Influence of Diameter, Length, and Chirality of Single-Walled Carbon Nanotubes on TheirFree Radical Scavenging Capability

Annia Galano*Departamento de Quımica, UniVersidad Autonoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col.Vicentina, Iztapalapa, C. P. 09340, Mexico

ReceiVed: May 18, 2009; ReVised Manuscript ReceiVed: August 18, 2009

Density functional theory calculations have been used to model the influence of diameter, length, and chiralityof single-walled carbon nanotubes (SWCNT) on their free radical scavenging activity. SWCNTs with widedistributions of different diameter, length, and chirality are proposed to have good free radical scavengingactivity in the gas phase and in nonpolar environments. Therefore, they can be used as free radical traps withpotential application in environmental and biological systems. In general, thinner tubes are expected to havebetter antiradical activities. However, the curvature of the tubes seems to modify the antiradical activity ofarmchair nanotubes. Therefore, for wide distributions of tube diameter, the zigzag SWCNTs are expected tobe more efficient for free radical scavenging purposes than the armchair ones. The length of the tubes onlyhas a minor influence on the free radical trapping efficiency of SWCNTs. From the results reported in thiswork, thin and zigzag nanotubes are recommended as those with the best antiradical activity, regardless oftheir length.

Introduction

Carbon nanotubes (CNTs) are fascinating molecules that haveimpacted broad areas of science and technology.1–7 Their wideapplicability and peculiar properties arise from their uniquestructure. CNTs constitute large arrays of conjugated doublebonds, and therefore they are expected to show great electrondonor and acceptor capabilities. This particular feature makesthem particularly reactive toward free radicals, which are highlydangerous to human health and environment. Therefore, thecapability of CNTs to act as efficient free radical scavengers isa promising attribute that can be applied to fight these damagingspecies. Despite the importance of such application, very littleresearch has been devoted to it. In fact, there are only fourreports on this subject so far.8–11

Chronologically, Watts et al.8 were the first to report thatmultiwalled carbon nanotubes (MWCNT) can act as antioxidantsas well as halogen absorbers. These authors found that theoxidation of polystyrene, polyethylene, polypropylene, andpoly(vinylidene fluoride) is retarded by the presence of carbonnanotubes. Shortly after, Fenoglio et al.9 observed that when incontact with hydroxyl or superoxide radicals, MWCNTs exhibita remarkable radical scavenging capacity. After these twoexperimental results, the first and only previous theoreticalinvestigation on this subject was performed.10 The reactions ofa (5,5) singled-walled carbon nanotube (SWCNT) fragment withsix different free radicals were modeled, and it was concludedthat SWCNTs can act as free-radical sponges based onthermodynamic and kinetic considerations. Moreover, it wasfound that once a first radical is attached to the tube, furtheradditions are increasingly feasible. The most recent work onthis topic experimentally confirmed that SWCNTs are potentantioxidants.11 In the same work, cytotoxicity assays also showedthat SWCNTs have little or no toxic effect on cell viability,which is very important for biological applications.

When CNTs are synthesized, a mixture of tubes with differentdiameter, length, and chirality is obtained.12 Actually producingSWNTsofdefinedstructures isamajor technologicalchallenge.13,14

Therefore, now that we know that CNTs can efficiently act asfree radical scavengers, the next questions are if their diameter,length, and chirality affect this valuable property and how.Accordingly, it is the main aim of the present work to addressthese questions.

Computational Details

Electronic structure calculations have been performed withthe Gaussian 0315 package of programs. Full geometry optimi-zations and frequency calculations were carried out for all ofthe stationary points using the B3LYP hybrid HF-densityfunctional and the 3-21G basis set. No symmetry constraintshave been imposed in the geometry optimizations. The energiesof all of the stationary points were improved by single pointcalculations at B3LYP/6-311+G(d) level of theory. Thermo-dynamic corrections at 298 K were included in the calculationof relative energies. Spin-restricted calculations were used forclosed shell systems and unrestricted ones for open shellsystems. Local minima were identified by the number ofimaginary frequencies (NIMAG ) 0). It seems worthwhile toemphasize the fact that any theoretical model aiming to makepredictions concerning practical applications must be analyzedin terms of Gibbs free energies, which implies the necessity ofperforming frequency calculations that are particularly expen-sive. Accordingly, it seems a better compromise to performfrequency calculations at a low level of theory than increasethe level and analyze the results only in terms of electronicenergy.

The stationary points were first modeled in the gas phase(vacuum), and solvent effects were included a posteriori bysingle point calculations using a polarizable continuum model,specifically the integral-equation-formalism (IEF-PCM)16 atB3LYP/6-311+G(d) level of theory, with benzene as solvent* Corresponding author. E-mail: agalano@prodigy.net.mx.

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10.1021/jp904646q CCC: $40.75 2009 American Chemical SocietyPublished on Web 10/07/2009

for mimicking nonpolar environments. Polar environments werenot included because pure carbon nanotubes are not expectedto be soluble in such media.

Results and Discussion

Single-walled carbon nanotubes (SWCNTs) are cylindricalmolecules composed of carbon atoms that can be thought of asrolled-up graphene sheets. Their structures can be unambigu-ously defined by a chiral vector that represents the roll-updirection:

where a1 and a2 denote equivalent lattice vectors of the graphenesheet, and n and m are integers (0 e |m| e n) (Figure 1).

Finite SWNTs fragments of extreme chirality (armchair andzigzag) with diameters ranging from 0.4 to 1.1 nm have beenselected for the present study. The thinnest tubes were selectedwith diameters ≈ 0.4 nm because it is the smallest experimen-tally achievable diameter.17 Different lengths ranging from 0.7to 2.0 nm (from 3 to 8 hexagons long) have also been testedfor the thinnest tubes: (3,3) and (5,0). The dangling bonds atthe ends of the nanotubes have been saturated by hydrogenatoms to avoid unwanted distortions. The SWNTs free radicalscavenging activity has been modeled through the reaction ofthese fragments with the methoxyl radical (OCH3). Thesereactions have been computed in the gas phase as well as inbenzene solution, aiming for environmental and biologicalapplications, respectively.

The tubes have been selected in such a way that in everycase there is an armchair and a zigzag fragment of similardiameter (Table 1). This selection has been made for faircomparisons accounting for the effect of chirality. The diameters(D) reported through this Article have been estimated (in nm)according to:

Each addition product has been modeled with the free radicalattached to a central hexagon of the tube (Figure 2) to prevent

unwanted interactions with H atoms at the end of the tubes.The most relevant geometrical parameter associated withformation of the adducts is the C-O distance corresponding tothe newly formed bond (r1). Another geometrical parameterthat might be interested to analyze is the O-C distance in themethoxy moiety (r2), particularly relative to its value in thereacting O-CH3 radical (1.430 Å, at the used level of theory).

The influence of the SWCNTs diameter and length on thisbond distance is shown in Figure 3. The shortest d(C-O) wasfound for the thinnest tubes, for both armchair and zigzagnanotubes. In addition, a regular trend was observed, indicatingthat as the diameter of the tube increases so does the d(C-O)distance. It seems logical to assume that an upper limit valuemust exist. Even though it was not reached with the studiedfragments for the wider tubes, the d(C-O) seems to be nearsuch limit. For SWCNTs with diameters up to ∼0.7 nm, thenew formed bond was found to be larger for zigzag nanotubesthan for the corresponding armchair ones. This differencepractically vanishes for tubes with diameters g 0.96 nm. Thelength of the tubes influences the magnitude of d(C-O) to amuch less extent. In fact, the maximum variation of d(C-O)with diameter was found to be 0.04 and 0.03 Å for armchairand zigzag fragments, respectively, while the maximum variationof d(C-O) with length is only 0.004 and 0.003 Å. A slightzigzag pattern arises as the length of the tubes increases.However, the variations are so small that it can be consideredthat the d(C-O) distance remains unchanged, at least for thelengths considered in the present study. There is no reason toexpect a sudden change in this behavior for longer tubes.

The energy barriers have not been computed in the presentwork, because it was already proposed that the reactions ofpristine carbon nanotubes with the OCH3 radical are diffusioncontrolled.10 This is because such reactions are barrierless interms of enthalpy and have a very low barrier in terms of Gibbsfree energies of reaction (∆Gq ≈ 4 kcal/mol); therefore, thiswork only focuses on Gibbs free energies of reaction, whichcontrolled the products formation under equilibrium conditions.

The Gibbs free energies of reaction (∆G), at 298.15 K, for•OCH3 additions to the studied (n,0) and (n,n) fragments (threehexagons long), are reported in Table 2. For the gas phase, theywere performed using a standard state of 1 atm, as calculatedfrom the Gaussian program outputs. However, for reactions insolution, the reference state has been changed from 1 atm to 1

Figure 1. Definition of roll-up vector as linear combinations of basevectors a1 and a2. Zigzag: θ ) 0 (n,0). Armchair: θ ) 30 (n,n). Chiral:0 < θ < 30 (n,m).

TABLE 1: Diameters (nm) of the Studied (n,0) and (n,n)Nanotubes

tube diameter tube diameter

(5,0) 0.392 (3,3) 0.407(7, 0) 0.548 (4,4) 0.542(9,0) 0.705 (5,5) 0.678(10,0) 0.783 (6,6) 0.814(12,0) 0.940 (7,7) 0.949(14,0) 1.096 (8,8) 1.085

Ch ) (n, m) ) na1 + ma2 (1)

D ) 0.0783√n2 + m2 + nm (2)

Figure 2. Selected addition products. (A) Frontal view, (B) lateralview.

18488 J. Phys. Chem. C, Vol. 113, No. 43, 2009 Galano

M, and the solvent cage effects have been included accordingto the corrections proposed by Okuno,18 taking into account thefree volume theory.19 These corrections are in good agreementwith those independently obtained by Ardura et al.20 and havebeen successfully used by other authors.21–24 The expression usedto correct the Gibbs free energy is:

where n represents the total number of reactant moles. Accordingto expression 3, the cage effects in solution cause ∆G to decreaseby 2.54 kcal/mol for bimolecular reactions, at 298 K. Thislowering is expected because the cage effects of the solventreduce the entropy loss associated with any adduct formation,in reactions with molecularity equal to or larger than two.Therefore, if the translational degrees of freedom in solutionare treated as in the gas phase, the cost associated with theirloss when two or more molecules form a complex system insolution is overestimated, and consequently these processes areoverpenalized in solution.

All of the studied reactions were found to be exothermic,and most of them were found to be exergonic, regardless of thetube diameter (Table 2). The exceptions, with ∆G > 0, are theadditions to (6,6), (7,7) and (8,8) fragments in benzene solutions,and also to (5,5) in the gas phase. The feasibility of the studiedreactions was found to be increased by the presence of nonpolarsolvents, benzene in the present study; that is, the Gibbs free

energies of reaction are systematically more negative in benzenesolution than in gas phase. The dependence of the Gibbs freeenergies of reaction with the tube diameter is shown in Figure4A. It should be noticed that the present study is aiming topredict practical applications. In addition, addition reactions areinvolved, which have known entropy losses. Therefore, themagnitude that would determine the viability of the studiedprocesses is the Gibbs free energy.

From the results in Table 2, it stands out that zigzag nanotubesare systematically more reactive toward the OCH3 free radical,and probably toward free radicals in general, than theircorresponding armchair partners of similar diameter. This canbe explained by the fact that the highest occupied molecularorbitals (HOMO) of zigzag tubes are systematically higher inenergy than the HOMOs of the armchair tubes with equivalentdiameter. Therefore, the reactivity of the zigzag tubes towardelectrophilic radicals is higher than that of the correspondingarmchair tubes. Armchair, (n,n), nanotubes show a regular trendof decreasing their free radical scavenging activity as the tubesbecome wider. Zigzag tubes, on the other hand, show noindication of such trend. Apparently their reactivity toward freeradicals is less sensitive to the tube diameter than that ofarmchair SWCNTs. According to the results shown in Figure4A, for wide distributions of tube diameter, the zigzag structureis more efficient for free radical scavenging purposes.

The influence of the length of the tubes on their reactivitytoward free radicals has also been analyzed in terms of ∆H and∆G (Table 3). In this case, all of the reactions were found tobe exothermic and exergonic (but they all correspond to thethinnest fragments). The presence of the solvent also promotesthe studied reactions; that is, the exothermicity and exergonicityof the reactions are larger in benzene solutions than in gas phase.To help in visualizing any possible trend of the free radicalscavenging activity of the tubes with their lengths, a plot of∆G values versus the length in hexagons is shown in Figure4B. For the shortest tubes, the zigzag fragments show betterantiradical activity than do the armchair fragments. However,this tendency is inverted for tubes six, or more, hexagons long.However, actual SWCNTs are longer than those modeled inthe present study. Because for the (3,3) tubes the ∆G valuesdid not converge up to 8 hexagons, additional calculations havebeen performed for this particular case for tubes up and to 10hexagons long. For such lengths, it seems that the convergenceis achieved. In any case, what really matters is that all of theaddition processes were found to be energetically viable.

Figure 3. Distance of the formed C-O bond (A) as a function of the tube diameter, and (B) as a function of the tube length.

TABLE 2: Enthalpies (∆H, kcal/mol), Gibbs Free Energiesof Reaction (∆G, kcal/mol) Corresponding to OCH3

Additions to the Studied (n,0) and (n,n) Fragments (ThreeHexagons Long), and HOMO Energies (eV)

∆H ∆G HOMO

gas benzene gas benzene gas benzene

(5,0) -41.39 -40.31 -29.60 -32.95 -3.891 -3.839(7,0) -53.27 -52.64 -40.94 -44.74 -4.078 -4.004(9,0) -44.69 -43.81 -32.45 -35.99 -4.168 -4.102(10,0) -43.89 -43.19 -32.08 -35.81 -4.184 -4.118(12,0) -50.26 -49.34 -39.55 -43.06 -4.212 -4.152(14,0) -48.12 -51.28 -36.01 -43.59 -4.194 -4.078(3,3) -29.38 -28.75 -17.30 -21.10 -4.748 -4.738(4,4) -14.61 -13.95 -2.42 -6.19 -4.954 -4.918(5,5) -10.26 -9.70 1.90 -1.97 -4.727 -4.695(6,6) -6.42 -5.82 6.25 2.42 -4.612 -4.583(7,7) -4.58 -3.97 8.02 4.20 -4.527 -4.503(8,8) -3.11 -2.58 9.71 5.82 -4.464 -4.440

∆GsolVM = ∆Ggas - RT{ln[n10(2n-2)] - (n - 1)} (3)

Free Radical Scavenging Capability of SWCNTs J. Phys. Chem. C, Vol. 113, No. 43, 2009 18489

Therefore, thin nanotubes can be proposed as compounds withexcellent free radical scavenging activity, regardless of theirlength and chirality. They seem to be viable choices for bothbiological and environmental applications because the reactionsare exergonic in both the gas phase and benzene solutions.

Conclusions

Analyzing all of the previously discussed results together, itseems that some generalizations can be made. SWCNTs withwide distributions of different diameter, length, and chiralityare expected to have good free radical scavenging activity inthe gas phase and in nonpolar environments. Therefore, theycan be used as free radical traps with potential application inenvironmental and biological systems. In general, thinner tubesare expected to have better antiradical activities. However, thecurvature of the tubes seems to play an important role in theantiradical activity only for armchair nanotubes. Therefore, forwide distributions of tube diameter, the zigzag SWCNTs areexpected to be more efficient for free radical scavengingpurposes than the armchair ones. It was also found that thelength of the tubes only has a minor influence in the free radicaltrapping efficiency of SWCNTs. Taking into account all of these

findings together, thin and zigzag nanotubes are recommendedas those with the best antiradical activity, regardless of theirlength.

Acknowledgment. I thank Laboratorio de Visualizacion yComputo Paralelo at UAM-Iztapalapa for the access to itscomputer facilities.

References and Notes

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Figure 4. Gibbs free energy of reaction in benzene solution (A) as a function of the tube diameter, and (B) as a function of the tube length.Continuous lines represent benzene solutions, and dotted lines represent gas phase.

TABLE 3: Enthalpies (∆H, kcal/mol) and Gibbs FreeEnergies of Reaction (∆G, kcal/mol) Corresponding to OCH3

Additions to (5,0) and (3,3) Fragments from Three to SevenHexagons (h) Long

∆H ∆G

gas benzene gas benzene

(5,0) 3 h -41.39 -40.31 -29.60 -32.95(5,0) 4 h -44.53 -44.48 -32.93 -37.31(5,0) 5 h -39.67 -38.71 -27.69 -31.15(5,0) 6 h -30.55 -29.52 -17.96 -21.36(5,0) 7 h -23.19 -23.44 -9.49 -14.17(5,0) 8 h -22.89 -21.25 -10.00 -12.79(3,3) 3 h -29.38 -28.75 -17.30 -21.10(3,3) 4 h -28.10 -27.56 -15.91 -19.80(3,3) 5 h -32.27 -31.59 -20.49 -24.24(3,3) 6 h -36.87 -36.34 -25.72 -29.62(3,3) 7 h -29.01 -28.39 -16.52 -20.34(3,3) 8 h -35.61 -34.82 -23.89 -27.53(3,3) 9 h -31.46 -31.01 -19.03 -23.02(3,3) 10 h -31.39 -30.68 -18.99 -22.71

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