Research Article Mass Transport Induced by Heat Current in Carbon Nanotubes

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1 Nanomaterials Volume 2013, Article ID , 4 pages Research Article Mass Transport Inuce by Heat Current in Carbon Nanotubes Wei-Rong Zhong, 1 Zhi-Cheng Xu, 1 Ming-Ming Yang, 1 an Bao-Quan Ai 2 1 Department of Physics an Siyuan Laboratory, College of Science an Engineering, Jinan University, Guangzhou , China 2 Laboratory of Quantum Engineering an Quantum Materials, ICMP an SPTE, South China Normal University, Guangzhou , China Corresponence shoul be aresse to Bao-Quan Ai; aibq@scnu.eu.cn Receive 26 September 2013; Revise 15 November 2013; Accepte 22 November 2013 Acaemic Eitor: Miguel A. Correa-Duarte Copyright 2013 Wei-Rong Zhong et al. This is an open access article istribute uner the Creative Commons Attribution License, which permits unrestricte use, istribution, an reprouction in any meium, provie the original work is properly cite. Transport of helium atoms in the carbon nanotubes is investigate in the presence of temperature graients. The heat current flowing along the carbon nanotubes can inuce a stable irecte transport of helium; it is emonstrate that the heat current ensity rather than the temperature graient performs as a funamental physical factor to the mass transport. We provie an alternative route to control the mass transport by using heat. Our results reporte here are also relevant for unerstaning the transition from thermal energy to mechanical energy. 1. Introuction The stuy of transport is always a challenge issue with incalculable value to us. Thermal an mass transports are the two important transports an have attracte substantial concerns [1]. In thermal transport, thermal conuction is the transfer of heat energy by microscopic iffusion an collisions of particles or quasiparticles within a boy ue to a temperature graient. The mass transport refers to the orientate flow of particles. Even if thermal transport is a eviation from mass transport in physical principle, researchers are always trying to fin out their inherent relationship [2, 3]. Recently, an experimental result shows that thermal graients can rive the subnanometer motion of cargoes along carbon nanotubes (CNTs) [4]. Another numerical result shows that the fullerene encapsulate in carbon nanotubes canalsoberivenbytemperaturegraients[5]. More an more stuies focus on nanoparticle manipulation using heat [6 8]. A moel of carbon nanotubes fille with fullerene (C60) reporte that the temperature can pumping large particles [9]. The Langevin moel of a thermally -riven oublewalle nanotubes motor has escribe the ynamics of nanoelectromechanical evice activate by heat [10]. It was also reporte that the velocity of C60 inuce by temperature graients ha a linear relationship with heat flux [6]. These few previous efforts suggest that the heat originate from temperature graients can inuce the motion of particles. However, the unerline physics of mass transport riven by heat is still not so clear. In this paper, we will stuy the carbon nanotubes fille with helium (He) atoms an investigate the transport of He atoms inuce by the heat flowing through the CNTs. By constructing the relationship between the mass flux an the heatcurrent,wetrytorevealsomefunamentalphysicsabout theenergytransportanitstransformation.theobtaine results are of significance for unerstaning the thermally inuce mass transport in quasi-one-imensional materials anmaybeusefulforcontrollingthemasstransport. Figure 1 shows the carbon nanotubes fille with He atoms. HereweuseHeatomsasthefillingsjustbecauseoftheirstable chemical properties. Two heat baths (with temperature T H an T C, resp.) are connecte to the two sies of the CNTs. The two ens of the CNTs are fixe to avoi their spurious global rotation. The fixe region an the heat baths occupy one layer an six layers of atoms, respectively. In orer to keep a stable number of helium atoms, the perioic bounary is applie for He atoms along the axial irection of the CNTs. ThatmeansaheliumatomwillbeinsetinoneenoftheCNTs whenanotherheliumatomgoesoutofanotherenofthe CNTs. In our simulations, we have use classical molecular

2 2 Nanomaterials T H Heat current T C Mass flux Figure 1: Diagram of the carbon nanotubes (fille with helium atoms, the green balls) coupling to two heat baths (the re an blue balls). The temperatures of the re part an blue part are T H an T C, respectively. As T H > T C, the heat current will flow from the left sie to the right sie. Accoringly, a mass flux inuce by the temperature graient will occur along the axial irection of the CNTs.ThelengthofCNTsis12nm. ynamics metho base on the Tersoff-Brenner potential [11] of carbon-carbon (C C) boning interactions. The Lennar- Jones(LJ)potentialsform[12, 13] H LJ (r ij )= A rij 6 + B rij 12 (1) is use for van er Waals interactions of He He an He C couplings. The parameters of LJ are A = ev Å 6 an B = ev Å 12 for He He interaction an A = ev Å 6 an B = ev Å 12 for He C interaction, respectively. The equations of motion for atoms in either the left or right Nosé-Hoover thermostat are [14, 15] t Γ= 1 Q [ i t p i =F i Γp i, p 2 i 3N Ck B T 0 2m i 2 where p i is the momentum an F i is the force applie on the ith atom; Q = 3N C k B T 0 τ 2 /2, whereτ is the relaxation time, which is set to 1ps. Γ is the ynamic parameter of the thermostat; T(t) is the instant temperature of the heat baths at time t, which is efine as (m Ci /3k B )(V x (t) 2 + V y (t) 2 + V z (t) 2 ), where V(t) is the time-epenent velocity; T 0 (T H or T C )is the set temperature of the heat baths. N C is the number of the atoms in the heat baths, k B is the Boltzmann constants an m C is the mass of the carbon atom. The set temperatures of the heat baths, T H an T C,areplaceinthetwoens of the CNTs an the temperature graient is enote by T = ΔT/L = (T H T C )/L, wherel is the length of the CNTs. For the convenience of comparison, we use the average temperature 300 K, which is near the room temperature. The atoms between the two thermostats follow Newton s law of motion: t r j = p j m, ], (2) t p j =F j, (3) where j runs over all of the atoms between the two thermostats. We integrate these equations of motion by Verlet metho [16]. The time step is 0.55 fs. Generally, as shown in Figure 1, the heat current can stabilize aroun the set value when Temperature graient (K/nm) N H =50 N H = 108 Figure 2: Temperature graient epenence of average velocity of HeatomsinarmchairCNTsforifferentiametersoftheCNTs.The mass ensities of He in (5, 5), (7, 7), (10, 10), an (12, 12) are 66.39, 33.89, 16.6, an 16.6 amu/nm 3,respectively. the temperature graients are applie to the CNTs after 2 ns. At the same time, the mass flux riven by heat current occurs along the axial irection of CNTs. The heat bath acts on the particle with a force Γp i ;thusthepowerofheatbathis Γp 2 i /m C,whichcanalsoberegareastheheatfluxthat comes out of the high temperature heat bath an is injecte into the low temperature heat bath. The total heat flux injecte fromtheheatbathtothesystemcanbeobtainebyj h = i [ Γp 2 i /m i] = 3ΓN C k B T(t), wherethesubscripti runs over all the particles in the thermostat [17]. The average velocity of He is obtaine by V a =(1/N H ) N H i V i,where V i is the velocity of the ith helium atom, means a time average, an N H is the total number of He atoms. The mass fluxisefineas J m =ρ H m H V a = N Cm H V, (4) L where m H is the mass of single He atom an ρ H is the mass ensity of He in CNTs. When applying the temperature graients on the CNTs, astableflowingofheatomsalongcntswilloccur.figure 2 shows the temperature graient epenence of average velocity of He atoms for ifferent iameters of CNTs. To consier the iameter epenence of CNTs on the mass transport, here we stuy armchair chirality of the CNTs (5, 5), (7, 7),,an.Obviously,theaveragevelocityincreases with temperature graient. However, the average velocity of He atoms epens on the iameter of CNTs with slight irregularities. From our moel, when applying temperature graient on CNTs, the motion of He atoms occurs with a heat current flow from the hot heat baths to the col heat baths along

3 Nanomaterials Heat current (μw) Figure 3: Heat current epenence of average velocity of He atoms in armchair CNTs for ifferent iameters of CNTs. The CNTs are the same as in Figure 2. the surface of CNTs. If one uses the heat current, which is correspons to the temperature graient, to plot the x-axis, one woul fin an organize result comparing to Figure 2. As shown in Figure 3, if the heat current flowing through thecntsisthesame,thecntswithchiralityofcan rive higher average velocity of He atoms than that of (7, 7). When the iameter of armchair CNTs increases, the ability to rive the motion of He atom reuces. Then it is not ifficult to fin the conflicts between temperature graients an heat current. In orer to solve the conflicts, we plot the heat current ensity as the transverse axis an the average velocity as the longituinal axis. As illustrate in Figure 4, the curves for ifferent iameters as shown in Figure 3 all run together an the average velocity in the CNTs is proportional to the heat current ensity via the CNTs. This relationship is inepenent of the iameter as well as the length of CNTs. In Figure 4, wealso provie the results of two zigzag CNTs, (20, 0) an (16, 0). When the riving heat current ensity ranges from about 2 to 2 uw/nm 2, the linear relationship between average velocity an heat current ensity is still vali. This inicates that the heat current ensity etermines the average velocity, which may be inepenent of the structure of the CNTs. Since the mass flux is obtaine from (3), which means that the mass flux oes not epen on the cross section area, then the mass flux is proportional to the average velocity as well as the heat current ensity. In summary, we have stuie the temperature graient riven mass flux in the CNTs using nonequilibrium molecular ynamics. It is reporte that relationship between mass flux an heat current ensity rather than average velocity versus temperature graients can escribe the funamental physics of temperature graient inuce mass transport better. Our results try to connect energy transport an mass transport from a new point of view, which woul help Heat current ensity (μw/nm 2 ) Armchair Zigzag (16,0) (20,0) Figure 4: Average velocity versus heat current ensity for ifferent chiralities, iameter, an lengths of CNTs. The heat current ensity is obtaine by J = J h /S, wherej h is the total heat flux injecte from the heat bath to the system an S istheareaofcrosssection of CNTs, respectively. The mass ensity of He in (16,0) an (20, 0) is 16.6 amu/nm 3. researchers unerstan the physical mechanism of transport. Although we emonstrate a universal relationship between heat an motion, more physical properties such as the transfer efficiency nee to be aresse in etail. Even so, our results are an illumination to control mass flux by using heat conuction. Acknowlegments The authors woul like to thank Siyuan clusters for running a part of our programs. Wei-Rong Zhong thanks Y. Xiao at City University of Hong Kong for his contribution in plotting. This work was supporte in part by the National Natural Science Founation of China (Grant nos , , an );thenaturalsciencefounationofguangong Province, China (Grant nos an S ); the PCSIRT (Grant no. IRT1243); an the Funamental Research Funs for the Central Universities, JNU (Grant no ). References [1] K. F. Rinne, S. Gekle, D. J. Bonthuis, an R. R. Netz, Nanoscale pumping of water by AC electric fiels, Nano Letters, vol. 12, no. 4, pp , [2] M. J. Longhurst an N. Quirke, Temperature-riven pumping of flui through single-walle carbon nanotubes, Nano Letters, vol. 7, no. 11, pp , [3] H. Somaa, K. Hirahara, S. Akita, an Y. Nakayama, A molecular linear motor consisting of carbon nanotubes, Nano Letters, vol.9,no.1,pp.62 65,2009.

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