Electrostatic gating of a nanometer water channelJingyuan Li*†, Xiaojing Gong†, Hangjun Lu†‡, Ding Li†, Haiping Fang†§, and Ruhong Zhou§¶�

*Department of Physics, Zhejiang University, Hangzhou 310027, China; †Shanghai Institute of Applied Physics, Chinese Academy of Sciences, P.O. Box800-204, Shanghai 201800, China; ‡Department of Physics, Zhejiang Normal University, 321004 Jinhua, China; ¶IBM Thomas J. Watson ResearchCenter, Yorktown Heights, NY 10598; and �Department of Chemistry, Columbia University, New York, NY 10027

Edited by Ann E. McDermott, Columbia University, New York, NY, and approved January 9, 2007 (received for review June 1, 2006)

Water permeation across a single-walled carbon nanotube (SWNT)under the influence of a mobile external charge has been studiedwith molecular dynamics simulations. This designed nanoporeshows an excellent on–off gating behavior by a single externalcharge (of value �1.0e): it is both sensitive to the available chargesignal when it is close (less than a critical distance of 0.85 Å or abouthalf the size of a water molecule) and effectively resistant tocharge noise, i.e., the effect on the flow and net flux across thechannel is found to be negligible when the charge is >0.85 Å awayfrom the wall of the nanopore. This critical distance can beestimated from the interaction balance for the water molecule inthe SWNT closest to the imposed charge with its neighboring watermolecules and with the charge. The flow and net flux decayexponentially with respect to the difference between these twointeraction energies when the charge gets closer to the wall of theSWNT and reaches a very small value once the charge crosses thewall, suggesting a dominating effect on the permeation propertiesfrom local water molecules near the external charge. These find-ings might have biological implications because membrane waterchannels share a similar single-file water chain inside thesenanoscale channels.

carbon nanotube � molecular switch � nanogate

The transportation of water molecules across nanometer waterchannels in membranes plays a key role in biological activities

(1–8). It has been recognized that the existence of the chargedresidues in these water channels greatly reduces the permeation ofprotons across the channel but maintains quite stable water flows(4, 5, 9, 10). Moreover, because charges are indispensable in bothmembrane proteins and physiological solutions inside and outsidethe cells, it is also important to understand how external chargesinfluence the water permeation.

By using molecular dynamics simulations, the importance ofthe charged residues in channel proteins such as aquaporin(AQP) and Glpf on the behavior of water molecules inside thechannel has been studied recently (9–11). It has been found thatthe charged groups in the conserved NPA and ar/R regions thatdominate the energetics of water permeation in these regions caninterrupt the hydrogen bond along the water chain and generatethe electrostatic field to exclude proton transfer (9–13). Fur-thermore, very recently, the electrostatic environment of thewater channel has been found to be able to regulate waterpermeability, using mutational analysis (14).

However, the complex structure of biological channels andprotein–water interactions often make further investigations ofthe mechanism of biological water channels very complicated. Ithas been well recognized that simple nanochannels can be usedas model systems to exploit some of the primary behavior of thebiological water channels. In 2001, Hummer et al. proposed thatsingle-walled carbon nanotubes (SWNTs) can be designed asmolecular channels for water (15–18). They showed that the freeenergy of filling the single-file water chain in the SWNT issensitive to the small changes in the nanotube–water interaction,and the flow of the hydrogen bonded water chain throughnanotubes occurs in bursts. The authors also pointed out that thewater–nanotube interaction plays a significant role along withthe hydrogen bond interaction in the water chain inside the

SWNT in determining whether the tube is filled or empty(18–20). The single-file arrangement and the concerted move-ment of water molecules through the channel, together with theliquid–vapor transition in the channel due to the modification ofthe water–channel interaction, were thought to be the majorcharacters shared by the biological channels (15, 21–23). Re-cently, Zhu and Schulten (24) assigned charges to the atoms ofSWNTs (ntNPN) to mimic the biological channel and found thatsimilar dipole orientation of water molecules as in AQP could begenerated, along with a greatly reduced mobility for the waterchain inside the SWNT. The effects of homogeneous electricfield on the water chain polarization and the filling equilibriuminside the carbon nanotube were studied by Vaitheeswaran et al.(25). Dzubiella and Hansen (26) also found that a strong electricfield generated by an ion concentration imbalance can decreasethe critical radius Rc of hydrophobic nanopore for the waterpermeation. Zimmerli et al. (27) found that an increased fillingand a geometrical rearrangement of the single-file water chaininside the tube could result from the nonuniform electric fieldgenerated by static dipole moment induced from the curvatureof the carbon nanotubes.

Despite the great effect, the dependence of the dynamics ofwater molecules inside a channel on charges is still far from beingunderstood. In this study, a SWNT with an external positivecharge is used as a prototype to study the response to theindispensable charges as well as the possible charge noise nearwater channels. Molecular dynamics, which has been used widelyfor the studies of water dynamics in SWNT, in proteins, andin-between proteins (9–13, 15, 16, 28–35), is adopted here forthis work. Unlike the previous studies, where the charge is fixedat the carbon atoms of the SWNT (24), the charge we introducedhere has multiple positions and does not have to coincide withexact atom positions (5). Interestingly, in a very recent paper,Zimmerli et al. (27) have placed charges close to carbon atomsbut not on carbon atoms to generate a static dipole moment. Inaddition to the imposed charge, hydrostatic pressure is appliedin this study between two ends of the SWNT to investigate thenet flux change due to the imposed charge. Remarkably, we findthat the nanopore is an excellent on–off gate that is botheffectively resistant to charge noises and sensitive to availablesignals. This exceptional property largely comes from the stableand strong hydrogen-bond chain inside the channel, and thecritical charge distance for gating can be uniquely determined bycomparing the interaction energy of the water molecule in thechannel closest to the imposed charge with its neighboring watermolecules and that with the imposed charge. Interestingly,in-between the fully opened and fully closed states, the flow and

Author contributions: H.F. and R.Z. designed research; J.L., X.G., H.L., and D.L. performedresearch; J.L. contributed new reagents/analytic tools; J.L., X.G., H.L., D.L., H.F., and R.Z.analyzed data; and J.L., H.F., and R.Z. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS direct submission.

Abbreviations: AQP, aquaporin; PMF, potential of mean force; SWNT, single-walled carbonnanotube.

§To whom correspondence may be addressed. E-mail: fanghaiping@sinap.ac.cn orruhongz@us.ibm.com.

© 2007 by The National Academy of Sciences of the USA

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net flux decay exponentially according to the difference betweenthose two interactions, indicating that the local properties nearthe external charge dominate the permeation of the watermolecules. Meanwhile, the pattern of the single-file water chaininside the channel changes continuously from a completelyconcerted orientation, to two alternating orientations, and fi-nally to a completely bipolar orientation, as the external chargemoves closer to the wall of the SWNT. These findings fromsimple model systems might have implications in novel molecularswitch design, as well as biological water channels on the on–offgating mechanism, because they share a similar single-file watermolecule chain and bipolar orientation (9–11, 13). We believethat this excellent property is important for biological systems toachieve accurate information transfer in an environment full ofthermal fluctuations.

Results and DiscussionThe simulation framework is shown in Fig. 1. To mimic thebiological channels in a membrane, an uncapped, single-walledcarbon nanotube (36) 13.4 Å in length and 8.1 Å in diameter wasembedded along the z direction in a graphite sheet that subdi-

vides the SWNT and space into two equal parts. To study thebehavior of the water permeation across the channel due toexternal charges on or outside the channel, a positive charge witha quantity 1.0e was set to move on the same plane of the graphite.The radial distance of the imposed charge from the carbon atomsof the nanotube is denoted by �. The system without any externalcharges, namely the control system, is also prepared for thecomparison.

When two sides of a membrane have a same hydrostaticpressure but different concentrations of an impermeable solute,an osmotic pressure difference is established, and water flowsfrom the side with high solute concentration to the other side.Following the method proposed by Zhu et al. (37), and ourprevious paper (38), an external force is applied to each watermolecule along �z direction (z axis is defined to be along the axisof the SWNT with origin at the graphite plane) to obtain apressure difference between two ends of the SWNT. Thispressure difference is something like the osmotic pressuredifference (37) and is 181 MPa between two ends of the SWNTfor an additional acceleration of 0.1 nm�ps�2 at each atom (38).

As shown in Fig. 1, we set the imposed charge at differentdistances from the wall of the SWNT in our molecular dynamicssimulation to study the influence of external charge on waterflow and net flux. For each system with a different distance, a120-ns molecular dynamics simulation is performed. The last 110ns of the simulation were collected for analysis. Initially, there isno water molecule in the nanotube. The nanotube is rapidly filledby water molecules from the surrounding reservoir (15) in eachsimulation.

To our surprise, the water screening effect on the charge is sostrong that the average flow and net flux across the channel areapproximately equal to those in the control system when thedistance � is �0.85 Å (about half the size of a water molecule),as shown in Fig. 2. Here, the flow is defined as the total numberof water molecules leaving the SWNT (entered the nanotubefrom the opposite side) per nanosecond, while the net flux is thedifference of the numbers of water molecules leaving from theupper and bottom end (again entered from the opposite end) pernanosecond. Remarkably, the critical value �c � 0.85 Å is onlya little larger than half the radius of a water molecule (�1.4 Å),and charges outside this distance will have minimal effect on thewater dynamics inside the SWNT. Note that the interaction

A

B

Fig. 1. Simulation framework. (A) Snapshot of the simulation system (sideview). The dark gray cycles are the carbon atoms of the nanotube and thegraphite. The light gray point is the imposed charge, and the water moleculesare represented by lines. (B) Top view of the model channel system. There is nophysical hole in between the SWNT and the graphite plate. The gap betweenthe graphite plane and the SWNT is too small for a water molecule topenetrate.

Fig. 2. The averaged water flow (black) and net flux (gray) through thechannel with respect to �, together with those for the control systems (dashlines). � is the radial distance of the imposed charge to the centerline minus theradius of the SWNT. The flow is defined as the total number of watermolecules leaving the SWNT and entering the nanotube from the other sideper nanosecond, whereas the net flux is the difference of the numbers ofwater molecules leaving from the upper and bottom end, respectively, thatentered the nanotube from the other end, per nanosecond.

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energy of the water molecules in the SWNT with the imposedeffective charge is quite large, which reaches a value of about�20 kJ/mol. Thus, the permeation of the water moleculesconfined in the nanochannel can effectively resist to externalcharge noises when they are not very close. When � decreases towithin the critical distance, as shown in Fig. 2, the average flowand net flux decrease monotonically and sharply to about � �0.25 Å. At � � 0.25 Å, both the average flow and net flux are verysmall with values of 1.1 ns�1 and 0.8 ns�1. The average flow andnet flux further decrease slowly down to 0.7 ns�1 and 0.6 ns�1,respectively, at � � 0, showing that the channel is almost closed,consistent with the previous findings (24). We note that thedisplacement of the imposed charge for the transition from thealmost fully opened state (� � 0.85 Å) to a nearly closed state(� � 0) is only �0.85 Å. Thus, the single-file water chain in thenanochannel is also sensitive to the effective charge signal.

To understand the mechanism behind this excellent on–offgating with charge signals, we calculate the interaction energiesof the water molecule at position z inside the SWNT (total aboutfive such water molecules) with its neighbor water molecules,denoted by PWW, and the electrostatic potential with the imposedcharge, PWC. The results are shown in Fig. 3 A and B. As �decreases, the absolute value of PWC increases. It is interestingto find that, in the middle of the SWNT, PWC forms a valleywithin the region, which faces the position of the imposed charge,with a range of about one-fifth of the length of the SWNT.Consider that the average number of water molecules inside thechannel is 5.0 � 0.1, which is quite stable for different positions

of the imposed charge in this article, the z range of the valleycorresponds to about one water molecule facing to the externalcharge. For easy discussion, we denote the region with z coor-dinate ranging from �1.34 Å to 1.34 Å, which is about one-fifththe length of the channel, by the central-region, and the watermolecule in this region by the central-water-molecule hereafter.In the following we will find that the main properties of the flowand net flux, including the value of the critical value �c and thedecreasing of the flow and net flux, can be dominatinglydetermined by the hydrogen bonds and the dipole orientation ofthe water molecule facing to the imposed charge. PWW alsoweakens as � decreases.

Fig. 3C plots PWCC and PWW

C , the value of PWC and PWW/2,respectively, as a function of � at z � 0, where the imposed chargeis directly faced. PWW

C equals to the interaction energy of a watermolecule at z � 0 with either side of its neighboring watermolecules due to the symmetry. It is clear that PWW

C is strongerthan PWC

C when � is large (larger than �0.8 Å) and weaker thanPWC

C when � is small. Interestingly, PWWC � PWC

C at � � �c. Thetransition point can be determined from the competition be-tween PWW

C and PWCC . It is clear that the stronger the hydrogen

bond between the water molecules, the larger the value of PWWC ,

and correspondingly, the smaller the value of �c. The small valueof �c means that water molecules in the nanochannel caneffectively shield the external charge noise, thanks to the excep-tional property of water with strong hydrogen bond betweenmolecules.

A B

C D

Fig. 3. Water–charge and water–water interactions. (A and B) The interaction energies of a water molecule at z with the imposed charge, PWC (A), and withthe neighbored water molecules, PWW (B), for different radial distance �. (C) Values of PWC and PWW/2 at z � 0, denoted by PWC

C and PWWC , with respect to �. (D)

Decreasing of the average value of flow and the net flux with respect of PWWC � PWC

C . Exponential laws can fit the data very well in the interval of 0.25 Å � � �

0.75 Å.

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In the interval of 0.25 Å � � � 0.75 Å, which is below thecritical value �c, both the average flow and net flux can be fit toan exponential function with respect to (PWW

C � PWCC ) very well,

as shown in Fig. 3D.

Flow � f low0 � exp(�(PWWC � PWC

C )��f low)

NetFlux � f lux0 � exp(�(PWWC � PWC

C )��f lux),

where flow0 � 18.2 ns�1 and flux0 � 10.3 ns�1, respectively,slightly larger than the values of 16.2 ns�1 and 9.2 ns�1 for thecontrol system. �f low � �f lux � 14.7 kJ/mol, implying a similar rulegoverning the behavior of the flow and net flux. Importantly,both the critical value and the exponential laws clearly show thatthe flow and net flux in this � interval are mainly determinedlocally by the competition of the interactions that the watermolecule in the SWNT closest to the charge experiences with itsneighboring water molecules and with the external charge.

It has been widely recognized that the positive residues lying inthe central-region of the AQPs water channels results in bipolarwater orientations (4, 9, 10). The hydrogen bond chain was usuallyinterrupted by the charged residues which can exclude the protonpermeation but maintain a stable water flow (9, 10, 13). The bipolarwater orientation is also found in the SWNT for small � (morediscussions below for the differences between AQPs and thecurrent nanopore). Fig. 4A displays the distribution of the averageddipole orientation of water molecules inside the nanochannel forvarious �, where �� is the average of the angle between a waterdipole and the nanotube axis (z axis), and the average is taken over

all of the water molecules inside the tube (38). For the controlsystem and the systems with a large � (e.g., � � 1 Å), the value ofcos �� falls into two ranges, �1 cos �� �0.65 and 0.65 cos�� 1, resulting from the concerted dipole orientations of all of thewater molecules inside, either upward or downward. On the otherhand, there is only a single peak at cos �� � 0 for � � 0.5 Å,indicating a majority of the bipolar orientation of water chain insidethe nanochannel (see below for further description). When 0.5 Å � 1 Å, there are three peaks in the distribution of averaged waterdipole orientation, showing that the water molecules inside adopteither a uniform orientation or bipolar orientation, alternatively. As� decreases, the peak at cos �� � 0 increases and those at cos�� � �0.85 decrease.

To further characterize the dipole orientation of the water chain,the average value of cos �, �cos �, along the SWNT channel isshown in Fig. 4B, where � is the angle between a water dipole andthe nanotube axis (z axis), and the average is taken over all of thedata from simulations. All of the curves are symmetric with respectto the center (z � 0) of the SWNT, the position in the nanochannelclosest to the external charge. Transitions can be found at theboundary of the central-region, and the smaller the value of �, thesharper the transition. It is clear that �cos � � 0 everywhere insidethe SWNT when there is no external charge, because the proba-bilities are equal for both directions, either along the z axis or theopposite, for the dipoles of all water molecules inside the SWNT.As the external charge gets closer, ��cos �� at the outer-regionincreases. Here the outer-region is defined as the other two partsbesides the central-region in the nanochannel. At � � 0.5 Å, �cos �

A B

C D

Fig. 4. Water dipole orientation inside the SWNT. (A) Distributions of the averaged dipole orientation of water molecules inside the SWNT, �, for variousdistances �. The distribution has two peaks at about cos �� � �0.85 for � � 1 Å and a single peak at cos �� � 0 for � � 0.5 Å. (B) Profile of �cos � along the SWNTchannel. (C) Examples of the average values of �, denoted by ��, in three different regions for � � 1, 0.75, and 0.5 Å: central-region (black), other regions forpositive and negative z values (green and red). (D) Probability of bipolar orientation of all water molecules inside the channel. The red line is a linear fit forprobability � �1.91 � (� � 1.0).

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� �0.85 in the outer-region, indicating that the water dipoles in theouter-region are almost parallel to the axis of the SWNT. This isconsistent with the previous results on SWNTs (24) and the AQPchannels (9, 10). To characterize how the water molecules go fromthe concerted orientation to the bipolar orientation, we haveplotted in Fig. 4C some examples of the average values of �,denoted by ��, in three different regions, i.e., the central-region andother regions with positive or negative z values, respectively. As � �1 Å, �� falls in the same regions as for all three regions, consistentwith the concerted orientation behavior. When � � 0.5 Å, ��vibrates around 90° for the central-region and have values of �30°and 150° for the other regions, showing bipolar orientation. It isinteresting to find that when � � 0.75 Å, �� oscillates between theconcerted orientation and the bipolar orientation. To obtain aquantitative description on the transition from a concerted orien-tation to a bipolar orientation as � decreases from 1 Å to 0.5 Å, wehave computed the probability of bipolar orientation. Here weassume that the system shows a bipolar orientation when all of thewater dipoles in the outer-region point away from the center of theSWNT. The probability is calculated based on data from allsimulations. The result is shown in Fig. 4D. It is interesting to findthat the probability increases linearly from 8% to 98% when� decreases from 1 Å to 0.5 Å.

In AQPs the bipolar water order stops proton permeation butnot water transport. In the current nanopore, water flow can alsobe fully stopped, if the charge signal is too close. To some extent,the current charge signal is stronger (because of its single pointcharge nature) than that in biological channels where the positivecharge is spread over several atoms in lysine or arginine residues.Nevertheless, the current results show no apparent discrepancyon the bipolar water order and the water flow; in other words,it is possible to have both the bipolar water order and watertransport at the same time. As shown in Fig. 4D, the probabilityof bipolar orientation of water molecules inside the SWNTapproaches 1.0 when � � 0.5 Å or less. Meanwhile, even at thissmall charge distance of � � 0.5 Å, the average flow and net fluxstill have considerable values of 2.6 ns�1 and 1.9 ns�1, respec-tively (16% and 21% of those of the fully opened state), whichare comparable to the measured 3.9 � 0.6 ns�1 for AQP1 (3).Thus, it is feasible for the nanopore to have the flow and net fluxcomparable to the biological channels while maintaining thebipolar water order, which is linked to the exclusion of protontransfer in biological channels. It should be noted that the chargedistribution and the structure of AQPs are much more compli-cated (several charged residues can be involved with chargesspread to many atoms), and these charges effectively exclude theproton permeation but maintain a stable water flow by inducinga bipolar water orientation (4, 9, 10). In the present study, wefocus on the model nanopore with only one external charge(�1.0e, same as one basic residue) but probably stronger localelectrostatic strength on the nearest water molecule inside theSWNT.

The potential of mean force (PMF) is often used to charac-terize the behavior of water molecules inside the channel (39,40). Fig. 5A displays the PMF curves of water molecules alongthe axis of channel. The wave-like structure of PMF retains afterthe introduction of the imposed charge, but the peak-to-peak(min-to-max) value increases as � decreases. To further study therelationship of the PMF profile with the flow and net fluxquantitatively, the height of the barrier �G (41) is calculated.It is interesting to note that, in the region of 0 Å � � � 0.75 Å,the relationship can be fit to a power law very well with factorsof �f low � �1.85 (flow � 0.9 � �G�1.85) and �f lux � �1.61(flux � 0.9 � �G�1.61), respectively. Similar power law with afactor of �2 has been observed (41). We note that the expo-nential laws for the relations of the f low and net f luxwith (PWW

C � PWCC ) shown above, with a same factor found in the

z interval of 0.25 Å � � � 0.75 Å (see Fig. 3D), whereas the

power law observed here is available in the region of 0 Å � � �0.75 Å with different factors for flow and net flux. The physicalorigin for those laws is still unclear.

ConclusionThe single-file water molecules inside a SWNT have a transition-like behavior with a critical radial distance �c � 0.85 Å (the radialdistance from the SWNT wall for the external charge) under theinfluence of an external charge. When the radial distance ofthe imposed charge to the carbon atom of the SWNT � � �c, theaverage flow and net flux of the water across the channel arealmost the same as those without any external charge. The flowand net flux decrease as � decreases. When � � 0, the flow andnet flux are very small, showing that the nanochannel is effec-tively closed. This shows that the SWNT has distinguishedproperties as an excellent nano-controllable on–off gate forwater molecules under an external charge. Explicitly, on onehand, the fully opened state can effectively resist the externalcharge noise even if the charge is quite close to the channelboundary (as long as it is �0.85 Å away). On the other hand, thechannel is sensitive to effective charge signals once the distanceof the charge is 0.85 Å, from an almost opened state to a closedstate.

The strong hydrogen bonds between the water molecule in theSWNT closest to the charge, and its neighboring water moleculesplay the critical role on this important on–off gating behavior.The critical radial distance �c can be approximately determined

A

B

Fig. 5. PMF profiles for water inside SWNTs and their relationship with theflow and wet flux. (A) PMF profiles of water molecules along the axis ofchannel in several representative systems with � � 1.5 Å (black), 1 Å (blue), 0.75Å (red), 0.5 Å (magenta), and 0 Å (green). (B) Relationships of the flow and netflux with the height of the barrier �G in PMF profiles. The black and red linesare flow � 0.9 � �G�1.85 and flux � 0.9 � �G�1.61.

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by the balance of the interaction of this water molecule with itsneighboring molecules and with the external charge. In the statesbetween fully opened and closed, the flow and net flux decayexponential according to the difference between those twointeractions. This suggests that the local properties near theimposed charge dominate the water permeation across thechannel.

The water molecules in the SWNT show the bipolar orienta-tion for a small radial distance �. As � decreases from 1 Å, whichis slightly larger than the critical distance for the flow and netflux, the probability of bipolar orientation increases linearly withrespect to the radial distance �, and the water chain flips betweentwo states, the concerted orientation state and bipolar orienta-tion state. The probability of bipolar orientation reaches �100%before the channel is closed. In addition, the height of barrier inPMF profile (peak-to-peak value) increases monotonically as �decreases. The relationship of the height of the PMF barrier withflow and net flux can be fit to a power law very well, with powerfactors of �1.85 and �1.61, respectively. This indicates thestrong water orientational preferences induced by the chargelead to a substantial free energy barrier to water chain translo-cation of several kT, if the chain translocates in a concertedfashion.

The single-file water molecules chain and the strong hydrogenbonds between water molecules in the SWNT play crucial roleon the excellent on–off gating behavior of the channel. We arereasonably confident that biological water channels share theproperties of this simple nanochannel due to similar single-filewater molecules chain and bipolar orientation with charges onthe proteins (4, 9, 10). We believe that this excellent property isimportant for biological systems to achieve accurate informationtransfer in an environment full of thermal fluctuations.

System and MethodsThe 144-carbon (6,6) nanotube was formed by folding a graphitesheet of 5 � 12 carbon rings to a cylinder and then relaxed with

interactions between carbon atoms. The carbon–carbon inter-action parameters were adopted from the previous work byBrenner (42) using the Tersoff formulism (43). Periodic bound-ary conditions were applied in all directions. The distance of theimposed charge from the central axis of the SWNT ranges from5.55 Å to 4.05 Å. For the convenience of analysis, this distanceis denoted by � � r, where � is the radial distance of the imposedcharge from the carbon atoms of the nanotube; r � 4.05 Å is theradius of the channel. Thus, 0 � 1.5 Å. � � 0 implies thatthe charge has a same distance to the centerline with the atomsof the SWNT while its position may not coincide with any atomof the nanochannel. Numerically, we find that the axial angle ofthe imposed charge does not change the result much in thisarticle. The SWNT and the graphite sheet usually will deformbecause of the external charges by altering the electronic struc-ture of the channel atoms. Such polarization and deformationhave not been accounted for in our present simulations (23).

The molecular dynamics simulations were carried out at aconstant pressure (1 bar with initial box size Lx � 5.0 nm, Ly � 5.0nm, Lz � 5.0 nm) and temperature (300 K) with GROMACS 3.2.1(www.gromacs.org). Here the TIP3P (44) water model was applied.Periodic boundary conditions were applied in all directions. Theparticle-mesh Ewald method (45) was used to treat the long-rangeelectrostatic interactions. A time step of 2 fs was used, and datawere collected every 0.5 ps. In the simulations, the carbon atomswere modeled as uncharged Lennard–Jones particles with a cross-section of �CC � 0.34 nm, �CO � 0.3275 nm, and a depth of thepotential well of �CC � 0.3612 kJ�mol�1, �CO � 0.4802 kJ�mol�1

(15). To prevent the SWNT from being swept away, the carbonatoms at the inlet and outlet were fixed in the simulations.

We gratefully acknowledge valuable discussion with Jun Hu, DavidSilverman, and Bruce Berne. This work is partially supported by the IBMBlue Gene program; by grants from the Chinese Academy of Sciences,the National Science Foundation of China, the Foundation of Ministryof Personnel, and the Shanghai Supercomputer Center of China; and byMajor State Research Development Program Grant 2006CB 933000 andNational Basic Research Program Grant 2006CB 708612.

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