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. 2020 Oct 23;36(43):13104–13111. doi: 10.1021/acs.langmuir.0c02616

Superior Anchoring of Sodium Polysulfides to the Polar C2N 2D Material: A Potential Electrode Enhancer in Sodium–Sulfur Batteries

Muhammad Sajjad †,*, Tanveer Hussain ‡,§,*, Nirpendra Singh ∥,⊥, J Andreas Larsson †
PMCID: PMC7660946  PMID: 33095585

Abstract

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Despite the high theoretical specific energy in rechargeable sodium–sulfur batteries, the shuttle effect severely hampers its capacity and reversibility, which could be overcome by introducing an anchoring material. We, herein, use first-principles calculations to study the low-cost, easily synthesized, environmentally friendly, and stable two-dimensional polar nitrogenated holey graphene (C2N) and nonpolar polyaniline (C3N) to investigate their performance as anchoring materials and the mechanism behind the binding to identify the best candidate to improve the performance of sodium–sulfur batteries. We gain insight into the interaction, including the lowest-energy configurations, binding energies, binding nature, charge transfer, and electronic properties. Sodium primarily contributes to binding with the nanosheets, which is in accordance with their characteristics as anchoring materials. Sodium polysulfides (NaPSs) and the S8 cluster adsorb at the pores of C2N, where there are six electron lone pairs, one for each N atom. The polar C2N binds the NaPSs much strongly than the nonpolar C3N. In contrast to C3N, the charge population substantially modifies by adsorbing NaPSs on C2N, with a substantial charge transfer from the sulfur atoms. The calculated work function of 6.04 eV for pristine C2N, comparable with the previously reported values, decreases on adsorption of the NaPSs formed from battery discharging. We suggest that the inclusion of C2N into sulfur electrodes could also improve their issue with poor conductivity.

Introduction

The damaging effects of nonrenewable energy, like fossil fuels, on humans and the environment have triggered demands of clean renewable energy resources, which has put stress on the existing green energy storage devices like metal-ion (e.g., Li/Na-ion) batteries to keep up with the globe’s escalating needs. The low energy density and relatively high cost are other issues limiting the viability of metal-ion batteries for large-scale usage. Lately, alkali metal–sulfur batteries have emerged as a promising option, especially in high energy storage applications. The exceptionally high energy density (2600 Wh/kg) and theoretical specific capacity (1675 mAh/g) of lithium–sulfur batteries are manifold higher than the conventional metal-ion batteries.1,2 In addition to higher energy content, low toxicity and comparatively lower operational cost are other salient features associated with this class of batteries.3 However, considering the limited lithium resources in the earth’s crust, compared with the more abundant sodium, the utilization of the later could be an economically viable option. Moreover, being a member of the same group, both Li and Na would have similar chemistry. Therefore, sodium–sulfur would be a much cheaper alternative to lithium–sulfur for batteries.4,5

However, the development and commercialization of metal–sulfur batteries are plagued with several critical issues, like large volume expansion, poor electrical conduction of sulfur, and, most importantly, the so-called shuttle effect, where metal polysulfides dissolve into the electrolyte and are transported from the sulfur cathode to the metal anode.6 This dissolution of metal polysulfides results in the loss of active materials, and thus the capacity and reversibility of the battery are significantly hampered.7 Reduction in the Columbic efficiency and thermal effects are other pressing issues caused by shuttling of metal polysulfides between the anode and cathode.8,9 Therefore, actualization of metal–sulfur batteries relies on the active suppression of the shuttle effect. One of the most effective ways in this regard is the employment of an anchoring material capable of efficiently binding the metal polysulfides.

Two-dimensional (2D) nanostructures have been extensively studied in energy storage applications due to their intriguing properties like large surface area and exceptional structural, electronic, and mechanical properties.10−16 Introducing 2D nanostructures not only will help to suppress the shuttle effect by anchoring of metal polysulfides but also can improve the electric conduction of the sulfur cathode in metal–sulfur batteries. Many recent studies have reported different 2D materials as efficient binders for this purpose for lithium polysulfides. Recently, Li et al. used density functional theory (DFT) calculations combined with the van der Waals (vdW) interaction and solvent models (implicit solvation model and implicit self-consistent electrolyte model)17,18 to study the anchoring performance of a novel 2D transition metal–organic framework material, hexaaminobenzene-based coordination polymers (HAB-CPs), concerning intermediate dissolution related to lithium polysulfides.19 It was found among the studied systems that the vanadium-HAB-CP performed exceptionally well to suppress the shuttle effect in lithium–sulfur batteries. Wang et al. incorporated vdW correction in their DFT simulations to investigate the potential of bare, C- and S-functionalized vanadium carbide as anchoring materials for lithium–sulfur batteries.20 The authors found that V2CS2 was the most efficient MXene among the studied systems in binding the polysulfides. Freestanding 1 T MoS2/graphene heterostructures, synthesized through a facile one-pot hydrothermal process, are found to be highly efficient electrocatalysts for lithium polysulfides.21

Interestingly, very few studies have been conducted to investigate the binding properties of sodium polysulfides (NaPSs), the intermediate products of sodium–sulfur batteries. A handful of combined experimental and theoretical studies report the anchoring characteristics of NaPSs with graphite,4 S-terminated Ti3C2Tx MXene,22 and bilayer graphene.23 However, a detailed computational study explaining the intrinsic mechanism of the interaction of NaPSs with anchoring materials is nonexistent. Considering this gap, we have performed first-principles calculations based on DFT to study the anchoring properties of NaPSs (Na2S, Na2S2, Na2S4, Na2S6, and Na2S8) and the S8 cluster on the experimentally synthesized 2D materials nitrogenated holey graphene (C2N)24 and polyaniline (C3N).25 In addition to binding characteristics, structural changes, binding nature, and electronic and charge transfer properties are comprehensively studied.

Computational Details

To explore the anchoring properties of C2N and C3N toward the binding of NaPSs, we have performed DFT calculations with the Vienna Ab-initio Simulation Package.26 We have used the generalized gradient approximation exchange-correlation functional of Perdew–Burke–Ernzerhof,27 and plane-wave cutoff energy of 600 eV, using the gamma-centered k-mesh 6 × 6 × 1 (9 × 9 × 1) for self-consistent (non–self-consistent) calculations. We have employed the empirical DFT-D3 dispersion correction to include vdW interactions.28 The structural relaxation was considered to be converged when the Hellmann–Feynman forces are below 10–2 eV/Å for all atoms. We used 2 × 2 and 3 × 3 supercells of C2N and C3N, respectively, to study the adsorption of the NaPSs and the S8 cluster. Each model supercell in our study has 72 atoms in the 2D sheet. A vacuum of 20 Å in the out-of-plane direction was used to prevent artificial interactions due to the periodic boundary condition. The binding energies of NaPSs with the commonly used organic electrolytes 1,2-dimethoxyethane (DME) and 1,3-dioxolane (DOL) are also evaluated.

Results and Discussion

First, we briefly describe the structure of the studied 2D materials. The optimized lattice constant and C–N (two different types of C–C bonds) bond length in the C2N nanosheet are 8.33 Å and 1.34 Å (1.42 Å and 1.47 Å), respectively. The structure has a uniform distribution of pores and phenyl rings, both surrounded by sp2-hybridized N atoms.24 In contrast, the C3N nanosheet contains only phenyl rings surrounded by sp2-hybridized N atoms, such that the optimized lattice constant and C–N (C–C) bond length are 4.86 Å and 1.40 Å (1.40 Å), respectively. These values agree well with those reported previously.29−33 The structures and the 2D electron localization function (ELF) for the C2N and C3N nanosheets are shown in Figure 1. The ELF shows the in-plane covalent bonding as red regions of localized electrons between the neighboring atoms, in both nanosheets. However, C2N also has localized electrons (red regions) pointing toward the pores that are electron lone pairs located on the N atoms.

Figure 1.

Figure 1

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Optimized structure and 2D ELF plots of (a) C2N and (b) C3N. Brown and silver spheres represent C and N atoms, respectively. The 2D ELF plots of (c, e, f) Na2S adsorbed on C2N and (d, g) Na2S2 adsorbed on C3N. The total in-plane lattice parameters and bond lengths (C–N and C–C) are also indicated.

Before finding the suitable binding sites on the nanosheets for the NaPSs and S8 cluster, it is important to obtain their individual ground-state structure. Figure 2 shows their most stable geometries and the shortest Na–S and S–S bond lengths in the NaPSs and S8 cluster. All these species have three-dimensional cluster configurations and are not one-dimensional chains, as is often assumed, which has also been found in the case of lithium polysulfides.34 As can be seen from the figure, the Na–S bond lengths are getting longer (weaker) with the number of S atoms in the compound, which could play a role in how Na+ is regenerated from the Na2Sn series (n = 1–8). To find the most stable configuration of the adsorbed Na2Sn and S8 cluster, we tried all possible binding sites on the nanosheets C2N and C3N with different rotational configurations. The most stable adsorption configurations are shown in Figures 3 and 4, and the corresponding binding energies are reported in Table 1. The binding energy, Eb, has been computed from the energy difference between the adsorbed systems (Enanosheet + NaPSs/S8) and the sum of the pure nanosheet (Enanosheet) and isolated Na2Sn/S8 species (ENaPSs/S8), Eb = Enanosheet + NaPSs/S8 – (Enanosheet + ENaPSs/S8). We have used the ELF to determine the nature of binding of the NaPSs and S8 adsorbed on C2N and C3N because ELF is an efficient approach to distinguish between chemical bonding and physical binding.35 We present our findings for Na2S and Na2S2 adsorption on C2N and C3N, see Figure 1c–g, but the outlined conclusions are unchanged for the other NaPSs. It can be seen from comparing Figure 1a,c that the absorption of the NaPSs modifies the charge population in the vicinity of the interaction region for C2N but such modifications of the charge density cannot be seen in C3N (comparing Figure 1b,d). It is clear that both Na atoms are physically binding with the nanosheets. For C2N, the NaPSs and S8 adsorb strongest in and around the pores, which is in line with previous studies of impurity trapping.24 In the case of Na2S, a S–N covalent bond (1.76 Å) is formed, see Figures 1f and 3a, since the S atom does not have any other neighbors (cf. Na2S2 in Figure 3b). The rest of the polysulfides absorb through physisorption via ionic and vdW dispersion binding, as seen from Figure 1c,e,g. For all the NaPSs, one of the two Na atoms resides inside the big pore, and it is in accordance with the characteristics of using it as an anchoring material for which the pores interact with the metal atoms.6 The Na atom sitting inside the pore is not precisely at the center but has asymmetric binding distances with the N atoms. In the case of Na2Sn (n = 1, 2, and 4), the second Na atom is physically bound with two neighboring N atoms at the pore rim, which as a result are slightly pulled out from their equilibrium positions (most prominent in the Na2S case). For Na2S2 and Na2S4, the Na...N distances are equivalent (2.55 and 2.61 Å, respectively), but for Na2S, they are slightly different (2.42 and 2.48 Å). This strong interaction with the pore rim is the cause for the higher binding energies relative to those found for Na2S6 and Na2S8, where the second Na atom is only interacting with one N atom at a considerably longer distance due to steric hindrance by the larger number of S atoms. In contrast, the binding of the Na2Sn and S8 cluster to C3N is substantially weaker. This can be attributed to the polar nature of C2N; as clear from Figure 1, each big pore has six N atoms with electron lone pairs, making them efficient for impurity trapping as has also been shown experimentally.24 Therefore, we have found that C2N is a much better choice compared with C3N, to effectively retard the shuttle effect during the charging–discharging cycling of sodium–sulfur batteries. The strong binding of the NaPSs on C2N affects the absorbents, which can be seen in their prominent geometrical distortion compared with that on C3N (cf. Figures 3 and 4). It is also reflected by the Na–S bond length elongations when bound to C2N (see Figure 2). The effect is most pronounced for Na2S and Na2S2 and becomes less significant for n = 4, 6, and 8, which could be important for Na+ regeneration. The weakest binding appears for the unsodiated S8 cluster with a binding energy of 0.68 eV (see Table 1) through vdW dispersion only (see discussion below). Accordingly, it undergoes hardly any geometrical distortion with the S–S bond lengths (2.06 Å) remaining unchanged after adsorption. This is slightly larger than that of the S8 bound to C3N (0.50 eV), where it is parallel to the nanosheet while it is tilted toward the pore in C2N, such that the minimum binding distances are 3.85 and 3.43 Å, respectively. We have found that the bond lengths within the NaPSs do not change significantly after adsorption on C3N, reflecting their weak binding. Based on the spin-polarized calculations, we found that a negligible amount of total magnetic moment (0.10–0.32 μB) appears for the three cases of Na2S, Na2S2, and Na2S4 adsorbed on C2N. We have also investigated if the binding strength of the NaPSs is affected by the thickness of the nanosheet with bilayer C2N. Fortunately, we find that the binding energies are very similar to that of the monolayer (see Table 1) and are even increased by 0.02 to 0.07 eV. For bilayer C2N, we consider the lowest energy stacking as obtained in refs,30,31 and the most stable adsorption configurations are shown in Figure S1.

Figure 2.

Figure 2

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Bond lengths of the isolated and adsorbed NaPSs and S8 cluster and their relaxed geometries as free species (a) Na2S, (b) Na2S2, (c) Na2S4, (d) Na2S6, (e) Na2S8, and (f) S8. Yellow and green spheres represent Na and S atoms, respectively.

Figure 3.

Figure 3

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Most stable adsorption configurations on C2N for (a) Na2S, (b) Na2S2, (c) Na2S4, (d) Na2S6, (e) Na2S8, and (f) S8. Brown, silver, yellow, and green spheres represent C, N, Na, and S atoms, respectively.

Figure 4.

Figure 4

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Most stable adsorption configurations on C3N for (a) Na2S, (b) Na2S2, (c) Na2S4, (d) Na2S6, (e) Na2S8, and (f) S8. Brown, silver, yellow, and green spheres represent C, N, Na, and S atoms, respectively.

Table 1. Calculated Binding Energies (eV) of the NaPSs and S8 Cluster with the Nanosheets C2N and C3N and the Electrolyte Molecules DOL and DME.

  Na2S Na2S2 Na2S4 Na2S6 Na2S8 S8
monolayer C3N –0.56 –0.78 –0.69 –0.53 –0.70 –0.50
monolayer C2N –3.09 –3.13 –2.51 –2.39 –2.33 –0.68
bilayer C2N –3.11 –3.15 –2.54 –2.41 –2.36 –0.75
DOL –0.65 –0.82 –0.64 –0.60 –0.65 –0.18
DME –0.64 –0.88 –0.78 –0.98 –0.42 –0.20
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In sodium–sulfur batteries, during the electrochemical process, the polar electrolytes (DME and DOL) may cause undesirable shuttling of soluble NaPSs. Thus, the binding of the polysulfides with DME and DOL should be weaker than that with the anchoring materials; otherwise, they will dissolve into the electrolytes. The ground-state structural geometries of the NaPSs and S8 cluster with the electrolytes are given in Figure S2. Table 1 shows that the NaPSs are bound much stronger (more than three times) with the C2N nanosheet than with the electrolytes. On the other hand, C3N fails to meet this criterion. Thus, we suggest that C2N nanosheets would be an efficient anchoring material by limiting the solvation of NaPSs and immobilize them to alleviate the shuttle effect.

Because C2N outperforms C3N, we further explored the former nanosheet interaction with the NaPSs and S8 cluster in depth. To study the charge transfer, we have performed the Bader analysis36 and found that the NaPSs donate the electronic charge of between 0.34 and 1.48 e to C2N on adsorption (see Table 2). We have found that the charge is mainly accumulated (depleted) on S (Na) before absorption, whereas it is transferred substantially from the S atoms after absorption such that the charge on Na remains unaltered, except for a 0.12–0.14 e decrease in the case of Na2S. The charge transfer between the NaPSs and C2N enables ionic binding, responsible for the high binding energies (−3.09 to −2.33 eV). In the case of the unsodiated S8 cluster, an insignificantly small charge is transferred, and hence, it has the lowest binding energy (no ionic binding).

Table 2. Charge Rearrangement (in Electrons, e) on the Constituents of NaPSs/S8 Species before (after) Adsorption on C2Na.

  ∑S Na1 Na2 ∑
Na2S –1.48 (−0.26) 0.74 (0.86) 0.74 (0.88) (1.48)
Na2S2 –1.72 (−0.76) 0.86 (0.87) 0.86 (0.88) (0.99)
Na2S4 –1.70 (−0.71) 0.85 (0.88) 0.85 (0.86) (1.03)
Na2S6 –1.71 (−1.30) 0.85 (0.88) 0.86 (0.85) (0.43)
Na2S8 –1.70 (−1.39) 0.85 (0.88) 0.85 (0.86) (0.34)
S8 (0.01)     (0.01)
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a

Plus and minus signs are referred to as charge lost and charge gained. The first column is the sum of charges on the S atoms, and the last column equals the total charge donated to C2N.

Such massive charge transfer from the NaPSs to C2N leads to considerable changes in their respective charge densities, which can be seen with the help of charge density differences using the relation Δρ = ρC2N + NaPSs/S8 + (ρC2N + ρNaPSs/S8), where ρC2N + NaPSs/S8, ρC2N, and ρNaPSs/S8 are the electron densities of the adsorbed system, pure C2N, and isolated NaPSs/S8 species, respectively. As can be seen in Figure 5, there is charge rearrangement not only within C2N and the NaPSs but also between them, and this effect is largest when the charge transfer is largest. Thus, it is most prominent for the small NaPSs and is consistent with the higher binding energies (ionic binding). In addition, the charge depletion located along the Na−S bonds show that they are weakened while the accumulation between Na and N is a result of the charge transfer. As expected, the charge density difference (CDD) contribution is smaller for S8. However, because CDD has to be computed with the separated constituents at frozen structures from the adsorption, it is known that it can give results that are hard to interpret, especially when the interaction is unusually strong or very weak. For example, the ELF analysis shown in Figure 1c–g is needed to deduce if the polysulfides are bound chemically (only Na2S) or physically, which is difficult to tell from the CDD analysis.

Figure 5.

Figure 5

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Charge density difference after and before (a) Na2S, (b) Na2S2, (c) Na2S4, (d) Na2S6, (e) Na2S8, and (f) S8 adsorbed on C2N. Yellow and cyan colors correspond to charge accumulation and depletion, respectively. The isosurface value is 3 × 10–3 eÅ–3.

It is worth mentioning that the adsorption of the NaPSs alters the electronic properties of C2N, which has been studied through the electronic density of states (DOS). Figure 6 shows the total DOS of pristine C2N and that with NaPS adsorption. The pristine system has an energy band gap of 1.66 eV, which is consistent with the previously predicted value at the same level of DFT.37,38 Concentrating on the DOS, the adsorption of the NaPSs shifts the conduction band states below the Fermi level, causing an n-type doping effect due to charge transferred from the NaPSs to C2N, as found from the Bader analysis. Among others, poor conductivity of the sulfur cathodes is one of the most critical problems for the realization of efficient metal–sulfur batteries. We have found that C2N becomes metallic when adsorbed with NaPSs (as observed from the DOS values in Figure 6 a–e). This is very important because C2N anchoring layers incorporated into the sulfur cathode not only would suppress the shuttle effect but also could improve the conductivity of the sulfur cathode. Thus, C2N could potentially overcome another unwanted issue in metal–sulfur batteries. No prominent influence on the DOS is observed upon S8 adsorption, consistent with its weak vdW bonding and small charge transfer. It has already been shown in scanning Kelvin probe microscopy experiments that graphene experiences a substantial shift in the work function after molecular adsorption.39,40 To have a deep insight into the electronic properties of C2N, we calculated the work function (ϕ) of pristine C2N and that with NaPS adsorption, see Figure 7, using ϕ = Vvacuum – EF, where Vvacuum and EF are referred to as the electrostatic potential and the Fermi level. Vvacuum is calculated from the planar average of the electrostatic potential sufficiently far from the surface along the c-direction. We find that ϕ turns out to be 6.04 eV for pristine C2N, which is comparable with previously reported values (5.80 eV37 and 6.20 eV41). The adsorption of NaPSs renders significant changes in the electron density and the occupation due to the charge transfer. Hence, ϕ substantially decreases. In contrast, the S8 cluster adsorption does not lead to significant changes in ϕ as the charge transfer is minimal (0.01 e).

Figure 6.

Figure 6

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Total DOS of pristine C2N (top panel) and adsorbed with (a) Na2S, (b) Na2S2, (c) Na2S4, (d) Na2S6, (e) Na2S8, and (f) S8. The Fermi level is set at 0 eV.

Figure 7.

Figure 7

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Calculated work functions of the pristine and the polysulfide-adsorbed C2N nanosheets.

Conclusions

The anchoring role of polar C2N and nonpolar C3N nanosheets has been investigated by studying the entire sodiation process through computations at the DFT level. We have used the ELF to show that physical binding dominates at all the stages of sodiation except for Na2S adsorption on C2N, where a covalent bond is formed between the S atom and an N atom at the pore rim. The polar C2N outperforms the nonpolar C3N in terms of binding strength, which is attributed to more charge transfer to the former nanosheet, that is, between 0.34 and 1.49 e. This results in strong ionic binding contributions with binding energies between −2.33 and −3.09 eV. Bilayer C2N, instead of the monolayer, improves the anchoring behavior, but the improvement is limited as the binding energies do not increase substantially (0.02 to 0.07 eV). Charge density difference shows that the charge rearrangement occurs in both C2N and NaPSs and between them. The charge depletion located along with the Na–S bond shows that the bond is softened after adsorption. The adsorption of NaPSs gives rise to n-type doping in C2N and, hence, could be used to improve the conductivity of the sulfur cathode, whereas the S8 cluster does not modify the electronic features of the nanosheet. Considering the role of electrolytes, NaPSs weakly bind with DME and DOL than C2N, suggesting that the NaPSs will not dissolve into these electrolytes. The present study paves the way for a cost-effective C2N nanosheet as an anchoring material for high-energy and high-capacity sodium–sulfur batteries.

Acknowledgments

The authors thank the Knut and Alice Wallenberg Foundation, Kempe Foundations, Swedish Research Council (VR), and Interreg Nord for financial support. The authors are grateful for the allocation of time and resources at High Performance Computing Center North (HPC2N), National Supercomputer Center (NSC), and the PDC Center for High Performance Computing, through the Swedish National Infrastructure for Computing (SNIC). N.S. acknowledges the support from Khalifa University of Science and Technology.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.0c02616.

  • Most stable adsorption configurations on bilayer C2N for the sodium polysulfides and binding configurations of the sodium polysulfides with electrolytes (DME and DOL) (PDF).

The authors declare no competing financial interest.

Supplementary Material

la0c02616_si_001.pdf (330.4KB, pdf)

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