Density functional theory calculations for interactions between metal-free phthalocyanine and lithium polysulfides

Density functional theory calculations for interactions between metal-free phthalocyanine and lithium polysulfides

Journal of Power Sources 423 (2019) 34–39 Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/loca...

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Journal of Power Sources 423 (2019) 34–39

Contents lists available at ScienceDirect

Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

Density functional theory calculations for interactions between metal-free phthalocyanine and lithium polysulfides

T

KumChol Ria,∗, CholYong Yunb, CholJin Kimc, Jun Mad, KukChol Kime a

Department of Chemistry Science, Kim Il Sung University, Pyongyang, 999093, Democratic People's Republic of Korea Department of Physical Science, Kim Chaek University of Technology, Pyongyang, 950003, Democratic People's Republic of Korea c Department of Energy Science, Kim Il Sung University, Pyongyang, 999093, Democratic People's Republic of Korea d Department of Geology Science, Kim Il Sung University, Pyongyang, 999093, Democratic People's Republic of Korea e Department of Resource Development Machinery, Pyongyang University of Mechanical Engineering, Pyongyang, 999093, Democratic People's Republic of Korea b

H I GH L IG H T S

S is absorbed on metal-free phthalocyanine by electrostatic attraction. • LiLi-trapped phthalocyanine has both cation and anion adsorption sites. • Li and S atom of Li S interact with the N and Li atom of Li-trapped phthalocyanine. • Li-trapped phthalocyanine plays a beneficial role in anchoring of Li S . • Strategies for using metal-free phthalocyanine in Li-S batteries are presented. • 2 n

2 n

2 n

A R T I C LE I N FO

A B S T R A C T

Keywords: Lithium polysulfides Metal-free phthalocyanine Anchoring material Lithium-sulfur batteries Density functional theory calculation

Rechargeable lithium-sulfur batteries are one of the most promising candidates for next-generation energy storage systems with high theoretical specific capacity and energy density, but there is some major challenge in the application of theirs. Among them, the main issue is the shuttle reaction caused by the dissolution of lithium polysulfides into the electrolyte. Recently, nitrogen-doped carbon materials are attracting attention as inhibitors for the shuttle reaction. However, according to our humble opinion, it is not easy to control the nitrogen doping configurations of nitrogen-doped carbon materials as wish. The nitrogen doping configurations of nitrogendoped graphene are very similar to the structure of some organic compounds, especially metal-free phthalocyanine. From this, density functional theory calculations are performed for the bound configurations between lithium polysulfides and metal-free phthalocyanine to assess the availability of metal-free phthalocyanine as an inhibitor for the shuttle reaction. The results show that metal-free phthalocyanine has sufficient potential to be used as an anchoring material for lithium polysulfides.

1. Introduction Lithium-sulfur (Li-S) batteries, which have the high theoretical specific capacity of ∼1670 mAh g−1 and high theoretical energy density of ∼2600 Wh kg−1, are considered as one of the most promising candidates to replace Li-ion batteries used as energy storage systems for electric vehicles [1]. Furthermore, compared to Li-ion batteries, sulfur is abundant in nature, inexpensive than lithium, and more environmentally friendly than cobalt [2]. Despite these advantages, Li-S batteries have not yet been commercially successful because of important issues such as poor conductivity of sulfur and its discharge



product Li2S, damage of cathode by volume expansion during discharging, and shuttle reaction of lithium polysulfides (LiPs) [3]. The major challenge is the shuttle reaction occurs because Li2Sn (n = 4, 6, and 8) in LiPs produced during discharging is dissolved into the organic electrolytes such as 1, 3-dioxolane (DOL) and dimethyl ether (DME) [4,5]. The result is fatal problems such as irreversible loss of sulfur, low coulombic efficiency during charging and rapid capacity reduction [6]. To solve the above issues, the various strategies have been explored, including the many carbon materials (porous/hollow carbon, carbon nanofibers/nanotubes, graphene/graphene oxide) [7–9], heteroatomdoped carbon materials (porous/hollow carbon, carbon nanofibers/

Corresponding author. E-mail address: [email protected] (K. Ri).

https://doi.org/10.1016/j.jpowsour.2019.03.058 Received 18 December 2018; Received in revised form 4 March 2019; Accepted 15 March 2019 0378-7753/ © 2019 Elsevier B.V. All rights reserved.

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Brillouin zone. The Perdew-Burke-Ernzerhof generalized gradient approximations were used for the exchange-correlation potential [37,38]. All the bound systems including H2Pc monomolecular are calculated in the 20 × 20 × 20 Å3 supercell. The van der Waals correction was evaluated by the vdW-DF2 functional [39]. The self-consistent loops were performed until the total energy change between the adjacent iterating steps was smaller than 10−4eV. All atoms are allowed to relax until the residual force per atom became smaller than 0.02 eV/Å in the 20 × 20 × 20 Å3. Bader charge analysis was performed on some major systems [40,41]. The binding energies were calculated by the following equation.

nanotubes, graphene/graphene oxide) [10,11], polymer (polyaniline, polypyrrole) [12–14], and transition metal oxides (MnO2, TiO2, Ti4O7) [15–17]. Additionally, many computational chemistry methods such as density functional theory (DFT) calculations have been applied to investigate the immobilization of LiPs at the atomic scale [18–23]. Carbon materials such as carbon nanofibers/nanotubes and graphene are good substances with excellent electrical conductivity and high surface area, but their interaction with LiPs is a van der Waals attraction so that the immobilization of LiPs is insufficient. Unlike this, nitrogen-doped graphene is a remarkable material that imparts conductivity to sulfur and LiPs and simultaneously performs an anchoring of LiPs [24,25]. In nitrogen-doped graphene, negatively charged N atoms interact with Li atoms in LiPs to inhibit the dissolution of LiPs in the electrolyte and provide Li-ions enriched environment on the surface, resulting in improved performance of Li-S batteries [26–28]. To understand the origins of performance improvement in Li-S batteries based on nitrogen-doped carbon materials, Li-Chang Yin and coworkers investigated the interactions of LiPs and nitrogen-doped graphene with different nitrogen doping configurations by DFT calculations and reported four types of pyrrolic and pyridinic nitrogen doping configurations (those in the pink hexagons of Fig. 1) to play an important role in the adsorption of LiPs [29]. Nitrogen-doped carbon materials obtained by a variety of methods including chemical vapor deposition (CVD), thermal treatment, hydrazine hydrate treatment, and pyrolysis of nitrogen-containing polymers [30–32]. It would be ideal to obtain only nitrogen-doped carbon materials with four types of nitrogen doping configurations above-mentioned by these methods, but such control is considered difficult. We have noted that the four types of nitrogen doping configurations above-mentioned are structurally similar to some organic materials such as metal-free phthalocyanine (H2Pc) and porphyrin. Indeed, H2Pc and its derivatives have already investigated as a component of the cathode of Li-ion batteries due to their high chemical stability, excellent electrochemical property, and high Li-ion intercalation capacity [33–35]. From this, we thought H2Pc has enough potential to can be used as an anchoring material for LiPs and performed DFT calculations on the interaction of LiPs and H2Pc to confirm whether this assumption is possible or not.

EB = ETotal − (ESub + EAds ) where ETotal, ESub, and EAds are the energies of the total bound system, H2Pc (or DOL/DME), and sulfur/LiPs, respectively. In order to verify the validity of the cutoff energy and the cell size set in the calculation, the binding energy of 2 × 2 periodic structure (40 × 40 × 20 Å3 supercell, 244-atoms) for the bound system of Li2S and H2Pc was calculated at 2 × 2 × 1 Γ-centered k-point. The difference of the binding energies for the two bound systems (20 × 20 × 20 Å3 supercell with a single k-point, 40 × 40 × 20 Å3 supercell with 2 × 2 × 1 k-point) of Li2S and H2Pc is less than 15 mV. 3. Results and discussion The structure optimization of the sulfur molecule and LiPs was performed. Fig. S1 shows the optimized structure of the sulfur molecule and LiPs in the ground state. The sulfur molecule, S8, has a crown configuration with D4d symmetry, and the S-S average bond length of 2.10 Å, and S-S-S average bond angle of 109.1°. The Li2S and Li2S2 have a chain-like and closed chain configuration with C2v symmetry, and Li2Sn (n = 4, 6, and 8) are closed chain form with C2 symmetry. The average bond length between Li atoms and adjacent S atoms is 2.09 Å in Li2S, 2.23 Å in Li2S2, 2.38 Å in Li2S4, 2.37 Å in Li2S6, and 2.39 Å in Li2S8, and tend to increase according to the number of S atom. This result is consistent with previous investigations [29,42]. The Bader analysis of S8 and LiPs was performed. The Bader charge of sulfur atoms is almost zero in S8. The charge of Li atoms in LiPs is +0.87 to +0.88 and does not depend much on the types of LiPs. However, in LiPs excluding Li2S, the charge of an adjacent S atom bound with Li atom is −0.67 to −0.93 and decrease according to the number of S atom. There is almost no change in charge of the other S atoms. The results show that S atoms are a covalent bond in S8 and the bond between the Li atom and the adjacent S atom is almost ionic in LiPs. In DOL and DME, O atom and an adjacent C atom have a polar

2. Methods DFT calculations were performed by the Vienna ab-initio simulation package using the projector augmented wave method [36], the planewave cutoff energy of 500eV, and a single k-point at Γ to sample the

Fig. 1. Diagram of the idea that H2Pc can be used as an anchoring material for Li2Sn (n = 4, 6, and 8). The nitrogen doping configurations of nitrogen-doped graphene in the pink hexagons play an important role in anchoring of Li2Sn (n = 4, 6, and 8) [29]. The C, N, H, Li, and S atoms are denoted by dark brown, light blue, lavender blush, green, and yellow spheres, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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110.0° in the isoindole units with H atom, 1.36 Å (1.31 Å: the other side length) and 124.5° in the bridge connecting the isoindole units, respectively. The average bond length of N atom and Li atom is 2.14 Å (Table S2). The average bond lengths of N-C and N-H in Li-H2Pc are slightly increased compared to H2Pc, and the two H atoms of the isoindole units are relocated below the plane of the molecule. When Li atom trapped on H2Pc, some charges migrate from Li atom to N atoms (Fig. S5). However, the average charge increase of N atoms bound with Li atom is negligible as about 0.06, and the charge of Li atom calculated by Bader analysis is about +0.9 (Table S3). Consequently, Li-H2Pc has positively charged Li atom and negatively charged N atoms (Fig. S6), and this means cation adsorption sites (N atoms) and anion adsorption site (Li atom) coexist in Li-H2Pc. If Li atom and adjacent S atom of LiPs interact simultaneously with N atom and Li atom of Li-H2Pc, the binding energy can be increased. At first glance, this can be helpful in the anchoring of LiPs. From the above results, it is expected that the interaction between LiPs and H2Pc will be in two forms. (a) The positively charged Li atoms of LiPs interact with the negatively charged N atoms of H2Pc. (b) Li atom and adjacent S atom of LiPs interact simultaneously with N atom and Li atom of Li-H2Pc, respectively. The optimization of the bound configurations between S8/LiPs and H2Ps was performed, and the binding energies were calculated (Fig. 3 and Fig. S7). In fully optimized configurations, the binding energies of S8/LiPs and H2Pc are −0.58eV in S8, -1.05eV in Li2S8, -0.96eV in Li2S6, -0.82eV in Li2S4, -1.23eV in Li2S2 and -1.28eV in Li2S, respectively. The binding energies of Li2S/Li2S2 and H2Pc are about −1.2eV, and which are about 0.2–0.4eV larger than those of Li2Sn (n = 4, 6 and 8) and H2Pc. This is because there are two Li-N bonds in between Li2S/Li2S2 and H2Pc and only one that in between Li2Sn (n = 4, 6 and 8) and H2Pc. The binding energies increase again according to the number of n in Li2Sn (n = 4, 6, and 8) because of the increase in van der Waals attraction depending on the molecular size. Although the binding energies of Li2Sn (n = 4, 6, and 8) and H2Pc are larger than those of Li2Sn (n = 4, 6, and 8) and DME/DOL, the binding energies of Li2S4 and DME/DOL are −0.80eV (Fig. S3 (e, f)) and that of Li2S4 and H2Pc is only −0.82eV. As shown in Fig. 4, the binding energies of S8/LiPs and Li-H2Pc are −0.74eV in S8, -1.44eV in Li2S8, -1.37eV in Li2S6, -1.11eV in Li2S4, -1.47eV in Li2S2 and -1.80eV in Li2S, respectively. The binding energies of S8/LiPs and Li-H2Pc unquestionably increase than those of S8/LiPs and H2Pc. The cause will be related to the number of the bond between LiPs and Li-H2Pc. The positively charged Li atom of LiPs bonds with a negatively charged N atom of Li-H2Pc, and the negatively charged S atom of LiPs bonds further with the Li atom of Li-H2Pc. The Bader analysis for the bound systems between Li2Sn (n = 4, 6, and 8) and

Fig. 2. The optimized structures of (a) H2Pc and (b) Li-H2Pc in the ground state. The C, N, H, and Li atoms are expressed by dark brown, light blue, lavender blush, and green spheres, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

covalent bond, and the charge of O atoms calculated by Bader analysis has of about −1 (Fig. S2). The dissolution of LiPs into DOL and DME is a result of the interaction between Li atom of LiPs and O atom of DOL/ DME [43]. In the stable bound configurations, the binding energies of Li2Sn (n = 4, 6, and 8) and DOL/DME are −0.80 ∼ −0.86eV, and that in DOL is slightly larger than in DME (Fig. S3). The optimized structure of H2Pc is shown in Fig. 2(a). H2Pc is a macrocyclic aromatic compound having four isoindole units and has excellent thermal and chemical stability. The investigation on its structure was carried out in detail by many researchers [44–46]. In the ground state, the average bond length and angle of N atom and adjacent C atoms are 1.38 Å and 107.0° in the isoindole units without H atom, 1.39 Å and 112.4° in the isoindole units with H atom, 1.33 Å and 124.0° in the bridge connecting the isoindole units, respectively. The average bond length of N atom and a hydrogen atom in the isoindole units with H atom is 1.01 Å (Table S2). This result is consistent with the previous investigations [47,48]. In the H2Pc, all N atoms have a negative charge, specifically but about 0.12–0.28 more negative than O atoms of DOL/ DME (Fig. S4 and Table S3). Li-ion is adsorbed to the negatively charged N-dopants of nitrogendoped graphene, as shown in many previous theoretical and experimental investigations for applying nitrogen-doped graphene in Li-ion and Li-S batteries [49–51]. Likewise, Li-ion also can be trapped to H2Pc. Therefore, the optimization for Li-trapped H2Pc (Li-H2Pc) was performed (Fig. 2(b)). In the stable configuration of Li-H2Pc, the average bond length and the angle of N atom and adjacent C atoms are 1.39 Å and 106.6° in the isoindole units without H atom, 1.44 Å and

Fig. 3. The fully optimized configurations of (a) S8, (b) Li2S, (c) Li2S2, (d) Li2S4, (e) Li2S6, and (f) Li2S8 on the H2Pc. The C, N, H, Li, and S atoms are denoted by dark brown, light blue, lavender blush, green, and yellow spheres, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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Fig. 4. The fully optimized configurations of (a) S8, (b) Li2S, (c) Li2S2, (d) Li2S4, (e) Li2S6, and (f) Li2S8 on the Li-H2Pc. The C, N, H, Li, and S atoms are denoted by dark brown, light blue, lavender blush, green, and yellow spheres, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

H2Pc are merely by electrostatic attraction. The feature of the interactions between the LiPs and Li-H2Pc is the opening of the closed chain in Li2S6 and Li2S8 (Fig. 4(e, f)). One of Li-S bonds in the LiPs is broken, S atom bonds with Li atom of the Li-H2Pc, and Li atom bonds with N atom of Li-H2Pc. When LiPs is adsorbed on some anchoring materials, the opening of closed chains is also reported in the previous investigations [29,52]. In Li-Chang Yin and coworker report, when Li2S8 is adsorbed on the Li-trapped nitrogen-doped graphene with four pyridine nitrogen-dopant, one of Li-S bonds in Li2S8 is opened. Also, in the investigation of Ji Liang and coworker, when Li2S8 is adsorbed on polymeric carbon nitrides (p-C3N4), one of Li-S bonds in Li2S8 is opened and formed new Li (in Li2S8) – N (in p-C3N4) bond. The kinetic barrier of the LiPs redox reactions on the p-C3N4 has been significantly reduced, which has resulted in a better rate performance. Interestingly, they reported the cause was from the distortion of molecular configurations of the LiPs anchored on p-C3N4. LiPs are more strongly adsorbed to p-C3N4 than graphene surface, and the molecular configurations of LiPs are also altered due to strong electrostatic interactions. The smaller inter-phase distance between LiPs and p-C3N4 could reduce the electron transport barrier, and the strong electronegativity of N atoms in p-C3N4 induces a Li-rich environment near the surface of p-C3N4. In the bound systems of LiPs and Li-H2Pc, the bond length between S atom of Li2Sn (n = 4, 6, and 8) and Li atom of Li-H2Pc are 2.43 Å in Li2S8, 2.42 Å in Li2S6, and 2.49 Å in Li2S4, respectively, and the average bond length between Li atom of Li2Sn (n = 4, 6, and 8) and N atom of Li-H2Pc is 2.02 Å (Fig. S8(d, e, f) and Fig. S9(d, e, f)). Also, the distance between S8 and Li-H2Pc is (about) 2.60 Å, which is much smaller than (about) 3.5 Å between S8 and H2Pc (Fig. S9(a) and Fig. S8(a)). Overall, the inter-phase distance between S8/LiPs and LiH2Pc reduce than in S8/LiPs and H2Pc. In addition, the charge of N atoms in Li-H2Pc is about −1.13 ∼ −1.23, which is about 0.12–0.28 more negative than O atoms of DME/DOL (Fig. S2 and Table S3). Therefore, N atoms of Li-H2Pc will provide a favorable environment for the lithiation of S8 and Li2Sn (n = 2, 4, 6, and 8) by attracting Li-ions dissolved in the electrolyte during discharge and enriching the surface with Li-ions. From this, when Li2Sn (n = 6 and 8) interacts with LiH2Pc, the closed chain is opened, but it is considered this phenomenon will not negatively affect battery performance. In order to consider the solvation effect of the electrolyte on the bound systems of Li2Sn (n = 4, 6 and 8) and Li-H2Pc, taking Li2S4 as an example, the binding energies between Li2S4 and Li-H2Pc with additional electrolyte molecule (DME/DOL) were calculated according to Ref. [53]. As shown in Fig. 5(c), the binding energies of L2S4 and LiH2Pc with additional DME/DOL decrease slightly than that of Li2S4 and Li-H2Pc (−1.11eV), but they are still larger than those of Li2S4 and

Fig. 5. The fully optimized configurations of DME and DOL on (a) H2Pc and (b) Li-H2Pc. (c) The fully optimized configurations of Li2S4 on Li-H2Pc with additional DME/DOL. The C, N, H, O, Li, and S atoms are denoted by dark brown, light blue, lavender blush, red, green, and yellow spheres, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

H2Pc/Li-H2Pc shows that the charge of Li atom and an adjacent S atom in the Li2Sn (n = 4, 6, and 8) is almost constant before or after bound with H2Pc/Li-H2Pc (Fig. S8(d, e, f) and Fig. S9(d, e, f)). In other words, there is little charge transfer of between the two materials. This means that the interactions of between Li2Sn (n = 4, 6, and 8) and H2Pc/Li37

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during the actual operation of batteries where the electrode reaction proceeds at the electrolyte/electrode interface. The binding energies of Li2Sn (n = 4, 6, and 8) on DME/DOL and H2Pc/Li-H2Pc were compared (Fig. 6). The binding energies of Li2Sn (n = 4, 6, and 8) and Li-H2Pc are about 0.3–0.6eV larger than those of Li2Sn (n = 4, 6, and 8) and DOL/DME. So, how can H2Pc be used in Li-S batteries? H2Pc and its metal derivatives tend to agglomerate and thus dissolve very little in common organic solvents [54]. This suggests that the homogeneous distribution of H2Pc could be suppressed in the mixing process of H2Pc and other cathode materials. In other words, the use of H2Pc molecule itself at the cathode may be undesirable. From this, some strategies for using H2Pc in Li-S batteries are presented (Fig. 7). It is believed that H2Pc can be used in Li-S batteries as hybrid materials with graphene/carbon nanofibers [55,56], and as porous H2Pc polymer film (or separator) [57,58].

Fig. 6. The binding energies of Li2Sn (n = 4, 6, and 8) on DME/DOL and H2Pc/ Li-H2Pc. The blue-violet, green, orange and blue columns indicate the calculated binding energies of Li2Sn (n = 4, 6, and 8) and DME/DOL, and H2Pc/LiH2Pc, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

4. Conclusions DFT calculations were performed for the bound systems between S8/LiPs and H2Pc/Li-H2Pc. When Li atom is trapped on H2Pc, the cation adsorption sites (N atoms) and the anion adsorption site (Li atom) coexist in Li-H2Pc. Since Li and adjacent S atom of LiPs simultaneously interact with N and Li atom of Li-H2Pc, the binding energies between LPs and Li-H2Pc increase than those between LiPs and H2Pc. The binding energies between Li2Sn (n = 4, 6, and 8) and H2Pc are about −0.82 ∼ −1.05eV, whereas those between Li2Sn (n = 4, 6, and 8) and Li-H2Pc are about −1.1 ∼ −1.5eV, which is 0.3–0.6eV larger than those between LiPs and DOL/DME. In other words, the interactions between LiPs and Li-H2Pc play an important role in anchoring of LiPs. These results show that H2Pc has sufficient potential to improve the performance of Li-S batteries through various strategies such as hybrid materials with graphene/carbon nanofibers and porous H2Pc polymer films (or separator). Acknowledgments This work is supported by Kim Il Sung University, Kim Chaek University of Technology, and Pyongyang University of Mechanical Engineering of DPR Korea. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jpowsour.2019.03.058. References [1] P.G. Bruce, S.A. Freunberger, L.J. Hardwick, J.M. Tarascon, Nat. Mater. 11 (2011) 19–29. [2] A. Manthiram, Y. Fu, S.H. Chung, C. Zu, Y.S. Su, Chem. Rev. 114 (2014) 11751–11787. [3] C. Li, Z. Xi, D. Guo, X. Chen, L. Yin, Small 14 (2018) 1701986. [4] S.S. Zhang, J. Power Sources 231 (2013) 153–162. [5] Y.V. Mikhaylik, J.R. Akridge, J. Electrochem. Soc. 151 (2004) A1969–A1976. [6] A.F. Hofmann, D.N. Fronczek, W.G. Bessler, J. Power Sources 259 (2014) 300–310. [7] J. Park, S.H. Yu, Y.E. Sung, Nano Today 18 (2018) 35–64. [8] A. Manthiram, Y. FU, Y.S. SU, Acc. Chem. Res. 46 (2013) 1125–1134. [9] S. Evers, L.F. Nazar, Acc. Chem. Res. 46 (2013) 1135–1143. [10] S.S. Zhang, Inorg. Chem. Front. 2 (2015) 1059–1069. [11] T.Z. Hou, X. Chen, H.J. Peng, J.Q. Huang, B.Q. Li, Q. Zhang, B. Li, Small 12 (2016) 3283–3291. [12] G.C. Li, G.R. Li, S.H. Ye, X.P. Gao, Adv. Energy Mater. 2 (2012) 1238–1245. [13] W. Zhou, Y. Yu, H. Chen, F.J. DiSalvo, H.D. Abruña, J. Am. Chem. Soc. 135 (2013) 16736–16743. [14] G. Ma, Z. Wen, J. Jin, Y. Lu, X. Wu, C. Liu, RSC Adv. 4 (2014) 21612–21618. [15] X. Liang, C. Hart, Q. Pang, A. Garsuch, T. Weiss, L.F. Nazar, Nat. Commun. 6 (2015) 5682. [16] Z. Wei Seh, W. Li, J.J. Cha, G. Zheng, Y. Yang, M.T. McDowell, P.C. Hsu, Y. Cui, Nat. Commun. 4 (2013) 1331. [17] X. Tao, J. Wang, Z. Ying, Q. Cai, G. Zheng, Y. Gan, H. Huang, Y. Xia, C. Liang,

Fig. 7. Some strategies for using H2Pc in Li-S batteries. (a) A porous H2Pc polymer film (or separator), (b) The hybrid materials of H2Pc with graphene/ carbon nanofibers. The C, N, H, and O atoms are denoted by dark brown, light blue, lavender blush, and red spheres, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

DME/DOL (−0.80eV). The binding energies of Li-H2Pc and DME/DOL increase than those of H2Pc and DME/DOL due to the formation of Li – O bond (Fig. 5(a, b)), but still smaller than those of Li2Sn (n = 4, 6, and 8) and Li-H2Pc. Additionally, the binding energies between S8/Li2S/ Li2S2 and Li-H2Pc with additional DME/DOL were calculated (Fig. S10). They decreased than those in the absence of DME/DOL, but there was no specific tendency depending on each system. This suggests that Li-H2Pc can be used sufficiently as an inhibitor for shuttle reaction even

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