Ideal Oscillation of a Hydrogenated Deformable Rotor in a Gigahertz Rotation–Translation Nanoconverter at Low Temperatures

sensors

Article Ideal Oscillation of a Hydrogenated Deformable Rotor in a Gigahertz Rotation–Translation Nanoconverter at Low Temperatures

Bo Song 1 , Jiao Shi 1,2 , Jinbao Wang 3, Jianhu Shen 4 and Kun Cai 4,* 1 College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, China; [email protected] (B.S.); [email protected] (J.S.) 2 State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China 3 School of Port and Transportation Engineering, Zhejiang Ocean University, Zhoushan 316022, China; [email protected] 4 Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, VIC 3001, Australia; [email protected] * Correspondence: [email protected]

Received: 18 January 2020; Accepted: 23 March 2020; Published: 1 April 2020

Abstract: It was discovered that large-amplitude axial oscillation can occur on a rotor with an internally hydrogenated deformable part (HDP) in a rotation–translation nanoconverter. The dynamic outputs of the system were investigated using molecular dynamics simulations. When an input rotational frequency (100 GHz > ω > 20 GHz) was applied at one end of the rotor, the HDP deformed under the centrifugal and van der Waals forces, which simultaneously led to the axial translation of the other end of the rotor. Except at too high an input rotational frequency (e.g., >100 GHz), which led to eccentric rotation and even collapse of the system, the present system could generate a periodic axial oscillation with an amplitude above 0.5 nm at a temperature below 50 K. In other ranges of temperature and amplitude, the oscillation dampened quickly due to the drastic thermal vibrations of the atoms. Furthermore, the eﬀects of the hydrogenation scheme and the length of HDP on the equilibrium position, amplitude, and frequency of oscillation were investigated. The conclusions can be applied to the design of an ideal nano-oscillator based on the present rotation–translation converter model.

Keywords: nano-oscillator; rotation–translation converter; nanodevice; molecular dynamics; hydrogenation

1. Introduction Due to the extremely high in-plane/in-shell strength [1,2] and ideal inter-layer superlubrication [3–5], pure sp2 carbon materials, such as carbon nanotubes (CNTs) [6] and graphene [7], are widely adopted in the design and fabrication of nanodevices, such as nanomotors [8,9], nanobearings [3,10], nano-oscillators [11–13], and nanopumps [14]. Meanwhile, some of them have already been realized in nanofabrication. To ensure those nanodevices work normally, numerous driving methods, such as a thermally driven strategy [15,16], electrical strategy [9,17], and ﬂuid strategy [18,19], have been proposed. In 2000, several experiments [3,20,21] demonstrated the low interaction between adjacent walls of multi-walled CNTs (MWCNTs) by pulling the inner tubes out. Since then, extensive attention has been paid to CNT-based nano-oscillators [12,22–26]. Zheng and Jiang [11] initially proposed the model of an axial gigahertz oscillator from MWCNTs. Legoas et al. [27] presented a molecular dynamics study of nano-oscillation with respect to dynamical aspects, such as temperature, force, and energy

Sensors 2020, 20, 1969; doi:10.3390/s20071969 www.mdpi.com/journal/sensors Sensors 2020, 20, 1969 2 of 16 temporal fluctuations. However, even though the friction between two concentric CNTs is very low, the oscillation amplitude still dampens quickly [28,29]. How to generate a stable and sustainable oscillation is the major challenge for the practical application of an oscillator. Many researchers have tried to overcome the damping oscillation by introducing an external driven field [30,31], but this will interfere or even cover the original oscillation frequencies of the oscillator. To address this challenge, in 2014, Cai et al. [32] found that in an NVE (NVE: constant Number of atoms, constant Volume and Energy of system) ensemble, long-life stable oscillations can be generated by introducing a high-speed rotating rotor in the stator. However, an NVE ensemble is not as easily realized as an NVT (NVT: constant Number of atoms, constant Volume and Temperature of system) ensemble in a laboratory. When studying the dynamic response of a nanomotor made from triple-walled CNTs, Shi et al. [33] found the concurrence of oscillations and rotation of the rotors in the fixed outer tubes when the system was in an NVT ensemble. Cai et al. [34] further discussed the effects of the length of the inner rotor, the temperature, and the input rotational frequency of the middle rotor on the dynamic response of the inner rotor, and noticed that the inner rotor could oscillate periodically with a stable amplitude, especially at relatively low temperature. Different from the above works, Song et al. [35] presented a nanodevice called a rotation–translation system in an NVT ensemble. In their model, a deformable part (DP) made of graphene was connected to the CNT rotor. The DP deforms when the rotation-induced centrifugal force [36] is strong enough, and the axial translation of the rotor happens simultaneously. Unfortunately, DP may be self-bonded into a narrow ring under high rotational speed, which is unrecoverable and unstable. To solve this problem, Song et al. [37] hydrogenated the DP properly [38–41]. They found that the dynamic responses of DP and hydrogenated DP (HDP) at room temperature were very different, and proved the recoverability of the HDP. However, these two works could not generate ideal oscillation with a large amplitude. For a nanosystem that is placed in an NVT ensemble, random thermal vibration is intrinsic for atoms. Hence, temperature plays a critical role in the dynamic response and output signal of the system [34,42–44]. In general, a higher temperature means drastic thermal vibrations and more friction between adjacent walls of the MWCNTs. At a low temperature, the thermal vibration is weak and some novel phenomena may appear [34]. In the present work, a rotor with a recoverable HDP was placed in an NVT ensemble with a temperature under 150 K. The dynamic response of the system and the axial motion of the output end of the rotor were investigated via molecular dynamics simulations. Our results have great potential for the design of various nanodevices, such as high-speed digital and analog circuits, and memory cells.

2. Results and Discussion

2.1. Dynamic Behaviors for the Z2H6 System at an Extremely Low Temperature, e.g., 8 K When an input rotational frequency was suddenly applied on the rotor, the HDP deformed drastically in the first 2 ns, and therefore led to obvious fluctuations of the variation of potential energy (VPE) curves (Figure1a). After that, the amplitudes of the fluctuation of the VPE curves reduced and gradually tended toward being stable. In general, the mean value of the VPE of the HDP increased with the input rotational speed (ω), and a larger mean value indicates the deformation of the HDP was greater. Sensors 2020, 20, 1969 3 of 16 Sensors 2020, 20, x FOR PEER REVIEW 3 of 17

(a) 20 90  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 80 100 GHz 15 20 10

VPE (eV) VPE 5 10

0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.7 1.4 ns

(b) 40 100  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 90 100 GHz 35 ) 2 30 40 nm 

kg 25

( 30 20

MoI MoI 20 15 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.7 1.4 ns

1.5 50 (c)  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 40 100 GHz

1.0 20 ) Å

(

e 0.5 10

0.0 0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.7 1.4 ns

(d1)  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz 5.5 5.5 5.0 5.0 4.5

(nm) 4.5 4.0 d 4.0 3.5 3.0 3.5 -5.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.7 1.4 ns

(d2)  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz 5.5 5.5 3 periods 5.0 5.0 4.5

(nm) 4.5 Equilibrium 4.0 d position 4.0 3.5 Amplitude 3.0 3.5 -5.0 9.9 10.0 9.9 10.0 9.9 10.0 9.9 10.0 9.9 10.0 9.9 10.0 9.9 10.0 9.9 10.0 ns 1.4 1.6 ns

FigureFigure 1. Historical 1. Historical curves curves of dynamic of dynamic outputs outputs for the for Z2H6 the system Z2H6 system under di underfferent different rotation rotation frequencies at 8 K:frequencies (a) variation at 8 K of: ( thea) variation potential of energythe potential (VPE) energy of the (VPE) HDP, of ( bthe) moment HDP, (b) ofmoment inertia of (MoI) inertia of (MoI) the HDP aboutof the the z-axis, HDP about (c) eccentricity the z-axis, ( (ce)) eccentricity of the HDP (e from) of the the HDP z-axis, from (d1 the) thez-axis, axial (d1 translation) the axial translation of the R-rotor, d, andof (d2the) R the-rotor, amplified d, and ( viewd2) the of amplifiedd during view [9.85, of 10.00] d during ns “ZmHn”[9.85, 10.00] means ns “ZmHn” n columns means of n carboncolumns atoms on HDPof carbon with an atoms axial on length HDP of with Zm an are axial hydrogenated, length of Zm e.g., are Z2H6 hydrogenated, indicates e.g., six columns Z2H6 indicates hydrogenated six carboncolumns atoms hydrogenated on the HDP withcarbon a lengthatoms on of the Z2. HDP Details with of a thelength HDP of Z2. are D givenetails inof Sectionthe HDP3 .are given in Section 3. When the input rotational frequency is low, e.g., ω = 20 GHz, the VPE remained unchanged soon afterWhen 2 ns, the input which rotational meant frequency that the is shapelow, e.g., of ω the= 20 GHz, HDP the changed VPE remained slightly unchanged during soon rotation after 2 ns, which meant that the shape of the HDP changed slightly during rotation (Figure 2a). The (Figure2a). The reason was that the two hydrogenated parts on the HDP, i.e., the areas with reason was that the two hydrogenated parts on the HDP, i.e., the areas with internal carbon– internal carbon–hydrogen (C–H) bonds, were attached via the strong van der Waals (vdW) force, hydrogen (C–H) bonds, were attached via the strong van der Waals (vdW) force, and the centrifugal and theforce centrifugal was not high force enough was to not separate high enoughthem. However, to separate once them.ω reache However,d 30 GHz, once the centrifugalω reached force 30 GHz, the centrifugalon the HDP force was onstrong the enough HDP was to overcome strong enough the vdW to overcome force and separate the vdW the force C–H and area separates apart. the C–HSimultaneously, areas apart. Simultaneously, HDP was undertaking HDP was breathing undertaking vibration breathings (Figure vibrations2). This was (Figure the reason2). Thiswhy wasthe the reasonVPE why curves the VPEkept fluctuat curvesing kept. fluctuating.

Sensors 2020, 20, 1969 4 of 16 Sensors 2020, 20, x FOR PEER REVIEW 5 of 17

Figure 2. Configurations of the Z2H6 system under different conditions at 8 K: (a) ω= 20 GHz, (b) ω= Figure 2. Configurations of the Z2H6 system under different conditions at 8 K: (a) ω = 20 GHz, (b) ω 30 GHz, (c) ω = 50 GHz, (d) ω = 90 GHz, and (e) ω = 100 GHz. In (a), the HDP looked like a “ ,” and = 30 GHz, (c) ω = 50 GHz, (d) ω = 90 GHz, and (e) ω = 100 GHz. In (a), the HDP looked like∞ a “∞,” the two hydrogenated areas were in contact when ω was too low. As shown in (c), the vdW forces and the two hydrogenated areas were in contact when ω was too low. As shown in (c), the vdW forces led to an inward curvature of the HDP, but centrifugal force pulled the atoms back. Snapshots in (e) led to an inward curvature of the HDP, but centrifugal force pulled the atoms back. Snapshots in (e) illustrate that the system could collapse if ω was too large. illustrate that the system could collapse if ω was too large. However, the fluctuation amplitudes did not increase monotonously with the input rotational frequencyIn our duemodel to, the the complex R-rotor connect loads oned the with HDP. the HDP For example, directly. forTherefore, the system when with theω HDPin the deform intervaled alongof 30–40 the GHz, z-axis, the the VPEs R-rotor varied was with mov smalling correspondingly. amplitudes (Figure Therefore,2b). This the was distance because between the centrifugal the right edgesforce andof the vdW R-rotor force and on R the-stator2, HDPs i.e., were d, change not ind equilibrium.simultaneously. However, Figure 1 whend1 listsω the= 50history GHz, curves there ofwas d during no fluctuation rotation ofwith the the VPE HDP curve under after different 2 ns, which input impliedconditions. the It configuration was found that of HDPthe mean remained value ofunchanged d decrease (Figured monotonously2c). In this with case, increasing the centrifugal input rotation and vdW frequency. forces reached Meanwhile, an equilibrium there were state.some otherWhen novelω = 60 characteristics. GHz, the VPE For curve instance, started at to ω fluctuate= 20 GHz, again. the fluctuation Furthermore, of d itcould was evidentbe neglected that when after nothe moreω was than higher 2 ns, than i.e., 60the GHz, amplitude i.e., 70, wa 80,s ne andar zero. 90 GHz, This the implies VPE curvesthat the could right oscillateedge of withthe R- largerrotor haamplitudesd no translation (Figure during2d). For rotati example,on, which when demonstratesω = 90 GHz, that the valuethe configuration of VPE oscillated of the within HDP remain the rangeed identicalof 5.91–16.94 when eV. the For centrifugal the systems force with waωs lowin the but range the vdW of 70–90 force GHz, was thehigh centrifugal. force on the HDP was highOnce enough ω ≥ 30 butGHz the, the vdW centrifugal force could force not wa acts stablyhigh enough anymore, that and the the fluctuation HDPs rotated of d eccentricallystill existed evenand deformedafter reaching along a stable the z-axis state. simultaneously. If d fluctuated with This a large led to and the stable large amplitude deformation, a nanodevice, of the HDP e.g., and anobvious oscillator, fluctuations could be of made the VPE. from In addition,the present when model the under inputrotational such conditions. speed reached In Figure thes critical1d1 and value, d2, thei.e., amplitudes 100 GHz, the of the VPE d approachedcurves were 0.18,90 0.10, eV soon 0.00, after and 1.40.16 ns. nm It at is30, known 40, 50 that, and the 60 centrifugalGHz, respectively force is. ≈ However,proportional at 70, to the80, squareand 90 ofGHz,ω. Hence, the amplitudes when ω = bec100ame GHz, 0.51, the 0.57 centrifugal, and 0.58 force nm, onrespectively. the HDP was More so importantly, the oscillation amplitudes did not decrease during the simulation. Hence, the oscillations were highly sustainable and reliable. From Figure 2d, one can see that d periodically fluctuated between 3.53 nm and 4.70 nm when ω = 90 GHz (See Video S1 in the Supplementary

Sensors 2020, 20, 1969 5 of 16 strong that it pulled the HDP away from the z-axis and further stretched the R-rotor out of the R-stators. In other words, the system collapsed because of the drastic deformation of the HDP (Figure2e). In Figure1b, due to more atoms on the HDP moving away from the z-axis under the centrifugal force of rotation, the moment of inertia (MoI) curves reached higher mean values under higher rotational frequencies. Moreover, the inertia curves usually fluctuated around their average value, which indicates that the HDP shrunk along the z-axis under most conditions. In particular, the results of the inertia for ω 70 GHz changed periodically, accompanied with large amplitudes. Hence, one can ≥ conclude that high rotational speeds led to high centrifugal forces and further led to great deformation of the HDP. Deformation of the HDP led to a variation of the VPE and MoI. However, this does not mean that the eccentricity (e) of the HDP’s centroid varied simultaneously. If the whole rotor, i.e., the L-rotor, R-rotor, and the HDP, had an ideal symmetric deformation about the z-axis, then the value of e should be zero. If the HDP had a stable configuration and a constant eccentricity, then the value of e should be a positive constant. However, random thermal vibration of the atom always exists during the rotation of the HDP. Hence, even if the rotating part looked symmetric about the z-axis, thermal vibration still led to the eccentricity of the HDP (Figure1c). The value of e at ω = 20 GHz, averaged over time, was even bigger than that at 30 GHz due to the special irregular “ -shaped” configuration of the HDP ∞ under a low rotation speed (Figure2a). When ω reached 30 GHz or higher, the up and down layers of the HDP were no longer attached and deformed almost symmetrically. Hence, a lower eccentricity appears. The lowest value of e happened at ω = 50 GHz because the shape of the deformed HDP was highly symmetrical under the equilibrium centrifugal force and vdW force (Figure2c). However, as ω approached 60 GHz or higher, the stable mean values of e significantly increased but were lower than 0.25 Å. At 100 GHz, after 1.4 ns of rotating under extremely high centrifugal forces, the value of e exceeded 20 Å or even higher, which indicates that the HDP moved far away from the z-axis, which then resulted in the failure of the whole system. In our model, the R-rotor connected with the HDP directly. Therefore, when the HDP deformed along the z-axis, the R-rotor was moving correspondingly. Therefore, the distance between the right edges of the R-rotor and R-stator2, i.e., d, changed simultaneously. Figure1d1 lists the history curves of d during rotation with the HDP under different input conditions. It was found that the mean value of d decreased monotonously with increasing input rotation frequency. Meanwhile, there were some other novel characteristics. For instance, at ω = 20 GHz, the fluctuation of d could be neglected after no more than 2 ns, i.e., the amplitude was near zero. This implies that the right edge of the R-rotor had no translation during rotation, which demonstrates that the configuration of the HDP remained identical when the centrifugal force was low but the vdW force was high. Once ω 30 GHz, the centrifugal force was high enough that the fluctuation of d still existed ≥ even after reaching a stable state. If d fluctuated with a large and stable amplitude, a nanodevice, e.g., an oscillator, could be made from the present model under such conditions. In Figure1d1,d2, the amplitudes of the d curves were 0.18, 0.10, 0.00, and 0.16 nm at 30, 40, 50, and 60 GHz, respectively. However, at 70, 80, and 90 GHz, the amplitudes became 0.51, 0.57, and 0.58 nm, respectively. More importantly, the oscillation amplitudes did not decrease during the simulation. Hence, the oscillations were highly sustainable and reliable. From Figure2d, one can see that d periodically fluctuated between 3.53 nm and 4.70 nm when ω = 90 GHz (See Video S1 in the Supplementary Materials). Furthermore, from Figure3a, one can see that the oscillation frequencies of the d curves for a Z2H6 system with an amplitude over 0.5 nm increased with ω, e.g., they were 32.23, 34.62, and 37.56 GHz at ω = 70, 80, and 90 GHz, respectively. At 100 GHz, the d curves became negative after 1.4 ns, which means the R-rotor escaped from the R-stator2, and the system collapsed (See Video S2 in the Supplementary Materials). Sensors 2020, 20, x FOR PEER REVIEW 6 of 17

Materials). Furthermore, from Figure 3a, one can see that the oscillation frequencies of the d curves for a Z2H6 system with an amplitude over 0.5 nm increased with ω, e.g., they were 32.23, 34.62, and 37.56 GHz at ω = 70, 80, and 90 GHz, respectively. At 100 GHz, the d curves became negative after 1.4 Sensorsns, which2020, 20means, 1969 the R-rotor escaped from the R-stator2, and the system collapsed (See Video 6S of2 16in the Supplementary Materials).

40 40 (a) Effect of N H (b) Effect of LZ Z2H6 35 35 Z2H4 Z2H2 30 30 Z1H1

25 25 Z2H1 Z2H1 20 20

Oscillation frequency (GHz) frequency Oscillation 15 (GHz) frequency Oscillation 15 Z3H1 50 60 70 80 90 30 40 50 60 70 80  (GHz)  (GHz) Figure 3. Oscillation frequencies of the d curves with amplitudes higher than 0.5 nm during 9–10 ns Figure 3. Oscillation frequencies of the d curves with amplitudes higher than 0.5 nm during 9–10 ns obtained using a fast Fourier transmission (FFT) method: (a) effect of the hydrogenation scheme (NH) obtained using a fast Fourier transmission (FFT) method: (a) effect of the hydrogenation scheme (NH) on the HDP and (b) effect of the axial length of the HDP (Lz). on the HDP and (b) effect of the axial length of the HDP (Lz). 2.2. Axial Translational Motion in the Z2H6 System at 25 K, 50 K, and 150 K 2.2. Axial Translational Motion in the Z2H6 System at 25 K, 50 K, and 150 K For a nanosystem in a canonical NVT ensemble, temperature significantly affects its dynamic response.For a At nanosystem higher temperatures, in a canonical the atoms NVT inensemble, the present temperature system had significantly more drastic affects thermal its vibrations, dynamic whichresponse. influenced At higher the interaction temperature (friction)s, the atoms between in the the stators present and system rotors. ha Here,d more we investigated drastic therm theal axialvibration motionss, which of the influence R-rotord in the the interaction Z2H6 system (friction) at temperatures between the higher stators than and 8 K, rotors. i.e., 25 Here, K, 50 we K, andinvestigate 150 K (Figured the axial4). Comparedmotions of the with R- therotord incurves the Z2H6 at 8 Ksystem shown at intemperature Figure1d,s we higher found than that 8 K, the i.e.,d curves25 K, 50 at K 25, and K di ff150ered K slightly(Figure from4). Compar these curvesed with at 8the K, d and curves the curves at 8 K ofshownd still in fluctuated Figure 1d, orderly we found with considerablethat the d curves amplitudes at 25 K differ at highed rotational slightly from frequencies, these curves e.g., atω =8 K,70, and 80, andthe curves 90 GHz. of However,d still fluctuate whend theorderly environment with considerable temperature amplitudes increased at to high 50 K, rotational the amplitudes frequenc of theiesd, e.g.,curves ω = decreased 70, 80, and continually 90 GHz. withHowever, increasing whenω . the In addition, environment as the temperature temperature increase approachedd to 50 150 K, K, the the amplitudes amplitudes of of the the d curvescurves dampeneddecreased continually quickly and with reduced increasing to nearly ω. zero In addition, within 4 as ns. the Furthermore, temperature the approache Z2H6 systemd 150 at K, any the temperatureamplitudes of always the d collapsedcurves damp at 100ened GHz. quickly and reduced to nearly zero within 4 ns. Furthermore, the Z2H6From system the left at part any of temperature Figure5, one always can see collapse that thed at mean 100 GHz. values of d at 8 K, 25 K, 50 K, or even 150 K always decreased with the increasing ω, and there were no obvious differences among them.

(a) 25 K  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz This5.5 means that temperature had a slight inﬂuence on the mean value of d. However,5.5 in the right part of Figure5, the amplitude curves of d varied signiﬁcantly with temperature when 5.0ω was high. 5.0 The amplitude curve of d under 8 K was the highest among the four temperature cases.4.5 At 25 K,

(nm) 4.5 4.0 thed amplitude of d had a small decrease but was still higher than 0.5 nm at ω = 80 GHz and 90 GHz.4.0 After that, when the temperature was higher, e.g., 50 K, the amplitudes dropped to3.5 0.29, 0.10, 3.0 and3.5 0.24 nm at 70, 80, and 90 GHz, respectively. Finally, when the temperature approached-5.0 150 K, 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 1 2 ns the amplitudes under all the input rotation frequencies were nearly zero, which indicates that the d

(b) 50 K curves had = 20 neither GHz oscillations30 GHz 40 nor GHz fluctuations.50 GHz Hence,60 GHz temperature70 GHz influenced80 GHz the90 GHz amplitude100 of GHz the 5.5 5.5 d curves. 5.0 5.0 From the above, we concluded that the equilibrium positions of d were not influenced4.5 by the

(nm) 4.5 4.0 environmentald temperature but the amplitudes of the d curves, i.e., the oscillation of R-rotor, were very sensitive4.0 to the temperature. Hence, to obtain an oscillator with a high amplitude from3.5 the present 3.0 model,3.5 the temperature should be conﬁned to under 50 K. -5.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 1 2 ns

Sensors 2020, 20, x FOR PEER REVIEW 6 of 17

Materials). Furthermore, from Figure 3a, one can see that the oscillation frequencies of the d curves for a Z2H6 system with an amplitude over 0.5 nm increased with ω, e.g., they were 32.23, 34.62, and 37.56 GHz at ω = 70, 80, and 90 GHz, respectively. At 100 GHz, the d curves became negative after 1.4 ns, which means the R-rotor escaped from the R-stator2, and the system collapsed (See Video S2 in the Supplementary Materials).

40 40 (a) Effect of N H (b) Effect of LZ Z2H6 35 35 Z2H4 Z2H2 30 30 Z1H1

25 25 Z2H1 Z2H1 20 20

obtained using a fast Fourier transmission (FFT) method: (a) effect of the hydrogenation scheme (NH) on the HDP and (b) effect of the axial length of the HDP (Lz).

2.2. Axial Translational Motion in the Z2H6 System at 25 K, 50 K, and 150 K For a nanosystem in a canonical NVT ensemble, temperature significantly affects its dynamic response. At higher temperatures, the atoms in the present system had more drastic thermal vibrations, which influenced the interaction (friction) between the stators and rotors. Here, we investigated the axial motions of the R-rotor in the Z2H6 system at temperatures higher than 8 K, i.e., 25 K, 50 K, and 150 K (Figure 4). Compared with the d curves at 8 K shown in Figure 1d, we found that the d curves at 25 K differed slightly from these curves at 8 K, and the curves of d still fluctuated orderly with considerable amplitudes at high rotational frequencies, e.g., ω = 70, 80, and 90 GHz. However, when the environment temperature increased to 50 K, the amplitudes of the d curves Sensorsdecrease 2020d, 20continually, x FOR PEER withREVIEW increasing ω. In addition, as the temperature approached 150 K,7 of the 17 amplitudes of the d curves dampened quickly and reduced to nearly zero within 4 ns. Furthermore,

(c)Sensors 150 K 2020, 20, 1969 7 of 16  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz the5.5 Z2H6 system at any temperature always collapsed at 100 GHz. 5.5 5.0

5.0 (a) 25 K 4.5  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz 5.5 5.5 (nm) 4.5 4.0 d 5.0 4.05.0 3.5 4.5

3.0

(nm) 3.54.5 4.0

d -5.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 1 2 ns 4.0 3.5 3.0 3.5Figure 4. Axial motion of the R-rotor in the Z2H6 system with different inputs at temperature-5.0s higher 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 1 2 ns than 8 K: (a) at 25 K, (b) at 50 K, and (c) at 150 K.

(b) 50 K  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 5.5 100 GHz 5.5From the left part of Figure 5, one can see that the mean values of d at 8 K, 25 K, 50 K, or even 5.0 5.0 150 K always decreased with the increasing ω, and there were no obvious differences among4.5 them.

This (nm) 4.5 means that temperature had a slight influence on the mean value of d. However, in the4.0 right part d of Figure4.0 5, the amplitude curves of d varied significantly with temperature when ω wa3.5s high. The amplitudeSensors 2020, 20curve, x FOR of PEER d under REVIEW 8 K was the highest among the four temperature cases. At3.0 25 K,7 ofthe 17 3.5 -5.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 1 2 ns amplitude of d had a small decrease but wa s still higher than 0.5 nm at ω = 80 GHz and 90 GHz. After (c) 150 K  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz that,5.5 when the temperature was higher, e.g., 50 K, the amplitudes dropped to 0.29, 0.10, and5.5 0.24 nm 5.0 at 70,5.0 80, and 90 GHz, respectively. Finally, when the temperature approached 150 K, the amplitudes 4.5

under all the input rotation frequencies we re nearly zero, which indicates that the d curves had

(nm) 4.5 4.0 neitherd oscillations nor fluctuations. Hence, temperature influenced the amplitude of the d curves. 4.0 3.5 From the above, we concluded that the equilibrium positions of d were not influenced3.0 by the environment3.5 al temperature but the amplitudes of the d curves, i.e., the oscillation of R-5.0-rotor, were 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 1 2 ns very sensitive to the temperature. Hence, to obtain an oscillator with a high amplitude from the Figure 4. Axial motion of the R-rotor in the Z2H6 system with diﬀerent inputs at temperatures higher presentFigure model, 4. Axial the motiontemperature of the R should-rotor in be the confined Z2H6 system to under with different50 K. inputs at temperatures higher than 8 K: (a) at 25 K, (b) at 50 K, and (c) at 150 K. than 8 K: (a) at 25 K, (b) at 50 K, and (c) at 150 K.

From the left 5.4part of Figure 5, one can see 8 K that the mean values of d at 8 K,0.6 25 K, 50 K, or even 150 K always decreased with the increasing 25ω ,K and there were no obvious differences among them. 50 K 0.5 This means that temperature5.1 had a slight influence 150 K on the mean value of d. However, in the right part of Figure 5, the amplitude curves of d varied significantly with temperature when ω was high. The (nm) 0.4 d amplitude curve of4.8 d under 8 K was the highest among the four temperature cases. At 25 K, the amplitude of d had a small decrease but was still higher than 0.5 nm at ω = 80 GHz0.3 and 90 GHz. After that, when the temperature4.5 was higher, e.g., 50 K, the amplitudes dropped to 0.29,0.2 0.10, and 0.24 nm

at 70, 80, and 90 GHz, respectively. Finally, when the temperature approached 150 K, (nm) Amplitude the amplitudes 0.1 under all the input value ofMean rotation frequencies were nearly zero, which indicates that the curves had 4.2 d neither oscillations nor fluctuations. Hence, temperature influenced the amplitude0.0 of the d curves. From the above, 20we 30conclude40 50 d60 that70 the80 equilibrium90 20 30 40 positions50 60 70of d80 we90re not influenced by the environmental temperature but the (GHz) amplitudes of the d curves, (GHz) i.e., the oscillation of R-rotor, were very sensitive to the temperature. Hence, to obtain an oscillator with a high amplitude from the Figure 5. Mean values and amplitudes of d curves of the Z2H6 system between 9 ns and 10 ns at Figure 5. Mean values and amplitudes of d curves of the Z2H6 system between 9 ns and 10 ns at presentdiﬀ erentmodel, temperatures. the temperature should be confined to under 50 K. different temperatures.

2.3. Eﬀect of the Hydrogenation Scheme (NH) on the Axial Oscillation of the R-Rotor at 8 K 2.3. Effect of the Hydrogenation Scheme (NH) on the Axial Oscillation of the R-Rotor at 8 K In a previous simulation,5.4 N = 6, i.e., there 8 K were six lines of carbon atoms in0.6 each horizontal side H 25 K In a previous simulation, NH = 6, i.e., there were six lines of carbon atoms in each horizontal side of the deform part on the rotor, and they were 50 bonded K by hydrogen atoms. Due to0.5 the existence of the oflocal the C–H deform bonds, part the 5.1on horizontalthe rotor, and sides they became we re150 curved, bondedK which by hydrogen was veriﬁed atoms. by Due the simulationsto the existence above. of

the local C–H bonds (nm) , the horizontal sides became curved, which was verified by the simulations If we change the value of NH, what will happen to the output of the system? To demonstrate0.4 the eﬀect d aboveof N ,. weIf we subsequently change4.8 the value reduced of NH, fromwhat 6will to4, happen 2, and 1.to the output of the system? To demonstrate H H 0.3 the effectAccording of NH, towe the subsequently results in Figures reduce6 andd N7H, from one can 6 to see 4, that2, and the 1. output of the system depended on the hydrogenationAccording to the schemes.4.5 results Moreover,in Figures the6 and equilibrium 7, one can positionssee that the of doutputalways of decreased the0.2 system as depend the inputed onrotation the hydrogenation frequency increased. schemes. The Moreover, reason was the that equilibrium a larger centrifugal positions force of d led always to further decrease (nm) Amplitude deformationd as the 0.1 input rotation frequency value ofMean increased. The reason was that a larger centrifugal force led to further of the HDP with a4.2 higher rotational speed. Furthermore, at the same input rotational frequency, a smaller N induced a lower value of d. There were narrower areas on the0.0 horizontal sides that H 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90  (GHz)  (GHz)

Figure 5. Mean values and amplitudes of d curves of the Z2H6 system between 9 ns and 10 ns at different temperatures.

2.3. Effect of the Hydrogenation Scheme (NH) on the Axial Oscillation of the R-Rotor at 8 K

In a previous simulation, NH = 6, i.e., there were six lines of carbon atoms in each horizontal side of the deform part on the rotor, and they were bonded by hydrogen atoms. Due to the existence of the local C–H bonds, the horizontal sides became curved, which was verified by the simulations above. If we change the value of NH, what will happen to the output of the system? To demonstrate the effect of NH, we subsequently reduced NH from 6 to 4, 2, and 1. According to the results in Figures 6 and 7, one can see that the output of the system depended on the hydrogenation schemes. Moreover, the equilibrium positions of d always decreased as the input rotation frequency increased. The reason was that a larger centrifugal force led to further

Sensors 2020, 20, x FOR PEER REVIEW 8 of 17

Sensors 2020, 20, 1969 8 of 16 deformation of the HDP with a higher rotational speed. Furthermore, at the same input rotational frequency, a smaller NH induced a lower value of d. There were narrower areas on the horizontal remainedsides that inwardlyremained concave inwardly when concaveNH waswhen smaller. NH was Hence, smaller. the Hence, HDP deformedthe HDP deform easier undered easier the under same centrifugalthe same centrifugal force. Furthermore, force. Furthermore the critical, the rotation critical rotation speed for speed the schemesfor the schemes of Z2H6, of Z2H4,Z2H6, Z2H2,Z2H4, andZ2H2 Z2H1, and wereZ2H1 100, were 90, 100, 90, 90, and 90 70, and GHz, 70 respectively.GHz, respectively. Hence, Hence, the system the system with with a lower a lower value value of N ofH collapsedNH collapse atd a at lower a lower rotational rotational frequency. frequency.

(a) Z2H6  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 100 GHz 5.5 5 5.0

(nm) 4.5 4 d 4.0 3 3.5 -5.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.7 1.4 ns

(b) Z2H4  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 5.5 5 5.0

4.5 4

4.0 3 3.5 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10ns 0.0 0.5 1.0 ns

4.0 3 3.5

3.0 2 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0 2 4 ns (d) Z2H1 5.5  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 5 5.0 4 4.5

3 4.0 2 3.5 1 3.0 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10ns 0.0 0.1 ns Figure 6. Axial motion (d) of the R-rotor with different hydrogenation schemes on the HDP with Figure 6. Axial motion (d) of the R-rotor with different hydrogenation schemes on the HDP with different rotational frequencies at 8 K: (a) Z2H6, (b) Z2H4, (c) Z2H2, and (d) Z2H1. In the Z2H2 system different rotational frequencies at 8 K: (a) Z2H6, (b) Z2H4, (c) Z2H2, and (d) Z2H1. In the Z2H2 system with ω = 70 GHz, the “beat” phenomenon happened in the first 5 ns. with ω= 70 GHz, the “beat” phenomenon happened in the first 5 ns. It was evident that the system with ω > 20 GHz could always produce a valuable oscillation no matter the C–H scheme adopted. By comparing the amplitudes of the d curves in the right part of Figure7, one can see that for the HDP, the amplitude of d increased rapidly with ω. If ω was near the critical value over which the system collapsed, the oscillation amplitudes were higher than 0.5 nm (within the gray background in Figure7). Furthermore, the largest amplitude of the schemes of Z2H6, Z2H4, Z2H2, and Z2H1 were 0.58, 0.56, 0.63, and 0.63 nm, respectively. Hence, the system could act as a nano-oscillator if NH > 0. Furthermore, the value of NH did not influence the largest amplitude of the oscillations significantly. If we need a rotor with the HDP to generate a high amplitude with a relatively low input rotation speed, we can choose a lower NH. Furthermore, the oscillation frequencies of the d curves with amplitudes greater than 0.5 nm for different C–H schemes are shown in Figure3a. This figure demonstrates that the oscillation frequencies increased linearly with the rotation speed for a specific hydrogenation scheme. One can also see that the oscillation frequency was higher when the system had more lines of C–H bonds on the horizontal

Sensors 2020, 20, 1969 9 of 16 sides of the HDP, which implies that an oscillator with a certain period could be obtained by choosing a proper HDP. In the above analysis, we also found a “beat” phenomenon in the Z2H2 system when ω= 70 GHz at 8 K. By observing the trace of the system, we found that the HDP had both radial deformation and axial bending of the vertical sides of the HDP along the z-axis during the rotation with the rotor. We conclude that the “beat” phenomenon was mainly caused by the axial bending leftward (z ; red − arrow) and rightward (z+; blue arrow) alternatively during oscillating. According to the snapshots inserted in Figure8, when the bending direction of the vertical sides of the HDP was aligned with v, i.e., the velocity direction of the right end of the R-rotor, the amplitude of the d curves increased. Otherwise,

Sensorsthe amplitude 2020, 20, x decreased.FOR PEER REVIEW For example, between 1.92 ns and 2.33 ns, the amplitude increased ﬁrst9 of and 17 then decreased.

5.4 Z2H6 Z2H4 0.6 5.1 Z2H2 Z2H1 0.5

(nm) 4.8

d 0.4 4.5 0.3 4.2 0.2 Amplitude(nm) 3.9 Meanofvalue 0.1 3.6 0.0 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90  (GHz)  (GHz) Figure 7. Mean values and amplitudes of the d curves in the systems with diﬀerent hydrogenation Figure 7. Mean values and amplitudes of the d curves in the systems with different hydrogenation Sensorsschemes 2020, 20, atx FOR 8 K betweenPEER REVIEW 9 ns and 10 ns. 10 of 17 schemes at 8 K between 9 ns and 10 ns.

I5t was evident that the system with ω> 20 GHz could always produce a valuable oscillation no matter the C–H scheme adopted. By comparing the amplitudes of the d curves in the right part of Figure4 7, one can see that for the HDP, the amplitude of d increased rapidly with ω. If ω was near the critical value over which the system collapsed, the oscillation amplitudes were higher than 0.5 nm (within the gray background in Figure 7). Furthermore, the largest amplitude of the schemes of Z2H6, 3 Z2H4, Z2H2, and Z2H1 were 0.58, 0.56, 0.63, and 0.63 nm, respectively. Hence, the system could act as a nano-oscillator if NH > 0. Furthermore, the value of NH did not influence the largest amplitude of the oscillation2 s significantly. If we need a rotor with the HDP to generate a high amplitude with a 8/8/3 relatively low input rotation speed, we can choose9/7/2 3/9/ 7a lower NH4. /10/4

4.2 Furthermore, the8/9 /oscillation4 frequencies of the d curves with amplitudes greater 5than/4/11 0.5 nm for (nm) 1 4.0 differentd C–H schemes are shown in Figure 3a. This figure demonstrates that the oscillation frequencies3.8 increased linearly with the rotation speed for a specific hydrogenation scheme. One can also see0 that 3.6 the oscillation frequency was higher when the system had more lines of C–H bonds on the horizontal3.4 sides of the HDP, which implies that an oscillator with a certain period could be obtained-1 by3.2 choosing5/5/5 a proper HDP. 8/3/5 In the above D1analysis, I1 we also found a “beat”D2 I2 phenomenonD3 I3 in the Z2H2 system whenD4 ω I4= 70 GHz at 8 K. By observing1.95 the trace2.00 of the system,2.05 we fou2.10nd that 2.15the HDP ha2.20d both radial2.25 deformation2.30 and axial bending0 of the2 vertical4 sides of6 the HDP8 along the10 z-axis12 during the14 rotation16 with the18 rotor. We20 conclude that the “beat” phenomenon was mainlyTime (ns)caused by the axial bending leftward (z−; red arrow) andFigure rightward 8. “Beat” (z+ phenomenon; blue arrow) in thealternativelyd curves of during the Z2H2 oscillating. system with Accordingω = 70 GHz to at the 8 K. snapshots insertedFigure in Figure8. “Beat ”8, phenomenon when the bending in the d directioncurves of the of Z2H2the vertical system sides with ωof= the 70 GHzHDP at wa 8 K.s align ed with v, i.e., theThe velocity detailed direction variation of processes the right were end as of follows. the R-rotor In the, the increasing amplitude stage: ofwhen the dd curvesdecreased increase (v < 0d),. Otherwise,thereT werehe detailed ﬁve the “z amplitude variation” and ﬁve processesdecrease “z+” statesd were. For in the as example, follows. D1 period betweenIn (Figurethe increasing 1.928), and ns there stage: and were 2.33 when ninens, d thedecrease “z amplitude” andd ( twov < − − 0),increase there dwe firstre five and “z then−” and decrease five “z+”d. states in the D1 period (Figure 8), and there were nine “z−” and two “z+” states in the D2 period; when d increased (v > 0), there were eight “z−” and four “z+” states in the I1 period, and there were three “z−” and seven “z+” states in the I2 period. It seems there were more states of the bending direction of vertical sides of the HDP align with the direction of R-rotor; hence, the amplitude of d gradually increased. On the contrary, during the decreasing interval: from the D3 to the D4 period, when d decreased, the number of “z+” states increased from three to eleven; from the I3 to the I4 period, the number of “z−” states increased from four to eight. Hence, the amplitude of d reduced due to more opposite bending states of the HDP to the motion of the R-rotor.

2.4. Effect of the Length of the HDP with NH = 1 on Its Oscillation at 8 K Figures 9 and 10 show the axial movement of the R-rotor connected with the HDPs with different lengths (Lz). From Figure 9, as the length of the HDP in the z-axis increased, the critical rotational frequency dropped quickly. For example, the systems with Z1H1, Z2H1, and Z3H1 HDPs collapsed at 90 GHz, 70 GHz, and 40 GHz respectively. This was because the longest HDP had the lowest stiffness but the largest inertia and the largest centrifugal force when the rotation frequency was specified. Therefore, its shape changed the easiest and it had the largest deformation. For example, when ω increased from 20 to 30 GHz, the value of d reduced to 0.09 nm and 0.24 nm for the Z1H1 and Z2H1 systems, respectively. For the Z3H1 system, the reduction was even larger, i.e., over 0.70 nm. Before collapsing, the system could always reach its dynamically stable state within 6 ns, and had regular oscillations when ω was higher than 20 GHz.

Sensors 2020, 20, 1969 10 of 16

“z+” states in the D2 period; when d increased (v > 0), there were eight “z ” and four “z+” states in the − I1 period, and there were three “z ” and seven “z+” states in the I2 period. It seems there were more − states of the bending direction of vertical sides of the HDP align with the direction of R-rotor; hence, the amplitude of d gradually increased. On the contrary, during the decreasing interval: from the D3 to the D4 period, when d decreased, the number of “z+” states increased from three to eleven; from the I3 to the I4 period, the number of “z ” states increased from four to eight. Hence, the amplitude of d − reduced due to more opposite bending states of the HDP to the motion of the R-rotor.

2.4. Effect of the Length of the HDP with NH = 1 on Its Oscillation at 8 K Figures9 and 10 show the axial movement of the R-rotor connected with the HDPs with di fferent lengths (Lz). From Figure9, as the length of the HDP in the z-axis increased, the critical rotational frequency dropped quickly. For example, the systems with Z1H1, Z2H1, and Z3H1 HDPs collapsed at 90 GHz, 70 GHz, and 40 GHz respectively. This was because the longest HDP had the lowest stiffness but the largest inertia and the largest centrifugal force when the rotation frequency was specified. Therefore, its shape changed the easiest and it had the largest deformation. For example, when ω increased from 20 to 30 GHz, the value of d reduced to 0.09 nm and 0.24 nm for the Z1H1 and Z2H1 systems, respectively. For the Z3H1 system, the reduction was even larger, i.e., over 0.70 nm. Before collapsing, the system could always reach its dynamically stable state within 6 ns, and had regularSensors oscillations 2020, 20, x FOR when PEERω wasREVIEW higher than 20 GHz. 11 of 17

(a) Z1H1 = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 5.5 5

5.0 4

4.5 3 2 4.0 1 3.5 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.1 ns (b) Z2H1 5.5  = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 5 5.0 4 4.5

3 4.0 2 3.5 1 3.0 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.1 0.2 ns (c) Z3H1  = 20 GHz 30 GHz 5 40 GHz 5.0 4 4.5 3

4.0 2 3.5 1

3.0 0 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.1 ns Figure 9. Axial motions of the R-rotor connected with the HDPs with diﬀerent lengths at 8 K: (a) Z1H1 Figure 9. Axial motions of the R-rotor connected with the HDPs with different lengths at 8 K: (a) Z1H1 HDP, (b) Z2H1 HDP, and (c) Z3H1 HDP. HDP, (b) Z2H1 HDP, and (c) Z3H1 HDP. From the amplitudes of the d curves shown in Figure 10, one can see that the oscillation amplitude From the amplitudes of the d curves shown in Figure 10, one can see that the oscillation increased with ω, and the amplitude was higher when HDP was longer if ω was speciﬁed. The output amplitude increased with ω, and the amplitude was higher when HDP was longer if ω was specified. oscillations of the R-rotor with Z1H1, Z2H1, and Z3H1 HDPs had maximum amplitudes of 0.67, 0.63, The output oscillations of the R-rotor with Z1H1, Z2H1, and Z3H1 HDPs had maximum amplitudes and 0.53 nm when ω = 80, 60, and 30 GHz, respectively. For a system requiring a larger amplitude of 0.67, 0.63, and 0.53 nm when ω= 80, 60, and 30 GHz, respectively. For a system requiring a larger oscillation or a larger decrease of d with a lower rotation frequency, we can choose a longer HDP. amplitude oscillation or a larger decrease of d with a lower rotation frequency, we can choose a longer HDP. Furthermore, the statistical results of the oscillation frequencies in the d curves with amplitudes larger than 0.5 nm are given in Figure 3b. One can conclude that the oscillation frequencies increased as the length of the HDP decreased. For example, the oscillation frequency for the Z3H1 system at ω= 30 GHz was only ≈ 15 GHz. For the Z2H1 system, the oscillation frequencies were between 21 GHz and 24 GHz. For the Z1H1 system, the oscillation frequency of the R-rotor jumped to 29–31 GHz. Hence, by changing the length of the HDP, the system could produce axial oscillation with a wide range of frequencies.

5.4 Z1H1 (80, 0.67) 0.7 (60, 0.63) Z2H1 Z3H1 5.1 (30, 0.53) 0.6

(nm) 0.5 d 4.8

0.4 4.5 0.3

4.2 0.2 (nm) Amplitude Mean value of value Mean 3.9 0.1 0.0 20 30 40 50 60 70 80 20 30 40 50 60 70 80  (GHz)  (GHz)

Sensors 2020, 20, x FOR PEER REVIEW 11 of 17

(a) Z1H1 = 20 GHz 30 GHz 40 GHz 50 GHz 60 GHz 70 GHz 80 GHz 90 GHz 5.5 5

5.0 4

3 4.0 2 3.5 1 3.0 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.1 0.2 ns (c) Z3H1  = 20 GHz 30 GHz 5 40 GHz 5.0 4 4.5 3

4.0 2 3.5 1

3.0 0 -2.0 0 2 4 6 8 10 0 2 4 6 8 10 ns 0.0 0.1 ns

Figure 9. Axial motions of the R-rotor connected with the HDPs with different lengths at 8 K: (a) Z1H1 HDP, (b) Z2H1 HDP, and (c) Z3H1 HDP.

From the amplitudes of the d curves shown in Figure 10, one can see that the oscillation amplitude increased with ω, and the amplitude was higher when HDP was longer if ω was specified. The output oscillations of the R-rotor with Z1H1, Z2H1, and Z3H1 HDPs had maximum amplitudes Sensorsof 0.67,2020 0.63, 20, ,and 1969 0.53 nm when ω= 80, 60, and 30 GHz, respectively. For a system requiring a 11large of 16r amplitude oscillation or a larger decrease of d with a lower rotation frequency, we can choose a longer HDP. d FurthermoreFurthermore,, the statistical results of the oscillation frequencies in the d curves with amplitudes larger than 0.5 nm are given in Figure 3 3b.b. OneOne cancan concludeconclude thatthat thethe oscillationoscillation frequenciesfrequencies increasedincreased as the lengthlength ofof thethe HDP HDP decreased. decreased For. For example, example, the the oscillation oscillation frequency frequency for for the the Z3H1 Z3H1 system system at ω at= 30 GHz was only 15 GHz. For the Z2H1 system, the oscillation frequencies were between 21 GHz ω= 30 GHz was only≈ ≈ 15 GHz. For the Z2H1 system, the oscillation frequencies were between 21 GHzand 24and GHz. 24 GHz. For For the the Z1H1 Z1H1 system, system, the the oscillation oscillation frequency frequency of of the the R-rotor R-rotorjumped jumped toto 29–3129–31 GHz. GHz. Hence, by changing the length of the HDP, the system couldcould produce axial oscillation with a wide range of frequencies.

5.4 Z1H1 (80, 0.67) 0.7 (60, 0.63) Z2H1 Z3H1 5.1 (30, 0.53) 0.6

(nm) 0.5 d 4.8

0.4 4.5 0.3

4.2 0.2 (nm) Amplitude Mean value of value Mean 3.9 0.1 0.0 20 30 40 50 60 70 80 20 30 40 50 60 70 80  (GHz)  (GHz) Figure 10. Equilibrium positions (mean values of d) and oscillation amplitudes of the R-rotor connected with the HDPs that had diﬀerent lengths at 8 K between 9 ns and 10 ns.

3. Materials and Methods

3.1. Model In this work, the model shown in Figure 11 was adopted to design a nanoconvertor for translating rotation into motion. When a rotational speed, i.e., ω, is exerted on the left end of a rotor, the HDP deforms under a centrifugal force and moves away from the rotational axis of the rotor. Simultaneously, asymmetric van der Waals (vdW) forces on both surfaces of the HDP lead to a reverse deformation. When the two deformations reach a dynamic equilibrium state, the value of d will have a stable ﬂuctuation, which can be used to design a perfect nano-oscillator. For a deep understanding of the dynamic oscillation behavior of the R-rotor during rotation, more factors, including temperature, hydrogenation schemes (NH), and the length of HDP (Lz), were investigated using molecular dynamics simulations. Six HDP models with diﬀerent values of NH and Lz were considered. Except for the HDP, the sizes of the remaining components in the model remained unchanged. Furthermore, each carbon atom on the boundary of HDP and the ends of all three stators and the R-rotor was bonded with a hydrogen atom. The detailed parameters of the HDPs are listed in Table1.

Table 1. Initial parameters of the HDPs in the nanoconvertor in Figure 11.

Model LZ/Å NH Number of Atoms on HDP

Z1H1 26.99 1 960C + 96H (boundary) + 16H (NH) Z2H1 35.51 1 1128C + 112H (boundary) + 16H (NH) Z2H2 35.51 2 1128C + 112H (boundary) + 34H (N ) HDP H Z2H4 35.51 4 1128C + 112H (boundary) + 68H (NH) Z2H6 35.51 6 1128C + 112H (boundary) + 102H (NH) Z3H1 48.29 1 1380C + 136H (boundary) + 16H (NH) Sensors 2020, 20, x FOR PEER REVIEW 12 of 17

Figure 10. Equilibrium positions (mean values of d) and oscillation amplitudes of the R-rotor connected with the HDPs that had different lengths at 8 K between 9 ns and 10 ns.

3. Materials and Methods

3.1. Model In this work, the model shown in Figure 11 was adopted to design a nanoconvertor for translating rotation into motion. When a rotational speed, i.e., ω, is exerted on the left end of a rotor, the HDP deforms under a centrifugal force and moves away from the rotational axis of the rotor. Simultaneously, asymmetric van der Waals (vdW) forces on both surfaces of the HDP lead to a reverse deformation. When the two deformations reach a dynamic equilibrium state, the value of d will have a stable fluctuation, which can be used to design a perfect nano-oscillator. For a deep understanding of the dynamic oscillation behavior of the R-rotor during rotation, more factors, including temperature, hydrogenation schemes (NH), and the length of HDP (Lz), were investigated using molecular dynamics simulations. Six HDP models with different values of NH and Lz were considered. Except for the HDP, the sizes of the remaining components in the model remained unchanged. Furthermore, each carbon atom on the boundary of HDP and the ends of all three stators Sensors 2020, 20, 1969 12 of 16 and the R-rotor was bonded with a hydrogen atom. The detailed parameters of the HDPs are listed in Table 1.

FigureFigure 11. Initial11. Initial schematic schematic of of a a rotation–translation rotation–translation nanoconvertor nanoconvertor with with a hydrogenated a hydrogenated deformable deformable part (HDP)part (HDP) on theon the rotor rotor from from carbon carbon nanotube nanotube (CNT)(CNT) (6, (6, 6). 6). ωω is isthe the input input rotational rotational frequency frequency exerted exerted on theon left the edgeleft edge of theof the L-rotor. L-rotor.d, d the, the output output ofof the system system,, is is the the axial axial distance distance between between the right the rightedges edges of theof R-rotorthe R-rotor and and the the R-stator2 R-stator2 from from CNT CNT (11,(11, 11). The The right right edge edge of ofthe the R-rotor R-rotor has hasa translational a translational velocityvelocity of v ofduring v during the the deformation deformation of of thethe HDP.HDP. On the the internal internal side sidess of ofthe the up upandand down down layer layerss of of the HDP, the NH lines of neighboring carbon atoms were hydrogenated. NH was no more than six. the HDP, the NH lines of neighboring carbon atoms were hydrogenated. NH was no more than six. The rotorsThe rotors were we madere made from from a (6, a 6)(6, CNT,6) CNT, and and stators stators from from a (11,a (11, 11) 11) CNT. CNT. The The dimensiondimension unit is is Å Å.. “//z” “//z” means parallel to z-axis. means parallel to z-axis.

3.2. Methodology Table 1. Initial parameters of the HDPs in the nanoconvertor in Figure 11.

Model LZ/Å NH Number of Atoms on HDP

3.2.1. Features of theZ1H1 HDP 26.99 1 960C + 96H (boundary) + 16H (NH)

Z2H1 35.51 1 1128C + 112H (boundary) + 16H (NH) To reﬂect the state of the HDP, its potential energy was recorded. In particular, the variation of Z2H2 35.51 2 1128C + 112H (boundary) + 34H (NH) the potentialHDP energy (VPE) illustrates the change of its state. The concept of the VPE of a HDP can be Z2H4 35.51 4 1128C + 112H (boundary) + 68H (NH) calculated by subtractingZ2H6 the35.51 current potential6 energy 1128C from + its 112H initial (boundary) value, + i.e., 102H (NH)

Z3H1 48.29 1 1380C + 136H (boundary) + 16H (NH) VPE(t) = PE(t) PE(t ), (1) − 0 where PE(t) and PE(t0) are the potential energy of the HDP at time t and t0 (

XM MoI(t) = m x2 + y2 , (2) i i i t i=1 where xi, yi, and mi are the coordinates and mass of the ith atom in the HDP with a total of M atoms. For a deformed HDP, the value of MoI depends on two factors, i.e., the eccentricity (e) and the deformation of the component. If the component has a small eccentricity, the degree of deformation of the HDP can be illustrated by the variation of the MoI. The eccentricity of the deformed HDP can be deﬁned as: v tu 2  2 XM  XM m y   mixi   i i  e(t) =   +   . (3)  mi   mi  i=1 t i=1 t Sensors 2020, 20, 1969 13 of 16

The centrifugal force on a HDP can be expressed as:

M M * X * X * * * F = F = m ω ω r , (4) C Ci i × × i i=1 i=1

* * where F Ci is the centrifugal force applied on atom i in the HDP, and ri is the vector from atom i to “o”, * i.e., the origin of reference in coordinates xyz. The direction of F Ci is normal to the z-axis.

3.2.2. Flowchart of the Molecular Dynamics Simulation The molecular dynamics simulation approach was adopted to investigate the deformation behavior of the rotor during rotation. The simulations were carried out on the large-scale atomic/molecular massively parallel simulator (LAMMPS) [46]. In this study,considering electric neutrality,the interaction between the carbon and/or hydrogen atoms was evaluated using the AIREBO potential, which contains three items, i.e., item one is the reactive empirical bond order (REBO) part for describing the bond-ordered short-range interaction, item two is the torsion part to consider the dihedral eﬀect in the local deformation, and the ﬁnal item is the Lennard–Jones potential (L-J) [47] to describe the vdW interaction between two atoms with a distance smaller than 1.02 nm. The force can be expressed as:

FvdW = ∂UL J/∂rij , (5) − where UL-J is the L-J potential energy and rij is the distance between atoms i and j. For each simulation, it contained the following five major steps: Step 1: Create the model of the nanoconvertor with a specific HDP. Step 2: Reshape the initial configuration of the model by minimizing its potential energy with the steepest descent method. Step 3: Fix the three rings of atoms on the left edge of the L-rotor and four rings of atoms on each stator; then, relax the rest of the system in a canonical (NVT) ensemble using a Nose–Hover thermostat at a given temperature for 100 ps. The time step was 0.0005 ps. Step 4: Provide a specified rotational frequency on the left end of the L-rotor, which was previously fixed. The time step was modified to be 1 fs. Step 5: record the necessary physical quantities of HDP including VPE, MoI, e, and d for postprocessing.

3.2.3. Fast Fourier Transmission The output curves of d may have obvious fluctuations during the rotation of the system at finite temperatures. To accurately describe the vibration, the fluctuation frequencies of the d-t curves were analyzed using the fast Fourier transmission (FFT) approach [48,49] using the following equation:

XI d(t) = A sin(2π Ω t + φ ), (6) i · i · i i=1 where Ai is the ith order of amplitude, Ωi is the eigenfrequency, and φi is the corresponding phase angle. In this study, all the transmissions were operated on the last 1000 ps of the curves.

4. Conclusions Using a molecular dynamics simulation approach, we investigated the dynamic response of a rotation–translation nanoconvertor, which contained a rotor and three stators. The rotor had three parts, i.e., the L-rotor and R-rotor for inputting rotation (ω) and outputting axial motion (d), respectively, and the two parts were connected by an internally hydrogenated deformed part (HDP). After a series Sensors 2020, 20, 1969 14 of 16 of numerical tests of the physical quantities of the HDP and the axial output of the R-rotor at a low temperature, the following five conclusions were drawn. First, at extremely low temperatures, e.g., 8 K, the configuration of HDP remained unchanged with a low rotational speed due to the two hydrogenated parts on the HDP curve that were attached together via a strong van der Waals force. Once the centrifugal force was strong enough to overcome the van der Waals force, HDP displayed a breathing variation and the axial motion of the R-rotor occurred simultaneously. In particular, when ω was high enough, the R-rotor could oscillate with an amplitude over 0.5 nm in the present model. This characteristic can be applied to the design of an oscillator. Second, the mean value of the historical curve of d with respect to a specified ω depended slightly on the environmental temperature. However, its amplitude varied significantly with temperature, especially when ω was high. To obtain an oscillator with a high amplitude from the present model, the temperature should be lower than 50 K. Third, the hydrogenation scheme on the HDP (i.e., the value of NH) had a significant influence on the output of the system. At a specific temperature, the mean value of d always decreased with increasing of ω. If ω was fixed, a smaller NH induced a lower mean value of d. Furthermore, the system could always generate large-amplitude oscillations when NH > 0. Moreover, the “beat” phenomenon was found and its mechanism was revealed. Fourth, the length of the HDP along z-axis (Lz) also had a significant effect on the dynamic behavior of the system. A system with a longer HDP could produce an oscillation with a larger amplitude, even at a lower rotation frequency. Final, ω, NH, and Lz all influenced the oscillation frequency of the R-rotor, i.e., the oscillation frequency could be adjusted in a wide range by changing the input rotational speed of the rotor and/or hydrogenation scheme and/or the length of the HDP. For the potential fabrication of our system, some essential techniques are demonstrated below: First, create a double-walled CNTs with a perfect structure and certain chirality using one of a range of methods, such as conventional arc-plasma methods or chemical vapor deposition. Second, create the major parts of the system, stators, and tubes on the rotor, e.g., by electrical-breakdown technique. Third, form an HDP by hydrogenating the inside of a CNT with a large radius; potential methods that could be used include chemical vapor deposition, chemisorption, and an electrical-breakdown technique. Finally, merge the HDP on the rotor to form a system, as shown in Figure 11.

Supplementary Materials: The following are available online at http://www.mdpi.com/1424-8220/20/7/1969/s1, Video S1: Z2H6-T = 8 K- ω = 90 GHz-during [9.9, 10] ns.avi; Video S2: Z2H6-T = 8 K- ω = 100 GHz-during [1.46, 1.66] ns.avi. Author Contributions: Conceptualization, J.W. and K.C.; data curation, B.S.; funding acquisition, J.W.; investigation, B.S.; methodology, J.S. (Jiao Shi); software, B.S.; supervision, J.S. (Jianhu Shen); writing—original draft, K.C.; writing—review and editing, J.S. (Jiao Shi) and J.S. (Jianhu Shen). All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Plan, China (grant no. 2017YFC0405102); the National Natural Science Foundation, China (grant no. 11372281); and the State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China (grant no. GZ18111). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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