Article pubs.acs.org/JPCC
Noncovalent Functionalization with Alkali Metal to Separate Semiconducting from Metallic Carbon Nanotubes: A Theoretical Study Nannan Li,†,⊥ Geunsik Lee,‡,⊥ Jae Won Yang,† Heeyoung Kim,§ Min Sun Yeom,§ Ralph H. Scheicher,∥ Jai Sam Kim,† and Kwang S. Kim*,‡,† †
Department of Physics, Pohang University of Science and Technology, San 31, Hyojadong, Pohang 790-784, Korea Department of Chemistry, Pohang University of Science and Technology, San 31, Hyojadong, Pohang 790-784, Korea § Department of Application and Support, Supercomputing Center, Korea Institute of Science and Technology Information, 245 Daehak-ro, Yuseong-gu, Daejeon, 305-806, Korea ∥ Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden ‡
S Supporting Information *
ABSTRACT: Despite intense studies of carbon nanotubes for decades, the separation of semiconducting and metallic single-walled carbon nanotubes (SWNTs) remains to be one of the most important tasks to be resolved. Here we demonstrate that a K atom binds the semiconducting SWNTs more strongly than the metallic SWNTs, while this binding strength hierarchy is reversed for a K+ ion, consistent with experimental reports. This was shown by first-principles calculations, which properly describe the van der Waals interactions, and the origin of such results is explained. These results could be exploited as useful guidance toward separating semiconducting and metallic SWNTs via noncovalent functionalization.
C
should be a useful guidance to experimentalists. Due to the noncovalent character, the binding energy difference depending on the type would be expected to be rather small. However, this difference can be exploited to separate the semiconducting and metallic SWNTs unless the difference is too small. In this regard, it requires an accurate prediction relying on a firstprinciples method. In theoretical prediction, there are two major challenges. In noncovalent bond systems, the van der Waals (vdW) interaction plays a significant role and the image charge effect of an adsorbed molecule on the tube is very important. If the periodic boundary condition is adopted, the unphysical interaction between the periodic images affects the binding energy significantly,18 so it should be carefully treated as addressed by Makov and Payne.19 Due to such difficulties, the literature results are sometimes not consistent with each other, as indicated by Lugo-Solis and Vasiliev.18 In this report, by using a first-principles method, accurate predictions of the binding energies between K/K+ and different types of SWNTs are made. The vdW interaction, the image charge effects of K/K+ on semiconducting and metallic SWNTs, and the periodic image effects arisen from the periodic boundary condition are treated properly.
arbon nanotubes have been studied extensively due to their extraordinary mechanical, chemical, and electronic properties. Their diverse applications including composites,1 energy storage,2 biological and chemical sensors,3,4 flexible electronics,5 and nanoelectrodes6 have been reported. However, as-synthesized carbon nanotubes are of various diameter and chirality, which dramatically affect the electronic and optical characteristics. For example, single-walled carbon nanotubes (SWNTs) are metallic when the chiral vector (n, m) satisfies n − m = 3 × (integer); otherwise they are semiconducting with the gap size inversely proportional to the tube diameter7 except for ultrathin SWNTs which turn out to be metallic due to the presence of some sp3 character in the C atoms on the high curvature of the tube.8 In this regard, the separation of semiconducting tubes from metallic tubes is one of the most important issues to be resolved for practical application in electronic device industry. Various methods at either postgrowth or growth stage have been reported to separate metallic tubes from semiconducting ones,9 such as dielectrophoresis,10 ion-exchange chromatography,11 densitygradient ultracentrifugation,12 cloning approach,13 and electrical breakdown.14 In spite of continuing advances,15−17 achieving high purity and high yields at low cost remains a challenge. In aspects of affordability and scalability, a promising method will be exploiting selective noncovalent functionalization of SWNTs in solvent and subsequent ultracentrifugation. The prediction of noncovalent bonding strength in molecule−SWNT complexes depending on the SWNT type © 2013 American Chemical Society
Received: December 16, 2012 Revised: January 26, 2013 Published: January 30, 2013 4309
dx.doi.org/10.1021/jp3123902 | J. Phys. Chem. C 2013, 117, 4309−4313
The Journal of Physical Chemistry C
Article
The calculations are performed by using the Vienna Ab-initio Simulation Package (VASP).20 For modeling ion cores, we use projector augmented wave (PAW) pseudopotentials with 400 eV energy cutoff for the plane wave basis set, where potassium 3p, 4s and carbon 2s, 2p are treated as valence electrons. The exchange-correlation energy is calculated with the generalized gradient approximation (GGA) functional of the Perdew− Burke−Ernzerhof (PBE) type. Considering the importance of the dispersion interactions, we further include the vdW density functional (vdW-DF) within optB86b. We relax the structures in all directions until all forces in the system are less than 0.02 eV/Å, which gives a well converged binding energy. We note that the calculated binding energy tolerance is less than 0.1 kcal/mol for every case (see Supporting Information for details). We consider two different charge states of potassium (a neutral K atom and a positively charged K+ ion) interacting with a SWNT, which will be denoted as K/SWNT or K+/ SWNT, respectively. For each case, three kinds of SWNTs are considered, where two of them with (n, m) = (4, 4) and (5, 5) are metallic, and the other (8, 0) is semiconducting. The adsorbate is positioned at the hollow site on the tube as shown in Figure 1, because it was found to have the lowest total energy in this configuration. A cubic supercell with the periodic boundary condition is chosen, so our model consists of a square array of parallel infinitely long nanotubes with a large vacant space between tubes. It is crucial to consider the occurrence of unphysical interactions between induced dipoles or between monopoles in these systems. The binding energy for K/SWNT (K+/SWNT) is given as E BE = E K(K+) + ESWNT − E K/SWNT(K+/SWNT) +
(1)
+
Here EK(K ), ESWNT, and EK/SWNT(K /SWNT) are the total energies of an isolated K(K+), SWNT, and K/SWNT(K+/ SWNT), respectively, which are calculated with the same size of supercell. The unphysical interaction between periodic images is excluded for the transverse and longitudinal directions separately. Along the transverse direction, the multipole correction is made when we obtain EK(K+) or EK/SWNT(K+/SWNT). For the longitudinal direction, we extrapolate the values of EBE, which are obtained by increasing the periodicity along the tube axis L, in order to predict the vanishing interaction limit. For the charged system involving K+, the homogeneous background charge19 is added. Table 1 lists the calculated results for L∼30 Å. The optimized C−K or C−K+ bond length is about 3 Å, which indicates rather weak bonding of the noncovalent type. The electron transfer from alkali metal to SWNT obtained from the Bader analysis is close to 1 au for K and negligible for K+. The major interaction between K and SWNT is found to be of an ionic type. The binding energies in Table 1 show a distinctive behavior between K/SWNT and K+/SWNT. For K/SWNT, the semiconducting (8,0) tube has more binding energy than the two metallic tubes of almost the same diameter size. However, for K+/SWNT, both metallic tubes have larger binding energies than the semiconducting tube. Also the metallic tube of larger diameter has a larger binding energy from the comparison of (5,5) and (4,4). To demonstrate the significance of the vdW interaction in our systems, we also calculate the binding energy and the doped distance of each case without vdW interaction, whose results are also listed in Table 1. In every case, compared to the previous one, the doped distance is slightly larger, and the binding energy is significantly underestimated. By using the
Figure 1. (a) 3D structure of the potassium-doped (4, 4) SWNT; (b) top view of the structure; (c) side view of the structure; (d) side views of potassium-doped (5, 5) and (8, 0) SWNTs. L ∼ 30 Å.
same relaxed structure as vdW-DF calculation, written in the parentheses, the binding energies for K/SWNT and K+/SWNT without vdW-DF interaction is decreased by ∼4.5 and ∼2.5 kcal/mol, respectively. These results confirm that the vdW interaction plays a significant role and the K/SWNT and K+/ SWNT systems have different binding mechanisms. The binding energies in Table 1 are obtained with the dipole correction only along the transverse direction for the K adsorption case or with the monopole correction for the K+ case. It still contains an undesirable interaction along the tube axis due to the periodic boundary condition. In order to predict an intrinsic binding energy between K or K+ and an infinite length SWNT, we calculate the binding energies by varying the periodic length L from ∼20 to ∼50 Å. For the neutral K, only 4310
dx.doi.org/10.1021/jp3123902 | J. Phys. Chem. C 2013, 117, 4309−4313
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Table 2. The Linear Fitting of Binding Energy: Parameter a (Intrinsic Binding Energy in kcal/mol) and R2 Correlation Coefficient
Table 1. Calculated Binding Energies, Charge Transfer, and Geometries of K/K+-Doped (4,4)/(5,5)/(8,0) SWNTs Based on the Same Supercell Sizea nanotube type (4,4) (5,5) (8,0)
(4,4) (5,5) (8,0)
EBE (kcal/mol)
Δq (e)
L (Å)
K-Doped SWNTs −0.8983 29.56 40.41 35.96b (35.89) 40.46 −0.8989 29.55 35.97b (35.93) −0.8973 29.89 42.01 37.93b (37.88) K+-Doped SWNTs 0.0894 29.56 37.49 35.06b (35.00) 41.80 0.0886 29.55 39.22b (39.19) 34.32 0.0890 29.89 31.79b (31.74)
d (Å)
R (Å)
K:SWNT
K:(4,4)
K:(5,5)
K:(8,0)
2.98 3.01b 2.98 3.00b 2.90 2.92b
5.53(5.47)
a R2 K+:SWNT
40.91 0.988 K+:(4,4)
40.97 0.988 K+:(5,5)
42.40 0.989 K+:(8,0)
a R2
30.90 0.998
32.75 0.999
29.79 0.998
3.04 3.07b 3.03 3.06b 2.96 2.99b
5.35(5.47)
6.84(6.78) 6.37(6.30)
semiconducting tube (a ∼ 42.4 kcal/mol). For K+, the binding energies of the metallic tubes are larger than that of the semiconducting tube, which also increases with the SWNT diameter. From our results, the more favorable interaction for metallic and semiconducting SWNTs is reversed between the neutral (K) and ionic (K+) cases. This means that the governing interaction is different in noncovalent interactions between K/ SWNT and K+/SWNT, which are clarified below for each case. In the case of K/SWNT, an electron transfer from K to SWNT is a major origin for the dominant ionic interaction. From the band structures in Figure 3, one can clearly see that both metallic (5,5) and semiconducting (8,0) SWNTs are doped with electrons from K. For the metallic case (Figure 3a), the SWNT π bands remain intact. The band indicated by the red dots is not decoupled from other π bands. However, for the semiconducting case (Figure 3b), such a band is decoupled, which indicates quasi-localization of electron. We analyze how additional electrons from K are distributed in SWNTs by plotting the probability distribution of the states in the top valence band crossing the Fermi level. As shown in the bottom most panels, the additional electrons are homogenously distributed for the metallic SWNT, but they are more localized near K for the semiconducting one. This results in strong ionic interaction for the semiconducting SWNT. In the case of K+/SWNT, the K+ does not cause any doping on SWNT, which is also confirmed by the band structure calculations. Instead, electrons are being redistributed within SWNT, maintaining the charge neutrality. Thus, the binding of K+ with SWNT is dominated by the polarization. We consider an electrostatic model, in which a neutral tube of the radius a with the dielectric constant ε is interacting with a fixed point charge q outside at (b,0,0). We then calculate the interaction energy between a point charge q and the redistributed surface charge on the tube. The surface charge density σpol(a,θ,z) can be obtained as below by using the electrostatic boundary condition that the normal displacement field must be continuous at the boundary r = a via ε0Eout = εEin:21 q ε − ε0 σpol(a , θ , z) = − (b cos θ − a) 2π ε + ε0
6.83(6.78) 6.37(6.30)
EBE: binding energy. Δq: amount of charge transfer; (−) K loses electrons, (+) K+ gains electrons. L: length of carbon nanotubes. d: doped distance, the shortest distance between K (K+) atom and the nearest carbon atom of a SWNT. R: diameter of a SWNT after (before) the K/K+ atom/ion doped. bThe 1st, 2nd, and 3rd (in parentheses) values of EBE denote the vdW-DF energy at the vdW-DF optimized geometry, the DFT energy without vdW interaction at this level theory optimized geometry, and the DFT energy without vdW interaction at the vdW-DF optimized geometry, respectively. a
EK/SWNT contains an undesirable dipole−dipole interaction along the tube axis, thus the binding energy scales as L−3. However, the total energies of K+ and K+/SWNT contain the remaining leading interaction between monopole and quadrupole. The resulting binding energy also scales as L−3.19 Therefore the binding energy should exhibit a scaling behavior a + bL−3 for both K and K+ cases, as the plot against L−3 in Figure 2 shows a linear shape. From a linear fitting via a + bL−3, we obtain the intrinsic binding energy a at infinite L (L−3 → 0), which are listed in Table 2. Though the values are different, the trend in relative binding energy difference in Table 2 (L ∼ ∞) is similar to that in Table 1 (L ∼ 30 Å). For K, two metallic tubes exhibit less binding energies (a ∼ 41 kcal/mol) than the
(a 2 + z 2 − 2ab cos θ + b2)−3/2
(2)
Then, the Coulomb energy or binding energy between the tube and the point charge can be evaluated as σpol·q 1 1 dS Eb = − 2 4πε0 R
∫
Figure 2. Linear fitting results of calculated binding energy of K or K+ doped SWNTs. The blue curves are the fitting curves for each case; the black, red and green points are the calculated data. Our binding energy tolerance is less than 0.1 kcal/mol.
=
4311
q2
π ∞ ε − ε0 dθ a(b cos θ − a) 0 4π ε0 ε + ε0 0 × (a 2 + z 2 − 2ab cos θ + b2)−2 dz 2
∫
∫
(3)
dx.doi.org/10.1021/jp3123902 | J. Phys. Chem. C 2013, 117, 4309−4313
The Journal of Physical Chemistry C
Article
we obtain that the metallic tube with the larger radius a has the larger binding energy. Our result for K+/SWNT is consistent with the experiment by Arnold et al.,12 where after ultracentrifuging SWNTs in the salt of sodium chlorate with a charged face, the denser metallic nanotubes are separated from the semiconducting ones due to their selective bonding with the salt. It is commonly said that metallic SWNTs with a larger polarizability have a higher reactivity than the semiconducting counterparts. However, abnormal selective adsorptions of molecules such as amine22 and pyrene23 on semiconducting SWNTs have been observed. The reasons have been attributed to an oxidized SWNTs for amine, where it is more like a covalent bond system, and to atomic correlation effect for pyrene.24 In addition to these mechanisms, our result of K/SWNT clearly shows that in the ionic interaction system, the localized distribution of electron (or hole) transferred from a molecule results in a selective interaction toward the semiconducting SWNTs. In conclusion, we studied the noncovalent interaction strength between SWNT and K or K+ by using a first-principles method with vdW-DF. From our results, a K atom binds more strongly with the semiconducting SWNT than the metallic one, while this trend is reversed for a K+ ion. Generalization of the results on a neutral (K) or charged (K+) species interacting noncovalently with SWNTs could lead to providing a guidance toward separating semiconducting from metallic SWNTs. For example, noncovalent interaction driven complexation of highly ionic or highly charge-transferable organic or inorganic compounds with SWNTs could be utilized for such separation.
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ASSOCIATED CONTENT
S Supporting Information *
The binding energy convergence test was done by increasing the cutoff energy and k-points values. The figures show that the binding energy tolerance is smaller than 0.1 kcal/mol beyond the 400 eV cutoff energy or 1 × 1 × 11 k-points mesh. This means that 400 eV energy cutoff with 1 × 1 × 11 k-points, which are used in our calculation, provides a high accuracy in determining the binding energy. This material is available free of charge via the Internet at http://pubs.acs.org.
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Figure 3. Calculated band structures for (a) (5, 5) and (b) (8, 0) SWNTs. For each case, the pristine SWNT (left), the K-adsorbed SWNT (middle), the K+-adsorbed SWNT (right), and the isosurface of the charge density contributed by the quasi-local bands of Kadsorbed SWNT indicated as red dots (below). These charge density figures are from the side view of the calculation system (as in Figure 1c) with the isosurface level 0.004 e/Å3. The K atom is at the top on the midpoint of the figure.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions ⊥
Equal contribution.
Notes
The authors declare no competing financial interest.
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where dS = a dθ dz is the surface element. For a semiconducting tube which has a finite dielectric constant, it satisfies ε − ε0
