J. Phys. Chem. B 2005, 109, 6153-6158
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Theoretical Analysis of Fluorine Addition to Single-Walled Carbon Nanotubes: Functionalization Routes and Addition Patterns Gregory Van Lier,*,† Christopher P. Ewels,‡ Filippo Zuliani,§ Allesandro De Vita,§,| and Jean-Christophe Charlier†,⊥ Unite´ de Physico-Chimie et de Physique des Mate´ riaux (P.C.P.M.), UniVersite´ Catholique de LouVain (UCL), Place Croix du Sud, 1 Boltzmann, B-1348 LouVain-la-NeuVe, Belgium, Laboratoire de Physique des Solides, UniVersite´ Paris Sud, Building 510, 91405 Orsay, France, INFM-DEMOCRITOS National Simulation Center and Center of Excellence for Nanostructured Materials (CENMAT), UniVersity of Trieste, Italy, Physics Department, King’s College London, Strand, London WC2R 2LS, United Kingdom, and Research Center in Micro- and Nanoscopic Materials and Electronic DeVices (CERMIN), UniVersite´ catholique de LouVain (UCL), Belgium ReceiVed: September 4, 2004; In Final Form: December 1, 2004
We present a theoretical investigation on the chemical addition patterns governing the fluorination of single wall carbon nanotubes. Monte Carlo calculations based on a Hu¨ckel model suggest that fluorination is stabilized in a bandlike pattern due to electronic confinement effects on the tube bond network topology. Ab initio analysis of the fluorination of small nanotubes show that fluorine addition along the nanotube axis direction is favored by a mechanism of carbon framework distortion. The experimentally observed formation of fluorine bands may be thus explained in terms of multiple axial C2F rows expanding by contiguous axial addition.
Introduction In recent years, great attention has been devoted to the chemical functionalization of carbon nanotubes (CNs) in the development of a new class of materials with enhanced properties.1 However, the range of chiralities and diameters present in a general experimental sample of carbon nanotubes makes it difficult to analyze the addition products upon functionalization. Nonetheless, major advances in synthesis and purification methods2,3 have enabled rapid development of carbon nanotube chemistry.4 Chemical functionalization of nanotubes is important in the development of novel materials, notably to improve nanotube solubility and purification techniques. Functionalization also provides a route to improved matrix-nanotube bonding in nanotube composites. Fluorination of carbon nanotubes has been extensively studied both experimentally and theoretically.5 It enables solubilization of nanotubes in many solvents6 and can be used as a starting point for further chemical modification.6-9 The influence of fluorination on mechanical10 and electrochemical11-13 properties has also been investigated. Fluorine is an unusual chemical addend in that calculations predict it does not change the metallic character of certain nanotubes.14,15 Fluorinated nanotubes have potential application as electrodes in lithium electrochemical cells.11 Fluorination may also be useful for pyrolytic “cutting” of nanotubes to provide short tubes of controlled length.16 Fluorination can be achieved with both elemental fluorine17 or F2 gas.18 Although initial claims suggested carbon nanotubes * Author to whom correspondence should be addressed. Phone: +3210-47-26-17. Fax: +32-10-47-34-52. E-mail:
[email protected]. † Unite ´ de Physico-Chimie et de Physique des Mate´riaux, Universite´ Catholique de Louvain. ‡ Laboratoire de Physique des Solides, Universite ´ Paris Sud. § INFM-DEMOCRITOS National Simulation Center and Center of Excellence for Nanostructured Materials (CENMAT), University of Trieste. | Physics Department, King’s College London. ⊥ Research Center in Micro- and Nanoscopic Materials and Electronic Devices (CERMIN), Universite´ catholique de Louvain.
fluorinate up to a C1F1 ratio,19 more recent work shows that fluorination without deterioration of the nanotubes is only possible up to C2F.7,17,18,20 Kelly et al. presented different addition patterns for this degree of fluorination,21 and stable endohedral structures have been proposed but not yet achieved experimentally.10,15,22 Defluorination was performed upon sonication with anhydrous hydrazine as a reagent.6,17 Scanning tunneling microscopy (STM) images of fluorinated single-walled carbon nanotubes show a dramatic banded structure, attributed to fluorine adding over broad continuous regions, believed to follow a circumferential addition pattern.21,23 Various distinct features govern the chemical reactivity of carbon nanotubes, the effect of curvature, induced by rolling a single graphene layer to form the nanotube, the helicity and diameter of the nanotube, characterized by the direction in which the graphene is rolled, and the number of atoms around the circumference of the nanotube. Besides, for fluorination, the difference between addition patterns will be influenced by both the difference in fluorine-fluorine interaction and the strain induced upon the carbon framework. Nanotubes have only one type of carbon atom (all three-fold coordinated) and only two (in the case of armchair and zigzag CNs) or three (general chiral nanotubes) distinct symmetry-independent bonds. As these bonds are differently oriented with respect to the curvature of the nanotube body, they are expected to exhibit a different chemical reactivity.24,25 During fluorination, the fluorine atoms preferentially add next to each other.26 Thus, although fluorination can be achieved with both elemental fluorine17 or F2,18 the same nanotube addition patterns and ratios will be obtained with the two methods. The chemical reactivity will influence the subsequent addition patterns, together with the experimental reaction conditions and subsequent treatment of the fluorinated carbon material. Detailed analysis of the interplay of these parameters is important to improve the control of the fluorination process.
10.1021/jp046005q CCC: $30.25 © 2005 American Chemical Society Published on Web 03/01/2005
6154 J. Phys. Chem. B, Vol. 109, No. 13, 2005 In this work, we perform a theoretical analysis of the fluorination of carbon nanotubes to understand the addition process and the experimentally observed bands. Our description is based on fundamental quantum theory, spanning from tightbinding models to the more accurate full first principles (for a review, see ref 27). We start with a tight-binding investigation of fluorine addition to different types of infinite single-walled carbon nanotubes (SWCN) within a Monte Carlo scheme. The analysis focuses only on electronic confinement effects induced by different absorption patterns of fluorine and their link to curvature and helicity of SWCNs, neglecting all effects of carbon framework distortion. While this is fully justified in the cases of multiwalled carbon nanotubes (MWCNs) or large diameter SWCNs, distortion of the tube structures may be important elsewhere and is investigated further on in this work using first principles techniques. However, even at the simplest level of tight-binding modeling, we find a preference to form circumferential banded domains, consistent with the experimental results.21,23 This first study was followed by a more in-depth analysis performing ab initio calculations of circumferential and axial fluorine addition on (5,5) and (9,0) finite SWCNs, including tube distortion effects for a better description. At this level of theory, a clear preference for axial addition was found. To further understand fluorinated band growth, we performed an ab initio study of fluorine addition to a partially fluorinated (5,5) nanotube, predicting axial C2F domains to expand by contiguous axial addition with circumferential edges. Experimentally observed banding could thus be obtained upon an axial addition pattern. Theoretical Calculations Our tight-binding analysis (TB) is based on a modified Hu¨ckel model, in which the hopping integral β between nearest-neighbor carbon atoms is the only element used to construct the Hamiltonian matrix of the system. In this simple model, fluorinated carbon atoms are assumed not to participate in the π-bonding network, so that the hopping terms involving them is set to zero. Since the Hu¨ckel model is an independent particle model, we can easily obtain the total energy of the system from a single Hamiltonian matrix diagonalization for any given distribution of adsorbed fluorine atoms. Notice that this model only aims at representing direct on-top covalent C-F adsorption and does not include different absorption types or bonding characters such as bridging geometries or ionic adsorption. Also, deformations of the nanotube frame induced by fluorination are not described, so that the computed energy used in the Monte Carlo procedure is only due to the size and topology of the “free” islands of unfluorinated carbon atoms participating at any given time in the nanotube π-bonding network. The Monte Carlo trial step rearranging the fluorine atoms on the nanotube frame support is simply achieved by moving one randomly chosen F atom at a time to a free nearest-neighbor carbon atom (if any exists). We use a simple simulated annealing procedure to search for the minimum energy configuration for the fluorinated SWCN. We use a (5,5) and a (10,0) SWCN, with a section of 240 carbon atoms and a circumference of 20 atoms to see the effects of addition patterns on SWCNs of different helicity. The ab initio calculations were performed on open and closed finite (5,5) and (9,0) SWCNs of similar diameter, to maximize the effect of curvature. These systems all have approximately 150 carbon atoms, and the open nanotubes are hydrogenterminated. Energies are calculated with Hartree-Fock HF/321G using semiempirical AM1 fully optimized geometries. AM1
Van Lier et al. has successfully been applied for geometry optimizations in similar studies.28-30 For the final part of the study, a (5,5) open carbon nanotube with 190 carbon atoms was also considered, fully optimized at ab initio HF/3-21G upon fluorination. These calculations were performed using GAUSSIAN 03.31 Results and Discussion Ideal Systems: Tight-Binding Analysis. To analyze the addition patterns governing the fluorination of carbon nanotubes, ideal (5,5) and (10,0) SWCNs were considered using periodic boundary conditions. We first confront the energy of fluorine addition on zigzag and armchair lines for the two systems within our simple TB model. Our results indicate that armchair addition is more stable than a zigzag pattern and suggest a general preference to form periodic circumferential domains. To initiate the Monte Carlo (MC) annealing procedure in a high-coverage situation, the fluorine atoms are placed on the nanotube so that domains of unfluorinated carbon atoms with predefined shapes are left on the nanotube body. Namely, we start with a single, a double, and a triple ring around the circumference of the nanotube and a spotlike domain (Figure 1). In a first set of simulated annealing calculations, we progressively increase the fictitious temperature kBT to span the range from 0.3 to 1.0 eV, with a temperature increase of 7 × 10-9 eV per MC step. As the width of the unfluorinated domain increases from one simulation to the next, the temperature needed to break off fluorine domains also increases. Comparing 64 unfluorinated carbon atoms forming a triple ring and a spotlike domain (Figures 1a and 1b), we find the spotlike domain is less stable than the triple ring and thus more subject to thermal rearrangement (Figure 2). This suggests that even if fluorine atoms adsorb on the SWCN surface leaving spotlike domains of free carbon atoms, these domains may reassemble spontaneously into (multiple) rings in order to minimize electronic confinement effects. We stress that, to this point, we have not taken the repulsion between fluorine atoms or strain effects induced in the SWCN carbon framework into account. Similar results are obtained switching to low-coverage conditions, with rings of adsorbed fluorine atoms forming on the SWCN surface. To further investigate the effects of electronic confinement induced by different fluorine addition patterns, we started novel simulations from a system containing only six fluorine atoms adsorbed on the same SWCN surface. Upon being annealed, these reorganize into a hexagonal pattern since hexagonal rings correspond to the lowest energy in our TB model. Fluorine atoms were further randomly added and allowed to diffuse one at the time from this point on, allowing the systems to evolve for a number of Monte Carlo steps compatible with equilibration of the position of all fluorine atoms on the SWCN between each “novel adsorption” event. The fluorine atoms were in all cases observed to build up connected domains starting from the hexagon initially present, whose shape evolves until eventually band-shape islands around the nanotube circumference are formed. We finally added an extra term in our Hamiltonian to penalize adsorption of fluorine atoms on carbon atoms whose nearestneighbor carbon atom adsorption sites are occupied by other fluorine atoms. Note that this condition ensures the C2F maximum experimental adsorption ratio. Even in this case, the adsorbed fluorine atoms are spontaneously seen to assemble in ring-shaped domains around the CN circumference. Ab Initio Analysis of Circumferential and Axial Addition. Initial ab initio calculations were performed on an infinite flat
Theoretical Analysis of SWCN Fluorine Addition
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Figure 1. Starting domains on our unrolled fluorinated (5,5) SWCN: (a) triple ring; (b) spotlike addition. Initial (b) and final (c) disposition of 64 unfluorinated spotlike packed carbon atoms from a Monte Carlo annealing at kBT ) 0.42 eV. The nanotubes are depicted with the chiral vector along the x direction and the tube axis along the y direction. Fluorinated carbon atoms are depicted as gray atoms, unfluorinated as white.
Figure 2. Total energies of the fluorinated (5,5) SWCN systems containing a triple ring (light) and a spotlike (dark) domain of unfluorinated carbon atoms as a function of temperature, obtained from Monte Carlo simulations, indicating a higher stability of the ring geometry (see text).
graphene sheet. The sheets were fluorinated at C2F (50%) and C4F (25%) coverage in zigzag and armchair lines. At 25% coverage, the energies were identical; however at 50% coverage, the armchair arrangement was 0.48 eV more stable per fluorine atom, consistent with the TB results. The 50% coverage zigzag introduced many new electronic states around the Fermi level whereas the armchair arrangement opened the gap. These results are consistent with graphene sheet edges where armchair edges are found to be more stable and semiconducting whereas zigzag edges are less stable and metallic.32 Further ab initio calculations were performed using SWCNs of different chirality, namely, a 150 C atom open (5,5), a 144 C atom open (9,0), and a 150 C atom closed (5,5) and (9,0) SWCN. The open nanotubes are hydrogen-terminated, giving C150H20 and C144H18 stoichiometry, respectively. A 1,2-addition path is followed, each time fluorinating the next carbon atom in a given direction, either circumferential (perpendicular to the tube axis) or axial (following the tube axis). In this way, the effect of curvature can better be incorporated as well as the difference between armchair and zigzag addition patterns depending on nanotube helicity. Figure 3 shows these patterns for fluorination of the 150 atom open (5,5) nanotube; the
Figure 3. Circumferential (normal) and axial (italic) addition order of fluorine atoms to a 150 carbon atom open (5,5) hydrogen-terminated nanotube (tube axis direction is from top to bottom).
numbering coincides with the addition order. Addition is started in the middle of the tube to minimize interaction with the hydrogenated tube ends. All calculations include full structural optimization of the atomic positions. Addition of fluorine to SWCNs is very exothermic. Although the reactivity of carbon nanotubes is lower than that of fullerenes, an exothermic energy release of approximately 60 kcal/mol is still found for each of the additions studied in this work, i.e., up to 18 (20) fluorine atoms for following a circumferential addition path in the case of a zigzag (armchair) nanotube (as compared to ∼100 kcal/mol for C6030). This is consistent with the ease of fluorination observed experimentally even at relatively low temperatures.17 Axial addition yields a lower total energy than circumferential addition for both the (5,5) and (9,0) nanotubes. This clearly demonstrates the effect of nanotube curvature on the bonding energy, since the more favorable axial addition follows a zigzag line on the (5,5) nanotube and an armchair line on the (9,0). This overrides the preference for armchair addition seen on flat sheets and within the TB model, where curvature effects are not present.
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Figure 4. Energy difference (eV) between axial and circumferential fluorination addition patterns for (5,5) C150H20 and (9,0) C144H18 open and closed C150 carbon nanotubes with respect to number of fluorine atoms added. Inset: Energy difference (eV) between the closed (9,0) and (5,5) C150 carbon nanotubes following circumferential addition with respect to number of fluorine atoms added.
We report in Figure 4 the energy differences for the different carbon nanotubes considered. Although axial addition is favored in all cases, the stabilization is greater for the closed (9,0) nanotube than that for the closed (5,5) nanotube. Thus, even though curvature dominates addition, the general preference for armchair addition over zigzag addition is still present. Comparing circumferential addition patterns between the closed (5,5) and (9,0) nanotubes (inset of Figure 4), we see that circumferential addition is more stable for the (5,5) SWCN, also favoring armchair rather than zigzag addition. Thus, even though curvature dominates addition, the general preference for armchair addition over zigzag addition is still present. Our results so far show a general preference for bandlike rather than spotlike addition. The ab initio results stress the influence of the strain of the carbon framework induced by fluorine, with preference for axial over circumferential addition, with underlying preference for armchair rather than zigzag addition in both SWCNs. Multiple addition is thus predicted to preferentially occur axially, in agreement with previous work.15,33 Subsequent Fluorine Addition. Axial addition ultimately leads to multiple axial strings of fluorine. The questions remain how such patterns propagate and how this correlates with the experimentally observed banding.21,23 C2F axial fluorination can extend onto an unfluorinated section of the nanotube, via either a single strand of 1,2-fluorine addition or contiguous extension of all of the existing strands. To test this, an open (5,5) SWCN, C190H20, was fluorinated at one end with 20 fluorine atoms in an axial C2F addition pattern. Subsequently, 10 fluorine atoms were then added, by either extending the existing addition pattern (contiguous addition) or adding the fluorine atoms as a single axial strand, growing out of the fluorinated part (Figure
5). Full HF/3-21G optimization predicts contiguous C2F addition to be 0.8 eV more stable than “single-strand” addition, i.e., 0.16 eV per F2 pair added. A “fully” fluorinated domain on a SWCN is thus predicted to expand via contiguous addition of fluorine, maintaining the banded structure. The choice of addition site will be guided by fluorinefluorine repulsion and the degree of distortion of the carbon nanotube, besides the electronic confinement effects discussed above. The distance between fluorine atoms of the same strand is often less than the fluorine van der Waals radius (2.7 Å), inducing repulsion. The single strand with its droplet cross section has a higher F-F distance, and thus fluorine-fluorine interaction favors single strands. But it is not the prevailing effect in determining the fluorination pattern. Fluorination changes the carbon from sp2-like to sp3-like coordination. This increases local carbon-carbon bond angles, as can be seen in the cross sections of Figure 5. Full C2F fluorination induces radial distortion of the nanotube. For the single strand, the effect is anisotropic and more severe, inducing a distortion of the tube cross section into a “droplet” shape.10 Such a radical distortion involves a significant strain mismatch at the interface with the fully fluorinated band, so that growing a single axial fluorination strand is associated to a significant elastic energy cost. The more regular C2F-fluorinated and the unfluorinated sections of a CN have a smaller relative mismatch. Also, growing the bandlike fluorination zone by increasing simultaneously all of the strand lengths just shifts the interface between the two sections, with no net increase of the elastic energy necessary to match them. In addition, a single strand increases the curvature at the opposite side of the nanotube, making this side more reactive, which is expected to further favor contiguous fluorination. To estimate
Theoretical Analysis of SWCN Fluorine Addition
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Figure 5. (5,5) C190H20F20 carbon nanotube fluorinated with 10 additional fluorine atoms as a single strand or extending an axial C2F addition pattern. Side views show radial deformation.
the energy associated with the nanotube framework distortion, we calculated the total energy of the C190H20F30 systems with the fluorine atoms removed and the original optimized geometry retained. Here, the C2F isomer structure was 1.3 eV more stable than the single-strand-isomer structure (single-point HF/3-21G). This confirms the higher elastic distortion cost associated to the single-strand structure, consistent with a prominent contribution of elastic effects in selecting bandlike adsorption. Namely, the growing out of a single fluorine strand is less favored than simultaneous growth of the distinct strands of the C2F region, due to the higher energy cost associated to the strain field of this addition pattern. We expect this to be even more important for fluorination of multiwalled carbon nanotubes, where inner layers will hamper radial deformation of the outer shell. Finally, we note that for initial addition-coalescence of two fluorine atoms only, a 1,4-circumferential-addition pattern is found most stable (position labeling as in Figure 3).34 If fluorination starts from this addition, then reorganization must occur upon subsequent addition to obtain axial rather than circumferential addition, consistent with the presence of low migration barriers.34 Conclusions In this article, the addition of fluorine to carbon nanotubes is investigated, to clarify the possible functionalization mechanisms in the development of new composite materials. Ideal systems were described using a simple Hu¨ckel-Monte Carlo model with a SWCN-Hamiltonian, neglecting carbon framework deformation induced by the fluorine addition, the effects which are expected to be minimal for MWCNs and large diameter SWCNs. Fluorine coverage shows the preferential formation of circumferential ring-shaped domains during fluorine adsorption due to quantum size effects related to π-state confinement on the unfluorinated tube regions. Ab initio analysis of graphene sheets shows preferential armchair line formation at high coverage, as found for SWCNs using a TB model. High exothermicity is predicted for fluorination of SWCN. For both (5,5) armchair and (9,0) zigzag, axial addition is preferred, with an underlying preference for armchair addition over zigzag. These results suggest that axial fluorination
is preferred for small diameter SWCNs, regardless of chirality. If a partly C2F-fluorinated nanotube is further functionalized, then contiguous axial propagation of the fluorinated region front is preferred over continued fluorination of a single axial strand, a result which is mainly due to strain-related effects. Fluorine addition is therefore expected to expand following an axial addition pattern over the nanotube surface rather than randomly in a spotlike pattern, but showing a sharp circumferential edge. The experimentally observed formation of fluorine bands may thus be explained in terms of multiple axial C2F rows expanding by contiguous axial addition. Thus, bandlike addition is reconciled with the energetic preference for an axial addition pattern. We note that low-temperature atomic force microscopy (AFM) may have sufficient sensitivity to distinguish between axial and circumferential banding and suggest that this may be a way to experimentally verify the fluorine arrangement in the fluorinated nanotube bands. Acknowledgment. G.V.L. and J.-C.C. acknowledge the National Fund for Scientific Research (FNRS) of Belgium for financial support. C.E. acknowledges funding from the EU Marie Curie Individual Fellowship Scheme. A.D.V. acknowledges funding from the EFS-EUROCORES-SONS-070 “Fun Smarts” Project. This paper presents research results of the ENABLE project financed by the Re´gion Wallone de Belgique. Parts of this work are also directly connected to the Belgian Program on Interuniversity Attraction Poles (PAI5/1/1) on Quantum Size Effects in Nanostructured Materials, to the “Action de Recherche Concerte´e” entitled “Interaction e´lectronphonon dans les nanostructures” sponsored by the Communaute´ Franc¸ aise de Belgique and to the FAME European network of excellence. References and Notes (1) Bahr, J. L.; Tour, J. M. J. Mater. Chem. 2002, 12, 1952. (2) Chiang, I. W.; Brinson, B. E.; Huang, A. Y.; Willis, P. A.; Bronikowski, M. J.; Margrave, J. L.; Smalley, R. E.; Hauge, R. H. J. Phys. Chem. B 2001, 105, 8297. (3) Chiang, I. W.; Brinson, B. E.; Smalley, R. E.; Margrave, J. L.; Hauge, R. H. J. Phys. Chem. B 2001, 105, 1157.
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