Functionalization of Single-Wall Zigzag Carbon Nanotubes by

Publication Date (Web): April 19, 2013 ... favorable for —COOH to adsorb in pairs on top of two neighboring carbon atoms that are bonded along the t...
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Functionalization of Single-Wall Zigzag Carbon Nanotubes by Carboxyl Groups: Clustering Effect Wissam A. Saidi* Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States ABSTRACT: Carboxylation of carbon nanotubes (CNTs) is a byproduct of acid oxidation treatments that are applied routinely for several purposes including cleaning of CNTs and as a first step of functionalization procedures. In this study, we employ density functional calculations to study the atomic and electronic structures of side-wall COOH-functionalized zigzag CNTs and elucidate their dependence on the tube diameter and the metallic or semiconducting character. Adsorption of a COOH group shows a covalent bonding character associated with a small charge transfer from the CNT to the carboxyl groups. The amount of charge transfer, as well as the binding energy, of the carboxyl to the CNT decreases with the tube diameter. We find that it is thermodynamically more favorable for COOH to adsorb in pairs on top of two neighboring carbon atoms that are bonded along the tube axis. This clustering effect becomes more favorable for larger diameter CNTs, because the difference in adsorption energy between isolated and pair carboxylation increases with tube diameter. Furthermore, we find that pair adsorption is not kinetically hindered and shows similar activation energies to that of the isolated adsorption. The electronic mechanism for the clustering effect is discussed.

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INTRODUCTION Carbon nanotubes (CNTs) in their pristine structure are quite unique in many aspects, but their full potential and major technological advances are based on their functionalized forms. During the functionalization process, chemical moieties that are appropriate to different potential applications are attached to the tube, thus marrying the exceptional electronic properties of the pristine CNTs with the diversity of organic chemistry.1−4 COOH-functionalization of CNTs is of particular importance, because it has been shown that the routinely applied oxidation treatments result in an increase in the number of surface carboxylic (COOH), carbonyl (CO), and hydroxyl ( COH) groups in the approximate proportions of 4:2:1.5 The abundance of these groups depend on the length of time and temperature of the oxidative treatment. Acid oxidation of CNTs, typically carried out using acids such as HNO3 and H2SO4 alone or in combination with peroxide,6−9 is a common chemical treatment that is often employed to remove metal impurities and amorphous carbon10 and to increase the solubility of the CNTs in water and solution. CNT oxidation is also applied for several other purposes. For example, oxidized CNTs are used as a first step in functionalization because the surface oxide groups can be used to attach organic and biorganic moieties.11 Furthermore, oxidation treatments using HNO3/H2SO4 have been shown to destroy single-wall metallic CNTs with diameters less than 11 Å while keeping the semiconducting ones intact.12,13 These treatments can be used to select between the two kinds of CNTs.14−16 Finally, the field of biomedicine, which is an emerging field for potential applications of CNTs, provides © XXXX American Chemical Society

additional impetus for studying CNTs in different acidic environments. Shortened CNTs that are often fabricated through chemical oxidation have been employed to shuttle various molecular cargos inside living cells, including proteins, short peptides, and nucleic acids.17,18 Also, carboxylated CNTs have been shown to have lower toxicity than the pristine tubes.19 The study of CNTs is experimentally particularly challenging considering the absence of analytically pure bulk samples. This makes quantum mechanical simulations of CNTs of prime importance for understanding and developing the chemistry of CNTs, considering the controlled environment of these simulations. There have been few density functional theory (DFT) investigations of carboxylated CNTs,20−24 and several issues remain uninvestigated. For example, it is known from experiments that harsh acid treatments destroy small diameter metallic CNTs;12 however the mechanism for the CNT dissolution is not completely understood. In this paper, we present an ab initio DFT investigation of the carboxylation process of single-wall CNTs where we focus on the adsorption of isolated and pair carboxyl groups. We limited our study to pristine CNTs with no carbon vacancies or topological defects that create deviations from the ideal hexagonal rings of the carbon network. Structural defects are known to increase the reactivity of the CNT. Also, we have not included solvent effects in our calculations despite their Received: January 26, 2013 Revised: April 18, 2013

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carboxyl group was found to be −1.06, −0.58, −0.62, and −0.63 eV for the four k-grids. The metallic (12,0) CNT shows slightly more sensitivity to the k-grid, which is not surprising considering its metallic nature. In this case, the binding energies obtained with the four k-grids are −1.27, −0.45, −0.52, and −0.55 eV, respectively. Because we are interested in applying the same computational model for all of the CNTs, we employed the (1 × 1 × 2) MK grid to keep the computations manageable for the large CNTs. Thus, our binding energies are accurate for less than 0.1 eV. The atom-projected density of states (PDOS) analysis is done using (1 × 1 × 8) MP k-grid. We used two repeat unit cells along the tube axis where the lattice constant is fixed at 4.32 Å. For the adsorption of one or two COOH groups per supercell, this would correspond to a relatively low COOH concentration of 0.5−2% per carbon atom. To investigate the carboxyl group adsorption in the isolated limit, we carried calculations with four and six repeat unit cells for (10,0) and (12,0) CNTs. For the single isolated adsorption, we find that employing the larger supercell decreases the binding energy of the two repeat unit supercells of both CNTs by ∼0.1 eV.

importance because this cannot be easily done in periodic DFT calculations. However, it is expected that solvent effects will not change the main conclusions of this study considering that there is a small charge transfer induced by the carboxylation, as we will show later. It should be noted that both the structural defects and solvent effects are believed to be more important in unveiling the detailed mechanism for the formation of carboxylic acids during the oxidation process. This was nicely illustrated recently for the HNO3 oxidation of a graphene sheet and a polycyclic aromatic hydrocarbon model using experimental observations and computational modeling.25 The DFT investigations of single and pair functionalization of COOH groups are systematically carried out for zigzag CNTs with diameters ranging from 7 to 16 Å. CNTs of this range of diameters can be produced, for example, from high pressure carbon monoxide HiPcO method. We show that there is a clustering tendency of the COOH groups evidenced by the more favorable adsorption energy of a pair of carboxyl groups than that of a single isolated adsorption. Also, we find that this clustering effect increases as the tube diameter increases. Besides the thermodynamic preference for pair adsorption, we find that the activation for pair carboxylation is not kinetically hindered and shows kinetic barriers that are comparable to those of the single isolated adsorption events. Therefore, pair adsorption should be the prevalent form of carboxylation. The electronic mechanism responsible for this clustering tendency is discussed.

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RESULTS AND DISCUSSION We limited the study to zigzag CNTs with chirality index n = 9, 10, 12, 14, 15, 16, and 18 with tube diameters between 7 and 16 Å. Zigzag CNTs are appealing for computational investigations because these keep the primitive unit cell size minimal. Additionally, both metallic and semiconducting characters can be realized in this family, where the CNTs are metallic with small bandgaps if n is divisible by 3 and semiconducting otherwise with a bandgap that is inversely proportional to the diameter. The binding energy of x carboxyl groups to the CNT is defined as

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COMPUTATIONAL DETAILS The DFT calculations are carried out using PWSCF.26 Core electrons are replaced by norm-conserving pseudopotentials,27 which are generated using OPIUM.28 The Kohn−Sham wave function is expanded in plane waves up to a cutoff of 680 eV. We used the generalized-gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE)29 in all of our investigations. Periodic boundary conditions are applied for the system using a supercell approach where the images in the nonperiodic directions (along x and y) are isolated from each other by more than 14 Å. The isolated carboxyl monomer is modeled using a cubic supercell with side length of 15 Å. In addition to the CNTs, we examined the COOH group interaction with graphene, which would correspond to the limit of the interaction with a very large diameter CNT. The graphene sheet was modeled using a 64 atom orthorhombic supercell with an inplane lattice parameters of 9.84 × 17.23 Å2 and with 20 Å vacuum in the nonperiodic direction. Geometry optimization was done using a convergence threshold of 0.01 eV/Å on the atomic forces and 10−6 eV on the energies in the self-consistent step. Calculations of the pristine CNT and of the CNTs with two COOH groups (with even number of electrons) are spin-averaged while those of the COOH group in isolation or with the CNT are spin polarized. We have checked that the spin-averaged calculations of the pair carboxylated CNTs are stable against a spin polarized solution for several CNTs in the six different adsorption configurations (cf., Figure 4). We also performed several tests to verify our computational framework including varying the vacuum spacing in the nonperiodic directions and the plane-wave cutoff. The grid used to sample the Brillouin zone (BZ) along Γ−X direction was determined by carrying test calculations using k = 0 (Γ-point), (1 × 1 × 2), (1 × 1 × 4), and (1 × 1 × 8) Monkhorst−Pack (MP) grids on (10,0) and (12,0) CNTs. For the semiconducting (10,0) CNT, the binding energy of the

E BE =

1 (ECNT + xCOOH − ECNT − xECOOH) x

(1)

where ECNT+xCOOH is the CNT energy with the adsorbed  COOH groups in the optimum geometry, ECNT is the pristine CNT energy, and ECOOH is the energy of an isolated carboxyl group. In the adopted notation, negative values of EBE indicate stable adsorption configurations. To gain further insight into the stabilizing forces for carboxylated CNTs, we partition the binding energy into E BE = ΔECNT + ΔECOOH + ΔE HB

(2)

Here, the first term, ΔECNT, is the CNT deformation energy defined as the energy difference between the CNT in the bonding configuration and the pristine CNT. The second term, ΔECOOH, measures the energy penalty due to the deformations from isolated geometry and interactions among the adsorbates and is defined as the energy difference between the carboxyl groups in the bonding configuration compared with that in isolation. The hybridization energy, EHB, is defined as the difference in energy between the total binding energy and the sum of ΔECNT and ΔECOOH so that eqs 1 and 2 are satisfied. ΔECNT and ΔECOOH are both destabilizing contributions to the total energy, while EHB is stabilizing. Adsorption of COOH Group. We find that the most favorable binding configuration corresponds to the case where the carboxyl carbon atom forms a direct bond with one CNT carbon atom, which agrees with previous studies.20,21,30,31 The CNT carbon atom is pulled out of the CNT nuclear framework B

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from the table, ΔECOOH is an order of magnitude smaller than ΔECNT and is the same for all of the tubes within 0.01 eV. ΔECNT and ΔEHB increases with the tube diameter, and this decreases the total binding energy. For example, comparing the (9,0) and (18,0) CNTs, both ΔECNT and ΔEHB increase by ∼0.2 eV, which leads to a decrease in the binding energy by ∼0.4 eV. The increase in ΔECNT and ΔEHB can be understood from the local change in the hybridization of the carbon atom that is bonded to COOH group from sp2 to sp3. This change is less favorable in large diameter CNTs that are closer to planarity, and hence have more sp2 hybridization character, than in small diameter CNTs where strong curvature effects weaken the sp2 network.32 From the COOH binding energy trends with tube diameter, it would be expected that the  COOH group will bind with a very small binding energy to a graphene sheet, which can be considered as a CNT with a very large diameter. Indeed this was verified to be the case with a binding energy of ∼0.025 eV. The COOH adsorption configuration is similar to what is shown in Figure 1. The covalent bonding nature between the COOH group and the CNT can be guessed from the small amount of electron charge transfer QCNT→COOH from the CNT to the COOH group, as shown in Table 1. The charge analysis is done using a Hirshfeld charge decomposition.34 Previously, charge transfer was also seen from the CNT to the COOH group for (8,0) CNT using Mulliken population analysis.21,24 The amount of charge transfer decreases as the CNT diameter increases, a trend that correlates with the weaker bonding of the COOH group as the CNT diameter increases. The charge transfer is small and ranges between ∼2 and 11 milli-e for the CNTs investigated. However, examining in detail the electronic charge rearrangement, we see that there is a more significant charge rearrangement within the COOH group. For illustration, Figure 2 provides an overview of the electronic charge rearrangement for the (14,0) CNT. Compared with an isolated carboxyl group, the nonhydroxyl oxygen gains 45 milli-e, the OH gains 6 mill-e, and the carbon atom loses 45 milli-e. Interestingly, the charge depletion or gain of the CNT atoms is not localized only at the carbon atom that is bonded to the COOH group, but also the neighboring carbon atoms show similar changes. In particular, the carbon atom bonded to COOH and its nearest neighbor along the tube axis have equivalent charge gain. Later, we will see that these two sites are the energetically preferable functionalization sites for a carboxyl pair. The charge analysis shows as expected that there is no charge gain or loss by the CNT carbon atoms that are more than two rings away from the adsorption site. The results for

with the C−COOH bond nearly perpendicular to the tube axis as shown in Figure 1. The sp2 hybridization of the CNT, which

Figure 1. Top and side views for the adsorption configuration of COOH on the sidewall of a (14,0) CNT. Hydrogen atoms are white, carbon atoms are turquoise, and oxygen atoms are red.

can be assumed by neglecting rehybridization and curvature effects,32 is locally disrupted due to the carboxylation resulting in an sp3 type bonding. We find that the hydroxyl group can rotate around the C−C and assume different binding configurations with an energy difference between them of less than 0.1 eV. Table 1 summarizes the adsorption energies for an isolated carboxyl group on the CNT surface. The adsorption distance is in very good agreement with previous studies, for example, d = 1.57 Å was obtained for the (8,0)21 and (10,0)22 CNTs. The binding energies are more sensitive to the computational model (e.g, k-grid and supercell) and the employed exchange− correlation functional, which explains somewhat the different results obtained previously. For example, Zha et al. reported a binding energy of 1.42 eV for the (9,0) and (10,0) CNTs. Wang et al. obtained a value of 0.92 eV for the (10,0) CNT.22 Using a computational model similar to the one employed in this study and a GGA-PBE DFT functional, Veloso et al.21 obtained 1.58 eV for the (8,0) CNT, while Al-Aqtash and Vasiliev23 obtained the smaller value of 0.97 eV. These two results are surprising considering that both are obtained using localized basis sets as implemented in Siesta.33 It is believed that the origin of this discrepancy is due to the basis-set superposition error (BSSE), which was accounted for in ref 23 but not in ref 21. From Table 1, the extrapolated planewave value for the (8,0) CNT from our study is consistent with the BSSE corrected value 0.97 eV.23 The COOH group binding energy, EBE, decreases as the CNT diameter increases making the carboxylation process less stable. This trend is consistent with the adsorption energies of other covalently bonded systems to the CNT surface, for example, Cl.31 To understand the bonding nature, Table 1 shows the three contributions to EBE as defined in eq 2. As seen

Table 1. Total Binding Energies for COOH along with Its Decomposition into ΔECNT, ΔECOOH, and ΔECOOH as Defined in Eq 2, Diameter (D) of the CNTs, Distance (d) between the CNT and COOH, and Amount of Charge Transfer (QCNT→COOH) from the CNT to COOHa

a

n

ΔECNT

ΔECOOH

ΔEHB

EBE

D

d

QCNT→COOH (milli-e)

9 10 12 14 15 16 18

0.97 0.98 1.02 1.04 1.06 1.06 1.07

0.08 0.08 0.08 0.08 0.08 0.08 0.08

−1.73 −1.64 −1.55 −1.50 −1.47 −1.44 −1.41

−0.68 −0.58 −0.45 −0.37 −0.33 −0.31 −0.26

7.1 7.9 9.5 11.0 11.8 12.6 14.2

1.57 1.57 1.58 1.58 1.58 1.58 1.56

−11.2 −9.4 −7.3 −5.9 −4.2 −4.0 −2.2

Energies are in eV, distances are in Å, and Q is in units of the elementary charge e (e > 0). C

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PDOS analysis shows that this extra electron is localized at the COOH group in the noninteraction limit, as it should be. Compared with the bottom of the pristine CNT bandgap, the band corresponding to the frontier spin-up occupied orbital of COOH is ∼1.3 eV lower in energy, while that of the frontier unoccupied spin-down orbital is ∼0.5 eV higher in energy. This empty orbital is mostly of p character and localized to a large extent on the carboxyl carbon atom. In the optimum binding configuration of COOH to the CNT (lower panel of Figure 3), the sharp molecular levels of the carboxyl group are broadened, which is a sign of the covalent bonding with the CNT. Examining the PDOS while the COOH group approaches the CNT (not shown), we can see that the sharp molecular orbitals of the carboxyl group remain almost intact as in the isolated limit for separations d > 3 Å between the two subsystems. For d < 3 Å, the sp3 hybridization causes the band corresponding to the half-filled orbital of the carboxyl group to broaden and move up in energy becoming closer to the bandgap lower edge in the optimum configuration, as shown in Figure 3b. The empty spin-down orbital of the carboxyl is still in the bandgap region, but now the sp3 hybridization results in an empty band with the corresponding orbital localized on the CNT and overlaps significantly with the band corresponding to the spin-down empty orbital of COOH. The overlap between these two bands would lead to the favorable bonding of an additional COOH group close the first one as we will discuss later. Functionalization in Pairs. To investigate potential clustering effects in COOH-functionalized CNTs, we examined the optimum binding configurations for a pair of carboxyl groups using six potential adsorption sites as shown schematically in Figure 4a. These six adsorption sites can be classified

Figure 2. Charge rearrangement for the optimum configuration of COOH on the sidewall of (14,0) CNT. The values in parentheses show the Hirshfeld charges of an isolated COOH. Charge is measured in milli-electron where the electron charge is negative. Hydrogen atoms are white, carbon atoms are turquoise, and oxygen atoms are red.

the charge analysis are consistent with the results obtained previously on (CH2)5COOH-functionalized (5,5) and (10,0) CNTs where the charges that were induced by the functionalization or due to extra electrons as in Birch reduction were also localized near the sp3 defect.35 The atom-projected density of states (PDOS) yields insight into the electronic nature of the binding mechanism and sheds light on why the COOH pair adsorption is more favorable than the isolated functionalization, as we will illustrate later. Figure 3

Figure 4. (a) A schematic of the six different binding configurations for a COOH pair on the surface of CNT where the first COOH group is adsorbed at the location of the red disk. (b) The six different binding configurations for a (14,0) CNT. Configuration 1 has the lowest adsorption energy. Only atoms close to the functionalization sites are shown. Hydrogen atoms are white, carbon atoms are turquoise, and oxygen atoms are red.

Figure 3. PDOS for the (10,0) CNT + COOH system. Spin-up channel is positive, while spin-down channel is negative. (a) PDOS in the noninteracting limit where the COOH is far from the tube. (b) PDOS of the CNT + COOH system in the optimum adsorption configuration. The inset shows the density of electronic states for the frontier orbitals between −4 and −2.5 eV projected onto the individual CNT C atoms that are shown in Figure 4a. Note that 1′ and 3′ are overlapping with almost the same projections.

according to their distance from the adsorption site of the first COOH group, indicated by “0” in Figure 4a. Configurations 1 and 1′ are at a distance a (≡ C−C bond length) from 0 where C1C0 is parallel to the tube axis; 2 and 2′ are at a distance of √3a from 0 with two C−C bonds apart where C2C0 is perpendicular to the tube axis; and 3 and 3′ are 2a away with three C−C bonds from 0 where C3′C0 is along the tube axis.

shows the orbital-decomposed PDOS for the (10,0) CNT. Other CNTs show essentially very similar behavior. The top panel of the figure shows the PDOS when COOH is very far from the surface (10 Å), that is, the two subsystems are noninteracting as can be guessed from the sharp atomic orbitals of the carboxyl group. The total CNT + COOH system is spin polarized with an extra electron in the spin-up channel. The D

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Table 2. Total Binding Energies in eV for Two COOH Molecules in the Six Binding Configurations That Are Shown in Figure 3a n

a

config

9

10

12

14

15

16

18

1 1′ 2 2′ 3 3′

−1.24 −1.05 −0.56 −0.52 −1.07 −1.15

−1.15 −1.02 −0.44 −0.52 −1.07 −1.05

−1.02 −0.92 −0.31 −0.31 −0.95 −0.96

−0.94 −0.84 −0.22 −0.20 −0.88 −0.90

−0.89 −0.80 −0.19 −0.19 −0.83 −0.86

−0.87 −0.78 −0.16 −0.17 −0.82 −0.84

−0.80 −0.72 −0.11 −0.11 −0.75 −0.80

Configuration 1 is the lowest in energy.

with tube diameter. Comparing the (9,0) and (18,0) CNTs, we can see that the adsorption energy per COOH group for the pair is a factor of 3 more favorable than the single COOH group for (18,0), while it is only a factor of 2 for the (9,0) CNT. Therefore, it would be expected that functionalization by a pair of COOH groups would be the dominant carboxylation mechanism during the oxidation process. The preference for pair over isolated adsorption has been reported for CNTs functionalized with hydrogen36 and recently for Cl.31 Also this was reported before for the phenyls on graphene and on CNTs,37 as well as for defected graphene nanoribbons.38 The clustering effect for carboxylated CNTs seems stronger than that of hydrogen and chlorine and comparable to that of the phenyls. For example, the adsorption energy for single and paired Cl atoms on sidewall of (9,0) CNT are, respectively, −2.0 and −2.25 eV/atom,31 giving a preference of only 0.24 eV/atom or 12.5% of the single adsorption energy. On the other hand, for the carboxyl group, the pair adsorption is favored by 0.56 eV or 82% of the single adsorption energy. To understand why configuration 1 is the most stable, we decomposed the total energy as shown in eq 2. We show in Table 3 the energy contributions for semiconducting and metallic CNTs with close diameters, (14,0) and (15,0) tubes, and an additional larger (18,0) CNT to show diameter dependence of the energetics. As seen from the table, configurations 2 and 3′ have the smallest ΔECNT, which we have verified to be also the case for the other CNTs. Although configuration 1 is the lowest in energy, it imposes the highest strain on the CNT with an energy penalty larger than 0.8 eV compared with configuration 2. The ΔECOOH penalty is substantial for some configurations and is the largest for configurations 2 and 3 and the smallest for configuration 1. It is interesting to note that the CNT deformation energy, ΔECNT, due to the adsorption of two COOH groups is not smaller or equal to twice the deformation energy due to a single COOH group. This result is somewhat surprising because it would have been expected that the first carboxylation event, which disrupts locally the CNT sp2 network and weakens the bonds between the neighboring carbon atoms of the functionalized site, will facilitate and expedite the second carboxylation event in its proximity to reduce the local strain. Therefore, it is not ΔECNT that favors the clustering effect and the pair functionalization but more ΔEHB. This can be understood from the PDOS analysis of the first carboxylation event. The PDOS analysis of Figure 3 shows that the sp3 rehybridization due to carboxylation leads to two bands, only one of them is occupied. The inset of Figure 3b shows that these two bands have fairly similar projections onto the carbon atoms that correspond to the six binding sites of Figure 3.

For illustration, Figure 4b shows the six configurations for the (14,0) CNT. Table 2 summarizes the binding energies per carboxyl group. As can be seen from the table, for all of the CNTs, the binding configuration 1 is the most stable, followed by 3′, 3, and 1′. Configurations 2 and 2′ are less stable than the other four configurations. From the trends in the adsorption energies, we note that the energy difference between the six adsorption configurations decreases as the CNT diameter increases. This is a consequence of the weakening of the curvature effects on the different adsorption configurations. In fact in the limit of a very large diameter CNT or graphene there will be only three different configurations, 1, 2, and 3 (1 and 1′ will be equivalent, and so on). The carboxyl groups’ tendency to bind in pairs to the CNT can be verified by comparing the binding energies of configuration 1 and that of an isolated COOH group. For convenience, we show the isolated and pair binding energies in Figure 5, all measured per COOH group. As can be seen

Figure 5. Binding energy, EBE, per carboxyl group for the isolated (marked as COOH in legend) and pair COOH groups for the six different configurations of Figure 3 plotted as a function of the inverse diameter. The dotted lines mark the metallic CNTs.

from the figure, pair adsorption in configurations 3′, 3, and 1′ in addition to 1 are all more favorable than that of an isolated carboxyl group. For instance, for the (9,0) CNT, the adsorption energy in the pair bonding configuration 1 is −1.24 eV/ COOH, while it is only −0.68 eV for a single isolated carboxyl group. It is also noteworthy that the clustering tendency is enhanced for larger diameter CNTs because the difference between the adsorption energy for pair or single carboxyl group increases E

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and COOH group fixed. We note in passing that these calculations can be more conveniently carried out using a nudged elastic band (NEB)39 approach, but considering the computational expense, we used instead the constrained optimization, which should yield very similar results considering the simplicity of the activation path. Figure 6 shows the potential energy curves for a single COOH adsorption event on four CNTs, including two

Table 3. Decomposition of the Total Binding Energy for (14,0), (15,0), and (18,0) CNTs into ΔECNT, ΔECOOH, and ΔECOOH as Defined in eq 2a config

ΔECNT

1 1′ 2 2′ 3 3′

2.89 2.36 2.06 2.26 2.24 2.14

1 1′ 2 2′ 3 3′

2.87 2.40 2.27 2.27 2.27 2.17

1 1′ 2 2′ 3 3′

2.86 2.48 2.11 2.29 2.34 2.22

ΔECOOH

ΔEHB

0.56 0.78 1.01 0.78 0.94 0.73

−5.32 −4.81 −3.52 −3.43 −4.95 −4.66

0.58 0.78 0.90 0.79 0.90 0.73

−5.24 −4.79 −3.56 −3.44 −4.84 −4.63

0.62 0.77 0.96 0.79 0.91 0.75

−5.10 −4.70 −3.30 −3.31 −4.73 −4.56

(14,0)

(15,0)

(18,0)

a

Figure 6. Reaction barrier for carboxylation of the (10,0), (12,0), (14,0), and (15,0) CNTs. The zero of energy is set for a very large separation between the CNT and the carboxyl group. Lines are to guide the eyes.

All energies are in eV.

semiconducting, (10,0) and (14,0), and two metallic, (12,0) and (15,0), CNTs. The transition state is located at ∼2.3 Å showing very little dependence on the tube diameter. The activation energies Ea are summarized in Table 4. For the

Furthermore, as seen from the inset, the carbon atom for adsorption configuration 1, C1, has the largest projection of the density of states for the two frontier bands, followed by carbon atoms C1′, C3, and C3′. This coincides with the ordering of the binding energies (cf. Table 2). Thus, when the adsorption of the second COOH group is activated by functionalizing the 1′ site, the half-occupied orbital, which has the largest projection on C1′, will be fully occupied leading to the favorable interaction. Activation and Desorption Energies of COOH. The adsorption of COOH pairs is energetically more favorable than isolated adsorption events and thus pair adsorption should be prevalent in the thermodynamic limit. However, there could be a significant kinetic hindrance for this process, which would make this mechanism not operative in the time span of the experiments. To address this, we can assume that pair carboxylation will take place in two steps where one carboxyl group functionalizes first the CNT surface, followed by another adsorption event in a bonding configuration as shown in Figure 4. To quantify the kinetic barriers, we calculate the activation energies for these two steps. We focus only on the most energetic pair configuration 1 because these calculations are prohibitively expensive. The activation energy, Ea, measures the relative ease to functionalize a CNT and is defined as the energy needed by the carboxyl group to overcome the adsorption barrier on the CNT surface. This can be determined as the energy difference between the energies of the isolated pristine CNT and  COOH group and the maximum energy as the carboxyl group approaches the CNT. To compute Ea, we mapped out the potential energy of the CNT + COOH system starting from the isolated limit where they are separated by a distance d ≈ 8 Å to the optimum binding configuration. The calculations are carried out using constrained optimization where all of the coordinates are relaxed keeping the distance between the CNT

Table 4. Activation, Ea, and Desorption, Ed, Energies (in eV) for Isolated and Pair Adsorptiona CNT (10,0) (12,0) (14,0) (15,0) (15,0)

Ea isolated COOH 0.10 0.14 0.23 0.23 COOH pair 0.27

Ed 0.78 0.59 0.60 0.56 1.16

a

For the isolated COOH group, the potential curves are shown in Figure 5.

(10,0) and (14,0) semiconducting CNTs, Ea is, respectively, 0.10 and 0.23 eV, while for (12,0) and (15,0) metallic CNTs, Ea is 0.14 and 0.23 eV. The activation energy increases with the tube diameter regardless of the tube metallic character. Additionally, it would have been expected that the (15,0) would have a larger Ea compared with (14,0) considering its larger radius, but as seen from the results both have similar values for Ea. This suggests that the metallic CNTs are easier to functionalize than the semiconducting ones, which is perhaps not very surprising considering that metallic CNTs are more reactive. The differences between the metallic and semiconducting CNTs, and the trends of Ea with tube diameter explain why only small diameter metallic CNTs are dissolved upon the oxidation treatment.12 The desorption energy Ed can also be computed knowing the transition state along the activation path and is defined as the energy difference between the transition and optimum F

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ACKNOWLEDGMENTS The author would like to thank A. Star for helpful discussions. Calculations are performed in part at the University of Pittsburgh Center for Simulation and Modeling. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number OCI-1053575.

configurations of the carboxyl group. The results are also summarized in Table 4. As can be seen from Figure 6, the desorption energy is also the sum of the binding energy and the activation energy, both of which show opposite trends with the tube diameter. Thus, it would be expected that for certain CNTs, the desorption energy will not vary much with the tube diameter. The potential energy curves of Figure 6 show that the  COOH group can also physadsorb to the CNT sidewall at a distance d > 4 Å from the CNT surface. However, both the adsorption energies and distances of these physadsorbed states are probably not very accurate considering that the present density functional is not able to capture long-range dispersion interactions, which are relevant for the description of the physadsorbed state. We also mapped the potential energy curve for the activation of a second COOH group for configuration 1. This is done only for a (15,0) CNT using constrained minimization. The activation and desorption energies are shown in Table 4. We note that the actual activation energy will presumably be smaller if obtained using NEB rather than using constrained minimization due to the complexity of the potential energy surface in this case as compared with the single adsorption case of Figure 6. Nevertheless, with constrained optimization we found an activation path that is comparable to that of an isolated COOH group. This shows that the pair adsorption is not hindered by kinetic barriers and thus should be the dominant form of carboxylation in oxidative treatments.

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CONCLUSION AND SUMMARY

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AUTHOR INFORMATION

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REFERENCES

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We employ density functional calculations to study the atomic structure, energetics, and electronic structure of side-wall COOH functionalized CNTs. We limited the study to zigzag CNTs with chiralities n = 9, 10, 12, 14, 15, 16, and 18 paying in particular attention to trends in tube diameter. We find that an isolated COOH group binds covalently in atop configuration to a sidewall carbon atom of the tube, disrupting locally the sp2 network and acquiring an sp3 hybridization. We found that this adsorption configuration induces a small charge transfer from the CNT to the carboxyl groups. The amount of charge transfer, as well as the binding energy, of the carboxyl to the CNT decreases with the tube diameter. The main finding of this study is that thermodynamically it is more favorable for  COOH to adsorb in pairs on top of two neighboring carbon atoms that are bonded along the tube axis. This clustering effect becomes even more favorable for larger diameter CNTs, because the difference in adsorption energy between isolated and pair carboxylation increases with tube diameter. We show also that this clustering tendency is not kinetically hindered compared with the isolated COOH adsorption. The study underscores the importance of the clustering effect for COOH groups as well as other radicals in interpreting the experimental data.

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. G

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