NANO LETTERS
Thermal Stability of Graphene and Nanotube Covalent Functionalization
2008 Vol. 8, No. 10 3315-3319
E. R. Margine* Laboratoire de Physique de la Matie`re Condense´e et Nanostructures (LPMCN), UMR CNRS 5586, UniVersite´ Claude Bernard Lyon 1, Baˆtiment Brillouin, 43 Bd 11 NoVembre 1918, 69622 Villeurbanne, France
M.-L. Bocquet Laboratoire de Chimie, UMR 5182, ENS Lyon, 46 alle´e d’Italie, 69364 Lyon, France
X. Blase Laboratoire de Physique de la Matie`re Condense´e et Nanostructures (LPMCN), UMR CNRS 5586, UniVersite´ Claude Bernard Lyon 1, Baˆtiment Brillouin, 43 Bd 11 NoVembre 1918, 69622 Villeurbanne, France and Institut Ne´el, CNRS and UniVersite´ Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France Received June 16, 2008; Revised Manuscript Received July 30, 2008
ABSTRACT We study kinetic factors governing the diffusion and desorption of covalently grafted phenyl and dichlorocarbene radicals on graphene and carbon nanotubes. Our ab initio calculations of reaction rates show that isolated phenyls can easily desorb and diffuse at room temperature. On the contrary, paired phenyls are expected to remain grafted to the surface up to a few hundred degrees Celsius. In the case of dichlorocarbene, no clustering is observed; at room temperature, the isolated radicals remain covalently attached to small-diameter nanotubes but desorb easily from graphene. Our results on the thermal behavior of side moieties on graphitic surfaces could be used to optimize the tradeoff between reactivity and conductance of nanotubes in the process of covalent functionalization.
A major challenge in expanding graphene and carbon nanotube (CNT) applications is the development of efficient synthesis methods that allow one to (a) obtain pristine CNTs with desired electronic properties or (b) chemically tailor graphene and CNT reactivity for applications in standard field-effect transistors, optical devices, or molecular recognition sensors. Chemical functionalization provides a promising route along these lines: the selection of metallic versus semiconducting tubes,1-3 the photosensibilization with grafted chromophores such as porphyrins or phtalocyanines,4 or the crucial improvement of the on-off ratio in graphene-based transistors5 have been recently achieved through covalent functionalization with appropriate moieties. A severe limitation of the covalent functionalization approach is that the disruption of the sp2 network strongly impairs the transport properties by significantly reducing the conductance of the substrate. Such an effect has been confirmed theoretically by several authors6,7 and can be compared to the rapid transition to a localization regime in the case of doped CNTs8 or nanowires,9 a problem that urged 10.1021/nl801718f CCC: $40.75 Published on Web 09/04/2008
2008 American Chemical Society
the development of alternative strategies such as core-shell doping techniques. An attractive way to overcome this problem, or better control it, has been demonstrated by removing grafted phenyl2,3,10,12-15 from the surface of CNTs through thermal annealing. Transport and Raman experiments revealed that for temperatures of the order of a few hundred Celsius, the vibrational and conductance properties of pristine tubes could be restored within a few hours. Therefore, this thermal treatment allows one to recover the initial properties of pristine CNTs after the selection, separation, and deposition steps and obtain devices assembled from functionalized CNTs with excellent electrical characteristics.10,14 At the theoretical level, the kinetics of desorption of phenyl moieties from graphene or nanotubes remains unexplored. A thorough understanding of the reaction pathways and temperature-dependent rate constants associated with the chemistry of desorption is certainly an important step to better control the reversibility of the grafting process and kinetically limit the number of adsorbed/desorbed groups. Further, as shown below, the comparison between theoretical
findings and experimental desorption results provides important information on the preferred adsorbed geometry of molecules. In this Letter, we present an extensive ab initio study of the reaction pathways, activation energies, and rate constants associated with the desorption and diffusion of phenyl radicals grafted onto graphene and nanotubes. Our results show that the diffusion and desorption of isolated functional groups can be easily achieved at room temperature on graphene and (10,10) tubes. The desorption rate constants of phenyls attached to the surface in pairs are dramatically smaller, indicating that higher temperatures are necessary to remove clustered moieties. Finally, the case of dichlorocarbene is considered. No pairing can be evidenced; however, even isolated moieties remain grafted at room temperature provided that the nanotube has large enough curvature to enhance the radical binding energy. Our simulations have been performed with a projectoraugmented-wave method16 within a generalized gradient approximation,17 as implemented in the VASP code.18 We use a plane-wave cutoff energy of 400 eV and spin polarization, a significant factor for the binding and activation energies. The desired initial and final states (isolated or paired phenyls, desorbed biphenyl, etc.) are fully relaxed to their minimum energy configuration until residual forces are less than 0.01 eV/Å. The minimum energy pathways are obtained with the climbing image nudged elastic band method (NEB);19 eight intermediate structures (images), constructed by linearly interpolating between the initial and final configurations, are simultaneously optimized along the reaction pathway until the forces in each image were smaller than 0.03 eV/Å. Such a scheme allows to automatically search for optimum (lowest energy) pathways and mechanisms connecting initial and final states. The saddle point structure was further refined by minimizing the forces until a 0.01 eV/Å value was reached. Quantum zero-point energy corrections to activation barriers are considered.20 The initial reactants (grafted substrates) and saddle points vibrational modes are calculated using finite differences in order to estimate the rate constants k within the harmonic transition state theory.21 Phenyl Radicals. We start by examining the case of an isolated phenyl grafted onto graphene.22 Our calculations demonstrate that this radical, which has a relatively low binding energy to graphene (-0.25 eV),23 needs to overcome an energy barrier Ea ∼ 0.60 eV to either desorb or diffuse, as shown in Figure 1 (details about the saddle point geometries are given in the figure caption). The similarity between the desorption and diffusion barriers suggests that there is no concerted bond-breaking/bond-re-forming mechanism in the diffusion case. The vibrational prefactor ν and rate constant k for desorption and diffusion are gathered in Table 1. At 300 K, the rate constants kRT for the two processes are very high: 3 × 103 s-1 and 2 × 104 s-1, respectively, which clearly indicate that at room temperature isolated phenyls will desorb and diffuse very easily. Grafting of one radical is known to enhance the reactivity of neighboring carbon sites2 which 3316
Figure 1. Left barrier: energy profile and atomic configurations of initial, intermediate, and final states for phenyl diffusion. Right barrier: energy profile and atomic configurations of initial and final states for phenyl desorption. Energies are in electronvolts; the carbon and hydrogen atoms are shown as gray and blue spheres. The graphene-phenyl distances at initial and transition states for diffusion (desorption) are 1.60 Å (1.60 Å) and 2.21 Å (2.24 Å).
Table 1. Computed Binding Energies, Eb, Activation Energies, Ea, Attempt Prefactors, ν, and Rate Constants, k, for Desorption Processes of Phenyl, Paired Phenyls, and Dichlorocarbene from Graphene and (n,n) Nanotubesa moiety phenyl
surface
Eb (eV)
Ea (eV)
graphene
-0.25
0.60
log(ν) (s-1)
log(kRT) (s -1)
log(kHT) (s-1)
13.6 3.5 (14.4) (4.3) phenyl (10,10) -0.73 0.87 14.5 -0.4 6.7 phenyl (5,5) -1.37 1.42 14.3 -9.5 1.9 p-phenyl graphene -1.51 1.98 16.0 -17.2 -1.3 o-phenyl graphene -1.25 1.66 15.1 -12.8 1.6 o-phenyl (5,5) -3.27 2.46 14.6 -26.7 -7.0 CCl2 graphene -0.03 0.59 12.9 3.0 CCl2 (5,5) -1.56 1.78 14.0 -15.9 -1.6 ak RT and kHT stand for rate constants at room and high (573 K) temperatures. Values for ν and k in parentheses are for the diffusion process.
suggests that isolated moieties might be rarely found just after synthesis. However, as shown below, the behavior of an isolated moiety will become of much relevance in the case of sequential desorption of paired configurations. Further, our results indicate that even if isolated addends are created during synthesis, they will either desorb or diffuse on the surface to form stable phenyl pairs (see below). This is an important finding since theoretical studies suggest that paired phenyls (divalent grafting) preserve a much larger conductance around the Fermi level as compared to isolated groups (monovalent grafting).6,7 On more general grounds, the further aggregation of phenyls in islands, the diffusion to the electrode/nanotube contact area, or the strong anchoring to native defects are mechanisms that now become relevant. This may explain the lack of complete reversibility that shows up after several desorption/adsorption cycles.10 The stronger bonding of phenyl pairs to graphitic surfaces has been previously demonstrated by total energy calculations.6,23 In good agreement with these studies, our simulations show that the binding energy of a phenyl radical in a para (p) (third nearest neighbor, bottom left Figure 2) or ortho (o) (first nearest neighbor) position goes up from -0.25 eV (isolated phenyl) to -1.26 and -1.00 eV, respectively.24 These results are consistent with the experimental observation11 that in the case of nanotube alkylation the 1,4-addition (para configuration) appears to be more common that the 1,2-addition (ortho configuration). This increased stability of paired phenyls together with the large diffusion rate of Nano Lett., Vol. 8, No. 10, 2008
Figure 2. Black curve: energy profile and atomic configurations of initial, intermediate, and final states for the desorption of a p-phenyl pair into biphenyl. Blue dashed curve: energy profile and atomic configurations of initial and final states for the desorption of one phenyl from the para state. Energies are in electronvolts; the carbon and hydrogenatomsareshownasgrayandbluespheres.Thegraphene-phenyl distances at the desorption saddle points of paired phenyls and single phenyl are 2.24 Å/2.24 Å and 1.60 Å/2.88 Å.
isolated radicals at room temperature strongly suggests that clustering of phenyls in pairs should take place on graphene. Our investigation of the desorption kinetics of a single phenyl from a paired state is done for the most stable para configuration. We find a barrier of ∼1.36 eV (blue curve Figure 2) which, combined with a vibrational prefactor ν ∼ 2.56 × 1014 s-1, gives a desorption rate constant kRT ∼ 4 × 10-9 s-1 at 300 K. Contrary to the case of an isolated phenyl, the desorption of a phenyl from a stable para configuration cannot take place at room temperature on graphene. However, such events are expected to occur at elevated temperatures13 within the experimentally relevant times: the rate constant at 573 K becomes kHT ∼ 3 × 102 s-1. Note that the single phenyl detached from the surface in this way may readsorb due to the very low energy barrier of 0.10 eV for the reverse reaction (see red dotted arrow, Figure 2). An alternative desorption reaction is the simultaneous detachment of two phenyl radicals with the subsequent formation of a stable biphenyl molecule (Figure 2, left to right). This final state is much more stable (by 3.35 eV, Figure 2) than the original configuration of paired phenyls on the graphene surface. However, the lowest energy pathway found for this reaction has an activation energy25 of 1.98 eV (full black curve Figure 2). With an estimated rate constant of 9 × 10-18 s-1 at 300 K, the desorption into biphenyl at room temperature can thus be excluded. Nevertheless, when the temperature is increased to 573 K, the rate constant becomes 6 × 10-2 s-1 and desorption of both phenyls from para configuration is expected to take place within minutes not hours as observed experimentally in the case of nanotubes. As compared to nanotube-based devices, this lesser thermal stability of functionalized graphene may come as a problem at high bias where device temperature is expected to increase markedly. Experimentally, the closest system to have been analyzed for desorption products is the diazonium-based functionalized nanotubes in an o-dichlorobenzene solution.15 In this case, dichlorobenzene-butylphenyl products were detected instead Nano Lett., Vol. 8, No. 10, 2008
of the dibutylbiphenyl pointing out toward the sequential desorption mechanism in Figure 2 (blue dash line). Similar experiments in a solvent-free environment are needed to check whether the simultaneous desorption of grafted radicals to produce the stable biphenyl may occur as depicted in Figure 2 (black line). We now turn to nanotube functionalization and study two armchair tubes27 of different diameters: (5,5), D ) 6.86 Å and (10,10), D ) 13.38 Å. Our calculated desorption barriers (Ea) for isolated phenyls shown in Table 1 can be correlated with average angle R formed by the phenyl radical with the three C-C backbonds on the surface (Rgraphene ) 106.39°; R(10, 10) ) 107.96°; and R(5, 5) ) 109.90°). In particular, the increase in desorption barriers from 0.60 eV in graphene to 0.87 eV in (10,10) and 1.42 eV in (5,5) nanotubes is nearly linear in R. With a vibrational prefactor of 3.35 × 1014 s-1 for (10,10) and 2.04 × 1014 s-1 for (5,5), the rate constants at 300 K are 4 × 10-1 s-1 and 3 × 10-10 s-1, respectively. Therefore, for standard diameter tubes such as (n,n) with n g 10, despite the effect of curvature, isolated phenyl radicals should, as in the graphene case, desorb and/or diffuse to form pairs or anchor to native defects at room temperature. Calculations of desorption barriers for nanotubes functionalized with a phenyl pair become prohibitively expensive. For this reason we study a reaction pathway for only one representative case: desorption of paired phenyls into biphenyl for the ortho configuration on the small-diameter (5,5) nanotube.28 We find an energy barrier of 2.46 eV, a vibrational prefactor of 3.61 × 1014 s-1, and a rate constant of 10-7 s-1 at 573 K. Therefore, paired phenyls on small diameter tubes are harder to desorb even at a few hundred degrees Celsius. Further, we estimate the desorption barriers of paired phenyls for the ortho state of a (10,10) tube using the linear relationship between the energy barrier and angle R revealed above. Interpolating between graphene and (5,5) ortho barriers, we obtain an activation energy of 2.01 eV for the ortho desorption of a (10,10) tube. For a typical prefactor of the order of 1014 s-1, these energy barriers lead to desorption rate constants of the order of 10-4 s-1 at 573 K. Therefore, desorption of paired phenyls at 573 K should take place within minutes for graphene and a few hours for commonly used nanotubes such as the (10,10), in good agreement with the experimental observations in this latter case.10,13 This ability of paired phenyls to remain grafted on graphene and nanotubes at ambient conditions, but desorb within a reasonable time scale at moderate temperatures, is central to the interest of such functional groups. As we now show in the case of dichlorocarbene radicals, other side moieties may not necessarily offer such a possibility. Dichlorocarbene. Our final calculations concern the important case of dichlorocarbene (CCl2) radicals.29 The reduced backscattering predicted for the so-called “open” configuration,7,31 where the adsorption of the CCl2 radical breaks a graphitic substrate C-C bond, thus restoring the π-conjugation, is a strong motivation for studying with much attention such side molecules. For graphene, the desorption barrier of an isolated CCl2 is ∼0.59 eV. The estimated rate constant at 300 K is 9 × 102 s-1 which again suggests that isolated 3317
calculations. X. Blase and E. R. Margine acknowledge support from the Agence National pour la Recherche under Contracts ANR-06-NANO-069-02 “Accent” and ANR-05BLAN-0282-02 “SupraDiam. Calculations have been performed at IDRIS (Orsay) and CIMENT (Grenoble). Figure 3. Energy profile and atomic configurations of dichlorocarbene desorption on graphene. Energy is in electronvolts; the carbon and chlorine atoms are shown as gray and green spheres. The C-C distances between the dichlorocarbene and the two substrate carbon atoms involved in cycloadition are 1.54 Å/1.54 Å and 1.82 Å/2.55 Å for initial and transition state.
radicals will easily desorb at room temperature from graphene. Any increase in the desorption barrier is unlikely since two CCl2 radicals do not pair on the graphene sheet and therefore no other possible scenarios to explore as in the case of phenyl.30 Therefore, contrary to paired phenyls, dichlorocarbene moieties are not viable candidates to functionalize graphene. Experimentally, it is known that CCl2 functionalized tubes are stable at room temperature.29 This raises a question: why isolated dichlorocarbene can be unstable on graphene and stable on nanotubes, while we showed that isolated phenyl was unstable on both graphene and tubes. The answer lies in the dramatic sensitivity of the carbene binding energy to curvature,31,32 an evolution that we expect to observe in the case of the desorption barrier as well. We find indeed that the energy barrier for CCl2 increases from 0.59 eV (graphene) to 1.79 eV in the case of a (5,5) tube, in agreement with a previous study.32 With a prefactor of 9.63 × 1013 s-1, we end up with a completely negligible rate constant of 1.35 × 10-16 s-1 at room temperature for the (5,5). One observes in particular that from graphene to the (5,5) tube, the desorption rate decreases faster in the case of dichlorocarbene as compared to isolated phenyls (see Table 1). This much larger sensitivity to diameter can be invoked to explain the stability of dichlorocarbene on nanotubes at room temperature, even though it is completely unstable on graphene. In conclusion, our analysis of the kinetics of desorption of covalently grafted side moieties on graphene and CNTs, such as phenyl or dichlorocarbene radicals, gives valuable information on the stability at room temperature and geometry of the side molecules. In particular, it is very unlikely that isolated phenyls will be found on graphene or nanotubes, while paired radicals will be present with important consequences on nanotube transport properties. Further, dichlorocarbene radicals, despite their potential in limiting the backscattering, cannot be used as grafting moieties for graphene due to a desorption barrier that decreases quickly with increasing CNT diameter. With desorption rates at 573 K of the order of 10-4-10-7 s-1 for paired phenyls on nanotubes and 10-2 s-1 for dichlorocarbene on a (5,5) tube, we suggest that controlled desorption may be an efficient way to monitor the number of radicals on the graphene or CNT surface for an optimal tradeoff between conductance and reactivity. Acknowledgment. The authors thank A. N. Kolmogorov for useful discussions and H. Lesnard for initiating the NEB 3318
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Nano Lett., Vol. 8, No. 10, 2008
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