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Electronic Properties of Carbon Nanotubes Intercalated with Li+ and Mg2+: Effects of Ion Charge and Ion Solvation Oleksandr M. Korsun,† Oleg N. Kalugin,*,† Andrey S. Vasenko,‡ and Oleg V. Prezhdo*,§ †

Department of Inorganic Chemistry, V. N. Karazin Kharkiv National University, Kharkiv 61022, Ukraine National Research University Higher School of Economics, Moscow 101000, Russian Federation § Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States ‡

S Supporting Information *

ABSTRACT: The influence of bare and solvated cations imbedded inside single-walled carbon nanotubes (SWCNTs) on the SWCNT electronic properties is studied by ab initio electronic structure calculations. The roles of ion charge and ion solvation are investigated by comparing Li + vs Mg 2+ and Li + vs its solvatocomplex with two ethylene carbonate (EC) molecules, [Li(EC)2]+. Two achiral nanotubes with similar radii but different electronic structure are considered, namely, the metallic, (15,15) armchair, and semiconducting, (26,0) zigzag, SWCNTs. The intercalation process is energetically favorable for both CNT topologies, with all bare cations and the solvatocomplex under investigation, with the doubly charged Mg2+ ion exhibiting the highest energy gain. Insertion of the bare ions into the SWCNTs increases the electronic entropy. The electronic entropy changes because the ions introduce new energy levels near the Fermi level. Those initially empty levels of the cations accept electron density and generate electronic holes in the valence band of both SWCNT topologies. As a consequence, the semiconducting (26,0) zigzag SWCNT becomes metallic, exhibiting hole conductivity. Solvation of the bare Li+ ion by EC molecules completely screens the influence of the ion charge on the SWCNT electronic properties, independent of the topology. The last fact validates the common practice of employing standard, nonpolarizable force field models in classical molecular dynamics simulations of electrolyte solutions interacting with CNTs. The strong dependence of the nanotube electronic properties on the presence of bare ions can be used for development of novel cation sensors for mass spectroscopy applications.

1. INTRODUCTION Functionalized carbon nanotubes (CNTs) attract significant attention due to their unique physical and chemical properties, stimulating experimental and theoretical studies and leading to a variety of promising applications. For instance, CNTs are used in transparent electrodes for organic light-emitting diodes, lithium-ion batteries (LIBs), supercapacitors, field-effect transistors, and other electronics components, catalytic and sensing devices, filters, mechanical and biomedical tools, and so on.1−3 CNT intercalation with metal cations, leading to the formation of either inner or outer CNT−ion complexes, provides facile means for controlling CNT electronic properties. Li−CNT systems can also improve the capacity of LIBs using both nanotube exteriors and interiors. Early theoretical studies of the Li-intercalated CNT ropes were performed by Zhao et al.4 It was found that both the nanotube interior and the interstitial space were susceptible to lithium intercalation. The nanorope was evaluated as a promising candidate for the anode material in LIB applications. Next, Kar et al.5 explored Li+ ion intercalation and insertion through carbon nanotube sidewalls and other regions. Simple models of five-, six-, seven-, and eight-membered rings were examined. Lithium ion favored © XXXX American Chemical Society

two positions: close to the wall inside the tube and outside of the tube. Energetic information was provided using simple models for different diameters. Movement of the cation(s) within single-wall tubes, in the interstitial zone, and within multiwall tubes was also studied and discussed. Subsequent theoretical investigations on single-walled carbon nanotubes (SWCNTs) were carried out by Garau et al.6,7 using an ab initio molecular interaction potential with and without polarization effects. The authors explored Li+ ion insertion through nanotube sidewalls. Ab initio calculations of the fully optimized CNTs were used to examine the topological defects, depending on the ring size.6 Similar calculations were also used to examine lithium incorporation into CNTs through the open end, depending on the nanotube diameter. Favorable interactions of Li+ with the six (n,0) open-ended zigzag nanotubes (n = 5−10) were studied and discussed.7 Li insertion during the arc discharge growth process was investigated by resonance Raman spectroscopy combined with ab initio calculations by Guerini et Received: July 26, 2016 Revised: September 27, 2016 Published: October 28, 2016 A

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The Journal of Physical Chemistry C al.8 The measurements were performed using a pair of SWCNT materials. One type of SWCNTs was prepared employing a Licontaining catalyst, while the other type was made without Li. The results showed that charge transfer from Li atoms into SWCNT bundles accompanied Li insertion. Calculations indicated that the transfer was governed by the Li-insertion rate in Li6C68. Udomvech et al.9 performed first-principles calculations on Li and Li+ adsorbed on CNT sidewalls. CNT diameters were varied by changing the chiral vectors from (6,0) to (12,0). The length of the (9,0) CNT was varied from 1 to 3 unit cells. Investigation of the potential energy surfaces suggested that both Li atom and Li+ cation preferred to localize near CNT sidewalls. Both Li and Li+ could easily diffuse along internal sidewalls, while diffusion along external sidewalls was hindered. Binding energies tended to depend on CNT chirality rather than diameter. In particular, they were different for CNTs with uneven and even chiral vectors (n,0). In addition, the binding energies depended on tube length but converged rapidly at 3 unit cells. The net charge on the Li atom inside CNTs was independent of whether the Li−CNT complex was neutral or charged. Li et al.10 carried out density-functional studies of adsorption and diffusion of various alkali-metal ions on surfaces of pristine and defective armchair SWCNTs. In pristine tubes, the position above the hexagon presented the most stable site for adsorption. Defects enhanced adsorption. All ions preferred to diffuse along the axial direction in pristine tubes. The diffusion energy barriers were low, less than 0.25 eV. In defective SWCNTs, axial diffusion was also energetically most preferable. The barriers increased only slightly and had little influence on diffusion, compared to pristine SWCNTs. Intercalation and diffusion of Li+ in CNT bundles were investigated using ab initio molecular dynamics (MD) by Song et al.11 They found that Li+ quickly penetrated inside CNTs and into the space between neighboring CNTs. When the Li+ ion density was low, Li+ ions tended to stay close to the nanotube ends. It was also discovered that Li+ ions could remain between two neighboring CNTs, presenting a new approach to Li+ ion intercalation and storage. Importantly, Li+ ions located between three neighboring CNTs experienced very strong adsorption potentials that were a factor of 4 larger than those of Li+ ions located along the central SWCNT axis. This result indicated that Li+ ions located between three neighboring CNTs would be very difficult to remove from a nanotube bundle, suggesting that Li storage capacity should be irreversible in this case. Therefore, controlling the distance between nanotubes can be utilized in order to hinder or promote irreversible intercalation. A new method for storing lithium, allowing the Li/C ratio to reach twice the highest ratio reported in the literature, was proposed by Tian et al.12 with the help of MD simulation. The main idea was to use SWCNTs to draw in lithium nanoparticles. The MD simulations showed that SWCNTs could repeatedly absorb and release lithium nanoparticles at certain temperatures, thus making this a practical method of lithium storage. In order to elucidate electrochemical Li+ ion storage with conducting and semiconducting SWCNTs, Kawasaki et al.13 explored several methods of generating sufficient amounts of semiconducting and metallic SWCNTs for electrochemical measurements. It was found using electrochemical charge− discharge measurements that reversible Li+ ion storage capacity of metallic SWCNTs was about 5 times greater than that of semiconducting SWCNTs. First-principles calculations were

performed by Wen et al.14 to study Li doping in a series of CNTs with different diameters and topologies. It was found that zigzag tubes with small diameters were energetically more favorable for Li doping than larger tubes. In contrast, almost all armchair tubes showed the same Li binding energy, especially for outside doping. These theoretical results suggested that small diameter zigzag tubes could be plausible candidates for LIB applications. The insertion of Li atoms into the channels formed by SWCNT bundles was investigated by Fagan et al.15 using an ab initio calculation. Relaxed geometric structures and electronic band structures were obtained. The results revealed that Li insertion modified the band structure by shifting the Fermi level, εF, to a region with a higher density of states and that the shift correlated with the rate of insertion. Petaccia et al.16 investigated the electronic properties of clean and lithiumdoped SWCNTs using several spectroscopic techniques. At 150 K, Li doping saturated at the Li/C ratio of about 0.06, causing a shift of the photoemission peaks toward higher binding energy by about 0.25 eV and an increase in the spectral intensity near the εF. The result was consistent with electron transfer from Li atoms and partial filling of the SWCNT conduction band. SWCNTs modified by Li+ and OH− ions via treatment with an aqueous solution of LiOH were investigated by Zhong et al.17 using the soft X-ray absorption and resonant emission spectroscopies. A valence state near the εF, induced by the charge transfer, was detected at the resonant excitation energy of 285.5 eV. The results indicated that SWCNT electronic properties could be tuned by Li+ adsorption. Recently, plane-wave density functional theory (DFT) calculations of the Li+ ion inside the quasi-infinite SWCNTs were reported by Korsun et al.18 It was shown for the first time that the electronic properties of zigzag SWCNTs can be tuned continuously from semiconducting to metallic by varying the location of the bare Li+ ion inside the nanotubes. It was also demonstrated that the Li+ ions have the biggest influence on the SWCNT electronic properties when they are located on the nanotube axis. For instance, the semiconducting SWCNTs can be made metallic by placing the Li+ ion exactly on the nanotube axis or close to it. When the Li+ ion approaches SWCNT internal walls, this effect is almost canceled out. Intercalation with bare ions can be achieved in practice only under very controlled conditions. In the majority of applications, such as in the LIBs, Li+ ions are surrounded by solvation shells, and counterions are also present. The ion solvation effects can be studied theoretically by considering solvatocomplexes instead of the bare ions. Solvatocomplexes can contain a variable number of solvent molecules, representing a solvated or partly solvated ion. Screening even by a few polar solvent molecules can notably decrease the polarizing action of bare cations on the CNT electronic subsystem. The present work compares the influence of bare cations with different charges and of a bare and solvated cation on SWCNT electronic properties. Both metallic, (15,15) armchair, and semiconducting, (26,0) zigzag, SWCNTs are considered (Figure 1, left). These tubes have fundamentally different electronic structure, as follows from the topological indexes. At the same time, they have very similar diameters. Thus, the internal radius of the (15,15) SWCNT equals 10.1710 Å, while the internal radius of the (26,0) SWCNT is 10.1845 Å.19 In order to investigate whether and how the ion charge influences the cation−SWCNT interaction, bare Li+ and Mg2+ ions are B

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energy of the system, FFEF, with “hot” electrons near the εF, corresponding to the electronic chemical potential, is given by eq 1 for the spin-unpolarized case. ⎛ ⎡ ε (k) − εF ⎤⎞ FFEF = −2kBTel ∑ ∑ wk ln⎜⎜1 + exp⎢ − i ⎥⎟⎟ kBTel ⎦⎠ ⎣ ⎝ i k δE XC + εFNel − Eel ‐ el + En ‐ n + E XC − n(r)dr δn(r)

∫

(1)

Here, kB, Tel, wk, εi(k), Nel, Eel‑el, En‑n, EXC, and n(r) are the Boltzmann constant, electronic temperature, k-point weights, molecular orbital energies, total number of the electrons, electronic and nuclear repulsion energies, exchange-correlational energy, and total electron density, respectively. The exchange-correlational energy was described by the gradient-corrected BLYP functional24,25 that was used earlier in the plane-wave pseudopotential DFT calculations of the CNT systems.18,26,27 The long-range dispersion correction term was applied according to Grimme.28 The core electrons of the simulated atoms were treated using the norm-conserving Troullier−Martins pseudopotentials.29 The nonlocal parts of the pseudopotential for the C and O atoms (l = 0) as well as for the Mg atom (l = 1) were represented in the Kleinman− Bylander form.30 The nonlinear core correction was enabled for Li and Mg in the atomic pseudopotential form.31 FEF is related to the DFT total energy, EDFT, and electronic entropy, Sel, according to the simple thermodynamic relation FFEF = EDFT − TelSel. Using the conventional expression for the EDFT term in the spin-unpolarized case leads to eq 2 for FFEF.

Figure 1. Side views of the pristine (15,15) armchair and (26,0) zigzag SWCNTs (left panel) and cross sections of the corresponding SWCNTs with bare Mez+ ions (Mez+ = Li+ and Mg2+) and the complex [Li(EC)2]+ ion (right panel). The cations are located exactly on the SWCNT axis.

considered. The ions are located at the nanotube axes (Figure 1, top right). The effect of the ion location on the SWCNT properties has been investigated previously.18 Because the Li+ and Mg2+ ions have small radii, they generate strong spherical electric fields. By attracting the surrounding electron density, they have the biggest influence on the SWCNT electronic structure when located exactly on the nanotube axis.18 In order to investigate the solvation effect, the SWCNTs intercalated by the bare Li+ ion are compared with the SWCNTs containing an extremely stable complex of Li+ with two ethylene carbonate (EC) molecules, [Li(EC)2]+ ion.20 These solvent molecules are highly polar and are oriented with the negative (carbonyl) groups toward the Li+ ion (Figure 1, bottom right). Such a linear [Li(EC)2]+ solvatocomplex with the EC molecules orthogonal to the internal walls of the SWCNTs should provide maximal screening of the strong polarizing action of the Li+ ion. In a realistic CNT containing an electrolyte solution, the EC molecules completely solvate the cation, and the resulting solvation shell is spherically symmetric on the average. By placing the [Li(EC) 2 ] + solvatocomplex symmetrically on the CNT axis with the EC molecules orthogonal to the CNTs walls, we represent a limiting case. Other orientations of the complex would reduce the screening. Comparison of the properties of the SWCNTs containing the bare Li+ and the complex [Li(EC)2]+ ions characterizes the effect of solvated cations that are present in real CNT filled by an electrolyte solution. The roles of the ion charge, Li+ vs Mg2+, and the ion solvation, Li+ vs [Li(EC)2]+, are investigated for both metallic (15,15) armchair and semiconducting (26,0) zigzag SWCNTs.

FFEF =

∑ ∑ wkfi (k)εi(k) − Eel ‐ el + En‐ n + E XC i

−

k

∫

δE XC n(r)dr − TelSel δn(r)

(2)

Here, f i(k) are the occupation numbers calculated from the Fermi−Dirac distribution function for the spin-unpolarized case (eq 3). −1 ⎛ ⎡ εi(k) − εF ⎤⎞ fi (k) = 2⎜⎜1 + exp⎢ ⎥⎟⎟ ⎣ kBTel ⎦⎠ ⎝

(3)

Using eqs 1 and 2, the total electronic entropy, Sel = ∑wkSk, and its k-components, Sk, can be represented as eqs 4 and 5, respectively. ⎛ ⎡ ε (k) − εF ⎤⎞ εFNel Sel = 2kB ∑ ∑ wk ln⎜⎜1 + exp⎢ − i ⎥⎟⎟ − kBTel ⎦⎠ Tel ⎣ ⎝ i k 1 ∑ ∑ wkfi (k)εi(k) + Tel i k (4)

⎛ ⎡ ε (k) − εF ⎤⎞ εFNel Sk = 2kB ∑ ln⎜⎜1 + exp⎢ − i ⎥⎟⎟ − kBTel ⎦⎠ Tel ⎣ ⎝ i 1 ∑ f (k)εi(k) + Tel i i

2. THEORETICAL METHODOLOGY 2.1. Theory. The quantum−chemical calculations were performed using the CPMD program, which implements DFT in a converged plane-wave basis set and describes the core electrons with pseudopotentials.21,22 The electronic structures of the pristine SWCNTs and the SWCNTs intercalated with the cations were investigated in the free energy functional (FEF) framework.23 Within this approach the Helmholtz free

(5)

The component of the electronic entropy corresponding to the center of the Brillouin zone or Γ-point, SΓ, can be calculated with high precision according to the relation SΓ ≡ Selw−1 Γ . C

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Table 1. Changes in Specific Free Energy Functional, ΔFFEF, and Specific Electronic Entropy, ΔSel, during Intercalation of the Li+, Mg2+, and [Li(EC)2]+ Ions into the (15,15) Armchair and (26,0) Zigzag SWCNTs, Resulting in the Formation of the ion@(15,15) and ion@(26,0) Intercalates ion@(15,15)

intercalate +

ion

Li −1

ΔFFEF, kJ·mol ΔSel, J·mol−1·K−1

−2.3 +0.02

Mg

2+

ion@(26,0) +

+

[Li(EC)2]

Li

−1.6 0

−1.9 +0.08

−10.6 +0.02

Mg2+

[Li(EC)2]+

−9.2 +0.05

−1.4 0

3. RESULTS AND DISCUSSION 3.1. Ion Intercalation. Table 1 presents changes in the specific free energy functional, ΔFFEF, and specific electronic entropy, ΔS el , during formation of the ion@SWCNT intercalates (ion = Li+, Mg2+, and [Li(EC)2]+). All ΔFFEF values are negative, indicating that the cation−SWCNT interactions are attractive. The absolute values of ΔFFEF are systematically larger for the metallic (15,15) armchair SWCNT than for the semiconducting (26,0) zigzag SWCNT-based intercalates. This fact can be explained by the higher polarizability of the armchair CNT. Substitution of the singly charged Li+ ion by the doubly charged Mg2+ ion increases the ΔFFEF magnitude almost 5-fold for both (15,15) armchair and (26,0) zigzag nanotubes. Thus, the attraction energy of cation intercalation changes nonlinearly with the ion charge. The ΔF FEF magnitudes for intercalation of the [Li(EC) 2 ] + solvatocomplex are of the same order, although slightly lower than those for the Li+@SWCNT intercalates. The smaller values can be rationalized by a lower polarizing action of the more extended linear [Li(EC)2]+ complex ion compared to the bare Li+ ion (Figure 1, right). The changes of ΔSel are positive for the bare Mez+ ions insertion and are zero for the [Li(EC)2]+ complex intercalation. Nonzero electronic entropy arises from a distribution of “hot” electrons near the εF energy level, including partial population of HOMO and LUMO states. The positive ΔSel values (Table 1) arise due to redistribution of the SWCNT electron density upon ion insertion that perturbs the initial SWCNT molecular orbital system. According to the entropy data, the bare Li+ and Mg2+ ions have the same influence on the electronic subsystem of the (15,15) armchair SWCNT, independent of the ion charge. The corresponding ΔSel values are significantly larger for the semiconducting (26,0) than for the metallic (15,15) SWCNT. Also, in the case of the (26,0) zigzag SWCNT, the singly charged Li+ ion has more impact than the doubly charged Mg2+ ion. The last two facts deserve an additional explanation that is given below. 3.2. Electronic Structure. To clarify the polarizing action of the bare Mez+ ion and [Li(EC)2]+ ion complex on the electronic structure of the investigated SWCNTs, the energies and occupation numbers of the electronic levels near the εF are considered in detail. The energy level diagrams for the pristine SWCNTs and ion intercalated CNTs, ion@SWCNTs, are shown in Figure 2. The diagrams in Figure 2a−d show that the HOMO and LUMO levels of the SWCNTs are 2-fold degenerated and can contain up to four electrons. Note that the nominal SWCNT HOMOs are not completely occupied in the presence of the bare cations (Figure 2b,c), due to the charge transfer. The nominal HOMOs and LUMOs correspond to the valence band top (or maximum) and conduction band bottom (or minimum), respectively. Because the band gap of the pristine (15,15) armchair SWCNT is small (see subsection 2.2 for

Quasi-one-dimensional periodic boundary conditions (PBCs) were applied in all simulations to mimic infinitely long CNTs. The calculations were performed in the tetragonal supercells containing several SWCNT unit cells,19 so that the supercell lattice constants along the tube axis, L, were as close as possible for the two SWCNTs under investigation. In particular, the L values were 7.3837326 and 8.5260 Å for the armchair and zigzag CNTs, respectively. The parameters of the simulation supercells were L, 30.0 and 30.0 Å in the x, y, and z directions, respectively. By extending the supercells up to 30.0 Å in the directions perpendicular to the nanotube axis we have minimized the interaction between the SWCNT periodic images. The same PBCs were used for calculations performed with the [Li(EC)2]+ solvatocomplex. The (15,15) armchair and (26,0) zigzag SWCNT simulation supercells contained 180 and 208 carbons correspondingly. In order to reproduce the Fermi−Dirac distribution functions in the vicinity of εF, 12 additional Kohn−Sham orbitals were included in the computations. Thus, 360 + 12 states were treated explicitly for the (15,15) armchair SWCNT, and 416 + 12 states were considered for the (26,0) zigzag SWCNT. The total number of electrons in the system did not change upon introduction of the bare Li+ and Mg2+ ions since the core electrons of the given ions were treated using pseudopotentials. The total number of Kohn−Sham orbitals was increased by 34 for the [Li(EC)2]+@SWCNT intercalates. The Li+@SWCNT, Mg2+@SWCNT, and [Li(EC)2]+@SWCNT simulation supercells carried the net positive charge of +1, +2, and +1, respectively. The neutralizing background charge was employed in these cases, in order to compensate the Coulomb repulsion among the periodic images of the simulated charged systems. 2.2. Validation. The convergence of the numerical results was validated (i) for the kinetic energy cutoff of the plane-wave basis set at the Γ-point (Figure S1, left) and (ii) for the Monkhorst−Pack k-points mesh32 in the Brillouin zone at the 80 Ry cutoff value (Figure S1, right), using the pristine (15,15) armchair and (26,0) zigzag SWCNTs. The 90 Ry plane-wave kinetic energy cutoff and the uneven 3 × 1 × 1 Monkhorst− Pack mesh at the electronic temperature of 298.15 K are used for subsequent discussion. See Supporting Information for the validation details. The energy gap and specific electronic entropy values at the Γ-point for the pristine SWCNTs were considered as the validation criteria of the used level of theory. The computed values of the band gap are 0.06 eV for the (15,15) armchair and 0.35 eV for the (26,0) zigzag SWCNTs, in agreement with topologies of the given nanotubes. The SΓ values computed using eq 5 per carbon are 7.5 × 10−8 and 1.0 × 10−9 Ha·K−1· atom−1 for the (15,15) armchair and (26,0) zigzag SWCNTs, respectively. The specific SΓ values confirm the fundamental difference in the electronic structure of the investigated SWCNTs. D

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Figure 2. Energy level diagrams of the pristine (15,15) armchair and (26,0) zigzag SWCNTs (a), the same SWCNTs containing the bare Li+ (b) and Mg2+ (c) ions, and the [Li(EC)2]+ ion complex (d). The levels are shown for the Γ-point. The gray dashes at 0 eV denote the Fermi level of a simulated system. The blue and red marks designate the HOMO and LUMO levels, respectively, as they exist in pristine SWCNTs (a−d). The pink marks indicate the levels arising due to the Li+ and Mg2+ ion intercalation; “Li” and “Mg” labels denote metal nonbonding levels (b, c). The green marks show CNT states close to the Mg level in the Mg2+@SWCNT intercalates. The “(2)” label indicates degeneracy order of the marked levels, particular to the Mg2+@(15,15) intercalate (c). The numerical values present occupation numbers of selected energy levels, calculated according to eq 3.

details), the occupation of its conduction band bottom is nonzero (Figure 2a, top). This is in full agreement with the metallic-like nature of the given nanotube. The conduction band bottom is empty in the formally semiconducting (26,0) zigzag SWCNT, at the used electronic and zero nuclear temperatures. As a consequence, all electrons of the (26,0) zigzag nanotube are collected in the valence band (Figure 2a, bottom). The HOMO and LUMO electron densities for the pristine (15,15) armchair and (26,0) zigzag SWCNTs are shown in Figure 3. The HOMOs and LUMOs have different spatial distributions. The extended regions of electron density in the HOMO of the (15,15) armchair CNT point in the circular direction, while similar density regions in the (26,0) zigzag CNTs point along the nanotube axis. The situation is reversed for the LUMOs. As a result, the (15,15) armchair HOMO resembles the (26,0) zigzag LUMO and vice versa. Intercalation of the investigated ions does not change the energy level diagrams of the SWCNTs, and their energy gaps remain equal to those of pristine SWCNTs (Figure 2a−d). Insertion of a bare Mez+ ion into the SWCNTs produces a new nondegenerated state near the εF (Figure 2b,c). The orbitals corresponding to the new states arise from the ns0 valence subshells for the ionized Li (n = 2) and Mg (n = 3) metal atoms. The electron densities of these nonbonding orbitals shown in Figure 4 support the last conclusion: orbitals have stype or spherical symmetry and localize primarily around the inserted cations with small tails extending onto the CNTs. Inside both SWCNTs, the Li orbitals are slightly larger than the

Figure 3. Electron density distributions of the LUMOs (top panel) and HOMOs (bottom panel) at the Γ-point for the pristine (15,15) armchair (left panel) and (26,0) zigzag (right panel) SWCNTs (the isodensity surface contour is 0.0004 e·Bohr−3).

Mg orbitals. The higher contraction of the Mg orbitals arises due to the larger net charge of the bare Mg2+ ion compared to the Li+ ion. E

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Figure 5. Total electron density distributions for the (26,0) zigzag SWCNTs containing the bare Li+ ion (left panel) and the [Li(EC)2]+ ion complex (right panel) (the isodensity surface contour is 0.0025 e· Bohr−3). The electron density is present on the bare Li+ ion (left panel) and is absent from the Li+ ion (lilac ball) imbedded into the [Li(EC)2]+ ion complex (right panel). Note that only the π-electron density contours appear next to the carbon atoms (gray balls), while the σ-electrons are not seen because of the chosen isodensity value and CNT periodicity. Figure 4. Electron density distributions of the Li (top panel) and Mg (bottom panel) nonbonding orbitals at the Γ-point for the (15,15) armchair (left panel) and (26,0) zigzag (right panel) SWCNTs containing the bare Li+ and Mg2+ ions, Mez+@SWCNT, respectively (the isodensity surface contour is 0.0004 e·Bohr−3).

SWCNT to the cations, making the CNT metallic. The solvent molecules (ECs) screen the polarizing action of the bare Li+ ion due to formation of chemical bonds between the Li+ ion and carbonyl oxygens and prevent the charge transfer. Distributions of the total electron densities in the Li+@(26,0) and [Li(EC)2]+@(26,0) intercalates are shown in Figure 5. The bare Li+ ion shows a spherically symmetric s-type density (Figure 5, left). In comparison, no such density is seen on the lithium imbedded inside the [Li(EC)2]+ ion complex (Figure 5, right). (Note that the picture excludes core electrons because pseudopotentials are used.) Instead, the oxygen’s lone electron pairs stretch to the sp-hybridized lithium orbitals and form two covalent bonds Li+ ← O by the donor−acceptor mechanism.

The energy level diagrams of the Li+@(15,15) and both Mg2+@SWCNT intercalates show that the metal levels are positioned below the nanotube HOMOs (Figure 2b, top, c). Being inside the SWCNT valence bands, the metal levels are almost fully occupied. In the case of the Li+@(26,0) intercalate, the Li level is positioned slightly above the valence band top and exactly at the εF (Figure 2b, bottom). The occupation numbers indicate that the ns0 orbitals of the Li+ and Mg2+ cations accept electron densities from the SWCNT valence bands (Figure 2b,c). The charge transfer generates a hole in the SWCNT, creating a possibility for p-type conductivity. This fact is more important for the semiconducting (26,0) zigzag than for the metallic (15,15) armchair SWCNT. The semiconducting (26,0) nanotube becomes conducting, when the bare Li+ and Mg2+ ions are placed near the nanotube axis. The hole conductivity of the (26,0) zigzag SWCNTs intercalated with the bare Mez+ should be higher in the doubly charged Mg2+ ion because almost twice as many electrons are transferred to the Mg level than to the Li level (Figure 2b,c, bottom). The ΔSel = 0 values for intercalation of the [Li(EC)2]+ ion complex presented in Table 1 have indicated already that the solvated cation has almost no influence on the electronic properties of both semiconducting (26,0) and metallic (15,15) SWCNTs. This conclusion is supported by comparison of the energy level diagrams of the pristine SWCNTs and the same SWCNTs intercalated with the [Li(EC)2]+ ion complex (Figure 2a,d). There are no differences between the energy diagrams for the pristine and intercalated CNTs, except for insignificant changes in the occupation numbers for the (15,15) armchair nanotube. Therefore, even partial solvation of the Li+ ion completely eliminates the cation’s influence (polarizing action) on the electronic properties of both metallic and semiconducting CNTs, though bare cations have a strong influence, in particular, on making semiconducting CNTs metallic. The strong polarizing action of the bare Li+ and Mg2+ ions modifies the electronic properties of the semiconducting (26,0) zigzag SWCNT. In particular, electrons are transferred from the

4. CONCLUSIONS Periodic FEF-DFT quantum−chemical calculations have been used to characterize the influence of charge and solvation of intercalated cations on the electronic properties of SWCNTs. Both metallic (15,15) armchair and semiconducting (26,0) zigzag SWCNTs have been considered. The pristine CNTs have been compared to the same CNTs containing the bare Li+ and Mg2+ ions as well as the [Li(EC)2]+ solvatocomplex. The results show that the intercalation process is energetically favorable for both CNT topologies and that it is more favorable for the metallic SWCNT due to its higher polarizability. As expected, the bare Mg2+ ion gives the highest energy gain upon intercalation. Insertion of the bare ions into the SWCNTs increases the total electronic entropy as a result of electron density redistribution. Entropy gains are notably bigger for the semiconducting (26,0) zigzag-based intercalates. The density redistribution occurs because the bare Li+ and Mg2+ ions introduce a new electronic level near the valence band top of the SWCNT. The orbitals of the new levels have a nonbonding nature. Electrons are transferred from the SWCNT valence bands to the metal cations, filling the introduced energy level and generating holes in the CNTs. The electron transfer process is particularly important for the (26,0) zigzag SWCNT because it enables p-type conductivity, making the initially semiconducting CNT metallic. The occupation numbers of the metal’s orbitals indicate that the p-type conductivity of the (26,0) zigzag SWCNT should be higher for the bare Mg2+ ion intercalation compared to the Li+ ion. F

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The Journal of Physical Chemistry C

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The electronic entropy does not change upon intercalation of the [Li(EC)2]+ solvatocomplex into both metallic and semiconducting SWCNTs. Since the electronic entropy characterizes occupations of states near the Fermi level, for instance the HOMO−LUMO equilibrium, it follows that insertion of the [Li(EC)2]+ solvatocomplex leaves the electronic state structure and state occupations near the Fermi level unchanged. Thus, the electronic properties of the CNTs filled with an electrolyte solution remain similar to the properties of pristine CNTs. The considered model of the [Li(EC)2]+ solvatocomplex represents de facto a partial solvated Li+ ion in LIBs. Even partial solvation completely eliminates the cation’s polarizing action on the CNT electronic properties, independent of the CNT topology. This observation directly validates application of classical force field models for representation of interactions of molecules and ions with CNT walls during molecular dynamics simulations of the confined ion−molecular electrolyte solutions. The obtained results can find a variety of applications. For instance, the changes in the CNT conductivity induced by the embedded cations can form the basis for development of ion sensors during mass spectroscopy experiments.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b07496. Convergence of the specific free energy functional and the specific electronic entropy with plane-wave kinetic energy cutoff and k-point mesh (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(O.N.K.) E-mail: [email protected]. Tel.: +380 50 3032813. *(O.V.P.) E-mail: [email protected]. Tel.: +1 213 8213116. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The calculations were performed using the “SCIT-4” computational cluster of the V. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine (http://icybcluster. org.ua). O.M.K. and O.N.K. acknowledge the Ministry of Education and Science of Ukraine for the financial support (Grant No. 0116U000834). O.V.P. is grateful to the U.S. Department of Energy for the financial support (Grant No. DESC0014429) and to the Photochemistry Center of the Russian Science Foundation, project No. 14-43-00052, for hospitality during manuscript preparation.

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REFERENCES

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DOI: 10.1021/acs.jpcc.6b07496 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.6b07496 J. Phys. Chem. C XXXX, XXX, XXX−XXX