J. Phys. Chem. C 2009, 113, 8959–8963
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Carboxylated Carbon Nanotubes under External Electrical Field: An Ab Initio Investigation Leandro B. da Silva,† Solange B. Fagan,*,† and R. Mota‡,§ A´rea de Cieˆncias Naturais e Tecnolo´gicas, Centro UniVersita´rio Franciscano, CEP 97010-032, Santa Maria, RS, Brazil, Departamento de Fı´sica, UniVersidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil, and International Center for Condensed Matter Physics, UniVersidade de Brası´lia, 70919-970, Brası´lia, DF, Brazil ReceiVed: December 10, 2008; ReVised Manuscript ReceiVed: March 27, 2009
Carboxylated semiconductor and metallic carbon nanotubes under transverse electrical fields are investigated through density functional theory based on first-principles calculations. The external field polarizes the system, resulting in an induced electric dipole moment toward the incident field with the modulus directly dependent on the field strength. The structural and electronic properties of the resulting system due to the orbital hybridization between the nanotube and COOH states are shown to be affected by the applied field. These results open new perspectives for different potential uses, such as to enhance the capacity of the composite to bind and characterize other substances, especially polar molecules, and as mechanisms to monitor the bound substances or control electron injection or detection, by varying the external field through a controlled application. Introduction Single-walled carbon nanotubes (SWNTs) have aroused huge curiosity in the scientific community due to their prominent features and number of potential applications. In the past years, SWNTs have been proposed as prototype structures for uses in electronics, sensing, filtering, probing, and biology, among many others.1 The practical application of SWNTs, otherwise, usually demands an enhancement or tuning of the SWNTs’ properties to obtain the desired physical and chemical characteristics. The improvement of SWNTs’ performance may be achieved by means of substitutional doping,2 covalent functionalization,3 adatoms,4 or due to vacancies.5 Theoretical predictions6-8 and experimental realizations9-11 have shown that organic radicals, such as hydroxyl and carboxyl, may mediate the interaction of the nanotube with organic substances. This is an important issue that has been extensively studied by several groups due to the potential applications in biochemistry and medicine.12,13 Besides, experiments have demonstrated that the electronic structure of the resulting systems is affected by the presence of these substances, which opens the possibility to design sensing devices by exploiting the interaction of carbon nanotubes with organic compounds.14,15 In addition to the electronic modulation due to chemical interaction between SWNTs and other molecules, transversal electric fields have been shown to affect the electronic structure of SWNTs. Tight-binding16-20 and density functional theory (DFT)21-23 simulations have reported the general trend of electronic band gap collapse in semiconductor SWNTs under transversal electric fields, although metallic tubes have their electronic band structures and densities of states essentially unaltered. * Corresponding author. E-mail:
[email protected], solange.fagan@ gmail.com. † Centro Universita´rio Franciscano. ‡ Universidade Federal de Santa Maria. § Universidade de Brası´lia.
On the basis of both covalent functionalization and SWNTs’ response to transversal electric fields, chemical sensors have been built.24-29 In these devices, a field effect transistor (FET) apparatus is designed in a way that biomolecules can be detected after a controlled variation of a gate potential. The changes in the conductance of the system are monitored and allow a signature of the binding specimen to emerge. In this work, we study through DFT-based methods the electronic properties of (8,0) and (5,5) carboxylated SWNTs under uniform transversal electrical fields. The recent work on functionalized SWNTs under external fields represents a new perspective in nanobiotechnology, which may be explored due to their large number of application possibilities. Our aim is to contribute to the clarification of the role of the external fields on the electronic structure of carboxylated SWNTs and to point out new perspectives in this rich area. Calculation Details The investigations of (8,0) and (5,5) carboxylated SWNTs under transversal electric fields were done through ab initio DFT-based simulations using the SIESTA code.30 The KohnSham orbitals were expanded in a double-ζ plus a polarization function set (DZP) as proposed by Sankey and Niklewski,31 confined by a potential defined through the energy-shift parameter, chosen as 50 meV. The ion-electron potential was replaced by a norm-conserving pseudopotential in the TroullierMartins scheme,32 and the exchange and correlation energies were determined by the generalized gradient approximation (GGA), as parametrized by Perdew et al.33 The reciprocal space integrals were replaced by summations over six special points, determined according to the Monkhorst-Pack method,34 and the electrical field is simulated by a sawtooth-type potential.30 The nanotubes were represented by unit cells of dimensions 50 × 50 × 8.52 Å3 (containing 68 atoms) and 50 × 50 × 7.47 Å3 (64 atoms) for, respectively, (8,0) and (5,5) species, chosen to guarantee periodic repetition and to avoid lateral tube-tube interaction. The field is applied perpendicularly to the tube axis,
10.1021/jp810878y CCC: $40.75 2009 American Chemical Society Published on Web 04/24/2009
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Figure 1. Representation of a unit cell and transversal electric field applied on the carboxylated SWNT.
TABLE 1: Electric Dipole Moment Moduli (in au) of Pristine and Carboxylated (8,0) and (5,5) SWNTs under Transversal Electric Fields applied field V/Å species
0.00
pristine, (8,0) 0.00 COOH, (8,0) -0.13 pristine, (5,5) 0.00 COOH, (5,5) -0.34
+0.05/-0.05 +0.20/-0.20 +0.40/-0.40 0.54/-0.54 0.68/-0.69 0.48/-0.48 0.23/-0.82
1.91/-1.91 2.10/-2.34 1.93/-1.93 1.83/-2.39
3.77/-3.77 4.52/-4.54 3.87/-3.87 4.01/-4.53
and the intensities are within the range of 10-2-10-1 V/Å, as used in previous calculations.16-23 The applied field is always parallel to the COOH radical, as shown in Figure 1. In previous calculations,17,21 it has been shown that the effects of external electrical fields on the electronic properties of the SWNTs depend strongly on the nanotube radius since, for instance, the electronic band gaps of the semiconductor systems collapse at a larger rate for tubes with a bigger radius. As a result, a correct comparison between semiconductor and metallic systems under transversal fields is only possible for equivalent radius nanotubes. This reason justifies our choice of (8,0), with a radius equals to 3.13 Å, and (5,5), with a radius of 3.39 Å, which are well-known semiconductor and metallic species, respectively. Results and Discussion Figure 1 shows a schematic view of the directions of the external electrical field (E) applied on the carboxylated SWNT unit cells. The electrical field is uniform, and its direction is always perpendicular to the tube axis. In terms of structural properties, the pristine nanotubes do not present important changes on the atomic arrangements when an external electrical field is applied. Although, in functionalized tubes, a contraction or expansion in the COOH-nanotube bonding distance is observed always toward the applied field, varying in the range of 1% relative to the no-field system.
Figure 3. Variation in charge density (∆F) for the carboxylated (a) (8,0) and (b) (5,5) SWNTs. The strength of the applied fields is 0.05 V/Å, and the surfaces are given in units of electrons/bohr3.
The external applied field has an important effect on the electrical polarization of the structures. Table 1 shows the electric dipole moments due to the transversal electric field on pristine and carboxylated SWNTs. Both (8,0) and (5,5) nanotubes are polarized, but with differences in the electrical dipole moduli in the range of 1-10%, depending on the field strength. In carboxylated SWNTs, the increase in dipole momentum is within the range of 4-26% relative to its corresponding pristine species. In Figure 2, the electric dipole moments versus applied electric fields for pristine and COOH-functionalized systems for both (8,0) and (5,5) SWNTs are shown. We observe, in all cases, a linear response on the electric moments to the external fields. In pristine (8,0) SWNTs, we found that the values are adjusted through linear regression by the function p ) 9.46E, where p is the dipole momentum modulus and E is the electric field modulus. In (8,0) carboxylated SWNTs, the adjusting function is p ) 11.31E - 0.07. In (5,5) SWNTs, the adjusting functions are p ) 9.67E for pristine (5,5) SWNTs and p ) 10.65E - 0.29 for (5,5) carboxylated SWNTs. Considering that the polarization vector is defined as dipole moment per unit volume and the angular coefficient of its corresponding function is the electric susceptibility, we conclude that the electric susceptibility of the system is increased when the system is COOH-functionalized. Additionally, in the absence of an electric field, COOH-functionalized SWNTs present a nonzero electric dipole moment. Our ab initio calculations give the values -0.13 au for (8,0) and -0.34 au for (5,5), although the values obtained
Figure 2. Electric dipole moment versus applied electric field on (8,0) and (5,5) pristine and COOH-functionalized SWNTs.
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TABLE 2: Total Mulliken Charge (in Electrons) on COOH Radical in Carboxylated (8,0) and (5,5) SWNTs under Transversal Electric Fieldsa applied field (V/Å) species
0.00
+0.05/-0.05
+0.20/-0.20
Mulliken charge on COOH for (8,0) SWNTs (in electrons) Mulliken charge on COOH for (5,5) SWNTs (in electrons)
17.12 (0.00)
17.11/17.13 (-0.01/+0.01)
17.07/17.16 (-0.05/+0.04)
17.02/17.20(-0.10/+0.08)
17.12 (0.00)
17.11/17.13 (-0.01/+0.01)
17.08/17.16 (-0.04/+0.04)
17.04/17.20 (-0.08/+0.08)
a
+0.40/-0.40
In parentheses, ∆q (in electrons) on COOH, taking COO-functionalized tubes at no field as reference.
Figure 4. Electronic band structures of carboxylated (a) (8,0) and (b) (5,5) SWNTs. Fermi energy is represented by the dashed line. The field strengths are given in V/Å with directions indicated in the inset figures.
from the linear regression are -0.07 au for (8,0) and -0.29 au for (5,5). The origin of these dipoles is due to charge transfers between COOH and SWNTs, as will be discussed later. We next present the charge density variation of carboxylated (8,0) and (5,5) SWNTs due to an external applied field. Such variation is defined as
∆F ) FE0 - F0 where F0 and F0E represent the electronic charge density of the system in the absence of external fields and under a transversal electric field of intensity E, respectively.
In both carboxylated (8,0) and (5,5) SWNTs, a variation in electronic charge density is observed, as it is shown in Figure 3. This variation is responsible for a charge separation on the surface, which may be pointed out as the origin of the internal electric dipole vector. It is observed that the variation in the electronic density follows the traditional picture, where negative charge is pushed in the opposite direction of the electric field vector. This effect can be better illustrated in terms of electronic population and charge transfers between the COOH radical and SWNT. In Table 2, we present the total Mulliken charges on COOH and charge variation in the COOH radical due to the electric field. It can be noted that, in the absence of an external field, the electronic population of the COOH radical, which has naturally 17 valence electrons (carbon 2s22p2, oxygen 2s22p4, and hydrogen 1s1), is increased by 0.12 electrons due to electronic transfer from the SWNT. This occurs in both (8,0) and (5,5) SWNTs, and it may explain the initial electric dipole moment, as listed in Table 1. The incident external field, otherwise, is responsible for new charge separations, leading to an increasing (decreasing) of COOH electronic population for negative (positive) external fields. The electric polarizations of the carboxylated SWNTs result in consequences on the electronic properties of the systems, as shown by the band structures in Figure 4. The interaction of the SWNTs with the COOH radical in the absence of external fields modifies the electronic band structures compared with the pristine tubes. The π and π* states in the (5,5) nanotube no longer cross at Fermi energy, and a defect level appears within the formed gap (Figure 4). In (8,0), the π and π* separation remains and, as in (5,5) SWNT, a defect level with small dispersion is presented. The defect levels present in both carboxylated (8,0) SWNTs and carboxylated (5,5) SWNTs are results of orbital rehybridizations occurring in the compounds due to the formation of a covalent bond between the SWNT surface and COOH radical. When COOH binds to the SWNT, a local structural distortion takes place, leading to a change of character from a sp2-like to a sp3-like hybridization in this site.8 The direction of the applied field has implications in charge distribution throughout the SWNT surface. The electric field acts directly on the electron density of the system, and the local lack or excess of charge determines the orbital geometry and, as a consequence, the defect level dispersion. For the carboxylated (5,5) nanotube, this dispersion increases for a negative field (see Figure 1 for a definition of field sign) and decreases for the positive one. Nevertheless, in the carboxylated (8,0) SWNT, the defect level dispersion increases for both positive and negative fields, although such dispersion is higher for negative fields compared with the positive field values. The modifications on the dispersion of the defective levels have consequences on the density of states (DOS) around the Fermi energy, as shown in Figure 5. In carboxylated (8,0)
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Figure 5. DOS of carboxylated (a) (8,0) and (b) (5,5) SWNTs under transversal electric fields. The Fermi energy was shifted to zero.
SWNTs (Figure 4a), a sharp peak at the Fermi energy is related to the defective level and remains when positive fields are applied (red line) but decreases significantly when the system is under negative fields (green line). In carboxylated (5,5) SWNTs (Figure 4b), however, the DOS around the Fermi level is sharp only when positive fields are applied. At a no-field regime and under negative fields, the DOS is lower and broader. Possible Jahn-Teller distortions and magnetic instabilities were investigated. The calculations with spin polarization do not show any magnetic instability since all stable configurations are nonmagnetic. On the other hand, all levels present the same dispersion on the Fermi energy, showing no Jahn-Teller distortions. Besides that, to present a Jahn-Teller distortion, a degeneracy should be involved, which is not the case in these systems. The characteristic behavior of carboxylated SWNTs under transversal electric fields opens a perspective for different potential uses. The polarization of the system may be used to increase the capacity of the composite to bind and characterize other substances, especially polar molecules.35 Besides, the dependence of the electronic properties on the direction of the applied field may be used as a mechanism to monitor the bound substance by varying the external field.36 Finally, other related applications, such as electron injection or detection, may be tuned by a controlled application of an external transversal electric field.37 Conclusions Carboxylated semiconductor and metallic SWNTs under transverse electrical fields were investigated through DFTbased first-principles calculations. The external field polarizes the system, inducing an electric dipole moment toward the incident field with the modulus directly dependent on the field strength. The defect level originated at the electronic band structure due to the orbital hybridization between nanotube and COOH states and is affected by the applied field. The energetic dispersions of the levels in (5,5) carboxylated SWNTs increase at negative fields and decrease at positive fields, whereas in the (8,0) one, the dispersions increase in both cases, at positive and negative fields. As a result, the DOS are modified: a sharp peak is observed around the Fermi energy for positive fields, whereas a decrease and a broadening in the DOS are observed for negative fields, in both (8,0) and (5,5) SWNTs. Our analysis about the carboxylated semiconductor and metallic carbon nanotubes under transverse electrical fields leads to the conclusion that the manipulation of the resulting systems in a stable way is feasible. A controlled application of a transversal electric field
may be used to enhance the capacity of the composite to bind substances, especially polar molecules, or as a mechanism to characterize bound substances and control electron injection and detection. Acknowledgment. The authors acknowledge Dr. A. Fazzio for the fruitful discussions; the Brazilian agencies CAPES, CNPq, FUNCAP, and FAPERGS for the financial support; and CENAPAD/SP for the computer time. References and Notes (1) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (2) Baierle, R. J.; Fagan, S. B.; Mota, R.; da Silva, A. J. R.; Fazzio, A. Phys. ReV. B 2001, 64, 085413. (3) de Souza Filho, A. G.; Fagan, S. B. Quim. NoVa 2007, 30, 1695. (4) Mota, R.; Fagan, S. B.; Fazzio, A. Surf. Sci. 2007, 601, 4102. (5) da Silva, L. B.; Fagan, S. B.; Mota, R.; Fazzio, A. Nanotechnology 2006, 17, 4088. (6) Zhao, J.; Park, H.; Han, J.; Lu, J. P. J. Phys. Chem. B 2004, 108, 4227. (7) Wang, C.; Zhou, G.; Liu, H.; Wu, J.; Qiu, Y.; Gu, B.-L.; Duan, W. J. Phys. Chem. B 2006, 110, 10266. (8) Veloso, M. V.; Filho, A. G. S.; Mendes-Filho, J.; Fagan, S. B.; Mota, R. Chem. Phys. Lett. 2006, 430, 71. (9) Kakadea, B. A.; Pillai, V. K. Appl. Surf. Sci. 2008, 254, 4936. (10) Vedala, H.; Roy, S.; Doud, M.; Mathee, K.; Hwang, S.; Jeon, M.; Choi, W. Nanotechnology 2008, 19, 265704. (11) Tasis, D.; Tagmatarchis, N.; Bianco, A.; Prato, M. Chem. ReV. 2006, 106, 1105. (12) Bianco, A.; Kostarelos, K.; Partidos, C. D.; Prato, M. Chem. Commun. 2004, 571. (13) Yu, X.; Munge, B.; Patel, V.; Jensen, G.; Bhirde, A.; Gong, J. D.; Kim, S. N.; Gillespie, J.; Gutkind, J. S.; Papadimitrakopoulos, F.; Rusling, J. F. J. Am. Chem. Soc. 2006, 128, 11199. (14) Yang, W.; Moghaddam, M. J.; Taylor, S.; Bojarski, B.; Wieczorek, L.; Herrmann, J.; Mc-Call, M. J. Chem. Phys. Lett. 2007, 443, 169. (15) Yang, W.; Thordarson, P.; Gooding, J. J.; Ringer, S. P.; Braet, F. Nanotechnology 2007, 18, 412001. (16) Zhou, X.; Chen, H.; Zhong-Can, O.-Y. J. Phys.: Condens. Matter 2001, 13, L635. (17) Kim, Y.-H.; Chang, K. Phys. ReV. B 2001, 64, 153404. (18) Li, Y.; Rotkin, S. V.; Ravaioli, U. Nano Lett. 2002, 3, 183. (19) Rocha, C. G.; Pacheco, M.; Barticevic, Z.; Latge´, A. Phys. ReV. B 2004, 70, 233402. (20) Pacheco, M.; Barticevic, Z.; Latge´, A.; Rocha, C. G. Braz. J. Phys. 2006, 36, 440. (21) Chen, C.-W.; Lee, M.-H.; Clark, S. Nanotechnology 2004, 15, 1837. (22) Tien, L.-G.; Tsai, C.-H.; Li, F.-Y.; Lee, M.-H. Phys. ReV. B 2005, 72, 245417. (23) O’Keeffe, J.; Wei, C.; Cho, K. Appl. Phys. Lett. 2001, 80, 676. (24) Kauffman, D. R.; Star, A. Chem. Soc. ReV. 2008, 37, 1197. (25) Wang, J.; Lin, Y. Trends Anal. Chem. 2008, 27, 619. (26) Star, A.; Gabriel, J.-C. P.; Bradley, K.; Gru¨ner, G. Nano Lett. 2003, 3, 459. (27) Besteman, K.; Lee, J.-O.; Wiertz, F. G. M.; Heering, H. A.; Dekker, C. Nano Lett. 2003, 3, 727.
Carboxylated Carbon Nanotubes (28) Chen, R. J.; Bangsaruntip, S.; Drouvalakis, K. A.; Kam, N. W. S.; Shim, M.; Li, Y.; Kim, W.; Utz, P. J.; Dai, H. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 4984. (29) Boussaad, S.; Tao, N. J.; Zhang, R.; Hopson, T.; Nagahara, L. A. Chem. Commun. 2003, 1502. (30) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejo´n, P.; Sa´nchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (31) Sankey, O. F.; Niklewski, D. J. Phys. ReV. B 1999, 40, 3979. (32) Troullier, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993.
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8963 (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (34) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (35) Picaud, F.; Girardet, P. Surf. Sci. 2008, 602, 235. (36) Goldsmith, B. R.; Coroneus, J. G.; Kane, A. A.; Weiss, G. A.; Collins, P. G. Nano Lett. 2008, 8, 189. (37) Gruneis, A.; Esplandiu, M. J.; Garcia-Sanchez, D.; Bachtold, A. Nano Lett. 2007, 7, 3766.
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