Ferroelectric Ordering in Ice Nanotubes Confined in Carbon

This mechanism is fundamentally different from the conventional one seen in ... In addition, it is found that vacancies in the ice nanotubes can induc...
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NANO LETTERS

Ferroelectric Ordering in Ice Nanotubes Confined in Carbon Nanotubes

2008 Vol. 8, No. 9 2607-2612

Chuanfu Luo,† Wei Fa,† Jian Zhou,† Jinming Dong,*,† and Xiao Cheng Zeng*,‡ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniVersity, Nanjing, 210093, China, Department of Chemistry and Nebraska Center for Materials and Nanoscience, UniVersity of Nebraska, Lincoln, Nebraska 68588 Received October 13, 2007; Revised Manuscript Received May 27, 2008

ABSTRACT The ice nanotubes with odd number of side faces formed inside carbon nanotubes (CNTs) are found to exhibit spontaneous electric polarizations along their tube axes by means of molecular dynamics simulations. The physical mechanism underlying the quasi-one-dimensional (Q1D) ferroelectricity is an interplay between the Q1D geometrical confinement of CNTs and the distinct orientational ordering of the hydrogen bonds dictated by the “ice rule”. This mechanism is fundamentally different from the conventional one seen in three-dimensional ferroelectric (FE) materials or in two-dimensional FE ice films. In addition, it is found that vacancies in the ice nanotubes can induce a net polarization normal to the tube axis.

Whether the bulk ice can or can not be a ferroelectric (FE) material in which each (dipolar) water molecule assumes a preferred alignment has been a fascinating topic for many years.1-4 Bernal and Fowler were the first to suggest that a proton-ordered ice structure, a form of FE ice, could be favored over proton-disordered ice according to the third law of thermodynamics.1 However, as Pauling correctly pointed out, there exists a huge number of water molecule arrangements, proportional to (1.5)N with N as the number of molecules. All of these arrangements are compatible with the “Bernal-Fowler” ice rules and can be adopted by the bulk ice, giving rise to a nonzero residual entropy.2 Nevertheless, a few experiments have shown evidence of net FE polarizations in ice films, because of the interaction between the ice layer and the underlying substrate, although only a tiny fraction (0.2%) of the molecules are aligned.5,6 Another possible approach to produce FE ice, e.g., ice XI, is by doping the hexagonal ice Ih with a few hydroxide ions to force internal dipole alignment and produce the ice XI. However, the degree of dipole alignment in the ice XI has not been unambiguously determined.7-9 Here, we propose a new route to achieve a FE ice, which is through the formation of single-walled ice nanotube (Ice-NT) inside a single-walled carbon nanotube (SWCNT). It is well-known that confinement of matter in the nanometer scale can induce new phase transitions not seen in the bulk.10,11 For example, water confined in quasi-one* Corresponding author. E-mail: [email protected] (J.D.) and xczeng@ phase2.unl.edu (X.C.Z.). † Nanjing University. ‡ University of Nebraska. 10.1021/nl072642r CCC: $40.75 Published on Web 08/07/2008

 2008 American Chemical Society

dimensional (Q1D) SWCNTs has attracted much interest because of its relevance to biology, geology, and materials science.12-21 Koga et al. revealed that water inside the SWCNTs with the diameter of 1.1-1.4 nm can freeze into n-gonal (n ) 4-7) Ice-NTs composed of a rolled square ice sheet.12-14 Their theoretical prediction had been later confirmed by neutron scattering and infrared spectroscopy measurements.22-24 It turns out that in nanoscale environment the behavior of confined water can be highly nontrivial as it can self-assemble into tubular structures rather than freezing into the bulk ice. Hence, water confined in SWCNTs offers great opportunity for finding new ice phases not seen in the bulk.25 Investigation of the size and dimensional effect on the ferroelectricity is another hot topic because of its fundamental importance and potential applications in nanoelectronics and optical devices.26-28 It is generally believed that there exists a critical size beyond which the material’s ferroelectricity will vanish because of the depolarization effect. The latter renders fabrication of nanoscale or Q1D FE materials very difficult. However, the Ice-NTs inside SWCNTs are likely to possess ferroelectricity because of their unique structure dictated by the “ice rule”, in which all water dipoles can align in a preferred direction. In this paper, we report molecular dynamics (MD) simulation evidence that an Ice-NT with odd number of side faces can exhibit spontaneous electric polarization along its tube axis. The microscopic mechanism underlying the spontaneous polarization is the interplay between the requirement of satisfying the ice rule for the hydrogen bonds of

Figure 1. Relaxed structures of Ice-NTs inside SWCNTs. The blue and red balls denote oxygen and hydrogen atoms, respectively. The 5and 7-gonal Ice-NTs have spontaneous electric polarizations along their tube axes, which are illustrated by b Pz and arrows.

water molecules and the Q1D confinement by the SWCNTs. In addition, influence of defect on the Ice-NTs’ polarization, particularly the polarization normal to the tube axis, is studied. The water-water interaction is described by the TIP4P model,29 in which the intermolecular potential energy is given by the short-range Lennard-Jones potential between the interaction sites and the long-range Coulombic potential treated by Ewald summation. The interactions between water molecules and SWCNTs are described by the Lennard-Jones potential and treated by the continuum model,30-32 in which the parameters were obtained from those of the TIP4P model and multiwalled carbon nanotubes based on Lorentz-Berthlot combining rules.33 A modified TINKER package34 was used for the MD simulations in which the velocity-Verlet algorithm for integration of equations of motion and the Berendsen thermostat algorithm were used. The time step was set to be 0.5 fs. The simulation was under constant volume and temperature (T) condition. The periodic boundary condition was applied along the axial direction with a fixed tube length (109.2 Å). The polarizations were calculated by summation of dipole moments of all water molecules. We chose four different zigzag SWCNTs, (14,0), (15,0), (16,0), and (17,0).36 Their diameters are 10.96, 11.74, 12.53, and 13.31 Å, respectively. During MD simulations, the temperature was lowered stepwise, from 450 to 100 K, and then raised up with the same T step. The MD simulation time for each given temperature was 2 or 20 ns near the phase transition. The total number of water molecules in the simulation box was 40 × n, where n ) 4, 5, 6, and 7, associated with the four chosen SWCNTs. Our simulation shows that Ice-NTs are formed at low temperatures, in which every layer is a n-gonal water ring 2608

with n ) 4-7 corresponding to the four SWCNTs, respectively. The relaxed structures and the polarization directions of certain Ice-NTs are shown in Figure 1. These structures are consistent with those obtained by Koga et al. as well as with those experimental results combined with MD simulations.12-15,22-24 As illustrated in Figure 1, the n-gonal IceNTs have n side faces. In particular, we found that the odd number-gonal (5- and 7-gonal) Ice-NTs have notable net polarizations along their axes, which are 0.351 and 0.347 eÅ per layer of water molecules, respectively, while the even number-gonal (4- and 6-gonal) ones are antiferroelectric (AFE). We also used the ab initio SIESTA35 program to calculate the polarizations of 4- and 5-gonal IceNTs, which are 0 and 0.464 eÅ per layer, respectively, confirming that the odd number-gonal Ice-NT is FE while the even number-gonal one is AFE. As is well-known, in order to identify a material to be ferroelectric, one has to show that the material can switch its polarization under an applied electric field in addition to the net polarization. So, we have also made a molecular dynamics simulation on the problem for the 〈5,0〉 Ice-NT with a spontaneous polarization b Pz along its tube axis as shown in Figure 1. After an opposite electric field is applied along the -z direction, it is found that its polarization can indeed be reversed under the applied external electric field in a period of about 1 ns, confirming the 〈5,0〉 Ice-NT to be FE. We further considered a bundle of the two FE 5- and 7-gonal Ice-NTs inside SWCNTs, arranged in a dense packed hexagonal 2D lattice with an interspace distance of 3.4 Å. The polarized rates are found to be 0.15 C m-2 and 0.12 C m-2, respectively, compared with 0.26 C m-2 for the FE bulk BaTiO3. Why can the odd number-gonal Ice-NT be FE? What is the microscopic mechanism of the FE phase transition in Nano Lett., Vol. 8, No. 9, 2008

Figure 2. Diffusion coefficient (D), potential energy per water molecule (Epot), which excluded the water-SWCNT interaction energy, and polarization per layer (Pz) versus temperature. The left and right panels correspond to the 5- and 7-gonal Ice-NTs, respectively. The red filled and blue unfilled circles indicate the heating and cooling processes, respectively. The statistic standard errors are shown by the error bars, and lines are to guide the eyes.

the Ice-NTs? In Figure 2, we show the diffusion coefficient (D), potential energy (Epot), and spontaneous electric polarbz|) versus T for the two ization along the tube axis (Pz ) |P FE Ice-NTs. The decrease of D to zero and a sudden drop of Epot at a temperature (Tc) clearly indicate that there exists a liquid-solid phase transition for the water inside SWCNTs. It can be seen from Figure 2 that the polarization Pz changes abruptly at the same Tc, showing a strong correlation between the FE-paraelectric and the solid-liquid phase transition for the Ice-NTs. Here, the FE-paraelectric transition is possibly a first-order transition; the ferroelectricity stems from the unique Q1D structure of Ice-NTs as well as the dipole orientations of water molecules. This new form of Q1D FE material can avoid the critical-size limitation of conventional low-dimensional FE materials since the microscopic mechanism for its ferroelectricity is fundamentally different from the soft-mode mechanism manifested in the traditional FE bulk materials, such as BaTiO3. For instance, unlike the conventional FE oxide, there would be no limitation of critical thickness for the FE ice tubes, both along the tube axis and along its normal. The underlying mechanism is mainly because (i) the water molecules entail their intrinsic dipoles and form a specific hydrogen bond network, imposed by the “ice rule” and (ii) of the nearly rigid confinement due to the SWCNTs, which should not be changed even at the nanometer scale. Our first-principles and MD simulations show that the finite tube length has little effect on the ice tube FE order. For example, it is found that a short fourlayer 〈5, 0〉 ice tube (actually, a small tube-like ice cluster) Nano Lett., Vol. 8, No. 9, 2008

Figure 3. Sketch of an unrolled 2D ice sheet with square lattices, satisfying the “Bernal-Fowler-Pauling ice rule”, in which the basis bh), and the axis vector (L b) vectors (a b1 and b a2), the chiral vector (C bh ) na are shown. C b1 + ma b2 characterizes a 〈n, m〉 Ice-NT (as an example, a 〈5, 1〉 Ice-NT is shown in this figure). The blue and red circles denote oxygen and hydrogen atoms, respectively. The square hydrogen-bond network is denoted by dashed lines, and the details are shown at the center by nine water molecules. The red arrow at a site denotes the dipole moment of a water molecule. The relative orientations, perpendicular and parallel, of two nearest water molecules are shown at the right.

has a FE polarization of ∼1.4 eÅ along the tube axis. We give more detailed discussion on the physics of the ferroelectricity of Ice-NT as follows. Like SWCNTs, an Ice-NT can be viewed as rolling a 2D square ice sheet simply described by a right-angle water molecular model as illustrated in Figure 3. As such, an IceNT can also be characterized by a pair of integer numbers 〈n, m〉. In this way, the three Ice-NTs shown in Figure 1 can be denoted as 〈4, 0〉, 〈5, 0〉, and 〈7, 0〉, respectively. However, unlike SWCNTs, Ice-NTs are molecular tubular structures rather than atomic ones. The 〈n, m〉 indices have a limitation in that they can only describe the mainframe of water molecular network but not the dipole orientations of water molecules, which are crucial for the description of the electric polarization of the Ice-NTs. The dipole moment of a water molecule (p b0) is 0.45 eÅ for the TIP4P model and 0.38 eÅ in vapor experiment. By assuming the 2D ice sheet obeys the “ice rule”, every water molecule lying on a line along one basis vector (a b1 or b a2 in Figure 3) has the same projective direction of its dipole moment to the basis vector. That is to say, there exist only two types of dipole orientations for two nearest water molecules, parallel or perpendicular, as illustrated in the right panel of Figure 3. To understand why the water molecules show preferred orientations as shown in Figure 1, we use a simple model to estimate the total energy E of an Ice-NT: E ≈ EF + EP. Here, EF is the energy of the mainframe of the water network, resulting from the “ice rule”, which involves both the intermolecular hydrogen bond and the Lennard-Jones potential energies. The EP is the dipole-dipole interaction energy, which affects the orientations of water molecules and is given by 2609

EP )

1 4πε

∑ ij

pi · f p j - 3(rˆij · f p i)(rˆij · f p j)

f

|f r ij|3

(1)

where ε is the permittivity, b pi (p bj) is the dipole moment of the ith (jth) water molecule, b rij is the displacement from the ith to the jth water molecule, and rˆij is its unit vector. In fact, the EF term is much larger than EP and nearly the same for all isomorphs of Ice-NTs. Thus, the total energy difference (∆E) between different isomorphs is mainly due to EP term (∆EP). Taking a pair of nearest water molecules as an example, in the 2D square ice sheet model, assuming |a b1| ) |a b2| ) r0, a perpendicular orientation has lower energy than a parallel one by p20/4πεr30, making two nearest water molecules prefer the perpendicular orientation over the parallel one. The ∆EP value will reduce substantially if farther dipole-dipole interactions are considered, but they do not change the conclusion that the perpendicular orientation for two nearest water molecules is preferred over the parallel one. We now discuss why only the Ice-NTs with odd number of side faces possess ferroelectricity. If only the orientations of the nearest pairs of water molecules are considered, the local water network of a 〈n, 0〉 Ice-NT can be classified into four types, a-d in the order of increasing potential energies, as shown in the upper panel of Figure 4. The type a has the lowest energy but has no net polarization, showing the AFE orders along both the tube axis and its perpendicular. Type a is favored when the Ice-NT is formed. The type b is polarized along the tube axis but still showing the AFE order along the perpendicular of tube axis, although it has slightly higher energy. The potential energy differences between the four types are very small. Taking 〈4, 0〉 Ice-NT as an example, the energy per water molecule of type b is only 2.1 meV higher than that of type a. The lower panel of Figure

Figure 4. Upper panel: four types of water molecule’s orientations in one side face of a 〈n, 0〉 Ice-NT. The red arrows indicate the orientations of water molecules. The potential energies of type a-d are in an increasing order, and so the type (a) is preferred. The lower panel: unrolled 2D hydrogen-bond network of two Ice-NTs, 〈4, 0〉 and 〈5, 0〉, for which the water molecules on the most right columns are in fact identical to those on the most left ones, and so their dipole orientations are indicated by the green arrows. The b Pz represents a whole spontaneous electric polarization along the axis. 2610

4 illustrates why a 〈5, 0〉 Ice-NT is FE while a 〈4, 0〉 one is AFE. A 〈4, 0〉 Ice-NT has 4 water molecules per layer with 2 upward and 2 downward, so it has no polarization at every layer. But, a 〈5, 0〉 Ice-NT has 5 water molecules per layer with 3 upward and 2 downward and, thus, has a net polarization along its tube axis due to the extra redundant upward water molecule. All of the layers have the same net polarization along the tube axis owing to the “ice rule” plus the EP term effect. Clearly, there must remain one FE side face of type b in the odd number-gonal Ice-NT, while in an even number-gonal Ice-NT there are only the AFE side faces of type a. This analysis can certainly be extended to other Ice-NTs. We conclude that an Ice-NT with odd number of side faces has at least one redundant polarized water molecule wire along its tube axis, giving complete spontaneous electric polarization. It is worth mentioning that our MD simulations predicted many other fast-quenched Ice-NTs, showing ferroelectricity no matter what odd or even number of side faces exist in them. These isomorphs of Ice-NTs only have slightly higher energies than those shown above and are also stable. They exhibit mainly type b side faces. If we cool the system fast under an external electric field, Ice-NTs with larger polarization than those discussed above may form. In real-world experiments, the orientations of water molecules can be detected by neutron scattering, and the ferroelectricity can be tested by second-order nonlinear optical coefficients. As shown above, regardless of the number of side faces, the perfect Ice-NTs display no FE polarization normal to the tube axis due to the antiferroelectric (AFE) ordering in this direction. It is interesting to see whether a defected IceNT would display FE polarization normal to the tube axis. As an example, we examined the influence of vacancies on the polarization of the 〈4, 0〉 and 〈5, 0〉 Ice-NTs at a vacancy density of one water molecule removed per four layers. The MD simulations show that the FE polarization normal to the tube axis is indeed induced by the vacancies for Ice-NTs with either an even or odd number of side faces (see Figure 5). This result provides additional evidence that there is no critical thickness for the FE Ice-NT along the direction of confinement, that is, the normal of tube axis. In the MD simulations, the influence of various vacancy distributions on the ice tube surface is included. The simulation results are given in Table 1 for two given types of vacancy distributions, named as type I and II. In type I, all of the vacancies are located periodically (every four layers) on a linear chain along ice tube axis. In type II, the vacancies are allowed to be randomly distributed on the entire ice tube surface. Clearly, as seen from Table 1, the vacancies not only induce the FE polarization normal to the tube axes in both defected 〈4, 0〉 and 〈5, 0〉 Ice-NTs, but also affect the FE polarization along the tube axes. For example, a FE polarization of 0.555 eÅ per four layers, normal to the tube axis, arises in the type I defected 〈4, 0〉 Ice-NT. More importantly, a FE polarization of 0.313 eÅ per four layers along the tube axis is also induced by the vacancies, which would be absent in a perfect 〈4, 0〉 Ice-NT with even number of side faces. For the defected 〈5, 0〉 Ice-NT, in addition to Nano Lett., Vol. 8, No. 9, 2008

ferroelectricity along their tube axes. This suggests a new route to produce FE ice. The underlying FE mechanism and behavior of phase transition differ fundamentally from traditional FE bulk materials, such as perovskite oxides. It is possible that similar type of FE mechanism exists in other nanoscale porous materials. It is also found that the vacancies can induce a net polarization normal to tube axis in the Ice NTs with either even or odd number of side faces. We finally note that the FE Ice-NTs may have potential application in fields such as highly sensitive sensors, nanoscale electric and optoelectric devices, and cell biology.

Figure 5. Schematic view of the defected 〈4, 0〉 and 〈5, 0〉 IceNTs, showing only a four-layer segment. The blue and red balls denote oxygen and hydrogen atoms, respectively. For clarity, the vacancy position is still occupied by a “phantom water molecule” (in gray color and highlighted by circle).

Table 1. Influence of Two Types of Vacancies on the Ferroelectric Polarizations of the 〈4, 0〉 and 〈5, 0〉

Ice-NTsa

〈4, 0〉 defected Ice-NT

Pjxy

〈5, 0〉 Pjz

Pjxy

Pjz

type I 0.555 0.313 0.573(0.575) 1.828(1.083) typeII 0.265 0.158 0.263 1.325 a Here, type I represents a defected Ice-NT, in which all of the vacancies are located periodically (every four layers) on a linear chain along the tube axis. Type II allows the vacancies in type I to be randomly distributed on j z and P j xy (in unit of eÅ) denote the polarization the entire ice tube surface. P per four layers along and normal to the tube axis, respectively. The data listed for the type II defected Ice-NTs are evaluated by averaging over 20 random configurations. Since the 〈5, 0〉 Ice-NT contains an FE side face of type (b), its type I results should be different when all of the vacancies are located on an AFE side face of type (a) from those on an FE side face of type (b). The results are given by the numbers outside and inside the parentheses, respectively.

the induced FE polarizations normal to the tube axis, the dipole moment along its tube axis is increased either, except that most vacancies are located on the side face b shown in Figure 4. Therefore, we can conclude that the FE polarization of the Ice-NTs with either an even or odd number of side faces can be induced by the presence of vacancies. Finally, we note that the helical Ice-NTs can also arise in the MD simulation when a faster cooling rate is used, even though the helical Ice-NTs have slightly higher energy. We expect that the helical Ice-NTs with an odd number of side faces are also ferroelectric along the tube axes. For example, we have performed a MD simulation of a 16 layer ice tube confined to a (15, 0) SWCNT, from which a helical Ice-NT with 5 spiral chains is obtained when the system is cooled from 300 to 150 K at a rate of 10 K/ns. The helical 〈5, 0〉 Ice-NT can still maintain its helical structure for additional 1 ns MD simulation, as shown in the supporting materials. The helical Ice-NT exhibits a polarization about 0.964 eÅ per four layers along the tube axis, less than that of the nonhelical 〈5, 0〉 Ice-NT (1.404 eÅ per four layers), as well as a net polarization of about 0.1 eÅ per four layers normal to its tube axis. In summary, the single-walled Ice-NTs inside SWCNTs with an odd number of side faces are found to exhibit Nano Lett., Vol. 8, No. 9, 2008

Acknowledgment. This work was supported by the Natural Science Foundation of China under Grants 10474035 and 90503012, and also from a grant for State Key Program of China through Grants 2004CB619004 and 2006CB921803. X.C.Z. is supported by grants from the US DOE (DE-FG0204ER46164), US NSF (CHE and CMMI), the Nebraska Research Initiative, and NSFC (Grant 20628304). Supporting Information Available: An example movie M1 to demonstrate the formation of a segment of 〈5, 0〉 ice nanotube in a (15,0) single-walled carbon nanotube. The water molecules are cooled from 400 K to 200 K at the rate of 5 K per 2 ns, and then quenched to 0 K at the rate of 10 K per 100 ps. Another example movie M2 is presented to show the evolution of a 16 layer helical 〈5, 0〉 Ice-NT with 5 spiral chains, which is obtained within the (15, 0) SWCNT under a faster cooling rate from 300 to 150 K at the rate of 10 K per 1 ns. And it still can maintain the helical structure for additional 1 ns MD simulations. For well-illustrating its helical structure, only a 12 layer segment of it is given, which clearly shows the stability of the helical structure 〈5, 0〉 IceNT at 150 K. And in order to see clearly its spiral chains, we present both the side and the top view of this helical structure in Figure S1a,b, respectively, and highlight one of the spiral chains in both figures in cyan. In both movies and in Figure S1, the big blue and small red balls denote the oxygen and hydrogen atoms, respectively. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

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Nano Lett., Vol. 8, No. 9, 2008