The Anchoring Effect of 2D Graphdiyne Materials for Lithium-Sulfur Batteries.

Systematic first-principles calculations are designed to investigate the interaction between isolated S8, lithium polysulfide (PS) Li2S n (n = 1-8, at different lithiated stages) clusters and two-dimensional (2D) graphdiyne (GDY) materials. By the calculations of their detailed interaction, we investigate the 2D GDY ability of trapping lithium PS clusters in order to evaluate the anchoring effect of 2D GDY materials for lithium-sulfur batteries. The theoretical results show that lithium PS intermediates/B-GDY systems have a moderate binding energy, indicating that the 2D B-GDY material is a suitable candidate for the anchoring materials of Li-S batteries. From the analysis of their charge density differences, the B-S σ bond and Li bond play an important role in the anchoring effect of 2D B-GDY substrates.

Introduction

In 1985, the first commercial lithium-ion battery (LIB) with lithium cobalt oxides as the cathode and petroleum coke as the anode was invented by Yoshino.[1] Since then, LIBs have played a crucial role in the electrochemical energy storage (EES) devices for the modern mobile information society and have become key components in design and development of new portable electronic products because of their easy design and higher energy density than that of a nickel–metal hydride battery.[2] However, there is still a large gap between LIBs and high-energy demands of large-scale storage systems such as battery electric vehicle (BEV) applications[3−5] due to the limited gravimetric (or volumetric) energy density, long charging time, safety problems, etc. The rise of BEVs poses a major challenge for EES devices and attracts extensive worldwide search for new battery technologies and battery materials with lower cost, higher energy density, longer cyclability, faster charge rate, and better safety. The energy density of a battery is related to the area under the voltage versus specific capacity curve. Also, the theoretical specific capacity (Q) of an active electrode material can be calculated according to Faraday’s laws of electrolysis. Higher theoretical specific capacity needs higher lithium percent composition of compounds. Among the light elements, sulfur (the most stable sulfur conformation S8) is extremely abundant and can react with lithium to form Li2S with a theoretical potential of 2.28 V versus Li/Li+.[6] So, it can theoretically produce as high as 1672 mA h g–1 of capacity and 2660 W h kg–1 of energy density, which are much higher than those of conventional LIBs.[6,7]

Due to the natural abundance of sulfur material, low cost, safety, and high energy density, Li–S batteries are considered promising and attractive for the next generation of EES. However, there are still several challenges hampering the practical application of Li–S batteries. First, both S8 and Li2S are electronic insulators. To change this insulating situation, a conductive carbon or metal is used as a coat to increase the conductivity.[8] Second, the volume of the active materials expands about 80% at the end of the discharging process because of different densities of sulfur (2.03 g cm–3) and Li2S (1.66 g cm–3).[9] This large volume expansion leads to battery cracking and fast capacity decay. So, a conductive buffer should be required to relieve the strain by volume change. Third, a lithium PS shuttle phenomenon exists in Li–S batteries. Previous studies show that the cathodic reaction of S8 is much more complex, and the transformation from S8 to the end member Li2S undergoes several lithium PS phases: Li2S, (1 ≤ n ≤ 8)[9,10] during the charge/discharge reaction:

The length of lithium PS chains gradually decrease during the discharging process. Among these lithium PSs, PS intermediates Li2S (n = 8, 6, 4) are highly soluble in organic electrolytes. Therefore, some dissolved long-chain lithium PSs diffuse to the Li metal anode and are reduced to short-chain PSs; a portion of short-chain PSs deposit at the anode and the other short-chain PSs go back to the cathode during the charging and discharging processes. This process is the PS intermediate shuttle phenomenon, which can lead to the loss of active materials, self-discharge and low Coulombic efficiency.[11,12] The shuttle effect lies in the high solubility of PS intermediates in electrolytes. So, extensive research has been carried out to prevent this shuttling effect, including the physical confinement and surface chemistry adsorption.[13] In 2009, Ji et al. made a breakthrough in Li–S batteries with high reversible capacities 1320 mA h g–1 using a highly ordered conductive mesoporous carbon–sulfur cathode[14] for trapping lithium PSs. Recently, several types of two-dimensional (2D) materials as sulfur host materials can effectively improve the electrochemical performance of Li–S batteries by trapping lithium PS intermediates at the cathode.[15]

Graphdiyne (GDY), a new carbon-based 2D material, was synthesized in 2010[16] with much larger pores than those of graphene. Furthermore, GDY can form a new large family graphen-n-yne by changing the number of C≡C triple bonds connecting aromatic rings (graph-1-yne is named as graphyne; graph-2-yne is called graphdiyne...). Moreover, the GDY family can also be considered as molecule-based covalent organic nanosheets (CONs), making GDY materials more versatile by tailoring the monomer molecules and allow programmed elemental doping,[17] as shown in Figure . Previous theoretical studies show that the GDY can adsorb lithium to form a LiC3 compound with twice the capacity of graphite;[18] the GDY family has small band gaps from 0 to 1.47 eV and a large charge carrier mobility of ∼105 cm2 v–1 s–1;[19] the energy barrier of lithium ion out-of-plane diffusion in GDY is 0.18 eV so that lithium ions easily cross the 12-C hexagon of GDY.[18] Also, recent experimental studies showed that the GDY film demonstrated an excellent electronic conductivity (2.56 × 10–1 S m–1, comparable to that of silicon) and high charge carrier mobility (2 × 105 cm2 v–1 s–1).[20] In addition, the large number of C≡C triple bonds makes GDYs with low atomic densities and high activity adsorb Li ions, molecules, and clusters. Li et al. showed that the sulfur cathode with hydrogen-substituted graphyne as host matrix (HsGY@S electrode) presents an excellent electrochemical performance.[21] As important allotropes of 2D carbon materials, none has been reported about the 2D GDYs’ ability of trapping lithium PSs. So, here, we have performed detailed first-principles calculations of the interaction between isolated S8, lithium PS Li2S (n = 8, 6, 4, 2, 1) clusters, and 2D GDY materials to evaluate the anchoring effect of 2D GDY materials for Li–S batteries. In this paper, we consider three types of theoretical graphynes (α-, β-, and γ-GY) and synthesized GDY together with several heteroatom-doped GDY materials.[17,22] Previous researches show that neither of the weak and strong anchoring materials are good for the performance of Li–S batteries.[23,24] The weak anchoring materials can not effectively prevent lithium PSs from dissolving into the DOL/DME electrolyte solvent, while the strong binding energy (larger than 2.0 eV) with lithium PSs leads to the decomposition of Li2S clusters. The moderate binding energy should be 0.8–2.0 eV.[23] Our calculated results show that the lithium PS intermediates/B-GDY system has a moderate binding energy, indicating that the 2D B-GDY material is a suitable candidate for the anchoring materials in Li–S batteries. Also, the chemical adsorption plays an important role in the lithium PS intermediate anchoring effect.

Figure 1

Basic structure models of several GDYs materials: (a) α-GY, (b) β-GY, (c) γ-GY, (d) GDY, (e) B-GDY, (f) bilayer B-doped-GDY: 2L-B-GDY, (g) Cl-GDY, (h) N2H-GDY, and (i) NH2-DGY. Brown balls denote carbon atoms. Balls with other colors represent the doped heteroatoms: the dark green, light green, gray, and pink balls represent B, Cl, N, and H atoms, respectively.

Results and Discussion

Figure shows the most stable structures of S8 and the lithium PS Li2S (n = 8, 6, 4, 2, 1) clusters optimized by the USPEX method. The calculated ground state of the sulfur cluster has a buckled octasulfur S8 ring with a D4 point group symmetry. Also, the optimized S–S bond length and S–S–S angle in the S8 cluster are 2.06 Å and 109.4°, respectively. The geometric parameters of calculated structures of the lithium PS Li2S (n = 8, 6, 4, 2, 1) are listed in Table . The optimized stable structures of lithium PS clusters are consistent with previous calculations.[24]

Figure 2

Illustration of the stable structures of calculated octasulfur S8 and Li2S Clusters: (a) S8, (b) Li2S8, (c) Li2S6, (d) Li2S4, (e) Li2S2, (f) Li2S. In the figure, the yellow and green balls represent sulfur and lithium atoms, respectively.

Table 1

Geometric Parameters of Optimized Stable Structures of the Lithium PS Li2S (n = 8, 6, 4, 2, 1)

lithium PSs	symmetry	S–S bond length (Å)	Li–S bond length (Å)	Li–S–Li bond angle (°)
Li2S8	C2	1.95–2.17	2.38–2.42	72.9
Li2S6	C2	2.06–2.10	2.33–2.39	68.7
Li2S4	C2	2.08–2.11	2.33–2.39	73.4
Li2S2	C2v	2.19	2.21	94.9
Li2S	C2v		2.09	113.2

The interaction strength between lithium PS intermediates and DOL/DME electrolyte solvent molecules was 0.74–0.79 eV, calculated with the DFT-D3 method of Grimme.[24] In order to prevent lithium PSs from dissolving into a DOL/DME electrolyte solvent, the binding energy between lithium PS clusters and anchoring materials should be no less than those values. The interaction strength between S8, lithium PS clusters, and GDY materials can be measured by the binding energy Eb, which is the energy difference between the total energy of PS cluster-GDY systems E(cluster+GDY) and the total energy summation of S8 or the PS cluster Ecluster and GDYs EGDY. Eb can be described by eq .

Interaction with GDYs

The calculated binding energy between S8, lithium PS clusters, and the GDY substrate by the DFT-D3 correction method of Grimme is shown in Table . We also calculate the binding energy of graphene with PSs at different lithiation stages for comparison. The binding energy of Li2S8/graphene is almost the same as that of S8/graphene and then decreases to a minimum binding energy of Li2S2/graphene (0.359 eV) as the Li–S battery is being discharged. At the end, the binding energy of Li2S/graphene increases to 0.668 eV. The binding energy curve of PSs/graphene versus PS clusters is similar to previous results of calculation.[23,25] The binding energy of lithium PS intermediate Li2Sn (n = 8, 6, 4,) on graphene is both smaller than that of Li2S and DOL/DME electrolyte solvent molecules (0.74–0.79 eV), although some limited special positions of amorphous graphene can induce a larger binding energy.[23] This is the main reason that the graphene substrate cannot effectively suppress the lithium PS intermediate shuttle effect.

Table 2

Binding Energy (eV) of S8, Lithium PS Li2Sn (n = 8, 6, 4, 2, 1) Clusters on the Monolayer Graphene and GDY Materials

PSs	graphene	α-GY	β-GY	γ-GY	GDY
S8	0.684	0.314	0.510	0.596	0.410
Li2S8	0.685	0.543	0.585	0.667	0.573
Li2S6	0.553	0.606	0.665	0.852	0.563
Li2S4	0.553	0.644	0.743	0.782	0.662
Li2S2	0.359	1.201	1.157	1.530	1.134
Li2S	0.668	1.653	2.043	2.279	1.739

From Table , the binding energy between S8; lithium PS clusters; and α-GY, β-GY, γ-GY, and GDY substrates shows a similar behavior. The binding energy grows gradually as octasulfur S8 is lithiated until a sharp increase at Li2S2 and Li2S. The binding energy between lithium PS clusters and GDYs contains a physical vdW interaction and chemical interaction. To investigate their interaction in detail, the ratio (R) of the chemical interaction is calculated, which can be described as R = EbPBE/EbPBE + vdW; EbPBE and EbPBE + vdW are the binding energy computed with the PBE functional (see Table S1 in the Supporting Information), and PBE + vdW is the D3 correction method of Grimme. The calculated chemical interaction ratio (R) of Li2Sn/GDY also increases from 14 to 39% at Li2S8 and Li2S6 with a binding energy of ∼0.6 eV and then a sharp increase to 79–91% for Li2S2 and Li2S/GDY with a binding energy of 1.2–2.3 eV. Therefore, the chemical interaction is the main source of their binding energy to enhance. Among the Eb of lithium PS intermediates, γ-GY has a relatively stronger interaction. Calculations show that only Li2S6/γ-GY has a little larger binding energy of 0.852 eV than that of the lithium PS intermediates/electrolyte. In a bilayer material system, one layer can introduce an inhomogeneous potential that affects the other layer (Figure S1). In our previous calculation of silicene or germanene/graphene bilayer systems,[26] the graphene substrate introduces an inhomogeneous potential, which leads to a variation in the bond angles of silicene or germanene, breaking the sublattice symmetry of silicene or germanene. Therefore, a band gap is opened at the Dirac points of silicene, germanene, and graphene bands in the bilayer systems. So, we add a second layer of GDYs under the GDY layer of PS clusters/GDY substrate systems with AB stacking to find whether the binding energy is enhanced. The binding energy between lithium PS intermediates and bilayer GDY substrates are also calculated (see Table S2). For 2L-γ-GY, the binding energy can be increased by 54–73 meV due to an additional inhomogeneous potential. Although the bilayer of GDY systems improve the ability of trapping PSs, the pristine GDY materials cannot effectively trap lithium PS intermediates according to the calculation result.

Interaction with Doped GDYs

Polar function groups introduced on carbon materials can increase the interaction between lithium PSs and substrate anchoring materials.[23] Several patterns of heteroatom-doped GDYs (see Figure ) have been synthesized recently.[17] Their binding energy with lithium PS intermediates is also calculated as shown in Table . In order to illustrate their relative values of binding energy, the values of Eb between S8, lithium PSs and GDYs versus various PS clusters are plotted as shown in Figure according to Tables and 3 and Table S2. In these heteroatom-doped GDYs, B-GDY has the largest binding energy with the lithium PS intermediates from 0.790 to 1.489 eV. Also, the corresponding ratio of the chemical interaction is from 51 to 77%, indicating that the chemical adsorption plays an important role in the lithium PS intermediate anchoring effect. A second B-GDY layer also enhances their interaction. The calculated binding energy between 2L-B-GDY and lithium PS intermediates is from 0.854 to 1.577 eV larger than that of lithium PS intermediates/B-GDY monolayer systems. According to the binding energy classification of Zhang et al., the lithium PS intermediates/B-GDY system has a moderate binding energy, indicating that the 2D B-GDY material is a suitable candidate for the anchoring materials for Li–S batteries.

Table 3

Binding Energy (eV) of Lithium PS Intermediates Li2S (n = 8,6,4) on the Doped GDY Materials

PSs	Cl-GDY	N2H-GDY	NH2-GDY	B-GDY	2L-B-GDY
Li2S8	0.483	0.697	0.349	0.790	0.854
Li2S6	0.559	0.766	0.960	1.172	1.294
Li2S4	0.503	0.746	0.725	1.490	1.577

Figure 3

Binding energy between S8, lithium PSs and GDYs. The filled yellow zone indicates the interaction strength between lithium PS intermediates and DOL/DME electrolyte solvent molecules.

Charge Transfer between Lithium PSs and GDYs

To understand the interaction between lithium PSs and GDYs, the charge transfer between lithium PSs and the GDY or B-GDY substrate together with their charge density differences (CDD) is calculated. Based on the Bader charge analysis,[27] the charge transfer from Li2Sn (n = 8, 6, 4) to GDY is calculated to be 0.02, 0.10, and 0.32 electrons, respectively. There is only a little charge transfer from Li2S (n = 8, 6) to GDY, so their interaction is mainly determined by the vdW interaction with a binding energy of about 0.57 eV. As seen from Figure S2a–c, the CDDs of Li2S/GDY, the lithium of PSs and carbon of GDYs form a lithium bond, which is an analogue of the H bond.[28,29] These Li bonds explain the strong vdW interaction in the lithium PSs/GDYs system. As the sulfur is lithiated to Li2S2 and Li2S, the charge transfer from Li2S to GDY increases to 0.48 and 0.94 electrons. So, as the clusters are adsorbed on GDYs, the lithium PSs are positively charged, while the GDY substrate is negative. This charge separation enhances their electrostatic interaction.[23] So, when discharged to the Li2S2 and Li2S stages, the lithium PSs adsorption has its roots in this charge separation of PSs/GDYs, with a larger binding energy of 1.13–1.74 eV. Figure S2d–e shows that there is a large charge migration from S to C atoms except the lithium bonds. The charge transfer from Li2S (n = 8, 6, 4) to the B-GDY substrate is 0.44, 0.49, to 0.58 electrons, respectively, which is similar to that of the Li2S/GDY (n = 2, 1) system. Figure shows the CDD of the Li2S/B-GDY (n = 8, 6, 4) system. The charge density redistribution among C, B, and S1 atoms can be clearly seen in Figure . The Li1–S1 bond is weakened after the absorption on B-GDY. The B and S1 form a B–S σ bond, while Li1 and carbon form a strong Li bond. Meanwhile, in Li2S4/Cl-GDY(Figure S2f), neither a Cl–S σ bond nor a strong Li bond forms. So, these B–S σ bond and Li bond play an important role in the anchoring effect of B-GDY 2D materials.

Figure 4

3D charge density difference with an isosurface value of 0.005 e/Bohr3 of Li2S/B-GDY (n = 8, 6, 4). In the figure, the yellow and blue colors represent gaining and losing electrons, respectively.

Conclusions

In summary, the detailed interaction between isolated S8, lithium PS Li2S (n = 1–8) clusters and 2D GDY materials has been studied via first-principles calculations. The calculation results show that the lithium PS intermediates/B-GDY monolyer system has a moderate binding energy (0.790–1.490 eV). Additionally, the bilayer of B-GDY further improve the ability of trapping PS intermediates with a binding energy of 64–120 meV larger than that of the B-GDY monolayer due to an additional inhomogeneous potential, indicating that the 2D B-GDY material is a suitable candidate for the anchoring materials of Li–S batteries. From the analysis of CDD, the B–S σ bond and Li bond play an important role in the lithium PS intermediate anchoring effect of 2D B-GDY substrates.

Method

The first-principles calculations are performed using the Vienna ab initio simulation package (VASP)[30,31] based on the density functional theory (DFT).[32,33] In the computations, ion core valence wave functions are treated by the projector augmented wave (PAW) pseudopotential method,[34] and a cut-off energy of 600 eV is used for the plane-wave basis set of valence electron wave functions. The exchange-correlation function is described by the generalized gradient approximation (GGA) of the Perdew, Burke, and Ernzerhof (PBE) functional.[35] For the unlithiated S8 cluster on graphene, the physical vdW interaction plays a dominant role in adsorption.[23] So, in the simulations of the interaction between clusters and GDYs, the van der Waals (vdW) interaction is also included, which is solved by the DFT-D3 correction method of Grimme[36] and Becke–Jonson damping.[36,37]

The most stable structures of isolated S8 and lithium PS Li2S (n = 8, 6, 4, 2, 1) clusters are gained using the USPEX code,[38−40] based on an evolutionary algorithm. In order to eliminate the spurious interaction of 2D GDY materials, we use slab models of a supercell with 25 Å in the direction perpendicular to the 2D GDY plane, so the vacuums of PSs-cluster-GDYs systems are larger than 15 Å. In the PSs-cluster-GDYs systems, we consider all the GDY adsorption surface sites, such as on-top, bridge, and hollow sites of 2D GDYs with pymatgen open-source software[41,42] and several rotation configurations of lithium PSs, which are rotated by 90 and 180° along the x, y, and z axes of lithium PS clusters on GDYs. For structural optimizations, all atoms are relaxed until the energy and force change reach 10–5 eV/cell and 10–2 eV/Å, respectively.