Density functional calculations of structural and electronic properties of a BN-doped carbon nanotube

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Density functional calculations of structural and electronic properties of a BN-doped carbon nanotube N. Krainara

a,b

, S. Nokbin

a,b

, P. Khongpracha

a,b

, Ph.A. Bopp c, J. Limtrakul

a,b,*

a

Laboratory for Computational and Applied Chemistry, Physical Chemistry Division, Department of Chemistry, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand b Center of Nanotechnology, Kasetsart University Research and Development Institute, Bangkok 10900, Thailand c Department of Chemistry, Universite´ Bordeaux 1, F-33405 Talence Cedex, France

A R T I C L E I N F O

A B S T R A C T

Article history:

The attachment of a variety of nitrogen nucleophilic groups to BN-doped single wall carbon

Received 15 July 2009

nanotubes (SWCNTs) was characterized by quantum mechanical calculations at the DFT-

Accepted 1 September 2009

level. We found that the binding energies for all systems lie between 6.90 and

Available online 6 September 2009

30.13 kcal/mol and are in the order guanidine > arginine > ammonia > imidazole > chitosan > pyridine > m-nitroaniline, which is analogous to the pKa. m-Nitroaniline and pyridine grafted tubes display a smaller energy gap, 0.252 and 0.347 eV, respectively, compared to an isolated BN-doped SWCNT, 0.430 eV. For the other cases, the energy gaps did not change significantly, which is in keeping with the results for the densities of states (DOS). In the cases of m-nitroaniline and pyridine, electron density is seen at the Fermi level of both SWCNTs and probe molecules when the DOS is split into these two contributions, different from the isolated probe molecules. Thus, m-nitroaniline and pyridine attached to BN-doped SWCNTs increase the conductivity of the system. Ó 2009 Elsevier Ltd. All rights reserved.

1.

Introduction

Single wall carbon nanotubes have emerged as being of great interest due to a variety of fascinating properties, e.g., their field emission and electronic transport properties, a high mechanical strength, and their chemical properties. With 100 times the tensile strength of steel, a thermal conductivity better than all but the purest diamond, and an electrical conductivity similar to copper, but with the ability to carry much higher currents, they are very interesting indeed. In general, the properties of nanotubes with large enough diameters can be described by the ‘graphene folding’ approximation; we shall call this here the ideal behavior. Deviations from this ideal behavior can be expected for small diameters (large curvatures), where the discreteness of the atoms can no longer be neglected. Accurate theoretical investigations of

tubes with small diameters have recently become important since such tubes have now been produced by several methods [1,2]. On top of their excellent electrical properties, carbon nanotubes possess a high mechanical and chemical stability. While the latter is certainly advantageous from an application point of view, this attribute also imposes a severe hurdle for the development of methods allowing for a selective and controlled covalent functionalization. This explains why it was only within the past 3–4 years that a wider range of reliable functionalization schemes have become available [3]. Their ultrahigh surface-to-volume ratio makes CNTs also highly suited for investigating fundamental aspects of adsorption and diffusion properties [4]. For instance, the interior region offers a deep well for physical adsorption, which provides an ideal example of a micro-porous material. In

* Corresponding author: Address: Laboratory for Computational and Applied Chemistry, Physical Chemistry Division, Department of Chemistry, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand. Fax: +66 2 562 5555x2169. E-mail address: [email protected] (J. Limtrakul). 0008-6223/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2009.09.001

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particular, nanotubes represent an optimal testing ground for theoretical predictions on adsorption mechanisms in 1D matter. Moreover, the fact that all carbon atoms of the SWCNT are exposed to the surface leads to a high sensitivity of its electronic properties against the binding of atoms or molecules, whereby promising perspectives for sensor applications are opened. Furthermore, appropriate chemical functionalization could make significant contributions towards the hierarchical assembly of nanotubes into ordered functional architectures. However, no reliable method is currently available to produce extended ensembles of aligned nanotubes, in which each tube would be located at a desired location and connected to its neighbors in a well-defined manner. Nonetheless, recent advances in linking specific groups or molecules to nanotubes clearly testify to the strong potential of chemical functionalization, not only for tuning the tubes’ electronic properties, but also to enable their assembly into the more-complex architectures required for integrated device operation. Chemical functionalization usually imparts an increased solubility to the nanotubes, thus opening up new perspectives for solution-based chemical transformations and spectroscopy. The fast progress made in these directions has led to the prediction that the field of nanotube chemistry will successfully rival that of the fullerenes. One intriguing example is a specifically designed amphiphilic peptide which enables SWCNT to self-assemble into fibers containing nanotubes aligned along the fiber axis [5]. This approach represents a promising alternative to methods that involve tube alignment during the growth [6]. Finally, several potential biomedical applications are emerging for functionalized SWCNTs, including their use as scaffold for the directed growth of neuron cells [7]. The special properties of SWCNTs have also attracted the interest of many analytical chemists in the field of electrochemical sensors. The relevant sensing mechanisms are attributed to the conductance change caused by a charge transfer between the tubes and adsorbed molecules [8–10]. As found in experiments, adsorbed molecules affect the electronic transport properties of SWCNTs via physisorption and chemisorption. However, some biomolecules cannot be detected by intrinsic CNT devices [11] since they cannot be adsorbed on the surface. Thus, considerable experimental and theoretical work has focused on improving the sensing performance of SWCNTs for various molecules by doping or functionalizing the tubes [8,12–18]. During the past few years, several methods for the covalent functionalization of SWCNTs have been established that allow atoms or molecules to persistently anchor to the carbon framework [19,20]. The intact sidewall, where the curvature, and hence strain relief, is considerably smaller than at the caps, has a smaller driving force for the formation of tetragonal carbons. As a consequence, sidewall functionalization in general requires quite ‘‘hot’’ addends. The electronic, chemical and mechanical properties of CNTs can be tailored by replacing some of the carbon (C) atoms with either boron (B) or nitrogen (N). If B (which has one electron less than C) or N (one electron more than C) replaces some C atoms, a p- or n-type conductor can be formed. From a chemical point of view, these doped structures should be likely to react with donor or acceptor type molecules,

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depending on the doping. B or N doped CNTs can be obtained by the arc-method: by arcing either B- or N-graphite electrodes in an inert atmosphere, as described previously [21,22]. Laser [23] and CVD [24] methods have also been used for their production. Zhang et al. systematically studied the isomers of BNdoped on (5,5) armchair carbon nanotubes and found that the doping increases the redox and electron excitation properties [25]. Moradian and Azadi investigated the BN-doped (10,0) zigzag SWCNT using DFT calculations. They found that the energy gap of the system can be controlled by the boron and nitrogen concentrations, giving smaller energy gaps with increasing concentration. Moreover, they suggested that BNdoped SWCNT could be a potential candidate for making nanoelectronic devices [26]. From a chemical point of view, BN-doped SWCNT, especially at the boron doped position, would be expected to react with molecules consisting of the electron donor group. In this study we have thus characterized by quantum mechanical calculations at the DFT-level the attachment of a variety of nitrogen nucleophilic groups to BN-doped SWCNT. The binding energies, geometries and electronic properties, i.e., the energy gaps, the charge redistribution and the densities of states (DOS), are reported. Moreover, the electron-donating properties are also presented to clarify the nucleophilic strength by the pKa (acid dissociation constant) of all Lewis base molecules [27–32].

2.

Methodology

The model of the SWCNT (5,5) consists of 90 carbon atoms. At each end of the model, 10 terminating H atoms were added to preserve the sp2 hybridization structure of the carbon atoms at the edge of the tube, yielding C90H20 as our model. Fig. 1 shows the model of a single B–N doped onto the armchair SWCNT, where two adjacent carbon atoms were replaced by B and N atoms at the most stable positions reported in literature, giving the model BNC88H20. In order to investigate the functionalization of these systems, the effects of nitrogen nucleophiles (N-nucleophiles) were explored. Different types of N-nucleophiles (see Fig. 2), i.e., ammonia, arginine, chitosan, guanidine, imidazole, mnitroaniline and pyridine, were selected. We note here that all N-nucleophiles will be called R-group throughout this

Fig. 1 – Position of the R-group functionalization on the sidewall of the (5,5) SWCNT.

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Fig. 2 – Structures of the nitrogen nucleophiles.

article. These R-groups interact directly with the B atom due to its electron acceptor behavior. Full geometry optimizations of these systems have been carried out by means of density functional theory (DFT) calculations using the PBE exchange–correlation functional [33] implemented in the TURBOMOLE code. The standard split-valence polarization SV(P) (double-f with polarization) basis sets with (7s4p1d)/[3s2p1d] contraction were used for all atoms in the system. We report here the binding energies and exact bonding geometries for situations like the one seen in Fig. 1. The binding energies were calculated from Eb = E(BN–SWCNT/R-group) E(BN–SWCNT)  E(R-group), where E(BN–SWCNT/R-group), E(BN–SWCNT) and E(R-group) are the total energies of the complex of the BN-doped SWCNT and the nitrogen nucleophilic molecule, of the BNdoped SWNCT, and of the nitrogen nucleophilic molecule, respectively. The ‘‘pyramidalization angle’’ is discussed in simple terms to verify the alteration in pyramidalization and hybridization (sp2 ! sp3) undergone during the chemical transformation. The pyramidalization angle is defined as hP = (hrp  90)°, where hrp is the angle between the p-orbital axis vector and the three r-bonds at a conjugated carbon atom. hP suggests sp2 or sp3 hybridizations when it is 0° or 19.47°, respectively. Additionally, we also report the energy gap between the HOMO and LUMO states to elucidate the effect of the various R-groups. Finally, to gain insight into the electronic properties, we have performed electronic population analyses, concerning, e.g., the charge transfer (NPA analysis), the density of electronic states (DOS), and the atomic orbitals. These electronic properties were studied by single point calculations using DFT-PBE and Ahlrich’s pVDZ basis set [34], as available in the Gaussian 03 package [35]. The DOS plots were convoluted by the AOMix program [36].

3.

Results and discussion

3.1.

Structural geometry

The charge distributions and internuclear distances of the B– C, N–C, C–C parts of the BN-doped SWCNT are shown in Fig. 3.

The charge ranges between 0.586e and +0.832e, with e the elementary charge. The nitrogen atom has the largest negative charge while the boron atom has the highest positive one. Table 1 shows the optimized structural parameters for the BN-doped SWCNT and the corresponding adsorption systems (Fig. 4). The optimized B–N, B–C1 and B–C2 distances in the BN˚ , respectively, showing doped SWNCT are 1.46, 1.53, and 1.51 A an elongation of the bond distances compared to the C–C ˚ ) in the undoped SWCNT. Moreover, the \N–B– bond (1.43 A C1, \N–B–C2 and \C1–B–C2 angles are 118.0°, 118.6° and 114.7°, respectively, smaller than the corresponding \C–C–C angles in the undoped SWCNT (120°). These small changes (about 2.0°, 1.4° and 3.3° for the \N–B–C1, \N–B–C2 and \C1–B–C2 angles, respectively) induce a lesser stabilization of the sp2 hybrids, even though this characteristic is still preserved at this state. However, as we shall see, the sp2 hybridization can be changed to an sp3 one when the adsorption processes takes place. In the R-group/BN-doped systems, when the reaction has taken place, the distances between the R-groups and B (R–B) ˚ , depending upon the interacare in the range of 1.60–1.79 A tion strength. In most cases, stronger interactions correlate with shorter bonds. Furthermore, the B–N, B–C1 and B–C2 bond distances are lengthened and lie in the range of

Fig. 3 – Charge distribution in BN-doped (5,5) SWCNT given in elementary charges e.

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Table 1 – Structural parameters of BN-doped SWCNT grafted with N-nucleophiles. Distances in Angstrom, angles in degrees.

BN–SWCNT m-Nitroaniline Pyridine Chitosan Imidazole Ammonia Arginine Guanidine

B–R

B–N

B–C1

B–C2

\N–B–C1

\N–B–C2

\C1–B–C2

\R–B–N

\R–B–C1

\R–B–C2

– 1.79 1.67 1.70 1.64 1.69 1.60 1.61

1.46 1.52 1.54 1.54 1.55 1.54 1.57 1.57

1.53 1.59 1.60 1.61 1.60 1.60 1.61 1.61

1.51 1.57 1.58 1.58 1.59 1.58 1.59 1.59

118.0 111.8 109.9 109.3 109.7 110.8 108.3 108.2

118.6 113.8 112.0 112.1 111.9 112.9 110.4 110.5

114.7 110.0 108.3 107.3 108.0 109.0 107.2 107.0

– 105.1 105.7 106.5 106.6 105.9 107.2 108.2

– 108.3 112.1 112.2 111.0 109.6 110.4 109.6

– 107.5 108.9 109.2 109.7 108.5 113.3 113.2

Fig. 4 – Positions of the R-groups, B atom, N atom, C1 atom, and C2 atom on the sidewall of (5,5) SWCNT. ˚ , respectively. It is found that 1.52–1.57, 1.59–1.61 and 1.57–1.59 A these interatomic distances increase with increasing interaction strength between the R-group and the doped SWCNT. For example, guanidine shows the strongest interaction to the BN-doped SWCNTand gives R–B, B–N, B–C1, and B–C2 distances ˚ , respectively. In contrast, m-nitroof 1.61, 1.57, 1.61, and 1.59 A aniline (the least stable system) shows corresponding distances ˚ . The other systems show a similar of 1.79, 1.52, 159 and 1.57 A behavior, depending on their binding energies. To further explain our findings in terms of hybridization, we consider the modification of the angles in the BN-doped region. In all cases, these angles are reduced by the R-group, reaching values rather close to the ideal tetrahedral value of 109.47°, indicating that these systems exhibit an sp3 hybridization instead of the sp2 hybridization.

of their binding energies (Eb) defined above. Table 2 shows these energies for all systems studied. We find that the binding energies for all systems lie between 6.90 and 30.13 kcal/mol and are in the order guanidine > arginine > ammonia > imidazole > chitosan > pyridine > m-nitroaniline. The adsorption of guanidine leads to the most stable system with a binding energy of 30.13 kcal/mol, while the adsorption of m-nitroaniline is the least stable with an energy of only 6.90 kcal/mol. We find that the structures of the adsorbed molecules as well as their intrinsic electronic properties play an important role for the binding energy. We will discuss in more detail the charge redistribution in the electronic properties section. We report the relationship between binding energies and the pKa of the complexes in Fig. 5. We found that the pKa value, taken from Refs. [27–32], is directly proportional to the binding energy, or, in other words: the higher the basicity, the larger the binding energy. It is worthy to note that in some molecules like pyridine and imidazole bind strongly to the BN-doped SWCNT and are even comparable to their proximate molecules (chitosan and ammonia). This is due to the fact that in pyridine and imidazole molecules, the nitrogen atom is in five or six aromatic rings with sp2 hybridization, while the nitrogen atom in ammonia and chitosan is with sp3 hybridization.

3.3. 3.2.

Electronic properties

Binding energies and pKa

In this study, the chemical interactions of nitrogen nucleophiles (R-group) and BN-doped SWCNT are reported in terms

In order to evaluate the electronic properties we calculated the charge redistribution and the electronic density of states (DOSs).

Table 2 – pKa-values, interaction energies (in kcal/mol), HOMO–LUMO energy gaps (in eV) and their reduction (in percent) in the BN-doped SWCNTs with various adsorbates. R-groups m-Nitroaniline Pyridine Chitosan Imidazole Ammonia Aiginine guanIdine

pKa

Eb (kcal/mol)

HOMO

LUMO

Eg (eV)

DEg (%)a

2.45 5.14 6.50 6.95 9.21 12.48 13.71

6.9 16.32 14.75 18.89 18.94 28.57 30.13

5.16 5.68 5.24 5.48 5.40 4.92 4.47

2.80 1.69 0.26 0.20 0.84 0.91 0.37

0.252 0.347 0.471 0.445 0.457 0.459 0.445

41.38 19.33 9.46 3.42 6.25 6.75 3.42

a Compared to the Eg value obtained for isolated BN-doped SWCNT, 0.430 eV.

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Fig. 7 – Charge distribution of isolated pyridine and of pyridine complexed with BN-doped SWCNT. Fig. 5 – Correlation between binding energies and pKa values of BN-doped SWCNT/N-nucleophiles complexes.

3.3.1.

Charge redistribution

Figs. 6 and 7 show the charge redistribution in selected systems, including the m-nitroaniline and pyridine complexes which have their HOMO–LUMO gaps reduced significantly as compared to the rest of the molecules (cf. Table 2). The charge redistribution, which was computed for all systems, was derived from the Natural Population Analysis (NPA) procedure. The results were partitioned into a contribution assigned to the BN-doped SWCNT and to the N-nucleophile part. The partial charge is the sum of the atomic charges in each part. The total charge of the BN-doped SWCNT part is negative (0.28e and 0.32e for the m-nitroaniline and pyridine systems, respectively) while the total charge of the N-nucleophile part is positive. Comparing with the isolated molecule, the total charge of the aromatic ring in the complex systems is more positive, indicating that electrons of the N-nucleophile ring are transferred to the doped SWCNT. It can be expected that only m-nitroaniline binds

loosely since the NO2 group withdraws electrons out of the aromatic ring and the NH2 group, hence weakening the basicity of the N1 atom. Another partitioning of the charge distribution, into the isolated m-nitroaniline molecule and the rest, shows that the total charge distribution at the NO2 group is negative (0.24e), while it is positive and neutral at the aromatic ring (+0.24e) and the NH2 group (0.00e), respectively. On the other hand, there is no electron withdrawing group attached to the pyridine ring, therefore, its N1 atom behaves as a stronger base than that of m-nitroaniline. In the cases of the chitosan, imidazole, and ammonia molecules, the electrons are more localized in a specific region, giving rise to more electron donor ability to N1. For the arginine and guanidine molecules. These molecules are quite similar due to their guanidinium group. Generally, guanidine prefers to behave in a resonance structure because of the conjugation between the double bond and the nitrogen lone pair electrons. Thus, the positively charged guanidium ion structure is preferred and enhances the electron donor capability of N1.

3.3.2.

Fig. 6 – Charge distribution of isolated m-nitroaniline and of m-nitroaniline complexed with BN-doped SWCNT.

Energy gap and densities of states

Table 2 shows the energy gap (Eg) of the R-group/BN-doped SWCNT systems. The calculated Eg is correlated with the binding energy Eb. The energy gaps, 0.25 and 0.35 eV, respectively, are smaller than that of an isolated BN-doped SWCNT, 0.43 eV; m-nitroaniline and pyridine thus should perform well as grafting molecules on BN-doped SWCNT. For the other cases, no significant changes of the energy gaps can be observed. Charge redistribution is found when aromatic Nnucleophiles are attached to the BN-doped SWCNT. This, however, does not occur for non-aromatic N-nucleophiles and, therefore, there is no change in the energy gap. From these results, one can expect that the pyridine derivatives may be useful for the functionalization or modification of BN-doped carbon-conducting materials for specific applications. This is due to their stability and the conductivity of the complexes. In order to consider the energy gap alteration in the complex systems, the electronic density of states (DOS) of the selected systems (m-nitroaniline, pyridine and guanidine) were

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carried out. The energy gap (Eg = 0.43 eV) of the bare BNdoped SWNT was selected as the reference. Figs. 8–10 show plots of the density of states of the BN–SWNT complexes (total density of states, TDOS) and their corresponding complexes (partial density of states PDOS) of m-nitroaniline, pyridine and guanidine [36]. In the complex systems, the energy gap characteristics have been changed due to the impurity states induced by probed molecules. From our results, two ultimate cases can be observed (cf. Table 2). As for mnitroaniline and pyridine, it is clearly seen that the impurities states occur in the region between the energy gap of the BN– SWNT system, leading to the reduction of their energy gaps (0.25 eV for m-nitroaniline and 0.347 eV pyridine) and thus increase the conductivity of the system. The guanidine is one of the non-aromatic N-nucleophiles where the energy gap is very slightly changed (it increases

Fig. 9 – Total density of states (TDOS) and partial density of states (PDOS) of m-nitroaniline complexed with BN-doped SWCNT.

by less than 3.5%) after grafting. The total and partial densities of states in the complex with guanidine are illustrated in Fig. 10. The TDOS of the complex is solely contributed by the BN-doped SWCNT and is the same as in the isolated BN-doped SWCNT. There are no visible impurity states in the energy gap of the BN–SWNT while the states appear further apart far from the gap (see Fig. 10c). Therefore, guanidine and other non-aromatic N-nucleophiles are not suitable for either grafting with the BN-doped SWCNT or for improving the conductivity of materials.

4. Fig. 8 – Total density of states (TDOS) and partial density of states (PDOS) of pyridine complexed with BN-doped SWCNT.

Summary and conclusions

We have carried out quantum chemical calculations to study the electronic properties of BN-doped carbon nanomaterials grafted with N-nucleophiles. The PBE density functional

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and pyridine. This results in an improvement of the conductivity of the material.

Acknowledgements This work was supported in part by grants from the National Science and Technology Development Agency (2009 NSTDA Chair Professor funded by the Crown Property Bureau under the management of the National Science and Technology Development Agency and NANOTEC Center of Excellence funded by the National Nanotechnology Center), Kasetsart University Research and Development Institute (KURDI), and the Commission of Higher Education, Ministry of Education under Postgraduate Education and Research Programs in Petroleum and Petrochemicals and Advanced Materials.

R E F E R E N C E S

Fig. 10 – Total density of states (TDOS) and partial density of states (PDOS) of guanidine complexed with BN-doped SWCNT.

theory (DFT) method with the def-SV(P) basis set and the RI approximation, as implemented in the TURBOMOLE code, was used. The degree of grafting the BN-doped SWCNT with N-nucleophiles (R-group) is reported in terms of binding energies (Eb). The relative order of the binding energies is directly proportional to the pKa values of the N-nucleophiles. The charge redistribution, derived from Natural Population Analysis (NPA), shows charge transfer when the BN-doped SWCNT is grafted with m-nitroaniline and pyridine. The BN-doped SWCNT acts as an electron acceptor and gains electrons from the grafted N-nucleophiles. The energy gap of the BN-doped SWCNT grafted with m-nitroaniline and pyridine decreases by about 0.25 and 0.35 eV, respectively, compared to that of the isolated BN-doped SWCNT, 0.43 eV. The partial density of states analysis indicates that the total density of states at the Fermi level increases when grafting with m-nitroaniline

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