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Density Functional Study of Interaction of Lithium with Pristine and Stone-Wales-Defective Single-Walled Silicon Carbide Nanotubes Xiao Wang and K. M. Liew* Department of Civil and Architectural Engineering, City University of Hong Kong, Kowloon, Hong Kong, SAR ABSTRACT: Interactions between a lithium atom or a lithium ion with pristine and Stone-Wales-defective (SW-defective) (5, 5) single-walled silicon carbide nanotubes (SiCNTs) were studied using density functional theory (DFT) with truncated nanotube models. The results show that the lithium atom or ion prefers to interact with defective SiCNTs, although the increase of binding energy for Li+ bonding with SiCNT is much smaller than that of the Li atom bonding with SiCNT. The molecular orbital energy level splits after a defect is created on the SiCNT, and along with localization of charge-electron density on the defect, it results in binding lithium more efficiently. Lithium always remains positively charged, irrespective of their charge state (neutral or cation) or the different rings that it interacts with. In addition, we also explore the possibilities of Li+ intercalation through the side-wall of SiCNT by examining the energy barrier. It is found that the barrier to insertion of Li+ through the ring of SiCNT depends on the ring size. The energy barrier of Li+ moving through the hexagon ring of perfect SiCNT was 7.02 eV, whereas it dropped to 2.5 eV when Li+ moved through the heptagon ring of the SW-defective SiCNT.

1. INTRODUCTION Carbon nanotubes (CNTs) are one of the most important nanomaterials because of their electronic, magnetic, and chemical properties and high-mechanical strength and flexibility,1−8 and they have been extensively studied both theoretically and experimentally since being observed by Iijima.9 Chemical doping of CNTs is a reaction procedure that is likely be accompanied by charge exchange between the host and the guest.10−12 This charge transfer is the key point that offers good opportunities for applications such as hydrogen storage,13 chemical sensors,14,15 and Li-ion batteries.12 Recent findings in the hydrogen storage field have revealed that alkali doped nanostructures can absorb higher percentages of hydrogen than pure nanotubes.16,17 A large number of publications have reported investigations of the interaction of lithium alkali with CNTs and the diffusion barriers inside− outside various types of CNTs18,19 or through structural defects,20,21 because of the great interest in rechargeable lithium batteries. Following extant research on CNTs, a wide field for research has opened up which enables the successful synthesis of other nanotubes, such as boron nitride nanotubes (BNNTs), ZnO nanotubes, and silicon carbide nanotubes (SiCNTs).22−24 SiCNTs, first synthesized in 2001,24 have many advantages over CNTs’ because of the high reactivity of their exterior surfaces facilitating sidewall decoration and stability at hightemperature.25 Due to their polar nature, SiCNTs can intrinsically be excellent sensors for detecting some harmful gases, such as CO, HCN,24 NO, NNO,26 NO2,27 and HCOH.28 Meanwhile, theoretical calculations show that the binding © XXXX American Chemical Society

energy of H2 increases by approximately 20% with SiCNTs compared with pure CNTs due to the partially heteropolar binding nature of the Si−C bonds.29 This makes SiCNTs more suitable for hydrogen storage. To further increase the binding energy of H2 to satisfy the requirements of the U.S. Department of Energy, in our previous study,30 the interaction between atomic lithium doped SiCNT and hydrogen molecules was studied. It was found that up to four H2 molecules can be attached to Li-adsorbed SiCNT with an average binding energy of 0.165 eV, which is close to the lowest requirement proposed by the U.S. Department of Energy. The higher hydrogen uptake of the Li doped SiCNTs is attributed to the formation of charged Li atom induced dipoles on the H2 molecules. It is seen that the Li atom plays a key role, as a “bridge”, and interacts with the molecule and the SiCNT simultaneously. Moreover, theoretical simulation of Li-intercalated SiCNT bundles indicated that both inside and the interstitial space of the nanotubes are susceptible to Li intercalation.31 This suggests that the SiCNT bundle is a promising candidate for use as the anode material in battery applications. Defects observed in CNTs32,33 are largely due to mechanical fractures or irradiation. These defects influence properties of CNTs in many aspects, including growth behavior, and mechanical, electrical and thermal properties.34−36 In addition to their structural significance, these defects have also been used as active sites for various processes, where adsorption strengths Received: August 1, 2012 Revised: November 20, 2012

A

dx.doi.org/10.1021/jp3076047 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Different binding sites of a single Li atom adsorbed onto a (5, 5) single- walled SiCNT. Gray, yellow and white balls denote carbon, silicon and hydrogen atoms, respectively.

where Eperfect and ESW are the total energies of a pristine SiCNT and an SiCNT with an SW defect, respectively. A larger formation energy corresponds to a more difficult formation of SW defects. After geometric optimization of such cluster models, the stable complexes were employed for studying adsorption of Li atom and Li ion. To study Li/Li+ adsorption with SW defective SiCNT, Li atoms or Li ions were placed at various locations on top of the SW defect sites or on the top of the new bonds created in defects of SiCNTs. The binding energy (Eb) between Li/Li+ and SiCNT or SiCNT with SW defects was defined as

and reaction products were found to depend strongly on the nature of orbital interactions. Lithium’s interaction with CNTs with defects has been studied extensively.20,21,37 However, until now, there have been no reports about interaction of lithium with SiCNTs and defective SiCNTs. Using the DFT molecular dynamics simulation, Wang et al. have reported that Stone− Wales (SW) defects could be created by low energy recoils in SiCNTs.38 Hence, to find new molecular storage materials, Li/ Li ion adsorption on pristine and SW-defective (5, 5) SiCNTs was studied, using the spin-unrestricted DFT method. Both adsorption strength and electronic structure were investigated to illustrate the property change of Li/Li+ caused by the SW defect in the substrate SiCNTs. Furthermore, lithium diffusion on the sidewall of perfect and SW-defective SiCNTs is also studied and presented here.

E b = E(Li/Li+ + tube) − E(tube) − E(Li/Li+)

where E(Li/Li++tube) is the total energy of the SiCNT with a Li/Li+ interacted and E(tube) and E(Li/Li+) are the total energies of the SiCNT with or without SW defect and Li atom or Li ion, respectively. By our definition, Eb < 0 corresponds to exothermic chemical adsorptions leading to minima stable toward dissociation into the SiCNT and bulk lithium. Endothermic energies Eb > 0 correspond to minima of adsorbed species which are thermodynamically unstable, relative to the host model and bulk lithium. Contribution of the zero-point vibrational energy (ZPE) to the total energy was not evaluated in this study. For all models, the SCF convergence limit was set to 10−6 a.u. on energy and electron density, and 0.001 Ha/Å on force. To clarify the electronic nature of the Li-doped SiCNT, the Hirshfeld charge43 analysis is computed and discussed.

2. COMPUTATIONAL DETAILS Density functional theory (DFT) based computations employed the generalized-gradient approximation (GGA) with the Perdew−Burke−Ernzerhof (PBE) correction implemented in a Dmol3 program.39−42 The basis sets used in the calculation were double numerical basis set plus polarization functional (DNP).39 And spin-unrestricted calculations were performed for all open-shell systems. In this work, armchair (5, 5) SiCNTs were employed for exploring adsorption of Li atom and Li ion. A model consisting of 45 carbon and 45 silicon atoms of nanotubes with H atoms capped at the ends of the fragment were applied to represent the SiCNT structure, resulting in a Si45C45H20 cluster model. These capped H atoms were used to avoid dangling bonds at the open ends. The Stone−Wales (SW) defective SiCNTs were generated by modifying the pristine Si45C45H20 cluster model shown in Figure 1 (SWD1: by a 90° rotation of a bridge Si−C bond and SWD2: by a 90° rotation of a zigzag Si−C bond). Each SW defect creates two pentagon and two heptagon rings, in which we named pentagon rings with C−C bond and Si−Si bond as 5-R1 and 5-R2, respectively. The same labels are used in two heptagon rings called 7-R1 and 7-R2. The formation energies of SWDs were evaluated by the following equation:

3. RESULTS AND DISCUSSION 3.1. Pristine and SW Defective (5, 5) SiCNTs. Optimized pristine and SW defective (5, 5) SiCNTs are shown in Figure 1. As our previous study showed, there are two nonequivalent Si− C bonds in pristine SiCNT: bridge Si−C bonds perpendicular to the longitudinal direction of the tube (e.g., the bond between C1 and Si2 atoms in Figure 1a) and zigzag Si−C bonds (e.g., the bond between C3 and Si2 atoms in Figure 1a). Bond lengths obtained are 1.794 Å for the bridge bonds and 1.798 Å for the zigzag bonds. These bond lengths are in fair agreement with those predicted in early theoretical studies.44−46 A 90° rotation of these two bonds results in two different SW defects:

Ef = ESW − Eperfect B



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the Type-1 SW defect (SW1) with a bridge bond rotation (Figure 1b) and the Type-2 SW defect (SW2) with a zigzag bond rotation (Figure 1c). All the relevant geometric data are listed in Table1. Like the SW defect in CNT and BNNT,47 the Table 1. Optimization Parameter of SW1 and SW2 Defective SiCNT bond length (Å)

SW1

SW2

C1−Si2 C1−Si4 Si2−C7 C−C Si−Si

1.742 1.847 1.802 1.460 2.260

1.770 1.869 1.804 1.462 2.279

formation of pentagons and heptagons violates the [4n + 2] aromatic rule and makes these defects electronically less stable, compared with the perfect hexagonal structure. Moreover, the formation of the new Si−Si and C−C bonds “frustrates” the atoms of the SW defect due to the unfavorable electronic interactions in direct donor−donor and acceptor−acceptor contacts. The electronic energies of SW1 and SW2 were calculated to be 2.881 and 2.588 eV higher (less stable) than the pristine SiCNT, respectively, which is a little lower than a previous study by Zhou et al.48 According to Wang et al.,38 the difference between formation energy of bridge and zigzag SW defects decreases as the diameter of the SiCNT becomes larger. Hence, together with this early study, the difference between of formation energy of SW1 and SW2 defects should primarily lie in the different rolling-up strains of these two defects. The formation of SW defects in SiCNTs has significant effects on their respective electronic structures, although all SiCNTs with SW defects still retain typical semiconductor characteristics. As shown in Figure 2, introducing SW defects in perfect SiCNT leads to new levels of the top valence band and the bottom conduction band. As stated in our previous report,30 the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the pristine SiCNT is calculated to be 2.277 eV, which is in good agreement with other theoretical results.48 Consequently, the HOMO−LUMO gaps of SiCNT with SW defects are reduced significantly, by 1.091 and 1.203 eV, respectively, for SW1-defective and SW2-defective SiCNTs. To clearly examine the characteristics of these new levels in defective SiCNTs, we plotted the electron density isosurfaces of the HOMO and the LUMO of defective SiCNTs (Figures 3 and 4). For perfect SiCNT, the HOMO is composed of p orbitals of C atoms and the LUMO mainly consists of p orbitals of Si atoms. In comparison with perfect SiCNT, for both defective SiCNTs, the HOMO originates mainly from C atoms in C−C bonds at the SW defects sites, whereas the LUMO are mainly from Si atoms in Si−Si bonds at the SW defects sites. Obviously, the reduction of the band gap of SiCNTs with SW defects is due to the localized island-like defect states appearing within the gap of the pristine SiCNTs, instead of the shifting of the original valence and conductance bands. This is similar to the case of BNNTs with SW defects reported by Chen et al.47 However, compared with defective BNNTs, SiCNT with SW defects show a much larger reduction of band gaps, which indicates that the newly formed C−C bonds and Si−Si bonds of SW defect sites are more unfavorable. In addition, the locality of these two new frontier orbitals improves the

Figure 2. Density of states (DOS) of (a) pristine (5, 5) SiCNT, (b) SW1-defective SiCNT, and (c) SW2-defective SiCNT. The Fermi level is in dotted line.

reactivity of the SW-defective SiCNTs compared with the pristine SiCNT. 3.2. Li Atom Adsorption on Pristine and SW Defective (5, 5) SiCNTs. As stated in the previous report, Li adsorption on the wall of pristine (5, 5) SiCNT results in two stable C



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Figure 3. Electron density isosurfaces of HOMO and LUMO for SW1 defective SiCNT. The isosurfaces of both HOMO and LUMO with values of +0.02 and −0.02 au are depicted in blue and yellow, respectively.

Figure 4. Electron density isosurfaces HOMO and LUMO for SW2 defective SiCNT. The isosurfaces of both HOMO and LUMO with values of +0.02 and −0.02 au are depicted in blue and yellow, respectively.

and the SW1 and SW2 structures are essentially the same, except for some minor differences. Because the frontier orbitals are localized around the defect sites, we then focus on the interaction between the Li atom and the SW defective region (atoms 1−16 in Figure 1c). Three adsorption products were obtained (Figure 5) when we studied the interaction between Li atom and SW2 defects. The vibrational frequencies, which were calculated for all three optimized structures, indicated that these structures were genuine minima. The most stable placement of Li atom is on top of the C−C bond which results in the LiSW2a structure (Figure 5a). In this structure, the strain due to the C−C bond frustration is released and the formation energy goes as high as 2.180 eV. Meanwhile, C1, C15, and Si2 atoms are found to stick out of the tube hypersurface markedly compared with the SW2defective SiCNT whose atoms at the defect site are fairly within the tube surface. Besides that, the C−C distance is elongated by insertion of Li, and the Si2−C1 length is also drastically increased (see Table 3). It is well-known that the change of HOMO−LUMO energy gap during the adsorption process can be related to the sensitivity of the adsorbent for a particular adsorbate. When the Li atom interacts with defective SiCNT, the introduction of the absorbate Li atom further narrows the HOMO−LUMO gap to 0.469 eV which indicates that SW defective SiCNTs express a higher reactivity to lithium adatom. For LiSW2a, the molecular orbitals (Figure 6) show that the Li 2s orbitals, C p orbitals, and Si p orbitals are highly hybridized together to compose the HOMO, whereas the HOMO-1 is composed of the π orbitals of the adjacent Si and C atoms and the pz orbitals of the C atoms in the defect area. Consequently, the HOMO and HOMO-1 are also highly localized. Generally speaking, in the open-shell system, the unpaired valence electrons will result in spin-splitting of molecular orbitals especially near the Fermi level. It is found from spin-DOS in

configurations, adsorbed on the top of C atom and on the hollow of the hexagon ring of SiCNT. The geometric parameters can be found in Table 2. The binding energies for Table 2. Binding Energies, the Shortest C−Li and Si−Li Bond Lengths, and Hirshfeld Charges (in e Units) of the (5, 5) SiCNT Doped with Li Atom Li and H2 at the same exterior side of SiCNT site

Eb (eV)

DC−Li

DSi−Li

Q

top of C atom center of hexagon

1.41 1.27

2.086 2.313

2.525 2.365

0.38 0.36

these two configurations are about 1.41 and 1.27 eV, weaker than the cohesive energy of bulk lithium, 1.7 eV.49 In addition, we also study the adsorption of Li on the outside of (4, 4), (6, 6), and (8, 8) SiCNTs to understand the relevance of the binding energy and the radius of the nanotubes. It is found that for (4, 4), (6, 6), and (8, 8) SiCNTs, the Li atom is still favorite for adsorption on the top of C atom of the SiCNTs, which is in good accord with that obtained from (5, 5) SiCNT. The binding energies of these systems are 1.47, 1.273, and 1.021 eV. It is obvious that the binding energy between SiCNT and Li atom is weaker than the Li cluster energy regardless of diameters of SiCNTs. Hence, to enhance the exterior activity of SiCNTs, SW defective SiCNTs are taken into account. It has been shown that CNTs and BNNTs with SW defects have higher reactivity than pristine nanotubes, so it is expected to have potential applications in lithium storage or as a media for the storage of hydrogen molecules for SiCNTs with SW defects. The adsorption of atomic Li on SW-defective SiCNT was studied only on the SW2-defective SiCNT, because compared with the SW1 structure, SW2 is energetically more favorable D



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Figure 5. Optimized geometries atomic Li-adsorbed SW2-defective (5, 5) SiCNTs. (a) LiSW2a, (b) LiSW2b, (c) LiSW2c. Gray, yellow, and purple balls denote carbon, silicon, and lithium atoms, respectively.

Table 3. Bond Lengths (in Å), Binding Energies (in eV), Partial Charges Q (in e unit), and HOMO-LUMO Gap (in eV) on Li for Li Adsorptions on SW2-Defective (5, 5) SiCNT at Different Sites Eb

C−C

C1−Si2

Li−C1

Li−C15

Q

HOMO−LUMO gap

LiSW2a LiSW2c

2.180 1.717 Eb

1.499 1.483 Si−Si

1.830 1.863 Si2−C7

2.092 2.243 Li−Si2

2.094 2.368 Li−Si12

0.35 0.33 Q

0.469 0.395 HOMO−LUMO gap

LiSW2b

1.925

2.275

1.909

2.484

2.774

0.33

0.305

Figure 6. (a) HOMO and (b) HOMO-1 band states for the LiSW2a complex. The isosurfaces of the HOMO and HOMO-1 band states are depicted with values of +0.03 and −0.03 au.

Figure 7a that the Li atom adsorbed on perfect SiCNT introduces one occupied energy band in the majority state as well as one unoccupied energy band with slightly higher energy in the minority state. However, when Li atom binds with SW defective SiCNT (Figure 7b), two pairs of adsorbate related states appear due to the larger deformation. Moreover, as different from Li absorbed on the pristine SiCNT, the LDOS of Li of LiSW2a spreads widely from −5 to −3 eV along with the PDOS of C atoms, which indicates a strong bonding interaction

between Li and the two nearby C atoms. In addition, the Fermi level of LiSW2a has no large change compared with SW2defective SiCNT or perfect SiCNT. This is also different from Li adsorbed perfect SiCNT which has a significant shift to a higher energy level. Hirshfeld charge analysis shows that 0.35 electrons are transferred from Li atom to SW2-defective SiCNT, especially, the two C atoms bond with Li. Because of the more localized electron density of SW-defective SiCNT created by distorted C−C and Si−Si bond, the charge E



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little to HOMO, which is also reflected in their DOS (Figure 9). Hence, on the basis of all computational results of Li atom adsorptions on SW-defective SiCNTs, we can conjecture that the defects in SiCNTs largely increase the binding energy and narrow the HOMO−LUMO gaps of the adsorbed systems. Atomic Li on a SiCNT with some SW defects will eventually relax into LiSW2a, LiSW2b, and LiSW2c structures due to their relatively high stability. This conclusion implies that fine-tuning of the reactivity of the adsorbed Li atom can be achieved through introducing defect sites. 3.3. Li+ Adsorption on Pristine and SW Defective (5, 5) SiCNTs. The lithium-graphite intercalation compound (LiGIC) has been extensively studied and widely used as the negative electrode in commercial lithium ion rechargeable batteries.50,51 In recent years, CNTs have been suggested to be one of the most promising candidates to replace the Li-GIC negative electrode. As a novel nanotube, SiCNTs exhibit good reactivity with Li atom. Hence, it is interesting and important to find out whether this new kind of nanotube could be a promising electrode in lithium batteries. So, after the Li atom, we investigated the Li+ ion interacting with perfect (5, 5) SiCNTs and the former defective ones. That means the Li’s outer shell consists of the degenerate s HOMO orbitals. Table 4 presents the calculated binding energies of Li+ ion interacting with different sites of the perfect (5, 5) SiCNT or SW2-defective SiCNT. Similar to the Li atom interacting with perfect (5, 5) SiCNT, there are two stable sites, on the top of the C atom and on the hollow of the hexagonal ring. The latter is more stable with higher binding energy (2.05 eV) this time. For that with SW2-defected SiCNT, three stable configurations exist, which are Li+ ion adsorbed on the top of C−C bond and on the hollow of the 5-R2 and 7-R1 rings of defected SiCNT. In these cases, it also seems the top of C−C bond is the most stable site with a higher binding energy of 2.377 eV compared with that on the hollow of 5-R2 and 7-R1 rings. From Table 4 it can be noticed that the Li+ ion interaction with the pentagonal and heptagonal ring is again energetically more favorable than the hexagonal ring. The same situation is also found in the case of Li+ ion binding to the perfect or SW-defective SiCNT on top of the C−C bond. However, this time, the gain in the binding energy is smaller than that of Li atom binding with perfect and SW-defective SiCNTs in all cases. Generally speaking, the interaction appears stronger and slightly affected by the deformation of SiCNT. Comparing both Tables 1 and 4, it is clear that the binding energies of the Li+ ion appear to be significantly larger than those of Li atom, despite the fact that the Li atom turns to be charged after the intercalation. The extra electron that exists in the case of the Li atom interacting with SiCNT destabilizes the system resulting in decreased binding energies. Li+ ion interaction with CNTs37 is wellknown as cation-π interaction.52 And in the case of Li+ ion interaction with SiCNT, Hirshfeld population analysis shows that the positive charge of the Li+ ion in the Li+-SiCNT systems is less than unity, indicating that charge transfer interaction in these systems is non-negligible. Hence, the cation-nanotube strong interaction could be attributed to two aspects, electrostatic interaction and the charge-transfer interaction.53 The charge-transfer interaction can be attributed to the interaction between the HOMO of the SiCNT system and the empty s orbital of the Li cation. Electrons transferred from the occupied 2p bonding orbital of SiCNT into the vacant 2s orbital of the Li+ ion result into an electron correlation, the

Figure 7. Spin-polarized DOS for (a) Li adsorbed on C site of perfect SiCNT and (b) Li adsorbed on SW-defective SiCNT with a LiSW2a sturcture. The Fermi level is plotted as the dotted line.

transferred from Li to the defective tube decreases a little compared with Li-adsorbed perfect SiCNT. In a word, LiSW2a is the most stable structure among the adducts of Li and SW2defective SiCNTs. The binding interaction of the complex from Li adsorption in the center of 5-R2 at the defect site is slightly weaker than that of LiSW2a with a binding energy of 1.925 eV. Adsorption of Li in the center of 5-R2 (LiSW2b) induces a noticeable Si2−C7 bond elongation (Figure 5b). In Figure 8a, the HOMO of LiSW2b is primarily composed of Li 2s orbitals and overlapped π orbitals of Si−C bonds, which is energetically higher than that of LiSW2a.The HOMO−LUMO gap further narrowed to 0.305 eV. Compared with LiSW2a, LiSW2b is more reactive and yet less stable. The adsorption of Li atom also induces band splitting into two pairs in-gap states. In addition, the Li atom can also be adsorbed in the center of 7-R1 (LiSW2c) with much weaker binding strength (1.717 eV). The HOMO of LiSW2c is primarily composed of π orbitals of Si−C bonds or 3p orbitals of Si atoms and Si−Si bond, whereas the HOMO-1 is composed of the remaining π orbitals of Si−C bonds and 2p orbitals of C atoms. It can be seen that Li atom contributes a F



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Figure 8. Plots of (a) HOMO, (b) HOMO-1, and (c) spin-polarized DOS of LiSW2b structure. The Fermi level is plotted as the dotted line, and the isosurfaces of the HOMO and HOMO-1 band states are depicted with values of +0.03 and −0.03 au.

Figure 9. Plots of (a) HOMO, (b) HOMO-1, and (c) spin-polarized DOS of LiSW2c structure. The Fermi level is plotted as the dotted line, and the isosurfaces of the HOMO and HOMO-1 band states are depicted with values of +0.03 and −0.03 au.

π−σ* interaction (where π is the HOMO of the SiCNT system and σ* is the LUMO of the cation). It has also been noticed that the defects of SiCNT affect dramatically the binding energy in the case of the Li atom but not in the case of the Li+ ion. We use the molecular orbital

theory to analyze this. The formation of a defect on a symmetric structure such as the perfect (5, 5) SiCNT causes splitting of the degenerate orbitals (Figure 2). The SOMO 2s electron of the Li atom can interact more easily with the defective SiCNT’s split orbitals rather than with the degenerate G



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promising candidates to be the negative electrode of rechargeable lithium ion batteries with the ability to store lithium not only on the exterior but also in the interior of them. Experimentally, lithium capacity of CNTs can be significantly increased by ball milling nanotubes into the fractured structure or chemically etching them to the short segments.18,54 Theoretical research has pointed out that lithium can easily diffuse not only to the exterior but also to the interior through the created defects or the open ends of such nanotubes.20,21 Hence, to investigate the possibility of SiCNT to be the new electrode of lithium ion batteries, we also need to investigate the diffusion-barrier for the perfect SiCNT and SiCNT with topological defects. In order to calculate the diffusion pathways for the Li ions, “adiabatic trajectory method”20 was used. In this method, the ion moves through a certain site above the rings of SiCNT to their surfaces with a constant speed in a given direction, while the total energy is monitored. Note that the ion is constrained to move in one direction only. All neighboring atoms are relaxed continuously in response to the Li ion motion. The calculated total energies show smooth variation along the diffusion pathways, indicating relative accuracy of the calculations.20 The energy barrier for lithium diffusion is defined as the difference between energy of configurations in which lithium is at the most stable and the most unstable positions on the diffusion pathway, which can be obtained as the peak heights in Figure 10. In case Li ion diffuses on the

Table 4. Binding Energy Values (eV), Charges Condensed to Li+ Ion, and HOMO-LUMO Energy Gaps (eV) of Li+ Interacting with Different Sites of Perfect and Defective SiCNTa interacting sites top of C atom center of hexagon top of C−C bond center of 5-R2 center of 7-R1 a

binding energy

charges

Perfect SiCNT 1.878 2.05 Defective SiCNT 2.377 2.076 2.188

HOMO−LUMO

0.56 0.43

1.933 1.9

0.48 0.41 0.43

1.149 0.897 1.137

The charges are in e.

orbitals of the perfect SiCNT. In the case of the Li+ ion interaction with the SiCNT, the contributions to the total interaction energy emerge from electrostatic and chargetransfer types. In the area where the defects are created, electron density is more localized compared to the perfect SiCNT. This can give a more ionic character to this interaction, which also can be used to explain the small increases of the binding energy in the cations’ cases. In Table 4, the HOMO−LUMO gap of the Li+ ion interacting with different sites of the perfect and defective SiCNTs is also presented. It can be easily observed from the table that whether the Li+ ion interacts with the perfect or defective SiCNTs, the gaps decrease due to the intercalation of the lithium ion. For instance, the HOMO−LUMO gap of the Li+ ion interacting with the hexagon of the perfect tube is 1.9 eV, which is 0.377 eV less compared with the perfect tube without Li+ ion intercalation. The gap of Li+ that interacts with heptagon of SW2-defective SiCNT also decreased to 1.137 eV relative to 1.203 eV of SW2-defective SiCNT. However, this change is again less than that observed in the Li atom doped SiCNT system. The Hirshfeld population analysis revealed that parts of the positive charge remains localized on the Li+ ion binding with either perfect or SW-defective SiCNT. Generally speaking, charge transfer in the alkali doped nanotubes depends on the oxidization state of the alkali which can be interpreted in terms of ionization potential. In the case of the interaction between the Li atom and the SiCNT, the ionization potential of the Li atom (Eion‑Li = 5.47 eV) is always lower than the perfect (Eion‑tube = 5.91 eV) or the defective SiCNT (Eion‑swtube = 5.61 eV). Hence, charges can be transferred from the Li atom to the tube. On the contrary, in the case of the interaction between the Li+ ion and the SiCNT, electron density is transferred from the SiCNT to Li+ ion, reversing the previous flow direction. In this situation, the second ionization potential of the Li atom or the first ionization potential of the Li+ ion (Eion‑Li+ = 76.23 eV) is much higher than the ionization potential of the perfect or the defective SiCNT. Thus, it is impossible for electrons to leave the Li+ ion and pass on to the SiCNT. The observed electron density transferred to the Li+ ion from the SiCNT is based on the effective nuclear charge of the Li cation. The tube “feels” a localized positive charge from the cations and attracts its electron density. Detailed analyses have been conducted for lithium adsorption energies in SiCNT and SW-defective SiCNTs. However, the key to superior battery performance using nanotubes lies in the ability of Li ions to enter and leave the nanotube interiors at a reasonable rate. CNTs are proved to be

Figure 10. Variation of energies by moving the lithium ion placed at a perpendicular distance of 2.6 Å from the front side to the center of the defect-free 6 ring of (5, 5) SiCNT.

exterior of perfect SiCNT, as the Li ion moves toward the center of the ring, the energies rise sharply and reach a maximum in the hexagon plane. Thus, the lithium ion has to cross an exceedingly high energy barrier to enter the tube through the hexagons of the side-wall of the tube. This barrier is estimated to be 7.02 eV which is lower than the energy barrier for the lithium diffusion through the defect free CNTs calculated by Nishidate et al.21 due to the steric effects. However, the relatively large energy barriers still prohibit Li diffusion through the walls of pristine SiCNT. Since it is difficult to synthesize uniform SiCNTs, we also investigate the energy barrier of lithium diffusion through (6, 6) and (8, 8) H



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deficiency provides a feasible pathway for Li to penetrate the tube wall.55 Although the energy barrier of 2.5 eV is still too high for lithium to get through the ring, the insertion process in SiCNTs has been predicted to become progressively easier as the structural defect becomes larger which has the same trend in the results of CNTs. In the results of lithium moves through the center of different rings of CNTs, the energy barrier decreases from 10.12 to 5.72 eV when the size of the ring changes from 6 to 7 based on the GGA results,21 which further dropped to 0.96 eV when the defective ring extends to enneagon. No doubt passage of the Li ion through the center of a ring is much easier for larger rings because the “holes” become larger and larger. Allowing the ring to deform facilitates the passage. Furthermore, the energy barrier for Li penetrating CNT walls can also be substantially reduced due to B doping55 and pyridinelike N doping.56 Hence, we may expect that SiCNT with large defects or other electron-deficient vacancy may much easier for lithium ion and may have promising applications in lithium ion batteries.

SiCNT. It is found that the variation of energies displayed in Figure 11 almost have the same trends with a little different of

4. CONCLUSIONS Spin-unrestricted DFT calculations were carried out to investigate the interactions between atomic and ionic Li and the pristine and SW-defective SiCNTs. For the Li atom adsorbed SiCNT system, the defects in SiCNTs largely increase the binding energy and narrow the HOMO−LUMO gaps because the SOMO 2s of the Li atom can interact more easily with the defective SiCNT’s split orbitals rather than with the degenerate orbitals of the perfect SiCNT. Also, the Li+ ion prefers to adsorb on defective SiCNT. However, the increase of binding energy between the Li+ ion and defective or perfect SiCNT is much smaller than that for the Li atom. In Li-rechargeable batteries, lithium ions get inside the carbon host (anode) during the charging process and are reversibly released in the discharging process. Thus the barrier height of the intercalation process is a crucial factor in battery activity. Hence, to explore the possibilities of this being a new electrode of lithium ion batteries, we also investigate Li ion intercalation through the side-wall of SiCNT. It is found that insertion of lithium ions through the side-wall of SiCNT seems energetically unfavorable like that happening in CNTs unless there are structural defects. The barrier height decreases from 10.4 to 2.5 eV as the ring size of the wall increases from pentagon to heptagon. Although the barrier energy of 2.5 eV is still very high for the Li ion penetrating the wall of SiCNTs, we may extend the defect to octatomic or introduce other electrondeficient vacancy to further decrease the barrier energy for application in Li ion batteries.

Figure 11. Variation of energies by moving the lithium ion placed at a perpendicular distance of 2.6 Å from the front side to the center of the defect-free 6 ring of (6, 6) and (8, 8) SiCNTs.

energy barrier. It indicates that the energy barrier of lithium diffusion has little dependence on the diameter of the tube. Next, we consider the Li ion moving on defective SiCNT. Here, we still consider Li diffusion on SW2-defective SiCNT only. Based on the adsorption results of Li ion interaction with defective SiCNT, Li ion is slowly brought to the center of the 5R2 and 7-R1 of Figure 12 from a distance of 2.6 Å. The

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Figure 12. Variation of energies by moving the lithium ion placed at a perpendicular distance of 2.6 Å from the front side to the center of the 5 and 7 ring of SW2 defective (5, 5) SiCNT.

Notes

The authors declare no competing financial interest.

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geometries of the tube were kept fixed at their optimized values. The intercalation energy increases to 10.4 eV when Li diffuses on the pentagon of SiCNT. On the contrary, when the Li ion moves through heptagon of SiCNT, the intercalation energy is lowered drastically from 7.02 eV to about 2.5 eV, as the ring size changes from 6 to 7. The existence of defect and electron

ACKNOWLEDGMENTS

The work described in this paper was fully supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 9041674, CityU 118411) and the China National Natural Science Foundation (Grant No. 11172253). I



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Article

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