Detailed investigation on single water molecule entering carbon nanotubes

Appl. Math. Mech. -Engl. Ed, 33(10), 1287-1300 (2012)Applied MathematicsDOI 10.1007/s10483-012-1622-8and MechanicsCShanghai University and Springer-VerlagBerlin Heidelberg 2012(English Edition)Detailed investigation on single water molecule entering carbonnanotubes*R. ANSARI，E. KAZEMI(Department of Mechanical Engineering, University of Guilan, Rasht 3756, Iran)Abstract The behavior of a water molecule entering carbon nanotubes (CNTs) is stud-ied. The Lennard-Jones potential function together with the continuum approximationis used to obtain the van der Waals interaction between a single-walled CNT (SWCNT)and a single water molecule. Three orientations are chosen for the water molecule as thecenter of mass is on the axis of nanotube. Extensive studies on the variations of force,energy, and velocity distributions are performed by varying the nanotube radius and theorientations of the water molecule. The force and energy distributions are validated bythose obtained from molecular dynamics (MD) simulations. The acceptance radius of thenanotube for sucking the water molecule inside is derived, in which the limit of the radiusis specified so that the nanotube is favorable to absorb the water molecule. The velocitiesof a single water molecule entering CNTs are calculated and the maximum entrance andthe interior velocity for different orientations are assigned and compared.Key words single-walled carbon nanotube (SWCNT), single water molecule, Lennard-Jones potential, force, energy and velocity distributions, acceptance radiusChinese Library Classification 03522010 Mathematics Subject Classification 81V55, 92E10IntroductionThe interest in carbon nanotubes (CNTs) continue to grow since the publication of theIijima's discovery paperl1l. CNTs possess many novel and unique physical and chemical prop-erties. Because of their nanoscale dimensions, hollow cylindrical shape, structure, composition,and porosity, nanotubes have potential applications in biomolecule separation devicesl2), molec-ular sensors3), encapsulation media for molecule storage and targeted deliveryl4 5, and channelsfor rapid fuid flows[6-8}.In recent years, the encapsulation of water inside nanoscale channels such as CNTs hasattracted the attention of researchers worldwide. Water transport inside hydrophobic channelsof CNTs represents a unique nanofuidic system9, which has great importance for biologicalactivity of macromolecules as well as for designing novel molecular devicesl10-12. The wateroccupancy of the channel was studied by Hummer et al.t9] based on the molecular dynamics(MD) simulations, and it was concluded that water molecules not only penetrate into but alsoare conducted through the nanotube. During 66 nanosecond, 1 119 water molecules enteredthe nanotube on one side and left on the other side, .ie of about 17water molecules per nanosecond passing through the中国煤化工99 cms-1)间。Predicted from the conventional fuid- fAow theory, Ma:MYHCNMHGhattheliquid* Received Nov. 28, 2011 / Revised Mar. 27, 2012Corresponding author R. ANSARI, Ph. D., E-mail: r. ansari@guilan.ac.ir.1288R. ANSARI and E. KAZEMIflow through a membrane composed of an array of aligned CNTs is four to five orders faster inthe magnitude. This high fuid velocity results from an almost frictionless interface at the CNTwall[13]. Wan et al.(14] used a simple hydrophobic nanopore as a prototype to study the responseof an on-off gate under continuous deformations by mechanical stress. Explicitly, an atom ofa single-walled nanotube is affected by an external force, which pushes this atom togetherwith its neighbor atoms to leave their initial equilibrium locations|14). Fang et al.15), in theirreview, examined some of recent advances in the dynamics of single fle water molecules insidevery narrow nanochannels. The work of Sansom and Biggin16l extended the understanding ofhow liquids behave at the nanoscale. The effect of the external structure on water permeationacross a single-walled nanochannel was studied by Gong et al.17] based on the MD simulations.These findings are expected to be helpful in the design of high-fux nanochannels and providean insight into the contribution of the lipid membrane to water permeation across biologicalwater channelsl7. Single-file transport of water into carbon nanotubes was experimentallydemonstrated by Cambre et al.18] for the first time through splitting the radial breathingvibration mode in Raman spectra of bile salt solubilized tubes when both empty (closed) andwater-filled (open-ended) tubes are present. One-dimensional ordered water molecules enteringand exiting from a carbon nanotube of a proper radius were studied via MD simulations by Qiet al.[19]. Their findings showed the possibility of controlling the water fAow by regulating thedipole directions of the water molecules inside nanochannelsl19).The single file water transport through a biomimic water channel consisting ofa (6, 6) CNTwith different types of external point charges was studied by the MD simulations by Zuo etal. [20]. The energetic analysis suggested that the water-water interaction determined by dipoleorientation configuration infuences the transport rate significantly. These findings can providecorrect biomimic understanding of water transport properties and will beneft the design ofefficient functional nanofuidic devicesl20]. The first-principle calculations for the hybrid systemsby water molecules confined inside a finite (6, 6) CNT were performed by Wang et al.l21, andthe tube water interactions were discussed in terms of the coupling energies, charge transfer,dipole moments, HOMO/LUMO distributions, and vibrational frequencies. Hilder and Hil2)outlined the concepts of an acceptance condition and the suction energy, and subsequentlyexamined the suction characteristics of a single water molecule entering a CNT.In the present study, the Lennard Jones potential function together with the continuumapproximation is used to obtain the van der Waals interaction between a single-walled CNT(SWCNT) and a single water molecule. Three orientations are chosen for the water moleculeas the center of mass on the axis of nanotube. The effects of both the nanotube radius andthe orientation of the water molecule on the distributions of force, energy, and velocity arefully examined. Also, the MD simulations are conducted to validate the results of force andenergy distributions obtained from the present model. The velocity of a single water moleculein different distances between center mass point and the left end of nanotube is calculated,and the maximum entering velocities for different orientations are assigned and compared. Thecomparison is studied between diferent orientations, and the best orientation is determinedaccording to the nanotube radius.2 Problem formulationThe non-bonded interaction energy between two interacting molecules can be obtained bydiscretely summing the interacting energy between each atom pair, i.e,E=E2中中国煤化工(1)MYHCNMHGwhere φ(Pij) is the potential function between atom i and atom j of two different moleculesplaced with the distance Pij from each other..Detailed investigation on single water molecule entering carbon nanotubes1289On the basis of the continuum approach, in which atoms are uniformly distributed over thesurface of the molecule, the double summation in Eq. (1) can be replaced by a double integral1SE=m7z .中()dSjdS2,(2)where η1 and 72 denote the mean surface densities between the two interacting molecules, andφ(p) is a potential function between two typical surface elements dSi and dS2 on each molecule.In the present study, we have an irregular shaped water molecule which can be stateddiscretely and a CNT which can be modeled by a continuous approach. The best formulationfor this model by using a hybrid discrete continuum approach23 leads toE=η(3)in which the mean surface density is assumed to be that of graphene, namely, 0.382x10-2 nm-2atom. The Lennard-Jones potential function φ(ρ) is represented as follows:A， B中(p) -pf p2.where A and B are attractive and repulsive constants, respectively. Their values are given forcarbon- oxygen and carbon-hydrogen in Table 1, respectively.It is noticeable that in both continum approximation and molecular dynamics approaches,the Lennard-Jones potential function given by Eq. (4) is lused to compute the (intermolecular)non- bonded interactions (as a force field) between two separate molecules (water moleculeand carbon nanotube), whose atoms are not linked by covalent bonds. In addition to theLennard-Jones potential, the Tersoff- Brenner potential function is also implemented in the MDsimulations to consider the energy of covalent bonds between the carbon atoms of each molecule.Table 1 Approximate Lennard-Jones constantsA/(eV.nm6 )B/(eV.nm12 )C-H14.945 x 10-614544.366 x 10-12C-O35.720x 10-662141.298x 10-12Consider a CNT with the radius a, the semi- infinite length is 0.1 nm and a water molecule :with the bond length is 0.1 nm, and H-O-H angle is 109.47° (see Fig. 1). Therefore, the exactcoordinates of atoms in the water molecule can be determined. Assuming that the mass centerof the water molecule is located on the nanotube axis, it can be calculated byCm=2Mwhere mi is the mass of each atorm in the molecule at the position ri, and M is the total massof the molecule.If we consider the base line at hydrogen atoms, the center of mass will be 0.051 28 nm.The global coordinate is considered to be at the left中国煤化工g.1) and thedistance between the global coordinate and the center3ssumed to beZ. Thus, the parametric equation of the nanotube isMYHCNMHG(acos0，asin0, zt),.1290R. ANSARI and E. KAZEMIand the coordinates of atoms in the water molecule can be generally stated as(ri， 0， Z+ zw,t),where i denotes the number of atoms in the molecule, which is three.2↑x↑A(r, zw,)a|2Zw ρCenter of massB(x,2)Fig.1 Single water molecule entering one CNTBased on the above discussion, the distance ρ can be defined asp2 = (acos0-r;)2 + (asin0)2 +(zt-(Z +zw))2.(5)Simplifying Eq. (5) yields0p=(a-ri)2 + 4ar;sin2号+(zt-(Z + zw,))2.(6)Since好= (a - r;)2 + 4ar; sin2号, Eq. (6) becomesp?=冷+(zt-(8 +2w.))2.(7)Equation (3) can be rewritten asE=na二了。”]。"(一条十B\)dzrd0.(8)Also, the van der Waals interaction force between the two molecules can be written asptot=-VE.Because of the symmetry of the problem, the prior equation can be simplified as8EF2*=-82(10)Thus,FEt=-na∞8(-命+晶)-dztd0,(11))Zwhere中国煤化工p∞8(-命+晶)J。8Z-dzt =之MH~T,W)CNMHG(12)in which H =-A, and H2= B..Detailed investigation on single water molecule entering carbon nanotubes12913 Results and discussionBased on the derived formulation in the previous section, the interaction behaviors of atomsof the water molecule for three orientations (see Fig. 2) with atoms of the nanotube are inves-tigated in the following aspects.0.051 28 nmBase lineCenter of massH~HD)I)*.H *.*.*(I)Fig.2 Schematics of single water molecule entering CNT with orientations (I), (II), and (II) andlocation of center of mass3.1 Interaction forceThe interaction force (FE*) between a single water molecule and an SWCNT is shown inFigs. 3- 12. The interaction force is a function of the distance between the center of mass of thewater molecule and the left end of the nanotube (negative Z indicates that the center of massis outside of the nanotube and vice versa).3.1.1 Validation of modelIn order to verify the continuum model developed herein, comparisons between the resultsfrom the present model and those from the MD simulations are made. It should be noted thatin the MD simulations conducted here, the Tersoff- Brennerl2425] potential function is used togive the energy of covalent bonds between the carbon atoms. A velocity-verlet algorithm26]is also used to integrate the equations of motion and a basic time step of 1 fs is employedto guarantee good conservation of temperature. The simulation is conducted in canonicalensemble, called NVT, at room temperature (300 K). The Nose Hoover thermostatl27] is utilizedin the simulation to keep the temperature constant at 300 K. Making use of this thermostatresults in less Auctuation of the system during the temperature stabilization.Figures 3-5 show the interaction forces for (5, 5)，(12, 1), and (13, 2) CNTs with radii0.339 nm, 0.49 nm, and 0.55 nm, respectively, for the three given orientations. These figuresprove that the present continuum model is accurate enough to predict the MD results.3.1.2 Discussion on diferent aspects of interaction forceIn Figs. 6-8, the results are plotted for each orien中国煤化工of nanotubes.Comparing the results of radii 0.339 nm, 0.49 nm,CHCNMH GSsrreported inRef. [22], it can be seen that the results obtained foecule entersnanotube with orientation II are reported in Ref. [22] for the case in which water moleculeenters nanotube with orientation I. As seen in Figs.6 and 7, in the radius like 0.348 nm, there.1292R. ANSARI and E. KAZEMI1.01.0-0.50.5 t0.0.0-0.5-0.5 |-1.0-1.5-1.5 t-2.0出-2.5-3.0-3.5-4.0.-1.0-050.00.5 101.5-1.5-1.0-0.5 0.0 0.5.0 1.5Z/nm- a = 3.30 (continwumn mode)a = 4.00 (continuumn mode)--- a = 8.30 (continum model)a = 4.90 (continuum model)--- a = 5.50 (continwum model) ---- a = 339 (MD slimulations)--a = 5.50 (continwum model)} -.. a = 3.39 (MD simulatons)---- a = 4.90 (MD simulations) - -- a = 5.50 MD simulations)---- a= 4.90 (MD simwlations) - _-- a = 5.50 MD simulations)Fig.3 Interaction force for single waterFig.4 Interaction force for single watermolecule entering nanotube with orimolecule entering nanotube with orien-entation I based on continum modeltation II based on continuum model andand MD simulationsMD simulations.0r0.6 t5 0.4e。高0.2-0.0 --0215-10-0.50.0 0.1.--- a = 330 (continwum model) --- a = 4.90 (continuum model)-a = 5.50 (continuum model) -- a = 3.39 (MD simulations)---- a= 4.90 (MD sinulations) --- a = 5.50 MD simulations)Fig.5 Interaction force for single water molecule entering nanotube with orientation III based oncontinuum model and MD simulationsare fuctuations which make local minimum points, and for others like 0.45 nm, the maximumpoints are observed. However, it is noticeable that these extremums take place in the samedistance from the left end of the nanotube depending on orientation I or II. For orientation I,these extremumns in all radii take place before entering the nanotube, and for orientation II, thephenomenon occurs after entering the nanotube. It is worth mentioning that these extremumsin both orientations occur while atoms of hydrogen are entering the nanotube. In other words,when Z is -0.05128 nm and +0.051 28 nm. However, this depends on the radius of the nanotube.When the diference between the nanotube radius中国煤化工T ncreases, thisextremum point occurs in a distance nearer to the leftlower than0.051 28 nm, as shown in Figs. 9 and 10.MYHCNM HGFigure 8 shows the infuence of the symmetric shape of molecule on the interaction forcewhile the center of mass is entering the nanotube. It can be seen that although the interaction.Detailed investigation on single water molecule entering carbon nanotubes1293.0 r1.0 r0.50.0 t0.0-0.5 I.0 F色-1.5-1.5-2.0-2.5- -3.0-3.0-35-10-0.50.005101.5-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Z/nmZ/mFig.6 Interaction force for single waterFig.7 Interaction force for single watermolecule entering nanotube with ori-molecule entering nanotube withentation Iorientation II1.00.8 |F 0.6---- 5.50 .三0.4-0.2---1.5-1.0-0.50.00.5 1.0 1Fig.8 Interaction force for single water molecule entering nanotube with orientation IIIforce is symmetric, some fuctuations also exist for some radii.According to Figs.6, 7, 9, and 10 for orientations I and II, when the differences betweenthe radius of the nanotube and that of the hydrogen atom are above 0.34 nm, the maximuminteraction force takes place while atoms with higher radius are entering the nanotube, andafter that, a reduction in the interaction force is seen. This means that the atom enteringthe nanotube first can affect the location of the occurrence of the maximum interaction force.For example, when oxygen enters the nanotube first, since its atomic mass is higher than thatof hydrogen, the maximum interaction force arises inside the nanotube as seen in Figs. 9 and10. When the differences between the radius of nanotube and the radius of hydrogen atomare below 0.34 nm, entering hydrogen has a negative effect on the interaction force. Besides,because of the decrease in the radius of entering atom (oxygen) will increase in the interactionforce, which occurs to some extent as illustrated in Figs. 6 and 7.According to Fig. 8, as mentioned before, for the existence of some radii fuctuations basedon the differences between the radii of hydrogen an中国煤化工between theinteraction force of Figs. 6 and 8 based on the radius ofMH.CN M H Gthe radius ofigs.11 and 12.The figures illustrate that when the radius of the nanhydrogen, the orientation III is better than orientation I, because when water is outside of thenanotube, the attractive force is greater, and when it is inside of nanotube, the repulsive force.1294R. ANSARI and E. KAZEMI0.80.0.70.620.5t-- a= 6.000.4 |-- a= 9.000.4a.3R 0.30.2 t0.20.10.:15 -1.0-0.5.0 1.5Z/nmFig.9 Interaction force for single waterFig.10 Interaction force for single watermolecule entering nanotube whenmolecule entering nanotube when dif-diferences between radius of nan-ferences between radius of nanotubeotube and radius of hydrogen atomand radius of hydrogen atom are aboveare above 0.34 nm for orientation I0.34 nm for orientation IIis greater (see Fig. 11). For differences above 0.34 nm, based on the results plotted in Fig. 12,orientation I is suggested..0r0.9Orentation IOrientation I.9.... Onientation m--- Orentation 1.850.6 t).6 t目0.5 |0.5 t它0.4s 0.3出0.3F0.2F).1 F0.0-1.5 -1.0 -0.5 0.0 0.5 10 1.55 -1.0 -0.5 0.0 0.5 1.0 1.5Z/hmFig.11 Diferences betweeninteractionFig.12 Differences between interaction force offorce of orientations I and III whenorientations I and III when a = 4.20a= 3.903.2 Discussion on concepts of energy and velocity3.2.1 Validation of modelBased on the MD simulations explained in subsection 3.1.1, the variations of energy arecompared with those of MD simulations to assess the accuracy of the present continuum model.Plots in Figs. 13 -15 are the energy associated with (5, 5), (12, 1), and (13, 2) CNTs for threeorientations. A close agreement between the continuum and MD simulations results confrmthe accuracy of the present model,3.2.2 Acceptance condition and suction energyThe concepts of acceptance condition and suction中国煤化工ed by Cox etal.[28). Condition specifies the minimum radius of theMHCNMHGmolecule canbe accepted. As seen in Figs. 6- -8, for some radii of nan: is negative,but it does not mean that the water molecule was repulsed by the nanotube and cannot enter it.The necessary condition for specifying the acceptance radius is given by Eq. (13), which shows.Detailed investigation on single water molecule entering carbon nanotubes12950.3).20.20.1 t0.1.0 r0.0-0.1 t旨-0.1-0.2 t-0.2-0.3-1.5-1.0-0.50.00.5 1.0 1.5-0415--1.0-0.50.00.51.0 1.5Z/rum- a ■3.39 (continuum model) - - a = 4.90 (continum modeD)- a = 5.50 (contruum mode) -_ a = 3.39 (MD simulations)_--- a= 5.50 (continuum model) __ a - 3.39 (MD simulationg)--- a = 4.90 (MD simulations) .-.. a = 5.50 (MD simulations)--- am 4.90 (MD simulations) --- a = 5.50 (MD simulations)Fig. 13 Energy of water molecule for orien-Fig.14 Energy of water molecule for orienta-tation I based on continuum modeltion II based on continuum model andand MD simulationsMD simulations0.00-0.05-0.10尔-0.15-0.20喜-0.25-0.30-0.35-0.40-0.4"1.5-1.0-0.50.0 0.5 1.0 1.5Z/nm-- a = 3.39 (contnuum model) --- a = 4.90 (continwum model)-- - a= 5.50 (continum model) --- a - 3.39 (MD simulations)---- a = 4.90 MD simulations) -- a = 5.50 (MD stmulatlons)Fig.15 Energy of water molecule for orientation II based on continuum model and MD simulationsthe energy of the molecule moving from Z= -∞to Z2 (Z2 is the point that interaction forceintersects Z- axies, it must have a positive value, and the interaction force after that must bealso positive) must be negative. In other words, based on Eq. (10), we know that the area underthe interaction force Z diagram is negative of energy. For absorbing water into the nanotube,the interaction energy must be negative so that the condition for acceptance of water moleculeby nanotube can be written as follows:pZzF(Z)dZ= E(-∞)- E(Z2)> 0.(13)Solving Eq. (13) shows that the acceptance radi for 0中国煤化工e 0.34780 nm,0.346 40 nm, and 0.327 90 nm, respectively (see Fig. 16)_ection 3.1, it isseen that the acceptance radius reported for orientatiCNMH(orientation II.For detailed investigation of these results, the velocity and energy of water molecule versus zfor diferent orientations are ploted in Figs. 17-22. The verification of the results of acceptance.1296R. ANSARI and E. KAZEMIenergy is obvious because all velocities for the radi above the acceptance radius are positive andenergy functions are negative, which confirm this theory. It is noticeable that in these figures,for some radii below the acceptance radius, the velocities reach zero inside the nanotube andthen increase. Also, the energy during entering the nanotube is positive, and after that givesnegative values, which means that nanotubes with these radi are favorouble to suck in thewater molecule, but additional external energy is needed. For example, in Figs. 17, 18, 20, and21 for a= 0.341 nm, this fact is seen. The same samples can be seen for orientation III for a= 0.335 nm. The concept of suction energy proposed in Ref. [28] is the energy needed for thenanotube exerting on the water molecule to suck it inside, and it is defined as follows:F(Z)dZ= E(-∞)- E(+∞)> 0.(14)0.3 FOnentationi营0.00.1 t岁-0.4-0.5-0.60.3200.3280.3360.3440.352a/nmFig.16 Acceptance energy for orientations I, II, and II25002000管1500二=a.1500 t...=6. .导10001000三500-1.5 -1.0 -0.50.0).5.0 1.5-1.5-1.0-0.50.0 0.5 1.0 1.5Z/nmZ/m .Fig.17 Velocity of water molecule for ori-Fig.18 Velocity of water molecule for orientaentation Ition IIFigure 23 shows the suction energy for different orientations of atoms in water molecules.The location where suction energy crosses horizontal axis gives the value of the minimumradius of the nanotube favorable to accept water m(中国煤化工; I and II, thevalue is 0.34067 nm, which is the same as reported iis 0.32244 nmfor orientation III. As seen in Fig. 23, the maximumCNMHGaions Iandnhappens when the radius of the nanotube is 0.390 nm which is close to the result of Ref. [22),and the value of the maximum suction energy is 0.566 eV. Figures 17 and 18 illustrate thatDetailed investigation on single water molecule entering carbon nanotubes129730000.30.2 t25000.1 t20000.0-0.1---a= 5.50器-0.21000-0.4 t-0.5-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-0.62/nm/nmFig.19 Velocity of water molecule for ori-Fig.20 Energy of water molecule for orientaentation IIItion I.3 r0.8.2-0.60.40.28 -0.1 t-0.2-0.3点-0.2-0.4-0.5.-.-.0-1.0-0.5 0.0 0.5 1.0 1.5~-1.0-0.50.00.51.0 1.5Z/nmFig.21 Energy of water molecule for orien-Fig.22 Energy of water molecule for orienta-tation IItion IIIin this radius, the velocity of water is the maximum and reaches from 1 687 m:s-1 (orientationI) and 1 686 m-s-1 (orientation II) in entry to a constant velocity of 2463 m:s-1 inside thenanotube. For orientation II, the maximum suction energy is about 0.6148 eV and takes placewhen the radius of the nanotube is 0.373 nm. Figure 19 shows the maximum velocity occursin this radius and the water molecule has the maximum entrance velocity of 1 783 m.s~ : 1 , andlastly reaches the maximum velocity 2 566 m.s- 1 inside the nanotube.3.2.3 Comparison of velocities for diferent orientations of water moleculeIn Figs.24 and 25, the velocities are compared for three orientations. It is obvious thatwhen the difference between the radi of atoms of water and the radius of the nanotube is below0:34 nm, the entrance velocity of orientation III is larger than others, and the velocity oforientation II is larger than that of orientation I (see Fig. 24). When this difference is morethan 0.34 nm, orientationsI, II, and III have the maximum entering velocity, respectively, butare very close to each other as shown in Fig. 25. .4 Conclusions中国煤化工C NMH G_Extensive studies on the variations of force, energy, duu Veuouluy uioulivuuons are carriedon by changing the nanotube radius and orientations of water molecule based on the Lennard-Jones potential function together with the continuum approximation. It is indicated that the.1298R. ANSARI and E. KAZEMI.8 r-OrientationI0.6.... Onientation IOrientation I0.4.2 t.0 F-0.40.300.350.400.45 0.50 0.55 0.60a/nmFig.23 Suction energy for orientations I, II, and III2500.... OnientationI2000- Orentation I- - Orientation m个1500里15001000三... OrientationI. Orientation I500- Orentation I1-1.5--1.0-0.50.0 0.5 1.0.5-1.5-1.0-0.5 0.0 0.5 1.0 1.5Fig.24 Comparison between velocities ofFig.25 Comparison between velocities of dif-different orientations whena= 3.48ferent orientations when a= 4.2shapes of the interaction force, energy, and velocity distribution are greatly dependent on theradius of the nanotube, the distance between the center mass of water molecule and the leftend of the nanotube, and the orientation of atoms of water molecule. Moreover, the diferencesbetween the radius of the nanotube and that of hydrogen are very significant in the behaviorof water molecule. Based on this investigation, an acceptance condition is given. The resultsshow that for orientations I, II, and III, the acceptance radii are 0.347 80 nm, 0.346 40 nm, and0.327 90 nm, respectively. However, in all the three orientations studied here, there is a limit forthe radius of nanotube in which the nanotube is favorouble to suck in water molecule, but addi-tional external energy is needed. This limit for orientation I is 0.34067 nm < a < 0.347 80 nm,for orientation II is 0.34067 nm < a < 0.34640 nm, and 0.32244 nm < a < 0.32790 nm fororientation II. Therefore, in these situations, it is needed and necessary to use nanotubes withradii below 0.34067 nm, and the only possible orientatin is orientation II. It is noticeablewhen the differences between the radius of the nanotube and the radius of hydrogen is below0.34 nm, the entrance and interior velocities of the water molecule in orientation III are sig-nifcantly higher than that of orientations I and II. Also, the enterance velocity of orientationII is more than that of orientation I, but reaches to the same velocity inside the nanotube.When the difference is above 0.34 nm, there is no sube中国煤化工1 the velocitiesof three orientations. However, the velocities of orieni:YHCNMH=those of orien-tation II, and the latter ones are also smaller than t. rthermore, themaximum entrance velocities for which the water molecule entering orientations I, II, and III are1687 m:s-1, 1 686 m-s-1, and 1 783 m-s-1, respectively. The water molecule reaches to a max-.Detailed investigation on single water molecule entering carbon nanotubes1299imum and constant velocity inside the nanotube, which is equal to 2463 m-s- 1 for orientationsI and II, and 2566 m-s- 1 for orientation II. It is worth mentioning that these maximum en-trance and interior velocities take place with the radius of 0.390 nm for orientations I and II and0.373 nm for orientations III.References[1] ljjma, S. 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