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Coupling Effect of Van Der Waals, Centrifugal, and Frictional Forces On PCCP View Article Online PAPER View Journal | View Issue Coupling effect of van der Waals, centrifugal, and frictional forces on a GHz rotation–translation Cite this: Phys. Chem. Chem. Phys., 2019, 21,359 nano-convertor† Bo Song,a Kun Cai, *ab Jiao Shi, ad Yi Min Xieb and Qinghua Qin c A nano rotation–translation convertor with a deformable rotor is presented, and the dynamic responses of the system are investigated considering the coupling among the van der Waals (vdW), centrifugal and frictional forces. When an input rotational frequency (o) is applied at one end of the rotor, the other end exhibits a translational motion, which is an output of the system and depends on both the geometry of the system and the forces applied on the deformable part (DP) of the rotor. When centrifugal force is Received 25th September 2018, stronger than vdW force, the DP deforms by accompanying the translation of the rotor. It is found that Accepted 26th November 2018 the translational displacement is stable and controllable on the condition that o is in an interval. If o DOI: 10.1039/c8cp06013d exceeds an allowable value, the rotor exhibits unstable eccentric rotation. The system may collapse with the rotor escaping from the stators due to the strong centrifugal force in eccentric rotation. In a practical rsc.li/pccp design, the interval of o can be found for a system with controllable output translation. 1 Introduction components.18–22 Hertal et al.23 investigated the significant deformation of carbon nanotubes (CNTs) by surface vdW forces With the rapid development in nanotechnology, miniaturization that were generated between the nanotube and the substrate. of devices from the microscale to nanoscale becomes feasible.1 Huang et al.24 found that a strain gradient in graphene can The concepts of typical nanodevices, such as the resonator,2–5 induce a non-zero net vdW force, which is sufficient to actuate oscillator,6–11 and rotary motor,12–16 have been proposed for over the directional movement of molecular mass on the graphene Published on 27 November 2018. Downloaded 1/16/2019 8:29:19 PM. a decade, and some of them have been realized in nanofabrica- surface. Besides, self-assembly of low dimensional materials is tion. For example, a nano-resonator has been used as a balance often controlled by vdW force.25–29 to measure the mass of a small molecule.4,5 The oscillator has a When relative sliding occurs between two components in a potential application in memory as an on–off. A few models for device, frictional force will affect the sliding state. In particular, the rotary nanomotor have been proposed, which may be applied the value of frictional force on the nanoscale increases with the to drive the motion of a nano vehicle. relative sliding speed.8,16,30–33 Friction even becomes a major On the nanoscale, the motion of a component in a system factor in the dynamic response of such devices as nano- depends on the external forces exerted. One of the forces is oscillators or nanomotors. Centrifugal force only appears on a van der Waals (vdW) force.17 Although not as strong as ionic or rotating component. For example, in a rotary nanomotor, the covalent bonds, vdW force always plays an important role in the atoms on the rotor are subjected to centrifugal force, which is mechanical properties, electrical transport properties, and the proportional to the square of the rotational speed. At gigahertz dynamic response of the nanodevices at interfaces between rotation, the rotor may be damaged due to heavy centrifugal force on the atoms.34–38 In this study, a model for a rotation–translation nano- a College of Water Resources and Architectural Engineering, Northwest A&F convertor is proposed potentially as a nano on–off or a sensor University, Yangling 712100, China. E-mail: [email protected] b Centre for Innovative Structures and Materials, School of Engineering, for measuring the rotational speed of the rotor. Considering the 2 RMIT University, Melbourne 3083, Australia excellent mechanical strength of sp carbon materials, e.g., 39 40 c Research School of Engineering, The Australian National University, ACT 2601, carbon nanotubes and graphene, and the extremely low Australia friction between neighbouring layers,32,33,39–43 we choose CNTs d State Key Laboratory of Structural Analysis for Industrial Equipment, as the rotor and stators in the system. Like origami,44 four Dalian University of Technology, Dalian 116024, China † Electronic supplementary information (ESI) available: Movie 1 – medium DP at graphene ribbons are used to form a deformable part (DP) for 500 K-input 50 GHz-[5, 5.18]ns.avi. Movie 2 – medium DP at 500 K-input 70 GHz- connecting both the input part and the output part of the rotors 45,46 [3.02, 3.09]ns.avi. See DOI: 10.1039/c8cp06013d (Fig. 1). Different from a traditional transmission system, This journal is © the Owner Societies 2019 Phys. Chem. Chem. Phys., 2019, 21, 359--368 | 359 View Article Online Paper PCCP Fig. 1 Schematic of a rotation–translation convertor with a deformable carbon rotor. At the left end of the L-rotor (the input part), an input rotational frequency, i.e., o, is exerted. ‘‘d’’ is the distance between the right edges of the R-rotor and the R-stator2, and it is the output of the system. Dimensions of the deformable part (DP) are labeled as Lx, Ly,andLz, respectively, with the unit of Å. Three DPs with different sizes are considered. as a rotational speed is applied on the input part of the rotor, it 2.2 Methods will also drive the rotation of the remaining parts. During The molecular dynamics simulation approach was adopted to rotation, the centrifugal force on the DP causes deformation find the deformation of configuration of the rotor during rotating. of the DP and synchronously produces translation of the output Simulations were accomplished using the open code LAMMPS.47 part. The effects of the vdW, centrifugal and frictional forces on The interaction among atoms in the carbon/hydrogen system is the dynamic behavior of the system are investigated by mole- described by the AIREBO potential.48 In each simulation, the cular dynamics simulations. initial configuration of the system is modified by minimizing its potential energy. Further, some atoms are fixed in their degrees of Published on 27 November 2018. Downloaded 1/16/2019 8:29:19 PM. 2 Model and methodology freedom, e.g., three rings of atoms on the left end of the rotor, four rings of atoms on each stator (Fig. 1). The next step is to relax the 2.1 Model of the rotary device system using a canonical (NVT) ensemble for 100 ps with a In this work, the model shown in Fig. 1 is adopted to illustrate timestep of 0.5 fs. After relaxation using the Nose–Hoover the vdW effect and the centrifugal effect on the nanoscale. In the thermostat,49,50 a specified rotational frequency is exerted on model, a deformable part (DP) made from graphene ribbons is the L-rotor at the atoms that were previously fixed in relaxation. used to connect the L-rotor and the R-rotor made from CNTs. During rotating, the timestep is set as 1 fs, and some essential Three CNT-based stators are fixed to constrain the motion of physical quantities, e.g., variation of potential energy (VPE), the rotors. At the left end of the L-rotor, a constant rotational centrifugal force of the DP, and displacement of the right end of frequency, o, is input. The distance between the right ends of the R-rotor, are recorded for analysis. The value of VPE can be the R-stator2 and the R-rotor is output to show the axial motion calculated by subtracting the initial value of potential energy of of the R-rotor. The detailed parameters are listed in Table 1. the component from its current value. Table 1 Initial parameters of the rotary system. Dimension unit: Å Component Chirality Radius Length Ring/layer Number of atoms L-rotor (6,6) 4.068 41.811 35 420C R-rotor (6,6) 4.068 95.921 80 948C + 12H L-stator (11,11) 7.458 12.298 11 242C R-stator1 (11,11) 7.458 12.298 11 242C R-stator2 (11,11) 7.458 12.298 11 242C Small DP 15.623(x) Â 16.664(y) Â 16.700(z) 4 104C Â 2(up + down) + 80C Â 2(left + right) Medium DP 24.145(x) Â 26.620(y) Â 26.520(z) 4 252C Â 2(up + down) + 228C Â 2(left + right) Large DP 32.666(x) Â 31.540(y) Â 31.540(z) 4 400C Â 2(up + down) + 376C Â 2(left + right) 360 | Phys. Chem. Chem. Phys., 2019, 21, 359--368 This journal is © the Owner Societies 2019 View Article Online PCCP Paper Temperature effects were considered by considering the that at 83 ps. In particular, the DP becomes a narrow ring, in system at low temperature (e.g., 8 K), room temperature (e.g., which the two sides of the ring attach. For the narrow ring, 300 K), and high temperature (e.g., 500 K). The input rotational it cannot deform further. This means that the rotor rotating at frequency of the L-rotor, i.e., o, was varied from 10 GHz to 60 GHz or higher frequency should have the same configuration, 100 GHz or higher if necessary. i.e., a narrow ring. To show the vdW effect on the deformation and output of At 8 K, the fluctuation of VPE tends to be less than 0.2 eV, the system, the VPE of the DP is defined and calculated using which is far less than that at 300 K or 500 K.
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