. The rotor will be actuated to rotate by the motor due to the interlayer van der Waals effects and the end effects. The MD simulation results show that, when the gas density is lower than a critical range, a stable signal of the rotor will arise on the output and the rotation transmission ratio (RRT) of RTS can reach 1.0, but as the gas density is higher than the critical range, the output signal of the rotor cannot be stable due to the sharp drop of the RRT caused by the large friction between helium and the RTS. The greater the motor input signal of RTS, the lower the critical working helium density range. The results also show that the system temperature and gas density are Citation: Zheng, P.; Jiang, W.; Qin, Q.; Li, D. Dynamic Behavior of the two main factors affecting the RTS transmission behavior regardless of the size of the simulation Rotation Transmission Nano-System box. Our MD results clearly indicate that in the working temperature range of the RTS from 100 K to in Helium Environment: A Molecular 600 K, the higher the temperature and the lower the motor input rotation frequency, the higher the Dynamics Study. Molecules 2021, 26, critical working helium density range allows. 5199. https://doi.org/10.3390/ molecules26175199 Keywords: rotation transmission nano-system; carbon nanotube; boron nitride nanotube; helium gas; molecular dynamics Academic Editor: Matteo Calvaresi

Received: 22 June 2021 Accepted: 24 August 2021 1. Introduction Published: 27 August 2021 Nanomachines have attracted a lot of attention recently with the rapid development of nanotechnology [1,2] and the urgent requirements in chemical and biological engineer- Publisher’s Note: MDPI stays neutral ing [3,4], especially after the 2016 Nobel Prize in Chemistry was issued to three scientists with regard to jurisdictional claims in published maps and institutional afﬁl- (i.e., Jean-Pierre Sauvage, Sir J. Fraser Stoddart, and Bernard L. Feringa) who have made iations. brilliant contributions to the ﬁeld [5]. The Nano-Electro-Mechanical System (NEMS) [6] is considered to be one of the important components in nanotechnology, which has the characteristics of quantum effect, interface effect, size effect, and so on. Carbon nanotubes (CNTs) show excellent mechanical [7,8], electrical [9,10], strain sensitive [11,12], and thermal [13,14] properties due to their special hexagonal structure, small size, low density, Copyright: © 2021 by the authors. high strength-to-weight ratio, and high hardness [15]. Therefore, CNTs have become the Licensee MDPI, Basel, Switzerland. most promising new type of nanomaterial in the construction of NEMS. In particular, This article is an open access article distributed under the terms and CNTs have two excellent mechanical properties, one is the extremely high modulus and conditions of the Creative Commons strength [16,17], and the other is the extremely low friction between adjacent layers of Attribution (CC BY) license (https:// multi-walled carbon nanotubes (MWCNTs) [18,19]. With the two extraordinary mechanical creativecommons.org/licenses/by/ properties, CNTs have found important potential applications for nano-devices such as 4.0/). nano-oscillator [20,21], nanobearing [22,23], and nanomotor [24,25]. The high modulus

Molecules 2021, 26, 5199. https://doi.org/10.3390/molecules26175199 https://www.mdpi.com/journal/molecules Molecules 2021, 26, 5199 2 of 15

and high strength of the carbon material guarantees the stability of the carbon components working at gigahertz, and the extremely low friction ensures that the relative movement between adjacent components could be easily maintained. According to the characteristics of motion, the nanodevices can be separated into two groups. One is linear nanodevices, e.g., nano-oscillator, and the other is rotary nanodevices, e.g., nanomotor. Rotary nanomotors, as an important component in providing power for the movement of nanodevices, need to be designed according to the service environment, and its movement should be controllable [26]. Due to the lack of precise experimental equipment and limitation of experimental technology and other objective factors, it is difficult to conduct experimental research on nanotubes. Fortunately, as a mature simulation method, the molecular dynamics (MD) method [27,28] has become an important method for researchers to study the related properties of nanotubes, and provides a powerful tool that satisfies some of the requirements for designing the nanomotors at a nano scale. In 2003, Fennimore et al. [24] observed the rotation behavior of CNTs through scanning electron microscopy in experiments for the first time. Since then, researchers have been using the rotation behavior of CNTs as driving components of nanodevices in the NEMS system. The driving force of rotary nanomotors could be provided by some external fields, such as light fields [29,30], electromagnetic fields [31,32], fluid fields [33,34], and thermal fields [23], etc. For instance, Barreiro et al. [23] investigated the transportation of cargoes at the sub-nanometer scale driven by temperature gradients along CNTs via experiments and MD simulations. Compared with the rotary nanomotors driven by the external fields, another type of rotary nanomotors [35,36] based on the MWCNTs without external field was subsequently proposed. The rotary nanomotors was in a gradientless temperature environment, the motion mechanism mainly relied on the inner tube, which loses geometric symmetry in the high temperature field to achieve the effect of rotation [35]. However, it was found that the rotation output signal has great randomness [23,24,29–36], and the uncontrollable output signal becomes a challenging problem that needs to be solved. Alternatively, Cai et al. [37,38] proposed a rotation transmission nano-system RTS consisting of an independent single-walled carbon nanotube (SWCNT) as a nanomotor and a group of coaxially arranged MWCNTs as nanobearing, in which the transmission of the rotation signal between the nanomotor and the nanobearing mainly depends on the interaction between adjacent ends. In addition, some researchers integrated nanomotor and nanobearing into another RTS model using a group of concentric MWCNTs [39–43]. Taking the advantage of the unique properties of boron nitride nanotube (BNNT) [44–48] and the excellent thermal and mechanical properties [49–51] of the heterogeneous CNT@BNNT, Zheng et al. [43] presented a novel RTS model of heterogeneous triple-walled nanotubes (TWNTs) based on CNTs and BNNT. The proposed RTS model was easier to control and the output signal was tunable in a wider temperature range, and the higher the system temperature, the higher the rotation transmission efficiency. The rotary nanomotors and RTSs in the work mentioned above were studied in a vacuum environment. In fact, nanodevices may need to be manufactured or work in a specific medium environment. Shi et al. [52] explored the efficiency of CNT-based RTS in water solution, and they manipulated the transmission efficiency of RTS through the water-rotor interaction in the water box. Cai et al. [53] and Shi et al. [54] studied the rotation behavior of nanomotors and nanorings in argon environments, respectively. The results show that in a higher temperature environment, the nanomotors and the nanorings have a higher rotation frequency than that at a lower temperature. Research data over the past decade shows that among all inert gases, especially helium, it has no anesthetic “side effects” such as xenon, allowing this specific gas to be used in many clinical ischemia/reperfusion situations [55]. On the other hand, helium is usually adopted to be a shielding gas in experiments. The rotational behavior of carbon monoxide in the helium environment was studied via the experimental method by Surin et al. [56]. Meanwhile, in a research similar to [56], Gupta [57] showed that the formation of CNTs and fullerene in a pure carbon arc in helium atmosphere may involve graphene bubbles. Jost et al. [58] investigated the Molecules 2021, 26, 5199 3 of 15

influence of the helium and nitrogen gas flow velocity and the laser pulse rate on the diameter distribution of SWCNTs. Hinkov et al. [59] also used helium and other gas as buffer gases to achieve the optical plasma temperature control during arc CNT growth. However, as far as we know, there is no report on the transmission characteristics of RTS in a helium environment. The purpose of this work is to explore the transmission behavior of the RTS proposed by Zheng et al. [43] in a helium environment. When the RTS works in a helium environment, randomly moving helium atoms will attract or repel the atoms on the nanotubes, thereby generating fluid friction and affecting the transmission performance of the RTS. Clearly, it can be concluded from aforementioned studies [43,53,54] that the temperature and gas densities have a significant influence on the nano-system in a medium environment. Therefore, using the classical MD method, the influences of the system temperatures, helium densities and simulation box sizes on the transmission behavior of RTS in a helium environment are especially investigated, aiming at providing guidance for the potential applications of RTS in nanodevices.

2. Results and Discussion In the RTS, the transmission behavior between the motor and the rotor mainly relies on the interaction between any two nanotube atoms, which includes interlayer van der Waals effects and end effects. The intratube interaction between atoms is a covalent bond, i.e., σ bond, while the intertube interaction is mainly due to the van der Waals force, i.e., π bond. The strength of the σ bond is much greater than that of the π bond. Around each intratube atom, except for the layer of atoms at both ends in the tube, there are three carbon atoms connected to it, which are connected by σ bonds, and each atomic bond is in a saturated state. However, there are only two atoms connected to the layer of atoms at the ends of the open-ended nanotubes, indicating that this layer of atomic bonds is not in an unsaturated state. After energy minimization, the rotor is in a state of equilibrium, and is then driven by the continuously rotating motor. Under the combining driving force of the interlayer van der Waals effects and the end effects between the tubes, the rotor starts to accelerate and rotate in the circumferential direction. The atom balance distance between the motor and the rotor is continuously destroyed due to the continuous rotation of the motor. At this time, the distance between the atoms in the equilibrium state increases and the atoms on the motor and the atoms on the rotor are attracted to each other under the combined action of the interlayer van der Waals effects and the end effects, leading the rotor to rotate in the circumferential direction due to the non-zero angular acceleration and oscillate in the axial direction. This relative movement also causes friction between the tubes. When the driving force and friction force reach a circumferential equilibrium, the rotor obtains a stable rotation frequency [43]. However, when the RTS works in a helium-filled zone, not only will there be friction between the motor and the rotor, but also the disordered movement of helium atoms will generate skin friction drag, which will affect the rotor’s motion behavior. Therefore, the rotor needs to completely overcome the friction between the tubes and the skin friction drag. If the driving force and the total friction reach a circumferential balance, the rotor can have a stable expected output speed. During the simulation, the rotation behavior of the motor and rotor is described by its rotation frequency. In order to describe the relative rotation between the nanotubes, we define the ratio of rotation transmission (RRT) between the motor and the rotor as RRT = ωr . When the value of RRT fluctuates around 1.0, the rotor is fully driven and will ωm rotate synchronously with the motor. When the value is less than 1.0, the rotor is not fully driven, its output speed will be less than the motor input speed.

2.1. Comparison of Two Heterogeneous Rotation Transmission Nano-Systems Figure 1 shows the curves of RRT for two RTS models with different rotor end structures in vacuum and helium environments. In this section, the size of the simulation box is set to 8 nm × 8 nm × 8 nm, ρ is 2.60 kg/m3, the input ωm is 200 GHz, and the system temperature is 300 K. It is found that when the RTS works in a vacuum environment, the RRT curves of the open-rotor RTS and the capped-rotor RTS almost coincide, and both Molecules 2021, 26, 5199 can reach 1.0 within 5.5 ns. Therefore, the end structure of the rotor does4 of not 15 affect the transmission behavior of the RTS in the vacuum environment. However, when the RTS works in a helium environment with ρ = 2.60 kg/m3, the highest RRT of the open-rotor RTStemperature and the capped-rotor is 300 K. It is found RTS thatcan whenonly thereach RTS ab worksout in0.49, a vacuum because environment, of the increase the in total RRT curves of the open-rotor RTS and the capped-rotor RTS almost coincide, and both frictionalcan reach resistance 1.0 within caused 5.5 ns. by Therefore, the action the end of helium structure atoms. of the rotor Compared does not with affect the the open-rotor RTS,transmission the response behavior time offor the the RTS RRT in the of vacuumthe capped-rotor environment. RTS However, reaching when 0.49 the is RTS shorter. worksRegardless in a helium of whether environment the RTS with ρworks= 2.60 in kg/m a vacuum3, the highest or helium RRT of environment, the open-rotor the motor andRTS rotor and will the capped-rotorswing eccentrically RTS can only during reach the about movement, 0.49, because and of the the increase center in of total mass will de- viatefrictional from the resistance center caused line to by a thecertain action extent. of helium Th atoms.is is one Compared of the important with the open-rotor factors that affect RTS, the response time for the RRT of the capped-rotor RTS reaching 0.49 is shorter. the stabilityRegardless of the of RTS whether struct theure. RTS worksThe larger in a vacuum the off-axial or helium rocking environment, distance, the motor the worse the stabilityand rotor of the will RTS. swing Figure eccentrically 2 depicts during the movement, time histories and the of center the ofoff-axial mass will rocking deviate motion of the rotorfrom the with center different line to a end certain structures extent. This in is th onee vacuum of the important and helium factors environment. that affect the It can be seenstability from Figure of the RTS 2 that structure. the degree The larger of the the off-axial rocking rocking distance, motion the of worse rotor the in a helium stability of the RTS. Figure2 depicts the time histories of the off-axial rocking motion of environmentthe rotor with is differentgreater endthan structures that in ina thevacuum vacuum environment and helium environment. due to the It caneffect be of helium atoms.seen The from off-axial Figure2 that rocking the degree distances of the off-axialof the open-rotor rocking motion in the of rotor RTS in working a helium in vacuum andenvironment helium environment is greater than are that about in a 0–0.38 vacuum Å environment and 0.2–0.8 due Å, to respectively, the effect of helium and those of the capped-rotoratoms. The are off-axial about rocking 0–0.2 distances Å and 0–0.25 of the open-rotorÅ, respectively. in the RTS The working off-axial in vacuumrocking distances and helium environment are about 0–0.38 Å and 0.2–0.8 Å, respectively, and those of the of the open-rotor are larger than those of the capped-rotor because helium atoms will run capped-rotor are about 0–0.2 Å and 0–0.25 Å, respectively. The off-axial rocking distances intoof the the inner open-rotor open-tube are larger rotor than when those ofthe the RTS capped-rotor is surrounded because by helium helium atoms atoms, will run as shown in the intoinset the of inner Figure open-tube 2b. The rotor helium when the atoms RTS is in surrounded the open-rotor by helium and atoms, the ascarbon shown atoms in on the rotorthe are inset not of in Figure the equilibrium2b. The helium distance, atoms in thewhich open-rotor causes and the the helium carbon atoms atoms to on attract the or repel the rotorinner are tube, not in leading the equilibrium a larger distance, off-axial which rock causesing the motion helium of atoms rotor. to attract However, or repel the off-axis the inner tube, leading a larger off-axial rocking motion of rotor. However, the off-axis swingswing of ofthe the capped-rotor capped-rotor inin the the helium helium environment environment is almost is almost negligible negligible compared tocompared to thatthat in the in the vacuum vacuum environment. environment. Therefore, Therefore, the capped-rotorthe capped-rotor RTS is more RTS stable is more than stable the than the open-rotoropen-rotor RTS RTS when when they work work in in a helium a helium environment. environment. So capped-rotor So capped-rotor RTSs will beRTSs will be adoptedadopted in inthe the subsequent subsequent MD MD simulations. simulations.

1.0

0.5

RRT ρ = 0 kg/m3 Capped-RTS 0.0 Open-RTS ρ = 2.60 kg/m3 Capped-RTS Open-RTS −0.5 0 5 10 15 20 Time (ns) FigureFigure 1. Time 1. Time histories histories ofof RRTRRT curves curves for thefor twothe RTS two models RTS withmodels different with rotor different end structures rotor end in structures in vacuumvacuum and heliumhelium environments. environments.

MoleculesMolecules 20212021, 26, 26x FOR, 5199 PEER REVIEW 5 of 15 5 of 16

1.4 3 (a) ρ = 0 kg/m (b) Capped-rotor 1.2 Open-rotor ρ = 2.60 kg/m3 1.0 Capped-rotor Open-rotor 0.8 0.6 0.4 0.2 0.0 Off-axial rocking motion of rotor (Å) 0 5 10 15 20 Time (ns) Figure 2. 2.(a )(a Time) Time histories histories of the of off-axial the off-axial rocking motion rocking of the motion rotor with of the different rotor end with structures different in end structures vacuumin vacuum and helium and helium environments, environments, and inset (b) atomicand inset diagram (b) ofatomic the open-RTS diagram at a certain of the moment. open-RTS at a certain 2.2.moment. Influence of Helium Density and Input Rotational Frequency of the Motor To investigate the influence of helium density ρ and motor input frequency on the 3 3 transmission2.2. Influence performance of Helium Density of RTS, ρ andis set Input from Rotational 0.65 kg/m Frequencyto 51.91 kg/m of the, andMotorωm is set toTo 50 GHz,investigate 100 GHz, the 150 influence GHz, and 200of helium GHz, respectively. density ρ The and system motor temperature input frequency on the is set to 300 K. Figure3a–d plot the RRT curves in a helium environment with different transmission performance of RTS, ρ is set from 0.65 kg/m3 to 51.91 kg/m3, and ωm is set to gas densities in case of ωm = 50 GHz, 100 GHz, 150 GHz, and 200 GHz, respectively. The results50 GHz, show 100 that GHz, as ρ increases, 150 GHz, meaning and 200 that GHz, more helium respectively. atoms enter The the system simulation temperature box, is set to the300 disordered K. Figure movement 3a–d plot of the more RRT helium curves atoms in willa helium generate environment greater skin friction with different drag, gas densi- leadingties in thecase transmission of ωm = 50 performance GHz, 100 ofGHz, RTS to150 become GHz, worse. and 200 It is GHz, manifested respectively. in two The results ways.show Onethat is as that ρ whenincreases,ρ is smaller meaning than a that certain more critical helium range, theatoms RRT enter of RTS the can reachsimulation box, the 1.0, but when ρ is higher than this critical range, the RRT drops sharply. It is noted that the criticaldisordered range reliesmovement on the input of more rotational helium frequency atomsωm ofwill the generate motor. It can greater be seen skin from friction drag, Figureleading3 that the when transmissionωm is 50 GHz, performance 100 GHz, 150 of GHz, RTS andto become 200 GHz, worse. the corresponding It is manifested in two criticalways. One density is that range when is 41.53–51.91 ρ is smaller kg/m than3, 15.57–16.87 a certain kg/m critical3, 2.60–6.50 range, the kg/m RRT3, and of RTS can reach 3 0.97–1.301.0, but kg/mwhen, ρ respectively. is higher Whenthan ρthisexceeds critical the criticalrange, range, the RRT the skin drops friction sharply. drag of It is noted that helium atoms to the RTS is increased. Although the rotor can be actuated by the motor, the drivingcritical force range is not relies enough on tothe completely input rotational overcome thefrequency total friction, ωm resultingof the motor. in the It can be seen motorfrom Figure and rotor 3 beingthat unablewhen toωm balance is 50 GHz, in the circumferential100 GHz, 150 direction, GHz, and so the 200 RRT GHz, of the the correspond- RTSing iscritical less than density 1.0. Another range way is is41.53–51.91 that compared kg/m with3, the15.57–16.87 RRT curves kg/m of the3, RTS 2.60–6.50 in a kg/m3, and vacuum0.97–1.30 environment, kg/m3, respectively. the RRT curves When fluctuate ρ exceeds greatly whenthe critical the RTS range, works inthe a heliumskin friction drag of environment with a gas density below the critical range, and they become disordered when thehelium gas density atoms is to above the theRTS critical is increased. range. Although the rotor can be actuated by the motor, the drivingAccording force to the is critical not enough density rangeto completely in Figure3, overcome Figure4 gives the the total critical friction, helium resulting in the densitymotor errorand rotor bar as being a function unable of the to input balance rotational in the frequencies circumferential of the motor. direction, We respec- so the RRT of the tivelyRTS is define less thethan area 1.0. under Another the curve way and is the that area compared above the curve with as the stable RRT and curves unstable of the RTS in a areas. It can be seen from Figure4 that as ω increases, the critical density range decreases, vacuum environment, the RRT curvesm fluctuate greatly when the RTS works in a helium which suggests that the RTS can work stably in a helium environment with a high ρ when itenvironment works at a low with motor a rotation gas density frequency, below and canthe onlycritical work range, in a helium and environment they become disordered withwhen a lowtheρ gaswhen density the RTS is works above at athe high critical motor rotationrange. frequency. According to the critical density range in Figure 3, Figure 4 gives the critical helium density error bar as a function of the input rotational frequencies of the motor. We respectively define the area under the curve and the area above the curve as stable and unstable areas. It can be seen from Figure 4 that as ωm increases, the critical density range decreases, which suggests that the RTS can work stably in a helium environment with a high ρ when it works at a low motor rotation frequency, and can only work in a helium environment with a low ρ when the RTS works at a high motor rotation frequency.

Molecules 2021, 26, x FOR PEER REVIEW 6 of 16

MoleculesMolecules 20212021, 26,, 26x FOR, 5199 PEER REVIEW 6 of6 15of 16

(a) ωm = 50 GHz, system temperature = 300 K (b) ωm = 100 GHz, system temperature = 300 K (b) ω1.5 = 100 GHz, system temperature = 300 K (a) ωm = 50 GHz,ρ system (kg/m 3temperature) = 300 K m 3 1.5 3 ρ (kg/m )1.30 2.60 1.0 3 1.30 5.19 2.60 10.38 5.19 20.76 10.38 31.15 1.0 2 20.76 41.53 31.15 51.91 0.5 2 41.53 51.91 0.5 RRT RRT RRT 1 RRT 0.0 1 0.0 3 ρ (kg/m3 ) ρ (kg/m ) 1.30 5.19 10.38 0 −0.5 1.30 5.19 10.38 0 −0.5 12.98 15.57 16.87 12.98 15.57 16.87 18.17 20.76 −1 −1.0 18.17 20.76 −1 0 5 10 15 20 −1.0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Time (ns) Time (ns) Time (ns) Time (ns) (c) ω = 150 GHz, system temperature = 300 K (d) ω = 200 GHz, system temperature = 300 K (c) ωm m= 150 GHz, system temperature = 300 K (d) ωm = 200m GHz, system temperature = 300 K 1.51.5 1.5 1.5

1.01.0 1.0 1.0

0.50.5 0.5 0.5 RRT RRT RRT RRT 3 3 0.00.0 3 0.0 0.0 ρ (kg/m ) ρ (kg/mρ (kg/m) 3) ρ (kg/m ) 0.65 0.97 1.30 1.30 2.60 2.60 0.65 0.97 1.30 1.30 1.95 1.95 −0.5−0.5 6.49 6.49 7.14 7.14 −0.5 0.5 − 2.60 3.89 7.79 7.79 10.38 10.38 2.60 3.89 5.19 5.19 1.0 − −1.0 −1.0−1.0 00 5 5 10 10 15 15 20 20 00 5 5 10 10 15 15 20 20 Time (ns) Time (ns) Time (ns) Time (ns) FigureFigure 3. Time 3. Time histories histories of RRT of at RRT 300 atK with 300 Kdifferent with different helium densities helium densities and motor and input motor rotation input frequencies: rotation frequencies: (a) ωm = 50 Figure 3. Time histories of RRT at 300 K with different helium densities and motor input rotation frequencies: (a) ωm = 50 GHz,(a) (ωb) ω=m 50 = 100 GHz, GHz, (b) ω (c) ω=m 100 = 150 GHz, GHz, (c) ωand= ( 150d) ω GHz,m = 200 and GHz. (d) ω = 200 GHz. GHz, (mb) ωm = 100 GHz,m (c) ωm = 150 GHz,m and (d) ωm = 200 GHz.m 60 60 50 3 50 46.72 kg/m 3

) 46.72 kg/m 3 40) 3 40 Unstable transmission area Unstable transmission area

(kg/m 30 ρ

(kg/m 30 ρ 20 16.22 kg/m3 20 16.22 kg/m3 Critical 10 4.55 kg/m3 Critical 10Stable transmission area 4.55 kg/m3 0 Stable transmission area1.135 kg/m3 0 50 100 1501.135 kg/m 200 3 50ω 100 (GHz) 150 200 m ω (GHz) Figure 4. The schematic diagram ofm the stable and unstable transmission areas of the RTS. FigureFigure 4. 4.The The schematic schematic diagram diagram of the of stablethe stable and unstableand unstable transmission transmission areas of areas the RTS. of the RTS. 2.3. Influence of the Size of Simulation Box 2.3.In Influence order to reflectof the Size more of accuratelySimulation the Box influence of ρ on the transmission performance of RTS, two sizes of the simulation box, i.e., 16 nm × 16 nm × 8 nm and 32 nm × 32 nm × 8 In order to reflect more accurately the influence of ρ on the transmission performance of RTS, two sizes of the simulation box, i.e., 16 nm × 16 nm × 8 nm and 32 nm × 32 nm × 8

Molecules 2021, 26, 5199 7 of 15

Molecules 2021, 26, x FOR PEER REVIEW 7 of 16

2.3. Influence of the Size of Simulation Box nm, areIn added order tofor reflect investigating more accurately the transmission the influence ofperformanceρ on the transmission of RTS in performance this section, in of RTS, two sizes of the simulation box, i.e., 16 nm × 16 nm × 8 nm and 32 nm × 32 nm × which the system temperature is 300 K and ωm is set to 100 GHz and 200 GHz, respec- 8 nm, are added for investigating the transmission performance of RTS in this section, in tively. For the same ρ, a larger simulation box has more helium atoms, as listed in Table 1 which the system temperature is 300 K and ωm is set to 100 GHz and 200 GHz, respectively. in SectionFor the 3.1. same Figureρ, a larger 5 depicts simulation the time box hist hasories more of heliumthe RRT atoms, curves as for listed RTS in under Table1 the in cases of differentSection 3.1 simulation. Figure5 depicts box sizes. the time From histories Figure of 5a,b, the RRT it can curves be found for RTS that under when the casesthe size of theof simulation different simulation box size boxis 16 sizes. nm × From 16 nm Figure × 85 a,b,nm itor can 32 benm found × 32nm that × when 8 nm, the the size critical workingof the ρ simulation range of RTS box sizeat the is corresponding 16 nm × 16 nm ω×m 8of nm 100 or GHz 32nm and× 20032nm GHz× are8 nm, both the 15.57– 16.87critical kg/m working3 and 0.97–1.30ρ rangeof kg/m RTS3, at respectively, the corresponding whichω arem of consistent 100 GHz and with 200 those GHz obtained are both 15.57–16.87 kg/m3 and 0.97–1.30 kg/m3, respectively, which are consistent with those from the simulation box size of 8 nm × 8 nm × 8 nm (Figure 3b,d). Therefore, the simulation obtained from the simulation box size of 8 nm × 8 nm × 8 nm (Figure3b,d). Therefore, the resultssimulation are independent results are independent on the size onof the sizesimulation of the simulation box. box.

ωm = 100 GHz ωm = 200 GHz 1.5 1.0 1.0

0.5 0.5 RRT RRT 0.0 ρ (kg/m3) 0.0 ρ (kg/m3) 0.65 0.97 −0.5 1.30 2.60 5.19 10.38 1.30 1.95 15.57 16.87 −0.5 2.60 3.89 −1.0 18.17 20.76 5.19 0 5 10 15 20 0 5 10 15 20 Time (ns) Time (ns) (a) ωm = 100 GHz ωm = 200 GHz 1.5 1.0 1.0

0.5 0.5 RRT RRT 0.0 0.0 3 ρ (kg/m3) ρ (kg/m ) 1.30 2.60 0.65 0.97 −0.5 1.30 1.95 5.19 10.38 −0.5 15.57 16.87 2.60 3.89 −1.0 18.17 20.76 5.19 −1.0 0 5 10 15 20 0 5 10 15 20 Time (ns) Time (ns) (b)

FigureFigure 5. Time 5. Time histories histories of the of the RRT RRT curves curves for RTSRTS under under the the cases cases of different of different simulation simulation box sizes: box (a )sizes: 16 nm (a×) 16 nmnm× × 816 nm, nm × 8 nm, andand ( (bb)) 32 32 nm ×× 3232 nm ×× 8 nm.

2.4. Influence of System Temperature The transmission behavior of the RTS at the 300 K has been analyzed in Section 2.2. It is well known that temperature is one of the major factors that affect the transmission performance of the RTS [43,53,54]. Hence, in order to investigate the influence of system temperatures on the transmission performance of RTS in helium environment, three temperatures of 150 K, 300 K, and 500 K are considered. Figure 3 shows that when the system temperature is 300 K in case of ωm = 50 GHz, 100 GHz, 150 GHz and 200 GHz, the corresponding critical working density range is 41.53–51.91 kg/m3, 15.57–16.87 kg/m3, 2.60–6.50

Molecules 2021, 26, 5199 8 of 15

2.4. Influence of System Temperature Molecules 2021, 26, x FOR PEER REVIEW The transmission behavior of the RTS at the 300 K has been analyzed in Section 2.28. of 16 It is well known that temperature is one of the major factors that affect the transmission performance of the RTS [43,53,54]. Hence, in order to investigate the influence of system temperatures on the transmission performance of RTS in helium environment, three kg/mtemperatures3, and 0.97–1.30 of 150 kg/m K, 3003, respectively. K, and 500 K areHowever, considered. when Figure the 3system shows temperature that when the drops to 150system K, the temperature critical working is 300 K density in case of rangeωm = of 50 the GHz, RTS 100 will GHz, be 150 reduced, GHz and as 200shown GHz, in the Figure 3 3 6. Itcorresponding can be seen from critical Figure working 6 that density when range ωm is is50 41.53–51.91 GHz and 100 kg/m GHz,, 15.57–16.87 the RRT could kg/m reach, 3 3 1.0 2.60–6.50when ρ range kg/m is, andlower 0.97–1.30 than 27.25–28.55 kg/m , respectively. kg/m3 and However, 3.89–5.19 when kg/m the3 respectively. system temper- How- ature drops to 150 K, the critical working density range of the RTS will be reduced, as ever, when ωm is 150 GHz and 200 GHz, the transmission performance of RTS in the he- shown in Figure6. It can be seen from Figure6 that when ω is 50 GHz and 100 GHz, the lium environment under the density range we studied ism very poor. At higher tempera- RRT could reach 1.0 when ρ range is lower than 27.25–28.55 kg/m3 and 3.89–5.19 kg/m3 tures, the thermal vibration of atoms/molecules in the system becomes more severe, and respectively. However, when ωm is 150 GHz and 200 GHz, the transmission performance the ofnonbonding RTS in the heliuminteraction environment at the adjacent under the ends density of the range rotor we and studied the motor is very becomes poor. At more energetic.higher temperatures,Therefore, when the thermalthe system vibration temperature of atoms/molecules rises within in a thecertain system range, becomes the inter- layermore van severe, der Waals and theeffects nonbonding and the end interaction effects atof theRTS adjacent increase, ends so ofthe the driving rotor and force the of the rotormotor increases becomes with more the energetic. increase Therefore,of temperature when the[43]. system The rotor temperature rotational rises speed within will a ac- celeratecertain as range, the environmental the interlayer van temperature der Waals effects rises and[53,54]. the end When effects the of system RTS increase, temperature so risesthe to driving 500 K, force although of the the rotor skin increases friction with dr theag increaseof helium of temperatureincreases with [43]. the The increase rotor in rotational speed will accelerate as the environmental temperature rises [53,54]. When the temperature, a higher critical working density range of RTS is allowed because of the system temperature rises to 500 K, although the skin friction drag of helium increases greaterwith driving the increase force in temperature,with the increasing a higher criticaltemperature. working Figure density 7 rangeshows of that RTS iswhen allowed the sys- tembecause temperature of the is greater 500 K driving and ωm force is 50 with GHz, the 100 increasing GHz, 150 temperature. GHz, and 200 Figure GHz,7 shows the critical 3 3 3 workingthat when gas density the system range temperature is 51.91–62.29 is 500 kg/m K and,ω 23.36–25.96m is 50 GHz, kg/m 100 GHz,, 7.79–12.98 150 GHz, kg/m and and 2.6–5.19200 GHz kg/m, the3, respectively. critical working Hence, gas density the system range is temper 51.91–62.29ature kg/m will 3seriously, 23.36–25.96 affect kg/m the3 ,critical 7.79–12.98working gas kg/m density3 and 2.6–5.19range of kg/m the RTS.3, respectively. Hence, the system temperature will seriouslyIn conjunction affect the with critical Figures working 3, 6gas and density 7, the influence range of the curves RTS. of the system temperature In conjunction with Figures3,6 and7, the influence curves of the system temperature and ωm on the critical working density error bar are drawn in Figure 8. They clearly and ωm on the critical working density error bar are drawn in Figure8. They clearly indicateindicate that that in in the the working working temperaturetemperature range range of the of RTSthe RTS from from 100 K to100 600 K Kto [ 43600], the K [43], thehigher higher the the temperature temperature and theand lower the thelower motor the input motor rotation input frequency, rotation the frequency, higher the the highercritical the working critical helium working density helium range dens allows.ity range allows.

(a) ωm = 50 GHz (b) ωm = 100 GHz, 150 GHz and 200 GHz 2 1.5 System temperature = 150 K System temperature = 150 K 3 ωm ρ (kg/m ) 100 GHz 2.60 1 1.0 100 GHz 3.89 100 GHz 5.19 100 GHz 6.49

RRT 100 GHz 7.79 0 RRT ρ (kg/m3) 0.5 150 GHz 1.30 1.30 5.19 150 GHz 2.60 150 GHz 3.89 24.66 27.25 −1 200 GHz 1.30 28.55 29.85 0.0 200 GHz 1.95 31.15 200 GHz 2.60 0 5 10 15 20 0 5 10 15 20 25 30 35 40 Time (ns) Time (ns)

FigureFigure 6. The 6. curvesThe curves of RRT of RRTat 150 at 150K in K a in helium a helium environment environment when when ( (aa)) ωωmm == 50 50 GHz, GHz, ( (b) ωm == 100 100 GHz, GHz, 150 GHz,GHz, and and 200 GHz. 200 GHz.

MoleculesMolecules 20212021,,26 26,, 5199x FOR PEER REVIEW 99 ofof 1516

(a) ωm = 50 GHz, System temperature = 500 K (b) ωm = 100 GHz, System temperature = 500 K

2 1.5 1.0 1 0.5

0.0

0 RRT RRT 3 ρ (kg/m3) ρ (kg/m ) −0.5 −1 5.19 10.38 5.19 15.57 20.76 31.15 −1.0 23.36 25.96 41.53 51.91 27.25 28.55 2 − 62.29 −1.5 29.85 31.15 0 5 10 15 20 0 5 10 15 20 Time (ns) Time (ns)

1.0 1.0

0.5 0.5 RRT RRT 3 0.0 3 ρ (kg/m ) ρ (kg/m ) 0.0 1.30 2.60 2.60 7.79 5.19 6.49 −0.5 12.98 14.28 −0.5 7.14 7.79 14.92 15.57 10.38 −1.0 0 5 10 15 20 05101520

Time (ns) Time (ns)

Figure 7. The curves of RRT at 500 K in helium environment when (a) ωm = 50 GHz, (b) ωm = 100 GHz, (c) ωm = 150 GHz, FigureMolecules 7. 2021 The, 26 , curvesx FOR PEER of REVIEWRRT at 500 K in helium environment when (a) ωm = 50 GHz, (b) ωm = 100 GHz,10 of ( c16) ωm = 150 GHz, and (d) ωm = 200 GHz. and (d) ωm = 200 GHz.

60 150 K ) 50 3 300 K 40 500 K (kg/m

ρ 30

Critical 10

0 50 100 150 200 ω (GHz) m

Figure 8. The relationship between the critical working helium density range and ωm at different Figure 8. The relationship between the critical working helium density range and ωm at different system temperatures. system temperatures. 3. Models and Methods 3.1. RTS Model In order to investigate the dynamic behavior of the RTS in a helium environment, a RTS made from CNT (5, 5)/BNNT (10, 10)/CNT (15, 15) in a helium-filled simulation box is set up, as shown in Figure 9. Figure 9a shows a heterogeneous TWNTs RTS made of CNTs and BNNT placed in the center of a simulation box with a boundary length of a × b × c in a helium environment. Figure 9b depicts two RTS models with different end structures of the rotor, one being the capped-rotor RTS model, and the other being the open- rotor RTS model. Figure 9c shows the construction parameters of the RTS model, where the inner CNT (5, 5) with a length of 6 nm and a diameter of 0.678 nm acts as rotor, the middle BNNT (10, 10) with a length 4 nm and a diameter of 1.356 nm acts as motor, and the two outer separated CNTs (15, 15) with a length of 1 nm and a diameter of 2.034 nm are fixed as stators. The inner and outer interlayer spacing are both set to 0.339 nm. The nanotubes of TWNTs in this model have a symmetrical layout along the z axis. The CNT stators are fixed during the MD simulations. ωm and ωr represent the rotation frequencies of motor and rotor, respectively. Table 1 lists the number of helium atoms corresponding to different helium densities ρ in the simulation box with different sizes.

Molecules 2021, 26, 5199 10 of 15

3. Models and Methods 3.1. RTS Model In order to investigate the dynamic behavior of the RTS in a helium environment, a RTS made from CNT (5, 5)/BNNT (10, 10)/CNT (15, 15) in a helium-filled simulation box is set up, as shown in Figure9. Figure9a shows a heterogeneous TWNTs RTS made of CNTs and BNNT placed in the center of a simulation box with a boundary length of a × b × c in a helium environment. Figure9b depicts two RTS models with different end structures of the rotor, one being the capped-rotor RTS model, and the other being the open-rotor RTS model. Figure9c shows the construction parameters of the RTS model, where the inner CNT (5, 5) with a length of 6 nm and a diameter of 0.678 nm acts as rotor, the middle BNNT (10, 10) with a length 4 nm and a diameter of 1.356 nm acts as motor, and the two outer separated CNTs (15, 15) with a length of 1 nm and a diameter of 2.034 nm are fixed as stators. The inner and outer interlayer spacing are both set to 0.339 nm. The nanotubes of TWNTs in this model have a symmetrical layout along the z axis. The CNT stators are fixed during the MD simulations. ωm and ωr represent the rotation frequencies of motor Molecules 2021, 26, x FOR PEER REVIEW and rotor, respectively. Table1 lists the number of helium atoms corresponding11 of 16 to different

helium densities ρ in the simulation box with different sizes.

Figure 9. RotationFigure transmission9. Rotation transmission nano-system (RTS)nano-system model made (RTS) from model CNT made (5, 5)/BNNT from CNT (10, 10)/CNT(5, 5)/BNNT (15, 15):(10, ( a) The RTS model in a10)/CNT helium environment, (15, 15): (a) The (b) RTS the RTSmodel model in a helium with different environment, rotor end (b) structures,the RTS model and with (c) the different structure rotor parameters of the RTS model.end structures, and (c) the structure parameters of the RTS model.

Table 1. The number of helium atoms corresponding to different helium densities ρ in the simulation box with different sizes.

0.65 0.97 1.30 1.95 2.60 3.89 5.19 6.49 7.14 7.79 10.38 12.98 14.28 14.92 15.57 16.87 18.17 20.76 ρ(kg/m3) 23.36 24.66 25.96 27.25 28.55 29.85 31.15 41.53 51.91 8 nm × 8 nm × 62.29 8 nm 50 75 100 150 200 300 400 500 550 600 800 1000 1100 1150 1200 1300 1400 1600 Number of atoms 1800 1900 2000 2100 2200 2300 2400 3200 4000 4800 0.65 0.97 1.30 1.95 2.60 3.89 5.19 10.38 15.57 ρ(kg/m3) 16 nm × 16 nm 16.87 18.17 20.76 × 8 nm 200 300 400 600 800 1200 1600 3200 4800 Number of atoms 5200 5600 6400 0.65 0.97 1.30 1.95 2.60 3.89 5.19 10.38 15.57 ρ(kg/m3) 32 nm × 32 nm 16.87 18.17 20.76 × 8 nm 800 1200 1600 2400 3200 4800 6400 12,800 19,200 Number of atoms 20,800 22,400 25,600

3.2. MD Method Initially, the helium atoms in the RTS model are laid out regularly in lines in the simulation box, and the boundaries for the global simulation box in each dimension are

Molecules 2021, 26, 5199 11 of 15

Table 1. The number of helium atoms corresponding to different helium densities ρ in the simulation box with different sizes.

0.65 0.97 1.30 1.95 2.60 3.89 5.19 6.49 7.14 7.79 10.38 12.98 14.28 14.92 15.57 16.87 18.17 20.76 ρ (kg/m3) 23.36 24.66 25.96 27.25 28.55 29.85 31.15 41.53 51.91 62.29 8 nm × 8 nm × 8 nm 50 75 100 150 200 300 400 500 550 600 800 1000 1100 1150 1200 1300 1400 1600 Number of atoms 1800 1900 2000 2100 2200 2300 2400 3200 4000 4800 0.65 0.97 1.30 1.95 2.60 3.89 5.19 10.38 15.57 ρ (kg/m3) 16.87 18.17 20.76 16 nm × 16 nm × 8 nm 200 300 400 600 800 1200 1600 3200 4800 Number of atoms 5200 5600 6400 0.65 0.97 1.30 1.95 2.60 3.89 5.19 10.38 15.57 ρ (kg/m3) 16.87 18.17 20.76 32 nm × 32 nm × 8 nm 800 1200 1600 2400 3200 4800 6400 12,800 19,200 Number of atoms 20,800 22,400 25,600

3.2. MD Method Initially, the helium atoms in the RTS model are laid out regularly in lines in the simulation box, and the boundaries for the global simulation box in each dimension are periodic. Consequently, at the beginning of the simulation, the structure is reshaped under minimized potential energy of the system by relaxing the system at the canonical NVT ensemble for 1 ns and the microcanonical NVE ensemble for 1 ns to obtain a reasonable layout of helium atoms with the RTS model, where N is the total number of particles in the system, V is the system’s volume, T is the absolute temperature, and E is the total energy in the system. As shown in Figure 10, it can be clearly seen that under a different system temperature, the total energy of the system is well converged during the relaxation. After the relaxation, the stators are fully fixed, and then the motor is applied with a continuous rotation at a given frequency through the command “fix move rotate”. This command essentially sets the angular velocity of each atom on the motor around the axis of rotation. The atoms on the rotor are free. The movement of rotor driven by the motor under the microcanonical NVT ensemble is recorded. For the systems of different system temperatures and different ωm, the time to reach equilibrium rotation frequency of the rotor is also different, and the specific range is also clarified by Zheng et al. [43]. In addition, when the speed of the motor increases, the time to reach equilibrium rotation frequency of the rotor also increases, so the total time for the simulation is 20 ns. The time step for all simulations is chosen to be 1 fs. LAMMPS [60] (Large-scale Atomic/Molecular Massively Parallel Simulator) is employed in the simulations. The interaction among carbon atoms on CNTs is evaluated by the AIREBO potential [61,62]. The interaction among boron atom and nitrogen atom on BNNT is evaluated by the Tersoff potential [63]. The Lennard-Jones (L-J) 12-6 potential function is used to describe the interaction of the C, B, N, and He atoms [64–66]. The L-J interaction can 12 6 σ σ be written as U(r ) = 4ε − (r ≤ rc), where r represents the distance i j ri j ri j ij ij between the atoms, ε is the well-depth, σ is the size parameter, and rc is the cutoff distance. The Lorentz-Berthelot mixing rule [67,68] is used to determine the well-depth and size parameters between any two atom types. The parameters of the L-J 12-6 potential listed in Table2. The cutoff distance of the L-J potential is 1.02 nm. Molecules 2021, 26, x FOR PEER REVIEW 12 of 16

periodic. Consequently, at the beginning of the simulation, the structure is reshaped under minimized potential energy of the system by relaxing the system at the canonical NVT ensemble for 1 ns and the microcanonical NVE ensemble for 1 ns to obtain a reasonable layout of helium atoms with the RTS model, where N is the total number of particles in the system, V is the system’s volume, T is the absolute temperature, and E is the total energy in the system. As shown in Figure 10, it can be clearly seen that under a different system temperature, the total energy of the system is well converged during the relaxation. After the relaxation, the stators are fully fixed, and then the motor is applied with a continuous rotation at a given frequency through the command “fix move rotate”. This command essentially sets the angular velocity of each atom on the motor around the axis of rotation. The atoms on the rotor are free. The movement of rotor driven by the motor under the microcanonical NVT ensemble is recorded. For the systems of different system temperatures and different ωm, the time to reach equilibrium rotation frequency of the rotor is also different, and the specific range is also clarified by Zheng et al. [43]. In addition, when the speed of the motor increases, the time to reach equilibrium rotation fre- Molecules 2021, 26, 5199 quency of the rotor also increases, so the total time for the simulation is 20 ns. The12 time of 15 step for all simulations is chosen to be 1 fs. LAMMPS [60] (Large-scale Atomic/Molecular Massively Parallel Simulator) is employed in the simulations.

600

500 −12,000 150 K nvt 300 K nvt 500 K nvt 400 150 K nve 300 K nve 500 K nve −12,050 300 −12,100

200 (eV) energy Total System temperature (K) 100 −12,150

0.00.20.40.60.81.0 Time (ns) Figure 10. Convergence of system temperaturestemperatures andand systemsystem totaltotal energiesenergies duringduring relaxation.relaxation.

The interaction among carbon atoms on CNTs is evaluated by the AIREBO potential Table[61,62]. 2. Lennard-JonesThe interaction parameters among boron for the atom interatomic and nitrogen van der Waals atom interactions. on BNNT is evaluated by the TersoffAtom potentiali-j [63]. The Lennard-Jonesε (eV) (L-J) 12-6 potential functionσ (nm) is used to describe the interaction of the C, B, N, and He atoms [64–66]. The L-J interaction can be writ- C-C12 6 0.00373 0.3400  σ   σ   U (r ) B-B= 4ε   −    0.00411 0.3453 i j N-N r   r   0.00628 0.3365  i j   i j   ten as He-He ( rij ≤ rc 0.00219), where rij represents the distance 0.2559 between the atoms, ε is theC-B well-depth, σ is the size 0.00391 parameter, and r is the cutoff 0.3427 distance. The C-N 0.00484c 0.3383 Lorentz-BerthelotC-He mixing rule [67,68] is used 0.00285 to determine the well-depth 0.2980 and size parameters betweenB-He any two atom types. The paramete 0.00300rs of the L-J 12-6 potential 0.3006 listed in Table 2. The cutoffN-He distance of the L-J potential 0.00370is 1.02 nm. 0.2962

3.3.Table Simulation 2. Lennard-Jones Strategies parameters for the interatomic van der Waals interactions. To investigateAtom i-j the influence of differentε (eV helium) densities (ρ) onσ the (nm transmission) performance of RTS, the RTS is placed in the original simulation box with a size of 8 nm × 8 nm × 8 nm, and the ρ is set from 0.65 kg/m3 to 51.91 kg/m3. The volume of RTS accounts for 2.65% of the simulation box, and the effective working volume of helium accounts for 97.32% of the simulation box. The system temperature is set as 300 K. To study the influence of system temperature on the transmission performance of RTS, three system temperatures, i.e., 150 K, 300 K, and 500 K are considered. The motor input rotation frequency (ωm) is set to 50 GHz, 100 GHz, 150 GHz and 200 GHz respectively. To study the influence of the simulation box size on the RTS, the period boundary value is set to 4 times and 16 times of the original simulation box, i.e., the size of the simulation box is 16 nm × 16 nm × 8 nm and 32 nm × 32 nm × 8 nm, respectively. In the case of the same ρ, a larger simulation box has more helium atoms. The ωm is set to 100 GHz and 200 GHz, and the system temperature is 300 K.

4. Conclusions In this work, we have conducted MD simulations to study the transmission performance of the heterogeneous rotation transmission nano-system (RTS) based on carbon nanotubes (CNTs) and boron nitride nanotube (BNNT) in a helium environment. Consider- ing the structural stability of the RTS model, we found that the capped-rotor RTS is more suitable for stable operation in a helium environment. Inﬂuences of some typical factors Molecules 2021, 26, 5199 13 of 15

such as system temperature, helium density, size of simulation box, and input rotation frequency of motor were especially investigated. The MD simulation results showed that when the gas density is lower than a critical range, a stable output signal of the rotor can be obtained and the rotation transmission ratio (RRT) of RTS can reach 1.0, but as the gas density is higher than the critical range, the rotor cannot output stably due to the sharp drop of the RRT caused by the large friction between helium and the RTS. The results also showed that the system temperature and gas density are two main factors affecting the RTS transmission behavior regardless of the size of the simulation box, which clearly indicates that in the working temperature range of the RTS from 100 K to 600 K, the higher the temperature and the lower the motor input rotation frequency, the higher the critical working helium density range allows. The research in this work could provide theoretical input for the application of this type of nanodevices in a gas environment.

Author Contributions: Conceptualization, W.J. and P.Z.; methodology, W.J.; software, P.Z.; validation, Q.Q.; formal analysis, P.Z.; investigation, P.Z.; resources, P.Z.; data curation, D.L.; writing—original draft preparation, P.Z.; writing—review and editing, W.J. and Q.Q.; visualization, D.L.; supervision, W.J.; project administration, W.J.; funding acquisition, W.J. and Q.Q. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant numbers 11772145 and 11772204. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772145 and 11772204). Conﬂicts of Interest: The authors declare no conﬂict of interest. Sample Availability: Samples of the compounds are not available from the authors.

References 1. Auffan, M.; Rose, J.; Bottero, J.Y.; Lowry, G.V.; Jolivet, J.P.; Wiesner, M.R. Towards a deﬁnition of inorganic nanoparticles from an environmental, health and safety perspective. Nat. Nanotechnol. 2009, 4, 634–641. [CrossRef][PubMed] 2. Yang, P.S.; Cheng, P.H.; Kao, C.R.; Chen, M.J. Novel self-shrinking mask for sub-3 nm pattern fabrication. Sci. Rep. 2016, 6, 29625. [CrossRef][PubMed] 3. Devadasu, V.R.; Bhardwaj, V.; Kumar, M.R. Can controversial nanotechnology promise drug delivery? Chem. Rev. 2012, 113, 1686–1735. [CrossRef] 4. Wang, H.; Pumera, M. Fabrication of micro/nanoscale motors. Chem. Rev. 2015, 115, 8704–8735. [CrossRef] 5. The Nobel Prize. Available online: http://nobelprize.org/nobel_prizes/chemistry/laureates/2016/press.html (accessed on 4 May 2021). 6. Berman, D.; Krim, J. Surface science, MEMS and NEMS: Progress and opportunities for surface science research performed on, or by, microdevices. Prog. Surf. Sci. 2013, 88, 171–211. [CrossRef] 7. Li, C.Y.; Chou, T.W. Elastic moduli of multi-walled carbon nanotubes and the effect of van der Waals forces. Compos. Sci. Technol. 2003, 63, 1517–1524. [CrossRef] 8. Zhou, X.; Zhou, J.J.; Zhong, O.Y. The strain energy and young’s modulus of single-wall carbon nanotubules calculated from the electronic energy-band Theory. Phys. Rev. B 2000, 62, 13692–13696. 9. Baughman, R.H.; Zakhidov, A.A.; Heer, W.A.D. Carbon nanotubes-the route toward applications. Science 2002, 297, 787–792. [CrossRef] 10. Kociak, M.; Kasumov, A.Y.; Gueron, S.; Reulet, B.; Khodos, I.I.; Gorbatov, Y.B.; Volkov, V.T.; Vaccarini, L.; Bouchiat, H. Supercon- ductivity in ropes of single-walled carbon nanotubes. Phys. Rev. Lett. 2001, 86, 2416–2419. [CrossRef][PubMed] 11. Qiu, W.; Kang, Y.L.; Lei, Z.K.; Qin, Q.H.; Li, Q.; Wang, Q. Experimental study of the Raman strain rosette based on the carbon nanotube strain sensor. J. Raman Spectros. 2010, 41, 1216–1220. [CrossRef] 12. Qiu, W.; Kang, Y.L.; Lei, Z.K.; Qin, Q.H.; Li, Q. A new theoretical model of a carbon nanotube strain sensor. Chin. Phys. Lett. 2009, 26, 080701. 13. Biercuk, M.J.; Llaguno, M.C.; Radosavljevic, M.; Hyun, J.K.; Fischer, J.E.; Johnson, A.T.C. Carbon nanotube composites for thermal management. Appl. Phys. Lett. 2002, 80, 2767–2769. [CrossRef] 14. Schoen, P.A.E.; Walther, J.H.; Arcidiacono, S.; Poulikakos, D.; Koumoutsakos, P. Nanoparticle trafﬁc on helical tracks: Ther- mophoretic mass transport through carbon nanotubes. Nano Lett. 2006, 6, 1910–1917. [CrossRef] Molecules 2021, 26, 5199 14 of 15

15. Lau, K.T. Interfacial bonding characteristics of nanotube/polymer composites. Chem. Phys. Lett. 2003, 370, 399–405. [CrossRef] 16. Treacy, M.M.J.; Ebbesen, T.W.; Gibson, J.M. Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 1996, 381, 678–680. [CrossRef] 17. Yu, M.F.; Lourie, O.; Dyer, M.J.; Moloni, K.; Kelly, T.F.; Ruoff, R. Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science 2000, 287, 637–640. [CrossRef][PubMed] 18. Cumings, J.; Zettl, A. Low-friction nanoscale linear bearing realized from multiwall carbon nanotubes. Science 2000, 289, 602–604. [CrossRef] 19. Zhang, R.; Ning, Z.Y.; Zhang, Y.Y.; Zheng, Q.S.; Chen, Q.; Xie, H.H.; Zhang, Q.; Qian, W.Z.; Wei, F. Superlubricity in centimetres- long double-walled carbon nanotubes under ambient conditions. Nat. Nanotechnol. 2013, 8, 912–916. [CrossRef][PubMed] 20. Jiang, W.G.; Zeng, Y.H.; Qin, Q.H.; Luo, Q.H. A novel oscillator based on heterogeneous carbon@MoS2 nanotubes. Nano Res. 2016, 9, 1775–1784. [CrossRef] 21. Lin, Y.W.; Jiang, W.G.; Qin, Q.H.; Chen, Y.J. A novel dual-signal output screwing oscillator based on carbon@MoS2 nanotubes. Appl. Phys. Express 2019, 12, 065001. [CrossRef] 22. Bourlon, B.; Glattli, C.; Bachtold, A.; Forró, L. Carbon nanotube based bearing for rotational motions. Nano Lett. 2004, 4, 709–712. [CrossRef] 23. Barreiro, A.; Rurali, R.; Hernandez, E.R.; Moser, J.; Pichler, T.; Forró, L.; Bachtold, A. Subnanometer motion of cargoes driven by thermal gradients along carbon nanotubes. Science 2008, 320, 775–778. [CrossRef] 24. Fennimore, A.M.; Yuzvinsky, T.D.; Han, W.Q.; Fuhrer, M.S.; Cumings, J.; Zettl, A. Rotational actuators based on carbon nanotubes. Nature 2003, 424, 408–410. [CrossRef] 25. Holek, I.S.; Reguera, D.; Rubi, J.M. Carbon-nanotube-based motor driven by a thermal gradient. J. Phys. Chem. C 2013, 117, 3109–3113. [CrossRef] 26. Ershova, O.V.; Lebedeva, I.V.; Lozovik, Y.E.; Popov, A.M.; Knizhnik, A.A.; Potapkin, B.V.; Bubel, O.N.; Kislyakov, E.F.; Poklonskii, P.A. Nanotube-based nanoelectromechanical systems: Control versus thermodynamic ﬂuctuations. Phys. Rev. B 2010, 81, 155453. [CrossRef] 27. Alder, B.J.; Wainwright, T.E. Studies in molecular dynamics. I. General method. J. Chem. Phys. 1959, 31, 459–466. [CrossRef] 28. Nosé, S. A unifed formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, 511–519. [CrossRef] 29. Tuzun, R.E.; Noid, D.W.; Sumpter, B.G. Dynamics of a laser driven molecular motor. Nanotechnology 1995, 6, 52. [CrossRef] 30. Král, P.; Sadeghpour, H.R. Laser spinning of nanotubes: A path to fast-rotating microdevices. Phys. Rev. B 2002, 65, 161401. [CrossRef] 31. Tu, Z.C.; Hu, X. Molecular motor constructed from a double-walled carbon nanotube driven by axially varying voltage. Phys. Rev. B 2005, 72, 3404. [CrossRef] 32. Wang, B.; Vukovic, L.; Kral, P. Nanoscale rotary motors driven by electron tunneling. Phys. Rev. Lett. 2008, 101, 186808. [CrossRef] 33. Kang, J.W.; Hwang, H.J. Nanoscale carbon nanotube motor schematics and simulations for micro-electro-mechanical machines. Nanotechnology 2004, 15, 1633–1638. [CrossRef] 34. Kang, J.W.; Hwang, H.J.; Lee, H.J.; Lee, J.H. Fluidic gas-driven carbon-nanotube motor: Molecular dynamics simulations. J. Kor. Phys. Soc. 2004, 45, 573–576. 35. Cai, K.; Li, Y.; Qin, Q.H.; Yin, H. Gradientless temperature-driven rotating motor from a double-walled carbon nanotube. Nanotechnology 2014, 25, 505701. [CrossRef][PubMed] 36. Cai, K.; Yu, J.Z.; Wan, J.; Shi, J.; Qin, Q.H. Conﬁguration jumps of rotor in a nanomotor from carbon nanostructures. Carbon 2016, 101, 168–176. [CrossRef] 37. Yin, H.; Cai, K.; Wei, N.; Qin, Q.H.; Shi, J. Study on the dynamics responses of a transmission system made from carbon nanotubes. J. Appl. Phys. 2015, 117, 234305. [CrossRef] 38. Cai, K.; Yin, H.; Wei, N.; Chen, Z.; Shi, J. A stable high-speed rotational transmission system based on nanotubes. Appl. Phys. Lett. 2015, 106, 602. [CrossRef] 39. Cai, K.; Yin, H.; Qin, Q.H.; Li, Y. Self-excited oscillation of rotating double-walled carbon nanotubes. Nano Lett. 2014, 14, 2558–2562. [CrossRef] 40. Shi, J.; Cai, H.F.; Cai, K.; Qin, Q.H. Dynamic behavior of a black phosphorus and carbon nanotube composite system. J. Phys. D Appl. Phys. 2017, 50, 025304. [CrossRef] 41. Jin, H.L.; Duan, H.Y.; Shi, J. Reversing rotation of a nanomotor by introducing a braking BNC nanotube. Comput. Mater. Sci. 2019, 159, 327–332. [CrossRef] 42. Zhang, X.N.; Cai, K.; Shi, J.; Qin, Q.H. Friction effect of stator in a multi-walled CNT-based rotation transmission system. Nanotechnology 2018, 29, 045706. [CrossRef] 43. Zheng, P.; Jiang, W.G.; Lin, Y.W.; Chen, Y.J.; Qin, Q.H.; Li, D.S. A novel rotation transmission nano-system based on Carbon@Boron- Nitride@Carbon heterogeneous nanotubes: A molecular dynamics study. Comput. Mater. Sci. 2021, 196, 110517. [CrossRef] 44. Lee, C.H.; Bhandari, S.; Tiwari, B.; Yapici, N.; Zhang, D.Y.; Yap, Y.K. Boron nitride nanotubes: Recent advances in their synthesis, functionalization, and applications. Molecules 2016, 21, 922. [CrossRef] 45. Wang, J.S.; Kayastha, V.K.; Yap, Y.K.; Fan, Z.Y.; Lu, J.G.; Pan, Z.W.; Ivanov, I.N.; Puretzky, A.A.; Geohegan, D.B. Low temperature growth of boron nitride nanotubes on substrates. Nano Lett. 2005, 5, 2528–2532. [CrossRef] Molecules 2021, 26, 5199 15 of 15

46. Grant, J.T.; Carrero, C.A.; Goeltl, F.; Venegas, J.; Mueller, P.; Burt, S.P.; Specht, S.E.; McDermott, W.P.; Chieregato, A.; Hermans, I. Selective oxidative dehydrogenation of propane to propene using boron nitride catalysts. Science 2016, 354, 1570–1573. [CrossRef] 47. Salvetti, A.; Rossi, L.; Iacopetti, P.; Li, X.; Nitti, S.; Pellegrino, T.; Mattoli, V.; Golberg, D.; Ciofani, G. In vivo biocompatibility of boron nitride nanotubes: Effects on stem cell biology and tissue regeneration in planarians. Nanomedicine 2015, 10, 1911–1922. [CrossRef] 48. Wu, H.S.; Jia, Y.F. Research progress of boron nitride nanotubes. Prog. Chem. 2001, 16, 6–14. 49. Jing, L.; Tay, R.; Li, H.L.; Tsang, S.H.; Huang, J.F.; Tan, D.; Zhang, B.W.; Teo, E.H.T.; Tok, A.L.Y. Coaxial carbon@boron nitride nanotube arrays with enhanced thermal stability and compressive mechanical properties. Nanoscale 2016, 8, 11114–11122. [CrossRef] 50. Jing, L.; Samani, M.K.; Liu, B.; Li, H.L.; Tay, R.Y.J.; Tsang, S.H.; Cometto, O.; Nylander, A.; Liu, J.; Teo, E.H.T.; et al. Thermal conductivity enhancement of coaxial carbon@boron nitride nanotube arrays. ACS Appl. Mater. Interfaces 2017, 9, 14555–14560. 51. Thamwattana, N.; Hill, J.M. Nanotube bundle oscillators: Carbon and boron nitride nanostructures. Physica B 2009, 404, 3906–3910. [CrossRef] 52. Shi, J.; Wu, P.W.; Li, X.; Cai, K.; Zhang, Y.Y. Efﬁciency of CNT-based rotation transmission nanosystem in water. Nanotechnology 2021, 32, 245401. [CrossRef][PubMed] 53. Cai, K.; Shi, J.; Yu, J.; Qin, Q.H. Dynamic behavior of a rotary nanomotor in argon environments. Sci. Rep. 2018, 8, 3511. [CrossRef] [PubMed] 54. Shi, J.; Li, Y.; Wang, A.; Cai, K. Rotational behavior of a nanoring protected by argon. Comput. Mater. Sci. 2018, 154, 132. [CrossRef] 55. Weber, N.C.; Smit, K.F.; Hollmann, M.W.; Preckel, B. Targets involved in cardioprotection by the non-anesthetic noble gas helium. Curr. Drug Targets 2015, 16, 786–792. [CrossRef][PubMed] 56. Surin, L.A.; Potapov, A.V.; Dumesh, B.S.; Schlemmer, S.; Xu, Y.; Raston, P.L.; Jager, W. Rotational study of carbon monoxide solvated with helium atoms. Phys. Rev. Lett. 2008, 101, 233401. [CrossRef] 57. Gupta, V. Graphene as intermediate phase in fullerene and carbon nanotube growth: A Young-Laplace surface-tension model. Appl. Phys. Lett. 2010, 97, 181910. [CrossRef] 58. Jost, O.; Gorbunov, A.A.; Ciacchi, L.C.; Pompe, W.; Liu, X.; Pichler, T.; Dunsch, L.; Golden, M.S.; Fink, J. Optical absorption study of factors inﬂuencing the carbon nanotube nucleation process. AIP Conf. Proc. 2001, 591, 341–344. 59. Hinkov, I.; Farhat, S.; Chapelle, M.L.; Fan, S.S.; Han, H.X.; Li, G.H.; Scott, C.D. Optical Plasma Control during ARC Carbon Nanotube Growth; NASA: Houston, TX, USA, 2001. 60. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1–19. [CrossRef] 61. Harrison, J.A.; White, C.T.; Colton, R.J.; Brenner, D.W. Molecular-dynamics simulations of atomic-scale friction of diamond surfaces. Phys. Rev. B 1992, 46, 9700–9708. [CrossRef] 62. Brenner, D.W.; Shenderova, O.A.; Harrison, J.A.; Stuart, S.J.; Ni, B.; Sinnott, S.B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 2002, 14, 783–802. [CrossRef] 63. Kinaci, A.; Haskins, J.B.; Sevik, C.; Cagin, T. Thermal conductivity of BN-C nanostructures. Phys. Rev. B 2012, 86, 115410. [CrossRef] 64. Hummer, G.; Rasaiah, J.G.; Noworyta, J.P. Water conduction through the hydrophobic channel of a carbon nanotube. Nature 2001, 414, 188–190. [CrossRef] 65. Hilder, T.A.; Gordon, D.; Chung, S. Salt rejection and water transport through boron nitride nanotubes. Small 2009, 5, 2183–2190. [CrossRef] 66. Lee, C.W.; Chernatynskiy, A.; Shukla, P.; Stoller, R.E.; Sinnott, S.B.; Phillpot, S.R. Effect of pores and He bubbles on the thermal transport properties of UO2 by molecular dynamics simulation. J. Nucl. Mater. 2015, 456, 253–259. [CrossRef] 67. Tomar, D.S.; Singla, M.; Gumma, S. Potential parameters for helium adsorption in silicalite. Microporous Mesoporous Mater. 2011, 142, 116–121. [CrossRef] 68. Rouha, M.; Nezbeda, I. Non-Lorentz-Berthelot Lennard-Jones mixtures: A systematic study. Fluid Phase Equilib. 2009, 277, 42–48. [CrossRef]