Understanding the interactions between lithium

Nano Energy 25 (2016) 203–210

Contents lists available at ScienceDirect

Nano Energy journal homepage: www.elsevier.com/locate/nanoen

Understanding the interactions between lithium polysulfides and N-doped graphene using density functional theory calculations Li-Chang Yin a, Ji Liang a, Guang-Min Zhou a, Feng Li a,n, Riichiro Saito b, Hui-Ming Cheng a,n a b

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China Department of Physics, Tohoku University, Sendai 980-8578, Japan

art ic l e i nf o

a b s t r a c t

Article history: Received 26 March 2016 Received in revised form 30 April 2016 Accepted 30 April 2016 Available online 2 May 2016

To understand the origin of the cycling performance improvement observed in lithium-sulfur (Li–S) batteries based on N-doped carbon materials, the interactions between lithium polysulfides (LiPSs) and N-doped graphene (N-G) with different doping configurations have been investigated by density functional theory calculations. It has been found that only N-G with clustered pyridinic N-dopants can strongly attract LiPSs with large enough binding energies to effectively anchor the soluble LiPSs, due to (i) an enhanced attraction between Li ions in LiPSs and pyridinic N-dopants and/or (ii) an additional attraction between S anions in LiPSs and Li ions captured by pyridinic N-dopants. This study has, for the first time, provided a fundamental understanding on the origin of the effective anchoring of LiPSs by N-doped carbon materials, which suppresses the shuttling of LiPSs and produces significant improvement in the cycling performance of Li–S batteries. These findings can also guide the design of more effective N-doped carbons or other N-rich materials for Li–S batteries, preventing the undesirable LiPS shuttling. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Lithium-sulfur battery Shuttling effect Density functional theory calculation Nitrogen-doping Graphene

1. Introduction Lithium-sulfur (Li–S) batteries are promising and attractive candidates for next generation portable or stationary power supplies due to their high theoretical energy density up to 2600 W h kg 1 [1–4]. Although Li–S batteries have been extensively studied during the past three decades [5–18], their practical application is still hindered by the rapid capacity decay and serious self-discharge caused by the dissolving and shuttling of soluble lithium polysulfides (LiPSs) in electrolytes [19–22]. The shuttling occurs when the interactions between LiPSs and the commonly used electrolyte solvents (e.g. 1, 2-dimethoxyethane (DME) and 1,3-dioxolane (DOL)) are stronger than those between LiPSs and electrode materials. In order to avoid the shuttling effect, carbon materials have been widely used in Li–S batteries not only as conductive additives, but also as spatial confiners, and anode protectors [23–26]. In particular, N-doped carbon was found to be able to anchor LiPSs [27–32], thus suppressing their shuttling and improving the cycling performance of a Li–S battery. For example, it was reported that N-doped graphene (N-G) with pyrrolic and pyridinic N-dopants could bind LiPSs more strongly with larger binding energies (Eb) than pristine graphene (p-G) [27–30]. An n

Corresponding authors. E-mail addresses: fl[email protected] (F. Li), [email protected] (H.-M. Cheng).

http://dx.doi.org/10.1016/j.nanoen.2016.04.053 2211-2855/& 2016 Elsevier Ltd. All rights reserved.

amino-functionalized reduced graphene oxide (r-GO) was also reported to be able to stabilize both sulfur and LiPSs by covalent bonding [33]. In addition, phosphorene was recently predicted to be a promising host to anchor LiPSs for Li–S battery cathodes [34]. However, considering (i) the many possible doping configurations that may exist in N-G and (ii) the difficulty of controlling the synthesis of N-G with specific doping configurations, it would be difficult to validate experimentally which doping configuration in N-G works as an effective immobilizer for LiPSs in a Li–S battery. Therefore, it is practically important to theoretically investigate the interactions between N-G with different doping configurations and the soluble LiPSs to obtain the optimal design of N-doped carbons for Li–S batteries. In this paper, a systematic density functional theory (DFT) study has been performed to understand the interactions between LiPSs and N-doped carbon, using N-G with different doping configurations as model materials. A van der Waals (vdW) correction is incorporated in the DFT calculation to calculate the Eb between LiPSs and N-G with different doping configurations, including isolated/clustered amino, graphitic, pyridinic, and pyrrolic N-dopants, for obtaining the intrinsic roles of different N-doping configurations on the suppression of the LiPSs shuttling in a Li–S battery. Our DFT results show that, except for graphitic N, other isolated N-dopants bind LiPSs more or less stronger than p-G. The calculated Eb between LiPSs and isolated amino, graphitic, pyrrolic, or

204

L.-C. Yin et al. / Nano Energy 25 (2016) 203–210

pyridinic N-dopant (0.56–1.18 eV) is smaller than or comparable to those between LiPSs and electrolyte solvent molecules (DME and DOL) (0.87–0.98 eV). This implies an insignificant effect of an isolated N-dopant on the suppression of LiPSs shuttling. On the other hand, it is found that a cluster of pyridinic N-dopants strongly binds to LiPSs with larger binding energies (1.23–3.57 eV) than those between LiPSs and electrolyte solvents. Consequently, clustered pyridinic N-dopants in N-G are effective immobilizers of soluble LiPSs, contributing to the cycling performance improvement of Li–S batteries using N-doped carbons in the cathodes.

2. Computational methods DFT calculations were performed using the projector augmented wave method [35,36] and a plane-wave (PW) basis set as implemented in the Vienna ab-initio simulation package [37]. The Perdew-Burke-Ernzerhof functional [38] for the exchange-correlation term was used for all calculations. The energy cutoff for the PW basis set was set to be 400 eV. Spin polarized calculations were performed for systems with an odd number of electrons. A large poly-aromatic hydrocarbon (PAH) molecule of C96H24 was used to represent graphene in a 30 30 20 Å3 supercell. Several N-Gs with different N-doping configurations were considered by substituting, removing, and/or adding relevant atoms based on the PAH molecule. Only the Γ point was used to sample the first Brillouin zone of this supercell for all calculations. For the geometry relaxations and energy calculations, vdW interactions were incorporated by the optB88 exchange functional [39,40], and this proved to be very important to accurately evaluate the interactions between S-containing clusters and pristine graphene [41]. All atoms are allowed to be fully relaxed in the fixed 30 30 20 Å3 supercell until the residual force per atom decreases to below 0.01 eV Å 1. The charge population was calculated by using Bader charge analysis [42,43]. In order to check the size and edge effects of the finite cluster, we also calculated the Eb by using a larger PAH molecule of C222H42 with six hydrogen terminated armchair edges and a periodic structure (a 7 7 1 supercell with a 2 2 1 Γcentered k-mesh). The difference in Eb between Li2S and p-G/N-G using different structures (e.g. C96H24, C222H42, and the 7 7 1 periodic structure) is less than 20 meV, which clearly shows that both the size and edge effects are negligible compared with the value of Eb between Li2S and p-G based on C96H24 (480 meV).

3. Results and discussion Several S-containing clusters, including S8, Li2S and Li2S2n (n ¼1, 2, 3, and 4), were considered in this work to investigate the interactions between sulfur/LiPSs and N-G/p-G. The optimized molecular structures of these clusters in their ground states are shown in Fig. 1. S8 has a puckered ring structure with the D4d symmetry, and the S–S bond length and S–S–S bond angle were calculated to be 2.10 Å and 109.1°, respectively. As for LiPSs, both Li2S and Li2S2 have C2v symmetry, while other LiPSs have C2 symmetry due to the lack of mirror symmetry. The shortest Li–S bond length in each molecule increases with increasing cluster size: 2.09 Å for Li2S, 2.23 Å for Li2S2, and 2.36 (2.35 and 2.38) Å for Li2S4 (Li2S6 and Li2S8), while the bond angle of Li–S–Li decreases: 131.9° for Li2S, 96.8° for Li2S4, and 73.5° (69.1° and 66.3°) for Li2S4 (Li2S6 and Li2S8). The calculated S–S bond lengths of Li2S4 are 2.13 Å for S1–S3 (S3–S4) and 2.17 Å for S2–S3, larger than that of S8 (2.10 Å) due to the less covalent character. The calculated S–S bond lengths of Li2S6 are 2.12, 2.11 and 2.14 Å for S1–S2 (S5–S6), S2–S3 (S4–S5) and S3–S4, respectively. The S–S bond lengths of Li2S8 are 2.11, 2.13, 2.09 and 2.14 Å for S1–S2 (S7–S8), S2–S3 (S6–S7), S3–S4 (S5–S6) and S4–S5, respectively. The optimized structures of S8, Li2S and Li2S2n (n¼ 1, 2, 3, and 4) obtained in this work are consistent with the previous calculations [44–46]. When a N atom is doped into graphene, there are three common bonding configurations in the carbon lattice, that is, graphitic N (NC), pyridinic N (NPD), and pyrrolic N (NPL) [47–55], as shown in Fig. 2. Additionally, amino N with two possible doping configurations, e.g. the NH2 group located at the edge (NA) or on the basal plane (NA′) of graphene as shown in Fig. 2, can be introduced into N-G by reducing graphene oxide under N-containing environments [56,57]. Interestingly, two graphitic N-dopants (N2C) have been observed to preferably occupy the same sub-lattices of graphene synthesized by chemical vapor deposition (CVD) [58,59]. Besides, N2PD (N2PL) denotes two neighboring pyridinic (pyrrolic) N atoms bonding into two adjacent six (five) member rings. It was also reported that native point defects (especially vacancies) and N-dopants (like NPD and NPL) attract each other and prefer to exist together in carbon nanomaterials, resulting in complex doping configurations with clustered N-dopants [60–63], such as two pyridinic plus one pyrrolic N (N2PD/PL), three pyridinic N (N3PD), three pyrrolic N (N3PL), and four pyridinic N (N4PD) dopants (Fig. 2). Except for N2C and NA′, the other N-dopants are located at edges or defective graphene sites, since the large structural distortion induced by N-doping is possible at these sites [60]. In fact, as shown in Fig. 2, N2PD/PL is composed of one pyrrolic and two pyridinic N atoms with four C vacancies, N3PD consists of three pyridinic N

Fig. 1. Fully optimized molecular structures of isolated S8, Li2S and Li2S2n (n¼ 1, 2, 3, and 4) clusters in the ground states. The S and Li atoms are denoted by yellow and purple balls, respectively. The symmetry groups, nonequivalent S–S/Li–S bond lengths and S–S–S/Li–S–Li bond angles of each cluster are also listed.


205

Fig. 2. Structural diagrams of p-G and N-G with different doping configurations. The full names of all abbreviations are given in the main text. The C, N and H atoms are denoted by green, blue and light blue balls, respectively.

atoms with four C vacancies, and N3PL (N4PD) consists of three pyrrolic (four pyridinic) N atoms with six C vacancies. The abundance of different doping configurations in N-G can be determined by the formation energy (Ef). Here, the Ef of different N-Gs is defined by the following equation,

E f =E t (N-G)−E t (p-G)+ nC μ C−nN μ N−nH μ H−nLi μ Li

(1)

where Et(p-G) and Et(N-G) denote the total energies of p-G and N-G, respectively. μC, μLi, μN, and μH are the chemical potentials of C, Li, N, and H atoms, respectively, which are taken as the total energy per C (Li) atom of graphene (bulk bcc lithium) for C (Li) and half of the total energy of an isolated N2 (H2) molecule for N (H). nC and nN (nH) respectively denote the number of the removed C and the added N (H) atoms in N-G with different doping configurations, and nLi denotes the number of Li atoms captured by the clustered N-dopants in N-G with complex doping configurations. According to Eq. (1), the Ef of p-G is naturally set to be zero and taken as the reference, and the calculated Ef of N-G with various doping configurations is listed in Table 1. As listed in Table 1, the Ef of NA gives the lowest value (0.14 eV) among all N-Gs. The lowest Ef of NA implies that NA is the dominant N-dopant if the N-G is prepared at low temperature (usually lower than 200 °C) under an

ammonia-containing environment, as reported in the previous work [56,57]. The calculated Ef of NA’ (1.91 eV) is much higher than that of NA, indicating that it is unlikely to obtain NA’ in N-G at low temperature. For the other three isolated N-dopants (NPD, NC, and NPL), the calculated values of Ef (0.63, 1.40 and 1.72 eV) are larger than that of NA. Therefore, these three N-dopants should be observed at relatively high temperatures. This result is consistent with the experimental observations that the amount of NA is remarkably decreased by annealing the N-doped carbon materials at high temperatures (Z 400 °C), leaving dominant dopants of NPD, NC, and NPL [56,57]. The lower Ef of NPD (0.63 eV) than those of NC and NPL (1.40 and 1.72 eV) means that NPD is the most dominant among these three N-dopants in N-doped carbon materials [64]. The origin of the large Ef of NPL (1.72 eV) can be attributed to the stronger in-ring strain at the pentagonal NPL site than that at the hexagonal NPD and NC sites, as implied by the longer N–C bond in NPL (Fig. S1). The Ef of N2 C was calculated to be 3.29 eV, much higher than those of NPD, NC, and NPL. This means that N2 C dopants can be obtained only at very high temperatures (4900 °C), as demonstrated by their observation in N-G prepared by CVD method [58,59]. As listed in Table 1, the Ef of N2PL (5.60 eV) is more than three times larger than that of N2PD (1.37 eV) due to the much

Table 1 The calculated Ef (eV) for N-G with different N-doping configurations. The values given in the parentheses are the Ef values calculated for N2PD/PL, N3PD, and N4PD after capturing Li atoms. Config.

NA

NPD

NC

NPL

NA′

N2PD

N2 C

N2PL

N3PL

N3PD

N4PD

N2PD/PL

EF (eV)

0.14

0.63

1.40

1.72

1.91

1.37

3.29

5.60

4.63

3.98 (0.19)

4.35 ( 0.28)

2.84 (1.61)

206


Table 2 The calculated Eb (eV) between different S-containing clusters and p-G/N-G. For comparison, the Eb between soluble LiPSs and electrolyte solvent molecules (DOL and DME) are also listed. Clusters

S8 Li2S Li2S2 Li2S4 Li2S6 Li2S8

Doping configurations

Electrolytes

NA

NC

N2 C

NPL

NPD

N2PD

N3PD

N4PD

N2PD/PLPL

p-G

DOL

DME

0.59 0.82 0.71 0.79 0.96 1.02

0.55 0.54 0.51 0.56 0.72 0.87

0.72 0.52 0.45 0.53 0.70 0.83

0.59 0.66 0.61 0.69 0.90 0.98

0.60 1.19 1.08 0.97 1.07 1.18

0.63 1.75 1.55 1.23 1.31 1.44

1.26 1.88 1.63 1.32 1.58 1.81

2.62 3.11 2.79 2.37 2.85 3.57

0.94 1.67 1.38 1.07 1.13 1.29

0.69 0.48 0.53 0.57 0.74 0.91

0.87 0.90 0.92

0.92 0.95 0.98

stronger in-ring strain at the pentagonal N2PL site than that at the hexagonal N2PD site. This can also be explained by the much longer N–C bonds at N2PL site than those at N2PD site, as shown in Fig. S1. The Ef values of N-Gs with complex doping configurations were calculated to be 2.84, 3.98, 4.35, and 4.63 eV for N2PD/PL, N3PD, N4PD, and N3PL (Table 1), respectively, and these are comparable to or larger than that of N2C (3.29 eV). This means that the thermodynamic stabilities of N2PD/PL, N3PD, N4PD, and N3PL are comparable to or lower than that of N2C, but still higher than that of defective graphene with more than one C vacancy (with Ef larger than 7.5 eV) [62,65,66]. The stability sequence for N2PD/PL, N3PD, N4PD, and N3PL obtained in this work is in agreement with other theoretical results [67,68]. Such complex doping configurations in N-G are always expected if N-doping is carried out on r-GO, considering the existence of many vacancies in r-GO [69]. Since nano-pores in r-GO have been proved to be effective for trapping Li ions during the operation of a Li ion battery [48] or a Li-air battery [67], we have also calculated the Ef of N-Gs with the complex doping configurations after trapping Li atoms. Interestingly, it is found that N2PD/PL, N3PD, and N4PD can respectively trap one, two and three Li atoms at the most. In the presence of Li atoms, the Ef is remarkably decreased to 1.61, 0.19 and 0.28 eV for N2PD/PL, N3PD, and N4PD, respectively, as given in the parentheses in Table 1. Here, the negative value of Ef for N4PD ( 0.28 eV) means that after capturing three Li atoms, N4PD is energetically more stable than p-G. The remarkable decrease of the Ef values of N2PD/PL, N3PD, or N4PD after capturing Li atoms indicates their strong ability to trap Li atoms. However, N3PL is found to be unable to trap Li atoms since all three pyrrolic N atoms are terminated by H atoms in this case, as shown in Fig. 2. Considering the extremely large Ef of N2PL and N3PL, it is very difficult to introduce these two N-doping configurations into N-G. Therefore, we do not consider these two doping configurations in the following discussion. In order to evaluate the interactions between LiPSs and N-G with different doping configurations, we have also calculated the binding energies between S-containing clusters (S8, Li2S and Li2S2n, n ¼1, 2, 3, and 4) and different N-Gs (or p-G), which are defined by:

Eb=E C-S−E C−ES,

(2)

where EC, ES, and EC-S are, respectively, the total energies of p-G/NG, one isolated S-containing cluster (S8, Li2S and Li2S2n, n ¼1, 2, 3, and 4), and a composite system of N-G/p-G bonded with different S-containing clusters. As for N-G with complex doping configurations of N2PD/PL, N3PD, and N4PD, EC and EC-S are the total energies of Li-trapped N-G and those of the composite structure of Li-trapped N-G bonded with S-containing clusters, respectively. 4. S-containing clusters with p-G The intermolecular interaction (i.e. vdW interaction) contains three parts: the Keesom orientation force (FO) due to the

permanent-permanent dipole interaction for polar molecules, the Debye induction force (FI) arising from the interaction between permanent dipole of a polar molecule and the induced dipole of a non-polar molecule, and the universal dispersion or London force (FD) due to the non-zero instantaneous dipole moments of all molecules [70]. Intuitively, the interaction between one isolated S8 molecule and p-G is only due to because the non-polar characteristics of both S8 molecule and p-G, and the interactions between LiPSs (polar molecules due to Li–S ionic bonds) and the p-G are due to both FI and FD, and those between LiPSs and N-G (with polarization induced by N-doping) are the sum of FD, FI, and FO if there is no charge transfer between LiPSs and N-G. According to Eq. (2), the calculated Eb between the S-containing clusters and the p-G increases from 0.48 eV for Li2S to 0.91 eV for Li2S8, then decreases to 0.69 eV for S8, as listed in Table 2. As we can see in Table 2, the Eb increases with increased cluster sizes of LiPSs. Since the interaction between one isolated S8 molecule and p-G mainly comes from FD, the larger Eb obtained between S8 and p-G is due to the larger size of S8 compared with Li2Sn (n r4). The larger Eb between Li2Sn (n¼ 6, and 8) and p-G than that between S8 and p-G can be attributed to both FD and FI, considering the similar size of Li2S6 and Li2S8 compared with S8. It should be noted that the Eb between one S3 cluster and p-G has been calculated to be 0.3 eV without including the vdW correction [71], which is smaller than that between one isolated S8 molecule and p-G (0.69 eV) due to the smaller size of S3 compared with S8 as well as the absence of a vdW correction in previous calculation. Moreover, the Eb between Li2S8 and p-G was calculated to be 0.8 eV without considering the vdW correction [45], which was re-calculated to be 0.91 eV after including the vdW correction in this work.

5. S-containing clusters with N-G Fig. 3 presents the fully optimized molecular structures of S8 on p-G and N-G. As shown in Fig. 3, the S8 molecule retains its puckered ring structure on p-G (Fig. 3a) and N-G with different doping configurations (Fig. 3b-g) except for Li-trapped N3PD and N4PD (Fig. 3h, i), on which the S8 molecule takes an opened ring structure. According to the calculated Eb (see Table 2), N-G with complex doping configurations of N2PD/PL, N3PD, and N4PD can effectively increase the binding strength between S8 and N-G due to the strong attraction between the S8 molecule and the Li atoms trapped by the clustered multiple N-dopants. Li-trapped N4PD shows the strongest binding (2.62 eV) to S8 due to the formation of Li–S bonds after ring opening, while NC, NA, NPL or NPD shows similar or even weaker binding with S8 compared with p-G, due to the smaller vdW contribution from only the edge atoms of N-G in these cases. As we can see in Table 2, the calculated binding energies between all N-Gs and LiPSs range from 0.45 to 3.57 eV, which are still much larger than the thermal fluctuation (26 meV per atom) at a typically expected operating temperature (300 K) of


207

Fig. 3. Fully optimized molecular structures of one isolated S8 on (a) p-G, and N-G with (b) NC, (c) N2C, (d) NA, (e) NPL, (f) NPD, and Li-trapped N-G with (g) N2PD/PL, (h) N3PD, and (i) N4PD. The calculated binding energies (Eb in eV) of one isolated S8 on p-G and N-G with different N-doping configurations are also given. The C, N, H, Li, and S atoms are denoted by green, dark blue, light blue, purple, and yellow balls, respectively.

the secondary Li–S batteries. Therefore, it is unnecessary to consider the thermal effect on the interactions between N-G and LiPSs in the first approximation. In order to identify the influence of different N-doping configurations on the interactions between LiPSs and N-G, the values of Eb given in Table 2 are plotted versus the amount of S in various LiPSs in Fig. 4. As for Li2S and Li2S2, which are insoluble in electrolyte solvents and could be regarded as the initial nucleating species for the subsequent discharge products (e.g. bulk Li2S and Li2S2) in a Li–S battery, we found that, except for NC and N2C, other doping configurations provide an obviously larger Eb with Li2S and Li2S2 than does p-G. Particularly, the doping configurations of NPD, N2PD, N2PD/PL, N3PD, and N4PD can provide a large Eb with both Li2S and Li2S2, which is more than twice that with p-G. Thus, these doping configurations would preferably induce inhomogeneous nucleation of the final discharge products on the surface of N-G during the charge/discharge of a Li–S battery. We have also noted that N-G with different doping configurations provides a smaller Eb with Li2S2 than with Li2S. This might be due to the large repulsion between the negatively charged N-dopants in N-G and the two negatively charged S atoms in Li2S2. As the main intermediate products during the charge-discharge of Li–S batteries, Li2Sn (3 rn r8) are soluble in electrolyte solvents due to their large values of Eb with the solvent molecules (DME and DOL). For example, the Eb values of Li2S4, Li2S6, and Li2S8 with DOL/DME were calculated to be 0.87–0.98 eV, which is larger than, or comparable to, those between them and p-G (0.57–0.91 eV) (see Table 2 and Fig. 4). This is the main reason for the rapid capacity decay (i.e. shuttling effect) and serious self-discharge of a Li–S battery using pristine carbon materials as electrodes. N-G has been believed to be able to effectively suppress the shuttling of soluble LiPSs [27–32], however, it is still unknown which N-doping configuration serves as the effective immobilizer for the soluble LiPSs. In fact, as we can see in Table 2 and Fig. 4, N-G with graphitic N (e.g. NC and N2 C) shows the smallest Eb with soluble LiPSs. As shown in Fig. 2, a graphitic N bonds with three C atoms, while an amino or a pyridinic/pyrrolic N atom bonds with only one or two C atoms. This would result in a large repulsion between the positively charged Li ions in LiPSs and the neighboring positively charged C atoms around the N-dopants at NC/N2C

Fig. 4. Plot of the calculated Eb between LiPSs and N-Gs with different doping configurations. For comparison, the Eb between LiPSs and p-G and those between soluble LiPSs and electrolyte solvents (DME and DOL) are also presented.

sites than those at NA and NPL/NPD sites [72]. Consequently, this would remarkably compromise the attraction between the positively charged Li ions in LiPSs and the negatively charged graphitic N, resulting in the smallest Eb of NC/N2C with soluble LiPSs (even

208


weaker than those between soluble LiPSs and p-G). On the other hand, larger values of Eb between soluble LiPSs and N-Gs with other doping configurations (NA, NPL, NPD, N2PD, N2PD/PL, N3PD, and N4PD) have been observed than those between LiPSs and p-G. However, the calculated Eb between soluble LiPSs and NA (NPL) is still smaller than, or comparable to, those between LiPSs and electrolyte solvents, e.g., 0.96 eV for Li2S6 with NA, 0.79 (0.69) eV for Li2S4 with NA (NPL), and 0.90 eV for Li2S6 with NPL. This implies that NA or NPL cannot provide a binding force that is strong enough to suppress the LiPSs shuttling. Different from NC, N2C, NA, and NPL, a slightly larger Eb was found between NPD and LiPSs (0.97–1.18 eV) than that between electrolyte solvents and LiPSs (0.87–0.98 eV), showing a moderate interaction between NPD and soluble LiPSs and its possible role in the suppression of the LiPSs shuttling [27– 32]. This mainly comes from the attraction between the positively charged Li ions in LiPSs and the more negatively charged pyridinic N (with 1.24 electrons) originated from the charge re-distribution of graphene upon N-doping [73], as well as the lower repulsion due to the absence of the positively charged H atom in this doping configuration, compared with other isolated N-dopants (especially for NA and NPL), as shown in Fig. S2. Apart from this, the interaction between LiPSs and N-G with pyridinic N can be further enhanced by increasing the number of the pyridinic N atoms. For example, the values of Eb for Li2S4, Li2S6, and Li2S8 with N2PD were calculated to be 1.23, 1.31, and 1.44 eV (Table 2), respectively. This result clearly shows the strong immobilizing effect of dual pyridinic N-dopants in N-G for soluble LiPSs. In the cases of complex doping configurations (N2PD/PL, N3PD, and N4PD) with trapped Li ions, as shown in Fig. 4, the interaction between them and LiPSs is significantly increased. The Eb between N-Gs with these doping configurations and LiPSs (e.g. 1.27 eV between Li2S4 and N2PD/PL and 3.07 eV between Li2S8 and N4PD) are much larger than the Eb between electrolyte solvents and LiPSs (Table 2). Such a strong binding should be able to effectively suppress the undesirable shuttling of LiPSs. The origin of the strong binding between soluble LiPSs and N-Gs with NPD, N2PD, N2PD/PL, N3PD, and N4PD can be understood by analyzing the fully optimized molecular structures of LiPSs on these N-Gs. For example, Li2S4 retains the ring structure on N-G with different doping configurations, except for N4PD with three trapped Li atoms, in which the Li2S4 ring is opened, as shown in Fig. 5. The calculated charge transfer (ΔQ) from N4PD to Li2S4 is 0.83 electrons in the case of Li-trapped N4PD, while a negligible ΔQ is obtained between Li2S4 and other N-Gs (Fig. S2). This means that, except for N4PD, the binding forces between different soluble LiPSs

and other N-Gs are mainly intermolecular interactions. As for N4PD, a significant charge transfer contributes to the additional interaction with LiPSs, resulting in the much increased Eb (2.37–3.57 eV) with LiPSs. It is well known that the Bader charge analysis method gives relatively large values of atomic charge comparing with others. In fact, we have also carried out the charge analysis using the Hirshfeld method [74]. By which the local charge of N atom in NPL (NPD) was calculated to be 0.08 (0.18) electrons. Since the absolute values of atomic charges are analysis method dependent, we cannot directly use the absolute values to make a quantitative conclusion. However, both results based on the Bader and the Hirshfeld methods give the same fact that N atom in NPD is more negatively charged than the N atom in NPL (See Fig. S2), we think that our discussions based on the Bader charge are justified for obtaining the same conclusion. The dependence of binding strength between LiPSs and N-G on doping configuration can be seen from Li-N/Li–S distances. As shown in Fig. 5, Li2S4 on NPD and N2PD gives the smallest Li-N distance (2.02 and 2.03 Å) among all cases considered, which is consistent with the large Eb obtained from Li2S4 on NPD and N2PD. In the cases of Li2S4 on N2PD/PL, N3PD, and N4PD, the Li–S and Li-N distances were calculated to be about 2.5 and 2.1 Å, respectively, similar to the Li–S bond length of LiPSs (2.36–2.41 Å) obtained in this work and the Li-N bond length (2.06 Å) in LiNH2 [75]. Apparently, apart from the attraction between the Li ions of Li2S4 and the negatively charged N-dopants, an additional attractive interaction exists between the negatively charged S of Li2S4 and the positively charged Li captured by the clustered multiple N-dopants, resulting in strong binding to the soluble LiPSs in these cases. On the other hand, in the cases of NC, N2C, and NPL, the smallest distances between Li2S4 and the N-dopants in N-Gs were calculated to be 3.23, 3.41, and 3.25 Å, respectively. This would result in the weak binding observed for Li2S4 on N-Gs with NC, N2C, and NPL. As for Li2S4 on NA, the Li-N distance (2.11 Å) is slightly larger than those between Li2S4 and NPD/N2PD (2.02/2.03 Å). However, the large repulsion of the Li ions by the two positively charged H atoms bonded to the amino N atom could strongly comprise the attraction between Li ions and amino N-dopants. It should be noted that the interactions between N-G and LiPSs might be relevant to other factors in a real electrochemical environment, such as electric potentials, ions, electrolyte solvents and so on. However, we did not consider these factors in this work for simplicity and this additional work will be a future study. Our DFT results have indicated that, among all considered N-doping configurations in N-G, only the clustered pyridinic

Fig. 5. Fully optimized molecular structures of Li2S4 on N-G with (a) NC, (b) N2C, (c) NA, (d) NPL, (e) NPD, (f) N2PD, and Li-captured N-G with (g) N2PD/PL, (h) N3PD, and (i) N4PD. The relevant Li-N/Li–S distances are presented. C, N, H, Li, and S atoms are denoted by green, dark blue, light blue, purple, and yellow balls, respectively.


N-dopants (N2PD, N2PD/PL, N3PD, and N4PD) can effectively anchor the soluble LiPSs and thus suppress their shuttling. Therefore, in order to improve the cycling performance of Li–S batteries by using N-G as an electrode material, it is necessary to find ways to introduce as many of these doping configurations as possible into the N-G by N-doping based on a specifically designed GO with suitable microstructures. To achieve this, several strategies can be considered. For instance, GO should be prepared with small sheet sizes or large pores to provide sufficient edge sites for doping of N2PD. GO should also contain abundant sub-nanometer pores with four to six C vacancies to offer the possibilities for doping configurations such as N2PD/PL, N3PD, and N4PD. In addition, GO could also be reduced in environments containing both N and Li, thus facilitating the formation of clustered N-doping configurations with trapped Li atoms. Apart from typical N-Gs, it is reasonable to expect that a large Eb for soluble LiPSs could be obtained by directly choosing the materials with a large number of pyridinic-like N atoms, such as polymeric carbon nitride (p-C3N4), as electrode materials for Li–S batteries. In fact, the calculated values of Eb between different soluble LiPSs and p-C3N4 are in the range of 1.45–1.74 eV, which are much larger than those between LiPSs and electrolyte solvents (0.87–0.98 eV). As predicted, we found that the Li–S system with a hybridized electrode consisting of p-C3N4 and graphene shows outstanding cycling performance with a capacity decay as low as ca. 0.037% per cycle and a coulombic efficiency of 100% [76].

6. Summary The interactions between LiPSs and N-G with different doping configurations have been systematically investigated by DFT calculations with vdW corrections. Except for graphitic N-dopants, N-G with other N-dopants can provide stronger binding with soluble LiPSs than p-G. However, only N-G with clustered pyridinic N-dopants binds soluble LiPSs much more strongly than the electrolyte solvents do, indicating their effective role in anchoring the soluble LiPSs. Our DFT results have thus shown that clustered pyridinic N-dopants in N-G are the intrinsic reason for the widely observed suppression of LiPS shuttling by N-doped carbon materials in Li–S batteries. This theoretical understanding of the interaction between S-containing clusters and N-G will shed light on the future design of electrode materials based on doped carbon for Li–S batteries with improved electrochemical performance.

Acknowledgments This work is supported by Ministry of Science and Technology of China (No. 2014CB932402), National Natural Science Foundation of China (Nos. 51472249, 51521091, 51525206, and U1401243), “Strategic Priority Research Program” of the Chinese Academy of Sciences (XDA01020304), the Key Research Program of Chinese Academy of Sciences (Grant No. KGZD-EW-T06), T.S. Kě Research Fellowship Program of Shenyang National Laboratory for Materials Science and China Postdoctoral Science Foundation (No. 2015M571342). R.S. acknowledges MEXT Grant Nos. 25107005 and 25286005. This work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe1(A). We also acknowledge the support from Shenyang Supercomputing Center (CAS). Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.nanoen.2016.04.

209

053.

References [1] A. Manthiram, S.H. Chung, C.X. Zu, Adv. Mater. 27 (2015) 1980–2006. [2] Y.X. Yin, S. Xin, Y.G. Guo, L.J. Wan, Angew. Chem. Int. Ed. 52 (2013) 13186–13200. [3] A. Manthiram, Y.Z. Fu, Y.S. Su, Acc. Chem. Res. 46 (2013) 1125–1134. [4] M. Barghamadi, A. Kapoor, C. Wen, J. Electrochem. Soc. 160 (2013) A1256–A1263. [5] R.D. Rauh, K.M. Abraham, G.F. Pearson, J.K. Surprenant, S.B. Brummer, J. Electrochem. Soc. 126 (1979) 523–527. [6] J. Shim, K.A. Striebel, E.J. Cairns, J. Electrochem. Soc. 149 (2002) A1321–A1325. [7] E. Peled, Y. Sternberg, A. Gorenshtein, Y. Lavi, J. Electrochem. Soc. 136 (1989) 1621–1625. [8] S.E. Cheon, K.S. Ko, J.H. Cho, S.W. Kim, E.Y. Chin, H.T. Kim, J. Electrochem. Soc. 150 (2003) A800–A805. [9] J.R. Akridge, Y.V. Mikhaylik, N. White, Solid State Ion. 175 (2004) 243–245. [10] S. Kim, Y.J. Jung, H.S. Lim, Electrochim. Acta 50 (2004) 889–892. [11] Y.J. Choi, K.W. Kim, H.J. Ahn, J.H. Ahn, J. Alloy. Compd. 449 (2008) 313–316. [12] J.W. Choi, J.K. Kim, G. Cheruvally, J.H. Ahn, H.J. Ahn, K.W. Kim, Electrochim. Acta 52 (2007) 2075–2082. [13] M.S. Song, S.C. Han, H.S. Kim, J.H. Kim, K.T. Kim, Y.M. Kang, H.J. Ahn, S.X. Gou, J. Y. Lee, J. Electrochem. Soc. 151 (2004) A791–A795. [14] J. Sun, Y.Q. Huang, W.K. Wang, Z.B. Yu, A.B. Wang, K.G. Yuan, Electrochim. Acta 53 (2008) 7084–7088. [15] Y.J. Jung, S. Kim, Electrochem. Commun. 9 (2007) 249–254. [16] J. Sun, Y.Q. Huang, W.K. Wang, Z.B. Yu, A.B. Wang, K.G. Yuan, Electrochem. Commun. 10 (2008) 930–933. [17] J.W. Choi, G. Cheruvally, D.S. Kim, J.H. Ahn, K.W. Kim, H.J. Ahn, J. Power Sources 183 (2008) 441–445. [18] B.H. Jeon, J.H. Yeon, K.M. Kim, I.J. Chung, J. Power Sources 109 (2002) 89–97. [19] Y.V. Mikhaylik, J.R. Akridge, J. Electrochem. Soc. 151 (2004) A1969–A1976. [20] S.E. Cheon, K.S. Ko, J.H. Cho, S.W. Kim, E.Y. Chin, H.T. Kim, J. Electrochem. Soc. 150 (2003) A796–A799. [21] S.S. Zhang, J. Power Sources 231 (2013) 153–162. [22] A. Manthiram, Y.Z. Fu, S.H. Chung, C.X. Zu, Y.S. Su, Chem. Rev. 114 (2014) 11751–11787. [23] J. Liang, Z.H. Sun, F. Li, H.M. Cheng, Energy Storage Mater. 2 (2015) 76–106. [24] J.B. Goodenough, Energy Storage Mater. 1 (2015) 158–161. [25] M.P. Yu, R. Li, M.M. Wu, G.Q. Shi, Energy Storage Mater. 1 (2015) 51–73. [26] W. Lv, Z.J. Li, Y.Q. Deng, Q.H. Yang, F.Y. Kang, Energy Storage Mater. 2 (2015) 107–138. [27] T.Z. Hou, H.J. Peng, J.Q. Huang, Q. Zhang, B. Li, 2D Mater. 2 (2015) 014011. [28] X.W. Wang, Z.A. Zhang, Y.H. Qu, Y.Q. Lai, J. Li, J. Power Sources 256 (2014) 361–368. [29] K. Han, J.M. Shen, S.Q. Hao, H.Q. Ye, C. Wolverton, M.C. Kung, H.H. Kung, ChemSusChem 7 (2014) 2545–2553. [30] Y.C. Qiu, W.F. Li, W. Zhao, G.Z. Li, Y. Hou, M.N. Liu, L.S. Zhou, F.M. Ye, H.F. Li, Z. H. Wei, S.H. Yang, W.H. Duan, Y.F. Ye, J.H. Guo, Y.G. Zhang, Nano Lett. 14 (2014) 4821–4827. [31] C. Wang, K. Su, W. Wan, H. Guo, H.H. Zhou, J.T. Chen, X.X. Zhang, Y.H. Huang, J. Mater. Chem. A 2 (2014) 5018–5023. [32] G.M. Zhou, E. Paek, G.S. Hwang, A. Manthiram, Nat. Commun. 6 (2015) 7760. [33] Z.Y. Wang, Y.F. Dong, H.J. Li, Z.B. Zhao, H.B. Wu, C. Hao, S.H. Liu, J.S. Qiu, X. W. Lou, Nat. Commun. 5 (2014) 5002. [34] J.X. Zhao, Y. Yang, R.S. Katiyar, Z.F. Chen, J. Mater. Chem. A 4 (2016) 6124–6130. [35] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953–17979. [36] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. [37] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169–11186. [38] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [39] J. Klimeš, D.R. Bowler, A. Michaelides, Phys. Rev. B 83 (2011) 195131. [40] J. Klimeš, D.R. Bowler, A. Michaelides, Condens. Matter Phys. 22 (2010) 022201. [41] Q.F. Zhang, Y.P. Wang, Z.W. Seh, Z.H. Fu, R.F. Zhang, Y. Cui, Nano Lett. 15 (2015) 3780–3786. [42] R. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, 1990. [43] G. Henkelman, A. Arnaldsson, H. Jónsson, Comput. Mater. Sci. 36 (2006) 354. [44] R.S. Assary, L.A. Curtiss, J.S. Moore, J. Phys. Chem. C. 118 (2014) 11545–11558. [45] B. Wang, S.M. Alhassan, S.T. Pantelides, Phys. Rev. Appl. 2 (2014) 034004. [46] L.J. Wang, T.R. Zhang, S.Q. Yang, F.Y. Cheng, J. Liang, J. Cheng, J. Energy Chem. 22 (2013) 72–77. [47] H.B. Wang, T. Maiyalagan, X. Wang, ACS Catal. 2 (2012) 781–794. [48] F.C. Zheng, Y. Yang, Q.W. Chen, Nat. Commun. 5 (2014) 5261. [49] X.W. Wang, G.Z. Sun, P. Routh, D.H. Kim, W. Huang, P. Chen, Chem. Sov. Rev. 43 (2014) 7067–7098. [50] J.T. Jin, X.G. Fu, Q. Liu, Y.R. Liu, Z.Y. Wei, K.X. Niu, J.Y. Zhang, ACS Nano 7 (2013) 4764–4773. [51] E.J. Biddinger, D.V. Deak, U.S. Ozkan, Top. Catal. 52 (2009) 1566–1574. [52] Y. Mao, H. Duan, B. Xu, L. Zhang, Y.S. Hu, C.C. Zhao, Z.X. Wang, L.Q. Chen, Y. S. Yang, Energy Environ. Sci. 5 (2012) 7950–7955. [53] S.B. Yang, L.J. Zhi, K. Tang, X.L. Feng, J. Maier, K. Müllen, Adv. Funct. Mater. 22

210


(1972) 3634–3640. [54] C.P. Ewels, M. Glerup, J. Nanosci. Nanotechnol. 5 (2005) 1345–1363. [55] J. Casanovas, J.M. Ricart, J. Rubio, F. Illas, J.M. Jiménez-Mateos, J. Am. Chem. Soc. 118 (1996) 8071–8076. [56] L.F. Lai, L.W. Chen, D. Zhan, L. Sun, J.P. Liu, S.H. Lim, C.K. Poh, Z.X. Shen, J.Y. Lin, Carbon 49 (2011) 3250–3257. [57] C.Z. Zhang, R. Hao, H.B. Liao, Y.L. Hou, Nano Energy 2 (2013) 88–97. [58] A. Zabet-Khosousi, L.Y. Zhao, L. Pálová, M.S. Hybertsen, D.R. Reichman, A. N. Pasupathy, G.W. Flynn, J. Am. Chem. Soc. 136 (2014) 1391–1397. [59] R.T. Lv, Q. Li, A.R. Botello-Méndez, T. Hayashi, B. Wang, A. Berkdemir, Q.Z. Hao, A.L. Elías, R. Cruz-Silva, H.R. Gutiérrez, Y.A. Kim, H. Muramatsu, J. Zhu, M. Endo, H. Terrones, J.C. Charlier, M.H. Pan, M. Terrones, Sci. Rep. 2 (2012) 586. [60] X.R. Wang, X.L. Li, L. Zhang, Y. Yoon, P.K. Weber, H.L. Wang, J. Guo, H.J. Dai, Science 324 (2009) 768. [61] Y. Fujimoto, S. Saito, Phys. Rev. B 84 (2011) 245446. [62] Z.F. Hou, X.L. Wang, T. Ikeda, K. Terakura, M. Oshima, M. Kakimoto, S. Miyata, Phys. Rev. B 85 (2012) 165439. [63] Z.G. Wang, X.Y. Niu, J. Xiao, C.M. Wang, J. Liu, F. Gao, RSC Adv. 3 (2013) 16775–16780.

[64] J.R. Pels, F. Kapteijn, J.A. Moulijn, Q. Zhu, K.M. Thomas, Carbon 33 (1995) 1641–1653. [65] J. Kotakoski, A.V. Krasheninnikov, K. Nordlund, Phys. Rev. B 74 (2006) 245420. [66] F. Banhart, J. Kotakoshi, A.V. Krasheninnikov, ACS Nano 5 (2010) 26–41. [67] J. Yu, Z. Zhou, ACS Catal. 5 (2015) 4309–4317. [68] M.Y. Yang, L. Wang, M. Li, T.J. Hou, Y.Y. Li, AIP Adv. 5 (2015) 067136. [69] C. Gómez-Navarro, J.C. Meyer, R.S. Sundaram, A. Chuvilin, S. Kurasch, M. Burghard, K. Kern, U. Kaiser, Nano Lett. 10 (2010) 1144–1148. [70] H. Margenau, Rev. Mod. Phys. 11 (1939) 1–35. [71] G.M. Zhou, L.C. Yin, D.W. Wang, L. Li, S.F. Pei, I.R. Gentle, F. Li, H.M. Cheng, ACS Nano 7 (2013) 5367–5375. [72] L. Yu, Dalian Institute of Chemical Physics (Ph.D. thesis) Chinese Academy of Sciences, 2012. [73] L.P. Zhang, Z.H. Xia, J. Phys. Chem. C. 115 (2011) 11170–11176. [74] F.L. Hirshfeld, Theor. Chim. Acta 44 (1977) 129–138. [75] H. Jacobs, R. Juza, Z. Anorg. Allg. Chem. 391 (1972) 271. [76] J. Liang, L.C. Yin, X.N. Tang, H.C. Yang, W.S. Yan, L. Song, H.M. Cheng, F. Li, Submitted.