Orientations of special water dipoles that accelerate water molecules exiting from carbon nanotube

Appl. Math. Mech. -Engl. Ed, 32(9), 1101-1108 (2011)Applied MathematicsDOI 10.1007/s10483-011-1484-xand Mechanics@Shanghai University and Springer -Verlag(English Edition)Berlin Heidelberg 2011Orientations of special water dipoles that accelerate water moleculesexiting from carbon nanotube*Wen- peng QI (亓文鹏)-,3，Yu-song TU (涂育松)尸，Rong zheng WAN (万荣正),Hai-ping FANG (方海平)1,3(1. Department of Physics, Shandong University, Jinan 250100,Shandong Province, P. r. China;2. Institute of Systems Biology, Shanghai University,Shanghai 200444, P. R. China;3. Shanghai Institute of Applied Physics, Chinese Academy of Scineces,Shanghai 201800, P. R. China)(Communicated by Shi-qing DAI)Abstract One-dimensional ordered water molecules entering and exiting from a carbonnanotube with an appropriate radius are studied with molecular dynamics simulations.It can be found that a water molecule near the nanotube end is more likely to be expelledfrom the nanotube if its dipole is almost perpendicular to the nanotube axis. The key tothis observation is that those water molecules are closer to the wall of the nanotube awayfrom the equilibrium position of the Lennar-Jones (LJ) potential. Thus, the interactionenergy for those water molecules is relatively high. There are two particular structures ofndicular water molecule depending on the dipole direction of the adjacent watermolecule in the nanotube. Although the probabilities of these structures are quite small,their contributions to the net fux across the nanotube end are approximately equal tothe predominant structures. The present findings further show the possibility of control-ling the water flow by regulating the dipole directions of the water molecules inside thenanochannels.Key words water, carbon nanotube, single fle water chain, Lennard- Jones (LJ)interactionChinese Library Classification 03522010 Mathematics Subject Classifcation 81V55, 92E101 IntroductionThe presence of water inside carbon nanotubesl-5, together with the existence of bio-logical water channelsl6 7, has greatly promoted the study of the water permeation throughnanochannelsl8 -19] and, in particular, the mass transportation induced by the thermo-migrationin carbon nanotubes20]. The mechanisms for the Aux generation in water- flld nanochannels* Received Apr. 29, 2011 / Revised May 24, 2011Project supported by the National Natural Science Foundation of China (No. 10825520) and theInnovation Program of Shanghai Municipal Education Commission (No. 11YZ20)Corresponding author Hai-ping FANG, Ph. D., E-mail: fanghaiping@sinap.ac.cn中国煤化工MHCNMH G1102Wen-peng QI, Yu song TU, Rong zheng WAN, and Hai-ping FANGcan be employed to study the coupling between the translational momentum and the rota-tional momentum using a generalized Navier- Stokes equation'21. Specifically, in the narrowchannels of appropriate radi, the water molecules form a single-file chainl12,22, and the electricdipole orientations are nearly aligned with the channel axis. Taking advantage of this singlefile structure, Wan et al.(23] found that the water molecules flowed through the nanochannelspontaneously in the dipole directions of the quasi one-dimensional (single-file) chain. Inspiredby biological channels, Gong et al.24] found that a charge distribution resulted in a unidirec-tional transportation of water molecules. In that system, the dipole orientations of the watermolecules inside the carbon nanotube were infuenced by the charge distribution. However, themechanism behind the fuxes of the water molecules across the nanochannels associated withthe particular dipole orientations has not been studied in detail.In this article, we study the events of water molecules entering and exiting from the narrownanotube by molecular dynamics simulations. It is found that a water molecule near the nan-otube end tends to be expelled from the nanotube if its dipole moment is almostto the nanotube axis. There are two structures of the perpendicular water molecule dependingon the dipole direction of the adjacent water molecule in the nanochannel. Although the proba-bilities of these structures are quite small, their contributions to the net Aux are approximatelyequal to the contributions from the predominant structures. These particular structures resultin the decrement in the Lennard- Jones (LJ) attraction between the water molecule and thenanotube. The LJ attraction compensates the energy lost caused by the water molecules enter-ing the nanotube. If the electric dipole of the adjacent water molecule points outward from thenanochannel, the decrement in the LJ attraction is 10.0 kJ/mol. If the dipole of the adjacentwater points inward, the decrement is only 4.0 kJ/mol These decrements in the LJ attractionresult in the easy expulsion of the water molecules near the nanotube end. We find that thehydrogen bond extension between the two water molecules in the frst structure is responsiblefor the large potential decrement. The present findings give a fundamental description of thewater molecules exiting from the carbon nanotube and show the possiblity of controlling thewater fow by regulating the dipole direction of the water molecules in the single fle chain thatis very important in applications, such 8s the desalination of seawater and the design of novelnano devices.2 System and simulation methodsAn uncapped armchair (6, 6) single-walled carbon nanotube (SWNT) with the length of1.34 nm and the diameter of 0.81 nm is embedded in a water container of the volume of4.50 nmx4.50 nmx4.50 nm. The simulation settings include maintaining the container at theconstant pressure (100 kPa) and temperature (300 K) using the Parrinello- Rahman methodl25]for the pressure coupling and the Nose Hoover!26 271 method for the temperature coupling withGromacs 4.0[28] and the TIP3P|29] model for water. A time step of 1 fs is used, and the dataare collected every 0.25 ps. In the simulations, the carbon atoms are modeled as the unchargedLJ particles with a cross section ofδcc = 0.340 nm, δco = 0.333 nmand a potential well depth[2| ofEco = 0.36 kJ/mol, eco = 0.48 kJ/mol.The carbon- carbon bond length of 0.140 nm and the bond angle of 120° are maintained by theharmonic potentials with the linear and angular spring constant set at 3.940x 109 kJ.mol 1.nm'中国煤化工MYHCNMH G.Orientations of special water dipoles that accelerate water molecules1103and 5.270x102 kJ.mol-1 .(°)-2, respectively. In addition, a weak dihedral angle potential isapplied to the bonded carbon atoms(2]. The simulations are performed for 300 ns with the last295 ns sampled for the analysis.In the following discussion, the water molecules closest to the ends are numbered as 1, andthe adjacent molecules inside the nanotube are numbered as 2 (see Fig. 1(a)). To quantitativelydescribe the water dipole orientation in the SWNT, an angle φi between the ith water moleculeand a unit vector along the central axis of the SWNT is calculated as ,-=-(品),where众is a unit vector aligned along the SWNT central axis and pointing outward theSWNT17I. Pi is the dipole of the ith water molecule (see Fig. 1(b)). The state .of the dipoledirection of a water molecule, Di, is defined as0°≤φ; < 65°,D;=-1， 115°<φ;≤180°,0，65°≤φi≤115°.In Fig. 1(a), the sticks (green) represent the SWNT. Some carbon atoms of the SWNT arenot shown or are drawn to be transparent for ease of demonstration. The water moleculesare shown with oxygen in red (dark balls) and hydrogen in light gray (light balls). The watermolecules outside the nanotubes are omitted in the figure. In Fig. 1(b), the dashed vertical linemarks the end of the SWNT, the two solid horizontal lines represent the wall of the SWNT,and the horizontal dot dashed line indicates the SWNT central axis. In total, we have fourstates shown in Fig. 2._S.........../Lp(2) Schematic(b) Typical structureFig. 1 Schematic of SWNT and serial numbers of water molecules and typical structure of two watermolecules near end of SWNTin1。(a)D\=Dz=1(b) D1=0 andDr=1(c)D.=D2=-1(d) D.=0 andD2=-1Fig. 2 Schematic diagram of water molecule structures in four states of diferent D1 and D2.中国煤化工MYHCNMH G.1104Wen-peng QI, Yu-song TU, Rong zheng WAN, and Hai- ping FANGThe dipole directions of the inside water molecules near the SWNT ends are recorded inevery frame. The numbers of the water molecules entering and exiting from the SWNT aredetermined by comparing the indices of the water molecules in the SWNT from two successiveframes.3 Results and discussionTable 1 shows the probability densities (p) of diferent water dipole orientation states, theaverage numbers of the water molecules entering (Nin) and exiting (Nout) from the nanotubeevery nanosecond in each dipole orientation state, the fux (F), and the net number of thewater molecules flowing through the nanotube end contributed by each state (Fp). The flux isdefined by the difference of the the numbers of the water molecules entering and exiting fromthe SWNT ends per nanosecond (F = Nout - Nin).There are four dipole orientation states in our simulation, which are numbered as I, II, II,and IV corresponding to the statesD1=D2=1; D1=0， D2=1; D1=D2=-1; D1=0， D2=-1,respectively (see Fig. 2). The probability of the state I, ρI, is 0.490. For the other states, pII is0.009, prul is 0.497, and ρTv is 0.004. The probabilities of the states II and IV are quite smallcompared with the predominant states I and II. However, the fuxes of the states II and IV, .denoted by Fir and Frv, have much larger values of 1 001.4ns- 1 and 1 395.7 ns-1 , respectively(here, the positive value of the fux indicates the water molecules exiting from the nanotube).Their values are much larger than those of the fuxes of the states Iand II(Fr= -12.6 ns~ 1 andFi= -19 ns~ 1). Consequently, the net numbers of the water molecules fowing through thenanotube end contributed by the states II and IV (FIp11 = 9.0ns-1 and Frvprv = 5.6 ns-1)per nanosecond are comparable切o the numbers contributed by the states I and III (FpI =-6.2 ns-1 and FIrp1Ir = -9.4 ns- l). There are some other possible water dipole orientationstates. However, they rarely occur for the water in nanotubes, and they have very smallcontributions to the net fux across the nanotube end (see Table A1 in Appendix A). .We also compute the energy values and the relative positions of the water molecules in theSWNT to understand the physics meaning behind the different ratios between Nout and Ninin these four states. The results are shown in Table 2. Here, PlJ is the average LJ potentialbetween the 1st water molecule and the SWNT, Eww is the average electric potential energybetween the 1st water molecule and the 2nd water molecule, d is the average distance of thewater molecule to the main SWNT axis (see Fig. 1(b)), Lh is the average hydrogen bond lengthbetween the 1st and the 2nd water molecules (see Fig. 1(b)), and S is the average distancebetween the 1st water molecule and the nearest end of the SWNT (see Fig. 1(b)).Table 1 Probability densities (p) of diferent water dipole orientation states, average numbers ofwater molecules entering (Nin) and exiting (Nout) from nanotube every nanosecond in eachdipole orientation state, fuxes (F, F= Nout - Nin) of diferent states, and net number ofwater molecules flowing through the nanotube end (F p) contributed by each stateD2Nout/(ns-1)Nn/(n-:s-1)Fp0.488487.8500.6-12.8 ..20.0091 178.4172.01006.4.00.495503.1-19.0-9.400.0041 550.8169.51381.3.6中国煤化]fYHCNMH G.Orientations of special water dipoles that accelerate watermolecules1105In the predominant states I and II, there are negligible diferences in Pu, Eww, d, andLn. Compared with the state I, Eww increases by about 4.0 kJ/mol, and Lh is extended byabout 0.007 nm in the state II. These variations stem from the hydrogen atoms of the 1st watermolecule approaching the hydrogen atoms of the 2nd water molecule shown in Figs. 2(a) and2(b). As a result of the extended Lh, the two water molecules move away from the SWNT axis.Compared with the state I, the distance between the 1st water molecule to the SWNT axisincreases by about 0.002 nm, and the approach of the water molecules to the SWNT inducesthe increment of PrJ by about 10.0 kJ/mol in the state II.Table 2 LJ potential between 1st water molecule and SWNT (Pus), electric potential energy between1st water molecule and 2nd water molecule (Eww), distance between 1st water molecule toSWNT axis (d), length of hydrogen bond between 1st and 2nd water moleculesh), anddistance from 1st water molecule to nearest ends of SWNT (S) for different water dipolestatesD)2Eww/(kJ mol-1)Ln/nmd/nmPus/(kJ.mol-1)S/nm1-27.4 .0.282-36.70.139-23.60.2890.065-26..0.1030.2810.062-34.60.1330- -27.9-30.50.089The same comparison between the state II and the state IV shows that there is no diferencein Eww and Ln in the two states except for a small increment in d of about 0.001 nm in thestate IV. The small increment comes from the diferent orientations of the hydrogen bond inthe two states shown in Figs. 2(c) and 2(d). As a result, P.s increases by about 4.0 kJ/mol inthe state IV compared with the state II.When the water molecules enter the SWNT, nearly two bydrogen bonds are lost. The LJattraction between the water molecules and the SWNT compensates for a part of the energyloss. Hummer et al.2 found that the water molecules were expelled from the SWNT by reducing the LJ potential depth. The increment in the potential P.s in the states II and IV canresult in a preference for the water molecules exiting ftom the SWNT. The water moleculesclose to the nanotube ends (i.e., with the small S) are easier to exit from the nanotube. Forthis reason, we find that the fux of the state IV is larger than the fux of the state II.The hydrogen bonds existing in the successive water molecules in the single fle chain are al-most aligned along the SWNT axis. As a consequence, the molecular dipoles are almost alignedwith this axis. It is convenient for the water molecules to rotate around these hydrogen bonds,and it is dificult to rotate their dipoles perpendicular to the SWNT axis. The precondition forD1 approaching the zero state is that the 1st water molecule needs to form a hydrogen bond as8 donor (contributing to its own hydrogen atoms) with a water molecule outside the SWNT.However, the water molecule has a triangle configuration (CHOH = 109.5°), and D1 = 0 bringsthe extension of Lh in the state II (D1 = 0 and D2 = 1) and diferent orientations of Lh in thestate IV (D1 = 0 and D2 = - -1), which results in different potential variations in these twostates.We remark that Fig.2 is only a schematic of physical situations that are very complex inreality. Here, it provides an aid in understanding the critical diferences, i.e., the variations ofLh, in the two dipole states.中国煤化工MHCNMH G1106Wen- peng QI, Yu-song TU, Rong zheng WAN, and Hai-ping FANG4 ConclusionsIn summary, the water molecule closest to the SWNT end tends to exit from the SWNTwhen its dipole is almost perpendicular to the SWNT axis. The reduction in the LJ attractionbetween the water molecules and the nanotube results in a preferential expulsion of these watermolecules from the SWNT. Furthermore, there are two structures of the perpendicular watermolecule depending on the dipole direction of the adjacent water molecule in the SWNT. In thefirst structure, the dipole of the adjacent water molecule points outward from the SWNT end,and the consequent extension of the hydrogen bond between the two water molecules forcesthe water moleculestoward the wall of the SWNT away from the equilibrium position of theLJ potential. In the second structure, the dipole points inward, and the reorientation of thehydrogen bond between the pair of water molecules forces the water molecules toward the wallof the SWNT away from the equilibrium position of the LJ potential. As the energy of the LJinteraction increases, the water molecules are easy to be expelled from the nanotube in thesetwo structures. We find that the first structure brings about the larger offset of the watermolecule toward the SWNT axis and a bigger decrement in the LJ attraction than the secondstate. The probabilities of these particular water dipole orientations are very small. However,their contributions to the net fux across the nanotube are approximately equal to those of thepredominant states.These particular water dipole orientations inside the SWNT have been found in the uni-directional transport of the water molecule by Gong et al.l24. These dipole orientations canhelp to control the transport of water molecules. Special water dipole orientations can help tomanipulate the biomolecules in nanotubes(30] and form the hydrophobic water monolayerl31].Our findings give a fundamental description of the water molecules exiting from the SWNTand a possible means to control the water flow by regulating the dipole direction of the watermolecules that have been formed into a single-file chain.Acknowledgements We would like to thank Dr. Hang-jun LU and Dr. Guang hong ZUO for theirsuggestions.References[1] Pan, z. W., Xie, s. S., Chang, B. H, Wang, C. Y., Lu, L., Liu, W., Zhou, M. Y., and Li, W. z.Very long carbon nanotubes. nature, 394(6694), 631 -632 (1998)[2] Hummer, G.,. Rasaiah, J. C, and Noworyta, J. P. Water conduction through the hydrophobicchannel of a carbon nanotube. nature, 414(6860), 188-190 (2001)[3] Cambre, S., Schoeters, B, Luyckx, Ss, Goovaerts, E, and Wenseleers, W. Experimental obser-vation of single fle water flling of thin single-wall carbon nanotubes down to chiral index (5,3).Phys. 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Lett, 103(13), 4 (2009)中国煤化工MHCNMH G1108Wen-peng QI, Yu-song TU, Rong zheng WAN, and Hai-ping FANGAppendix ATable A1Probability densities (p) of different water dipole orientation states, average numbers of watermolecules exiting (Nout) from and entering (Nin) nanotube every nanosecond in each dipole ori-entation state, fuxes (F, F= Nout一Nin) of different states, and net number of water moleculesflowing through the nanotube end (Fp) contributed by each stateDNoutNinFρ0.4876487.8500.6-12.8-6.210.0019604.8437.1167.70.30000.00.00.0 .0.00931 178.4172.81006.40.0003892.7192.1700.60.20.00401 550.8169.51381.30.0002576.457.6118.7-100.002055.9135.60.494803.1522.1- 19.0-9.4中国煤化工MYHCNMHG .