Finite-Size Effect and Wall Polarization in a Carbon Nanotube Channel Deyu Lu, Yan Li, Slava V. Rotkin, † Umberto Ravaioli, and Klaus Schulten* Beckman Institute for AdVanced Science and Technology, UniVersity of Illinois at Urbana Champaign, 405 N. Mathews, Urbana, Illinois 61801 Received September 4, 2004; Revised Manuscript Received October 7, 2004 ABSTRACT The electronic structure and dielectric screening of finite-length armchair carbon nanotubes are studied in view of their technical applications. For this purpose, a self-consistent tight-binding method, which captures the periodic oscillation pattern of the finite band gap as a function of tube length, is applied. We find the parallel screening constant E | to grow nearly linearly with the length L and to show little dependence on the band gap. In contrast, the perpendicular screening constant E ⊥ is strongly related to the band gap and converges for L > 10R (radius) to its bulk value. Our description is employed to study the wall polarization in a short (6,6) nanotube filled with six water molecules, a situation that arises with technical uses of carbon nanotubes as channels. Single-walled carbon nanotubes (SWNTs) can be classified as metallic, quasi-metallic, or semiconducting, depending on how they are wrapped up from graphene layers. 1 When SWNTs are shortened, their energy levels become quantized, which makes them suitable for applications such as quantum dots and single-electron transistors. 2 It has also been proposed that the small size and stable structure make short SWNTs good candidates for artificial nanoscale channels for transport of water, 3-6 protons, 7,8 ions, 9 or polymers. 10 Recent experi- ments using X-ray diffraction 11 and neutron scattering 12 provided insight into the properties of nanotube-confined water. The observations revealed a chain of water molecules wrapped by a shell of water, all encapsulated inside SWNTs with diameter around 1.4 nm. 12 These experiments confirm an earlier prediction that water can enter the hydrophobic interior of narrow SWNTs. 3-6 From the modeling point of view, artificial SWNT channels have been studied by means of molecular dynamics (MD) simulations, focusing on both filling and transport properties. 3-6 In the previous simulations, the interaction between water and the SWNT was usually treated through a short-range van der Waals potential, and little attention was paid to the polarizable nature of the SWNT. Unlike many biological channels, SWNTs are highly polarizable due to their delocalized π-electrons, which respond strongly to external fields. A study of screening effects of infinitely long SWNTs to an external point charge impurity has revealed that metallic nanotubes can effectively screen out the long- range Coulomb potential along the axial direction, while screening effects in semiconducting tubes are weaker. 13 Neglecting the polarization of SWNTs could be misleading because the filling and transport properties of water are sensitive to the water-SWNT interaction. 3 Therefore, knowl- edge of the dielectric response of finite-size SWNTs is essential for an understanding of water/ion/polymer perme- ation and for designing efficient SWNT channels. In recent studies, 7,8 density functional theory (DFT) calculations have been carried out in MD simulations to take into account the electronic degrees of freedom. However, the finite-size effect on the dielectric response is not well characterized in these studies, and further applications are prohibited by the high computational cost. In this work, we used a self-consistent tight-binding (TB) method to study the electronic properties of finite-length armchair nanotubes and observed how the screening behavior evolves from 0D to 1D as the tube length increases. We believe that our method can be efficiently combined with MD simulations to investigate nanotube-based channels. An infinitely long armchair nanotube is metallic, but a HOMO (highest occupied molecular orbital)/LUMO (lowest unoccupied molecular orbital) gap opens in finite-length tubes. First principle results from different groups 2,14,15 agree in that the gap oscillates as a function of tube length with a period of three sections. Interestingly, the obtained gap minima are nonzero, contrary to the prediction from TB theory with only nearest neighbor interactions. In the following we show that the period of oscillation can be explained by imposing the quantum box boundary condition and that the nonzero band gap minima can be reproduced by including third-nearest-neighbor (NN) inter- actions. For armchair SWNT segments with ideal geometry, * Corresponding author. E-mail: kschulte@ks.uiuc.edu. † Present address: Department of Physics, Lehigh University, 16 Memorial Drive East, Bethlehem, PA 18015. NANO LETTERS 2004 Vol. 4, No. 12 2383-2387 10.1021/nl0485511 CCC: $27.50 © 2004 American Chemical Society Published on Web 10/26/2004