Theoretical investigation of synergistically boosting the anchoring and electrochemical performance of lithiophilic/sulfiphilic transition metal carbides for lithium–sulfur batteries

Abstract

Lithium–sulfur (Li–S) battery is one of the most promising next-generation energy-storage systems with a high energy density and low cost. However, their commercial applications face several challenges, such as the shuttle effect caused by the soluble lithium polysulfide (LiPSs) intermediates and the sluggish sulfur redox reaction. In this article, we systematically investigated the anchoring and electrochemical performance of a series of transition metal carbides (TMCs: TiC, VC, ZrC, NbC, HfC, TaC) as cathode materials for Li–S batteries by theoretical calculations. The lithiophilic/sulfiphilic non-polar (001) surfaces of TMCs can offer moderate binding strength with LiPS intermediates, ensuring good performance of sulfur immobilization. These TMCs can also facilitate lithium diffusion, indicating the good rate performance of Li–S batteries. We also demonstrated that the studied TMCs can be classified into two classes according to their catalytic activity for Li₂S decomposition which originated from their different electronic structural features. Furthermore, TiC, ZrC, and HfC exhibited excellent bifunctional electrochemical activity through reducing the Gibbs free energy for sulfur reduction reactions (SRRs) and lowering the barrier for Li₂S decomposition which facilitates accelerating electrode kinetics and elevating utilization of sulfur. Our results offer a systematic approach to designing and screening non-polar materials for high-performance Li–S batteries, based on the rational electronic structure and lattice match strategy.

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1. Introduction

The increasing demand for energy storage devices in the flourishing sustainable fields of electric vehicles, portable electronic devices, and the large-scale storage of renewable energy has driven the development of high-performance rechargeable batteries. In the last few decades, lithium–sulfur (Li–S) batteries have attracted significant attention and experienced rapid growth because of their extraordinary theoretical energy density, cost-effectiveness and environmentally friendly nature, and are recognized as next-generation energy storage devices.^1–4 However, the commercial application of Li–S batteries is still hindered by some challenges, including the insulating nature of sulfur and lithium sulfides which will block the electron transfer, significant volume changes of sulfur materials during charging and discharging at the cathode, and the dissolution of intermediate lithium polysulfides (LiPSs) in the organic electrolyte during the cycling process.^5–7 The issues mentioned above will lead to the continual loss of active materials, fast capacity decay, low coulombic efficiency, severe self-discharge, and a poor battery lifespan.⁸

An omni-directional strategy has been considered to address the aforementioned issues of Li–S batteries, e.g. including (1) a blocking layer to block up the LiPSs’ shuttling path;^9,10 (2) a conductive matrix to promote electron transport;^11,12 (3) anode-protective additives to prevent parasitic reactions between LiPSs and the lithium metal anode;^13,14 (4) novel electrolyte configurations to regulate the dissolution and adsorption of LiPSs;^15,16 (5) a confinement framework to mitigate the S volume expansion during lithiation and suppress the dissolution of LiPSs;^17,18 (6) electrocatalyst materials to improve the decomposition kinetics of Li₂S;^19,20 (7) cathode anchoring materials to enhance the adsorption ability for LiPSs.^21,22

The transformation of long-chain LiPSs to short-chain sulfides contributes to the discharge capacity of Li–S batteries mainly. Therefore, the shuttle effect caused by the dissolution of long-chain LiPSs into the electrolyte has attracted particular attention. To address this problem, the most prevalent solution is to design and search for new cathode anchoring materials to confine the LiPSs and improve sulfur utilization. Carbon materials were selected due to their porous structure, large surface area, and excellent electronic conductivity.^23–25 However, the non-polar carbon surface could not offer moderate interactions with polar LiPSs to eliminate the shuttle effect completely. Meanwhile, polar materials, such as oxides and sulfides, show an excellent performance in suppressing the shuttle effect for the stronger polar interactions.^11,26,27 Unfortunately, the poor electrical conductivity of these materials leads to the slow conversion of these adsorbed LiPSs. Previous investigations on anchoring LiPSs have made significant progress but cannot restrain the shuttle effect. In addition, catalysts such as sulfides, oxides, and heterostructures were recently incorporated into Li–S batteries to alleviate the shuttle effect by accelerating the conversion kinetics of LiPSs.^19,20,28,29 Initially, adsorption and catalysis were only regarded as modulation methods separately. Recently, some research indicated that adsorption and catalysis coexist with each other, and both of them work together to enhance the electrochemical properties of Li–S batteries.^19,30

Because of the strongly sulfiphilic surface moieties, carbides always serve as anchoring materials to absorb LiPSs effectively. Transition metal carbides (TMCs) have been of great concern for a long time owing to their remarkable physical properties (e.g. extreme hardness, high melting points, and excellent electrical and thermal conductivity) and intriguing surface chemistry (as potential alternatives to noble-metal catalysts).^31,32 Undoubtedly, the unique combination of these properties originates from the electronic structure of TMCs, resulting in strong chemical bonds and interesting catalytic performance. Some previous experimental and theoretical studies verified that TMCs have been used as electrode materials for the oxygen reduction reaction, oxygen evolution reaction, hydrogen evolution reaction, CO oxidation reaction, NO reduction reaction, and water gas shift reaction in the field of fuel cells and related electrocatalytic applications.^33–37 TMCs also show the potential in improving the performance of sulfur cathodes, and some studies have shown that TMCs can boost the cycle life and stability of the sulfur cathode, even with high sulfur loading.^38–43 On the other hand, transition metal atoms in TMCs exhibit high catalytic activity for the conversion of LiPSs. Recently, there has been growing interest among researchers in utilizing carbide materials to address the shuttle effect and enhance the overall performance of Li–S batteries. Combining the experimental and theoretical methods, Peng et al. concluded that conductive TiC had strong interactions with LiPSs and played a crucial role in the redox kinetics of Li–S batteries.³⁸ Kim et al. showed that tungsten carbides (WC) can not only catalyze the disproportion of polysulfides, but also capture soluble LiPSs.⁴¹

Nevertheless, as far as we are concerned, a systematic theoretical understanding of the roles of TMCs in anchoring and conversion of LiPSs is still lacking. Inspired by the exciting experimental discoveries and theoretical predictions, the adsorption ability toward LiPSs, lithium diffusion behavior, the catalyst activation for Li₂S decomposition and the electrochemical performance for sulfur reduction reactions on a series of TMC surfaces have been systemically examined by first-principles calculations. The correlation between the electronic structure and the adsorption–catalytic behavior of the TMC surfaces has also been investigated. Our results show that all the non-polar TMC surfaces we investigated possess a moderate interaction with LiPSs, indicative of a remarkable sulfur immobilization, and the binding strength of LiPSs is sensitively dependent on the Li–C and S–TM interaction and the lattice constants of TMCs. In particular, the fast lithium diffusion and low activation energy barriers of Li₂S decomposition on the TMC surface benefit the rate performance and energy efficiency of Li–S batteries. Consequently, the different surface behaviors mentioned before are directly dependent on the intrinsic electronic structure characteristics of TMCs. We finally concluded that substituting the metal components in TMCs could regulate their electronic structure properties, and thus influence the adsorption–catalytic reactivity of such materials. Our findings provided the guidance for the use of non-polar TMC surfaces as the possible sulfur host for long cycling stability and promoted the conversion of LiPSs in Li–S batteries.

2. Models and computational methods

Spin-polarized calculations were carried out using the density functional theory (DFT) method as implemented in the Vienna ab initio simulation package (VASP).⁴⁴ The exchange–correlation functional with generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) combined with the projector-augmented wave (PAW) method was used to solve the Kohn–Sham equations.^45–47 The Kohn–Sham orbital has been expanded using a plane-wave basis set with an energy cutoff of 550 eV. The DFT-D3 method was used to accurately describe the van der Waals (vdWs) interaction between LiPSs and TMCs.⁴⁸ The Brillouin zone was sampled using a Γ-centered 5 × 5 × 1 k-point mesh with the Monkhorst–Pack⁴⁹ sampling method during geometry optimization, while a 15 × 15 × 1 mesh was used for electronic structure calculation. The climb-image nudged elastic band (CI-NEB) method⁵⁰ with five images was used to calculate the energy barriers and the diffusion pathways. More computational details are included in the ESI.†

3. Results and discussion

3.1 Geometric and electronic structure of the TMC (001) surface

First, the geometric and electronic structures of TiC, VC, ZrC, NbC, HfC, and TaC (the IVB and VB transition metal based carbides) surfaces were investigated systematically. The bulk TMCs have a cubic NaCl structure with a space group of Fm3m, in which each anion (cation) is surrounded by six cations (anions). The basic information of the optimized bulk TMCs is presented in Table S1,† which agrees with the previous results.^51–55 The non-polar flat (001) surfaces of the TMCs were selected as the substrate, which has been proven to be the most stable cleavage surface of TMCs among the low-index surfaces theoretically and experimentally.^56,57 Simultaneously, the thermal stability of the (001) surface of TMCs was confirmed by the ab initio molecular dynamic (AIMD) simulation in the canonical (NVT) ensemble with the time step set at 1 fs and temperature at 500 K for 10 ps and the detailed information can be seen in Fig. S1.† To investigate the (001) surface of TMCs, the TiC (001) surface was selected as an example due to their similar structures. The optimized TiC (001) surface, along with the possible adsorption sites, is displayed in Fig. 1a. The calculated bond lengths of TM–C, TM–TM and C–C in TMC (001) are shown in Table S1.† The TM–C bond lengths range from 2.084 to 2.356 Å, comparable to the Li–S bond length in LiPSs. The total and projected electronic density of states (DOS) plots are shown in Fig. 1b–c and Fig. S2,† respectively. Spin-polarized calculations were performed for all the systems. The symmetrical characteristics of the DOS plots for the spin-up and spin-down channels shown in Fig. 1b and the upper area of Fig. S2† reveal the nonmagnetic behavior of the TMCs. Moreover, all the TMC surfaces exhibit metallic features with a continuum of energy states and finite DOS at the Fermi energy. As shown in Fig. 1c and the lower area of Fig. S2,† both the TM and C atoms contribute to the finite DOS at the Fermi level. The excellent electronic conductivity of TMCs could address the low conductivity of sulfur and thus improve the electrochemical performance of Li–S batteries.

Fig. 1 (a) Top and side views of the TiC (001) surface; the bottom two layers in the red dashed line were fixed during the simulation. (b) and (c) The total and partial density of states plots of the TiC (001) surface.

3.2 The adsorption of S₈ and LiPSs on the TMC (001) surface

During the discharge/charge process, S₈ and Li₂S were reduced/oxidized into a series of LiPSs through the incorporation/separation of additional Li. Adsorption energy between the soluble LiPSs with the anchoring material is an important parameter to judge whether the shuttle effect can be suppressed effectively. To reveal the role of TMCs as effective anchoring materials for Li–S batteries, the adsorption behaviors of LiPSs on the TMC (TiC, VC, ZrC, NbC, HfC, TaC) surfaces were investigated systematically. The optimized geometry structures and the bond lengths of S₈ and LiPSs are shown in Fig. S3(a) and Table S2,† which are in good accordance with the previous calculations.⁵⁸ The preferred adsorption configurations of S₈ and LiPSs on the (001) facets of the above six TMCs are shown in Fig. 2 and Fig. S4–8,† which were evaluated from different adsorption sites and initial molecular orientations. The adsorption energy (E_ads) of LiPSs (or S₈) on TMCs was evaluated by eqn (1) (in the ESI†) and shown in Fig. 3a.

Fig. 2 The top and side views of the optimized adsorption structures of (a) and (e) S₈, (b) and (f) Li₂S₈, (c) and (g) Li₂S₆, (d) and (h) Li₂S₄, on the TiC (001) surface, respectively.

Fig. 3 (a) The adsorption energies of S₈ and LiPSs on TiC, VC, ZrC, NbC, HfC, and TaC (001) surfaces. The adsorption energies of the high and medium sulfur content LiPSs (i.e., Li₂S₈, Li₂S₆ and Li₂S₄) over the electrolyte solvent molecules (DME, DOL, 2DME, 2DOL) were also shown for comparison; (b) the ratio of vdWs interaction of S₈ and LiPS on TiC, VC, ZrC, NbC, HfC, and TaC (001) surfaces.

S₈ maintains a parallel adsorption configuration without any obvious deformation but with unconventional van der Waals adsorption (E_ads: ∼2.0 eV, adsorption distances: 2.60–2.84 Å) as shown in Fig. 2 and Fig. S4–7.† Four bottom S atoms of S₈ were atop TM atoms nonetheless, which will lead to the dissociation of S₈ on TaC. The stable adsorption configuration of S₈ was observed on the top of C atoms (as shown in Fig. S8a and e†). With regard to the adsorption of LiPSs, similar bonding characteristics with TMCs were obtained. Taking the TiC (001) surface as an example, the LiPSs exhibit a standing-up style with two Li atoms of LiPSs interacting with the surface C atoms to form Li–C bonds, and two S atoms of the LiPSs forming bonds with surface TM atoms, respectively (Fig. 2). Due to the rock–salt structure of the TMCs, LiPS was adsorbed on the TiC (001) substrate with a C₂ symmetry. In addition, the E_ads values ranging from 2.11 to 2.81 eV were found for S₈ and LiPSs on the TiC (001) surface which indicated that TMCs could offer moderate adsorption energies larger than those on graphene and transition metal sulfides (TMSs), similar to those on transition metal nitrides (TMNs) and transition metal oxides (TMOs).^59,60 As is known, for LiPSs on TMSs, only the TM or S atoms in TMSs are involved in the interactions. However, on TMCs, both the TM and the C atoms are involved in the interactions with LiPSs, which are similar to those on the TMNs and TMOs, thus endowing stronger binding strength. According to the results, the TMCs can effectively suppress the LiPS shuttling effect in Li–S batteries. The adsorption parameters of LiPSs on different TMCs are summarized in Tables S3–11,† respectively. Furthermore, considering that heavy elements such as Hf and Ta were involved in the studied TMC substrates. The DFT+U correction was used to evaluate the adsorption energies of LiPSs with the HfC, which was taken as an example for testing. We observed a slight change in the adsorption energies of LiPSs, while the trend in adsorption energies is well preserved, as illustrated in Table S12.† Hence, we believe that the chosen PBE/GGA is sufficient for elucidating the adsorption properties of heavy elements involved TMCs to LiPSs.

In order to prevent soluble LiPS dissolution into the electrolyte, stronger interactions between LiPSs and anchoring materials than those of solvent electrolyte molecules are essential. For this purpose, the adsorption of soluble LiPSs on the commonly used electrolyte solvents such as 1,3-dioxolane (DOL) and 1,2-dimethoxyethane (DME) was investigated. To describe the solubility characteristics of LiPSs more accurately, the binding of LiPSs with two DOL or DME molecules was also simulated. The most favorable configurations and adsorption energies of LiPSs on DOLs and DMEs are shown in Fig. S3(b–c),†Fig. 3(a) and Table S13.† The results demonstrated in Fig. 3(a) indicate that the adsorption energies of LiPSs on all TMC substrates are much higher than those of LiPSs on one or two electrolyte molecules (DOL&DME or 2DOL&2DME). Therefore, we could speculate that the shuttle effect could be well alleviated.

The difference in the E_ads of LiPSs on the surface of TMCs propels us to explore the mechanism of the anchoring effect. First, we analyzed the geometric features of LiPSs adsorbed on TMCs. As mentioned, both the Li–C and S–TM interactions contribute to the E_ads of LiPSs on the TMC substrate. For different LiPSs, as shown in Tables S9–11,† we can see that the Li atoms are found closer to the TMCs than the S atoms, and the shortest distance between Li in LiPSs and the surface decreases with decreasing number of S atoms. For a certain LiPS, taking Li₂S₈ adsorption as an example, the Li–C bond lengths are about 2.17 Å on TMCs. In comparison, S–TM bond lengths differ significantly from 2.55 to 2.70 Å for different TMCs, indicating that the S–TM interaction caused the difference in the E_ads values for different TMC interactions. The results are consistent with the previous research, which indicated that the interaction between sulfur-containing species and the anchoring materials could be dramatically enhanced by introducing TMs.^61,62 In summary, the improved interaction of non-polar (001) surfaces was attributed to lithiophilic and sulfiphilic characteristics of TMCs (i.e. the co-formation of S–TM and Li–C interaction).

To understand the adsorption mechanism of the TMC surfaces, the contributions of the vdWs and chemical interactions were evaluated by eqn (2) (in the ESI†) and visually illustrated in Fig. 3b. For the adsorption of S₈ on all TMCs, vdW interaction accounts for 58.59–94.38%. This phenomenon implies that chemical interaction contributes to the adsorption mechanism (except for the TaC surface). With the lithiation of S₈, the chemical interaction increased simultaneously. As a result, the ratio of vdW interaction between LiPSs and TMCs became smaller from of 31.88 to 56.53%. In summary, the anchoring behaviors were exhibited through a combination of vdW and chemical interaction for both S₈ and LiPSs, and the chemical interactions increased with deeper lithiation. To obtain further insights into the LiPS binding mechanisms, charge transfer and charge density difference (CDD) analyses were performed for LiPS adsorption on the TMCs. We considered the charge transfer of lithium and sulfur separately because both TM and the nonmetallic(C) atom were involved in the chemical interactions with S and Li in the LiPSs. The Li atoms lost charge and the S atoms obtained charge during the interaction process, and the charge transfer values are displayed in Fig. 4 and Table S14.† All of the LiPS adsorption systems exhibit similar charge transfer values, ranging from 1.67 to 1.69 e for Li atoms and from 1.05 to 1.29 e for S atoms. Comparatively, for the LiPS adsorption on the VC surface, the charge transfer of S is smaller than those on other TMCs, which demonstrates the weaker chemical interactions of LiPSs with VC (as shown in Fig. 3). Plenty of electrons were exchanged between the LiPSs with the TMC hosts, which was consistent with the moderate adsorption energy of the LiPSs. Specifically, this strong interaction is attributed to the cooperation of Li–C and S–TM chemical bonds.

Fig. 4 Charge transfer between the TMCs with Li atoms (a) and S atoms (b) in LiPSs which are in contact with TMCs.

To visualize the charge transfer characteristics, we performed CDD analysis for the adsorption of S₈ and LiPSs on TMCs, and the results are presented in Fig. 5a–d and Fig. S9–13,† respectively. For the adsorption of S₈, besides the charge transfer that occurred within S₈, electron-rich (yellow) regions appeared between S₈ and the TMC surfaces. The CDD results further explained the stronger E_ads of S₈ and the smaller adsorption distance than the conventional vdW adsorption strategy. A more detailed analysis of the crystal orbital Hamilton population (COHP) for the S and TM was conducted, and the results are shown in Fig. 5(e–h). The COHP and the corresponding integration values can efficiently measure the bonding strength of covalent bonds. Quantitative analyses based on COHP confirm the charge transfer analysis and CDD results. For the TiC surface, the spin-up and spin-down bands contribute equally to the four S–Ti bonds with a total integrated COHP (ICOHP) of −6.74. Thus, it can be concluded that there exists chemical covalent bonds between S₈ and the TiC (001) surface, resulting from the S–Ti interaction. Combined with charge transfer, CDD and COHP analyses, we can conclude that both vdW interaction and chemical interaction exist between S₈ and the TMC surface, except for the TaC surface. The CDD figures illustrate the accumulation of a great amount of charges between the LiPSs and the TMCs. Besides, lots of charges accumulated between the Li and C atoms, as well as between the S and TM atoms, which corroborates that both Li and S participated in a strong chemical interaction. The observed charge depletion and accumulation in the analysis are consistent with the charge transfer values from the Bader charge analysis. The COHP states of S–TM and Li–C have been plotted in Fig. 5(f–h) for the adsorption of Li₂S₈, Li₂S₆, Li₂S₄ on TiC (001) surfaces. The calculated ICOHP values of S–Ti interaction for different LiPS adsorption systems range from −3.60 to −3.19 (only for the spin-up state), which indicates the strong covalent interaction of S–Ti. According to the charge transfer analysis, a plenty of charge was transferred from Li to C, indicating a strong interaction between Li and C atoms. However, the ICOHP of Li–C interactions for different LiPS adsorption systems are relatively large. According to the basic theory of COHP, the COHP mainly measures the covalent bonding interaction. Therefore, the large ICOHP values for the ionic bonds are understandable. Combined with the large charge transfer from Li to C and the large ICOHP values for the Li–C bonds, we can conclude that the Li–C interaction belongs to ionic bonding. Overall, the strong interaction between LiPSs and TMCs mainly originated from the fact that both Li and S in LiPSs were involved in the interaction, resulting in the formation of strong Li–C ionic and S–TM covalent bonds. In contrast to most anchoring materials, the chemical interactions between the LiPSs and the non-polar (001) surface of TMCs are unique. Typically, for most materials, only one kind of atom in the anchoring materials participates in bonding with Li/S atoms in LiPSs. However, for the non-polar (001) surface of TMCs, both Li–C and TM–S contribute to the adsorption effect, resulting in a portion of the chemical interactions contributed by metal–S bonding in addition to Li–C bonding. As a result, the chemical interactions of LiPSs with the (001) surface of TMCs were stronger than some other anchoring materials.

Fig. 5 Side views of charge density differences (CDD) for (a) S₈, (b) Li₂S₈, (c) Li₂S₆, and (d) Li₂S₄ on the TiC(001) surface. Yellow and blue regions indicate charge accumulation and charge depletion, respectively. The calculated crystal orbital Hamilton population (COHP) for the adsorption of (e) S₈, (f) Li₂S₈, (g) Li₂S₆, and (h) Li₂S₄ on the TiC (001) surface. The integrated COHP values were inserted in the figure, and the dashed line indicates the Fermi level.

As known, lattice match between the adsorbate and substrate is one of the important factors in adsorption interaction.⁶³ Previous works have proved that the lattice constants of the substrate influence the adsorption of the adsorbate.⁶⁴ Here, the correlation between the lattice constants and the anchoring ability of TMCs was further explored. As shown in Tables S1 and S9,† there exists a monotonic relationship between the binding energy of Li₂S₈ and the lattice constants of these TMCs. Importantly, we found that with increasing lattice constants of TMCs, the anchoring ability to LiPSs increased monotonically. However, there is an anomalous result for TaC and NbC, since both the electronegativity of the TM and the lattice constants of TMCs contribute to the adsorption energy, and electronegativity plays an essential role in this case. Although the lattice constant of NbC is a little larger than TaC, the electronegativity of Nb is larger than Ta which implies that it would be more difficult for the S atom to get electrons from the substrate, resulting in a weaker S–Nb bond. In brief, for the NbC and TaC systems, the electronegativity of the TM and lattice constants may have synergistic effects on adsorption energy of LiPSs, which leads to the non-monotonic change of adsorption energy with the lattice constant.

An excellent electronic conductivity of the sulfur hosts could make up the intrinsically insulative nature of sulfur and LiPSs which can further improve the performance of Li–S batteries. Here, the total and projected density of states of S₈ and LiPSs adsorbed on the surface of TMCs were calculated to probe the conductive behavior of the systems and the results are shown in Fig. 6 and Fig. S14–18.† The figures demonstrate that although the sulfur-containing species are involved, a considerable amount of electron states exist at the Fermi level in the case of LiPSs adsorbed on TMCs. These results indicate that all the six TMCs can maintain their excellent metallic behavior during discharging and charging processes. Moreover, the metallic behavior of LiPSs adsorbed on TMCs originated from the abundance of electronic states at the Fermi energy level stemming from the d states of TM. Hence all the adsorbed systems possess good electrical conductivity mainly owing to the contribution of electrons from TM atoms, which is essential to expedite electrochemical reactions in Li–S battery systems.

Fig. 6 The total and projected density of states of S₈ (a), Li₂S₈ (b), Li₂S₆ (c), and Li₂S₄ (d) on the TiC (001) surface, respectively.

3.3 The diffusion of Li on the TMC (001) surface

In Li–S batteries, the Li-ion diffusion plays a critical role in transforming of LiPS species and the nucleation/decomposition of Li₂S. What is more, the rate capability of the Li–S batteries is also determined mainly by the adsorption and diffusion behavior of Li on the surface of the electrode materials. Therefore, the kinetic performance of TMCs acting as the sulfur hosts was further investigated by calculating the adsorption and diffusion barrier of lithium ions on TMCs. The diffusion barriers and pathways of Li atoms on the surface of TMCs were analyzed using the climbing image nudged elastic band (CI-NEB) method. Herein, the stable adsorption sites, diffusion paths of lithium ion on the (001) facet of TMCs and the minimum energy path (MEP) of Li-ion diffusion are presented in Fig. 7. All the possible adsorption sites for Li ion adsorption were checked carefully, and the detailed test data are listed in Table S15.† The results show that both the top sites of C and TM atoms are the stable adsorption sites, and the C-top is the most stable adsorption site. Therefore, the diffusion paths of Li-ions were designed from one of the C-top sites to another diagonally adjacent C-top site. There are three possible diffusion paths (as shown in Fig. 7b), i.e. Path I with the Li ion crossing the bridge site to the TM-top site, Path II with the Li ion crossing the hollow area constructed by two carbon atoms and TM atoms, and Path III with the Li ion crossing the top of the TM atoms. The calculation results show that for all TMC surfaces Path II has a relatively lower diffusion barrier. The diffusion barriers of Li ions on TiC, VC, ZrC, NbC, HfC and TaC are 0.09, 0.01, 0.33, 0.13, 0.27 and 0.15 eV, respectively, which are all smaller than the diffusion barrier of 0.30 eV on graphene,⁶⁵ except that on ZrC. Therefore, we conclude that the studied TMCs as host materials could facilitate the diffusion of Li ions, which improves the comprehensive performance of Li–S batteries.

Fig. 7 (a) Two possible adsorption sites of Li atoms on the TiC (001) surface; (b) the different diffusion paths of Li atoms on the TiC (001) surface; and (c and d) the diffusion barrier and the minimum energy paths of Li on TMC surfaces.

3.4 The decomposition of Li₂S on the TMC (001) surface

Li₂S is the final discharge product in the discharge process of Li–S batteries. However, the low electronic conductivity and high decomposition energy of Li₂S lead to a high overpotential and low rate capability. An excellent cathode catalyst that can reduce the decomposition barrier of Li₂S could enhance the overall reaction kinetics of the Li–S batteries. Therefore, the kinetic performance of TMCs acting as the sulfur hosts was further investigated by calculating the activation energy barriers of Li₂S decomposition on TMCs. Herein, the CI-NEB method was adopted to study the decomposition of Li₂S on the surface of TMCs. As shown in Fig. 8 and Fig. S19,† the overall decomposition process of the Li₂S molecule on different TMCs was considered as an intact Li₂S molecule decomposed into a LiS cluster and a single Li ion. The decomposition barriers of Li₂S on TiC, VC, ZrC, NbC, HfC and TaC are 0.57, 1.12, 0.65, 1.13, 0.64, and 1.10 eV, respectively. In contrast to the decomposition barriers of the natural free molecule Li₂S (3.39 eV) and that of graphene (1.81 eV),⁵⁸ all the TMCs have a remarkable catalytic activity in the decomposition of the Li₂S molecule. Significantly, TiC, ZrC, and HfC exhibit the most excellent catalytic ability to promote the decomposition of Li₂S effectively. According to the results, the decomposition processes of the Li₂S molecule on the TMC surface fall into two categories, which are attributed to the different Li₂S adsorption structures, as shown in Fig. 8. The adsorption of Li₂S on TiC, ZrC, and HfC (IVB transition metals based carbides) surfaces were achieved by the S atom in Li₂S bonding with the C atom in the surface. However, the adsorption of Li₂S on VC, NbC, and TaC (VB transition metal based carbides) surfaces was achieved by the S atom in Li₂S bonding with the transition metal (TM) atom in the surface. The underlying bonding and decomposition mechanism of Li₂S on the TMC surface was further investigated via electronic structure analysis. Since Ti, Zr, and Hf are in the same group (e.g. IVB) of the periodic table with the same number of electrons in the outermost partially filled atomic orbital shell, similar adsorption structures were obtained. V, Nb, and Ta are in the VB of the periodic table with the same number of electrons, which have one more valence electron than the transition metals in IVB. For Li₂S adsorption, the Li atoms in all systems bond by donating electrons to the nonmetal atom (carbon atom) of the surfaces. However, the S atom in Li₂S is bonding by accepting electrons from the surface atom. The V, Nb, and Ta in the VB group have one more valence electron than Ti, Zr, and Hf in the IVB group, which can more easily donate electrons to the S atom to form the S–TM bond. In contrast, on the TiC, ZrC, and HfC surfaces the S atom gets electrons from the C atom to create a strong S–C bond. As shown in Tables S3–8,† after the adsorption of Li₂S, the Li–S bonds were elongated. It should be noted that, on the TiC, ZrC, and HfC surfaces, the Li–S bond length increased by 0.33, 0.44, and 0.42 Å, respectively. Nevertheless, the Li–S bond length only increased by 0.11, 0.10 and 0.11 Å on the VC, NbC, and TaC surfaces. Therefore, the strong S–C bond weakens the Li–S bond in the Li₂S molecule, which leads to smaller decomposition barriers. The Bader charge analyses were performed for Li₂S adsorption on the TMCs. As shown in Table 1, for the adsorption systems of Li₂S on TiC, ZrC, and HfC, the substrates transferred more electrons to Li₂S than those in the VC, NbC, and TaC adsorption systems, which indicates a more vital chemical interaction between them. To reveal the origin of the above phenomena, the electronic properties of these TMC surfaces were calculated. The calculated total and partial density of states (DOS) plots illustrated in Fig. 9 were used to analyze the unique electronic structures for the non-polar (001) surface of TMCs, accordingly. The total DOS plots of two kinds of surfaces exhibit a significantly distinct peak at the Fermi levels with the TiC group peak featuring hybridization of metal Ti and nonmetal C states. In contrast, the case of the VC group has a clear majority of metal TM states. In addition, Bader charge analysis predicts charge transfer from TM to nonmetal C, and the charges of IVB metal (Ti, Zr, and Hf) in TMCs are slightly higher than those of the VB metal (V, Nb, and Ta) in TMCs due to the difference of electronegativity and electronic structure of the two groups of TM elements. In short, a fundamental difference between the two kinds of surfaces is their highest occupied levels with TiC (001) predominantly of nonmetal (C) nature and VC (001) primarily of metal (TM) nature.⁶⁶

Fig. 8 The optimized initial state (IS), transition state (TS), and final state (FS) of Li₂S decomposition on the (a) TiC, (b) VC, (c) ZrC, (d) NbC, (e) HfC, and (f) TaC (001) surfaces, respectively.

Fig. 9 The partial density of states of (a) TiC, (b) VC, (c) ZrC, (d) NbC, (e) HfC, and (f) TaC (001) surfaces, respectively.

Table 1 The charge transfer (Δq, in e) between the TMCs and Li₂S (the positive values of the charge transfer indicate that the charge is transferred from Li₂S to TMCs)

	TiC	VC	ZrC	NbC	HfC	TaC
Charge transfer between Li2S and TMCs (e)	0.921	0.537	0.805	0.439	0.821	0.439

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The intrinsic insulating properties of Li₂S will lead to sluggish charge transfer and electrochemical reaction kinetics during the charge/discharge process of Li–S batteries, which requires that the sulfur host should possess good electronic conductivity during the adsorption of Li₂S. The electronic conductivity of TMC surfaces before and after adsorption of Li₂S species was studied by calculating their total and projected density of states, shown in Fig. 9 and 10. It was found that, in all cases, there was no significant change in the DOS for all the TMCs regardless of Li₂S adsorption. Therefore, the electronic conductivity of the TMCs was retained even after Li₂S adsorption.

Fig. 10 The partial density of states of Li₂S on the (a) TiC, (b) VC, (c) ZrC, (d) NbC, (e) HfC, and (f) TaC (001) surfaces, respectively.

3.5 Sulfur reduction reaction (SRR) on the TMC (001) surfaces

To further understand the electrochemical performance of TMCs, the free energy diagrams of polysulfide conversion were considered. The overall SRR was based on the reversible formation of Li₂S from S₈ and Li. As shown in Fig. 11, the first steps for all TMC substrates are exothermic with the calculated Gibbs free energies ranging from −2.46 to −4.25 eV, corresponding to the reduction of S₈ to Li₂S₈ spontaneously. The other intermediate reaction steps from Li₂S₈ to Li₂S are endothermic with positive Gibbs free energies. The rate-limiting step in the overall discharge process can be classified into two classes, corresponding to the reduction step of Li₂S₄ to Li₂S₂ or Li₂S₂ to Li₂S, respectively. For the IVB group TMCs (e.g. TiC, ZrC, HfC), the rate-limiting step is the reduction step of Li₂S₄ to Li₂S₂. However, the rate-limiting step is changed to the reduction step of Li₂S₂ to Li₂S for the VB group TMCs (e.g. VC, NbC, TaC). In brief, we found that the Gibbs free energies of the rate-determining steps on the TMCs are moderate with values of less than 1 eV. The lower Gibbs free energies reveal that the SRR is more thermodynamically favorable on TMCs upon discharging, thereby improving the electrochemical performance of Li–S batteries.

Fig. 11 Calculated Gibbs free energy profiles of SRR on the (001) surfaces of TMCs.

4. Conclusions

In summary, based on first-principles calculations, we systematically explored the anchoring and catalytic ability of a series of TMCs for Li–S batteries. It was found that all the non-polar TMC (001) surfaces we investigated had a moderate adsorption ability to LiPSs. The DOS analysis for the adsorption systems of LiPSs on TMCs revealed their metallic properties. Besides, the low Li-ion diffusion barriers are essential to achieve high rate and reaction kinetics. Moreover, the activation barriers of Li₂S decomposition on the IVB group TMC (e.g. TiC, ZrC, HfC) surfaces are lower than those on the VB group TMC (e.g. VC, NbC, TaC) surfaces. Furthermore, the observed lower Gibbs free energy for SRR and decomposition energy barriers for catalytic oxidation of Li₂S enable accelerated formation and decomposition of Li₂S in both discharging and charging processes. To sum up, due to the excellent bifunctionality as anchoring and electrocatalytic ability, together with the intrinsic thermal and thermodynamic stabilities as well as the metallic conductivity of the TMC host materials, IVB group TMCs (e.g. TiC, ZrC, and HfC) are regarded as effective influential sulfur hosts to effectively improve the cycling stability of Li–S batteries. Our work sheds light on a strategy of using the non-polar TMC surface as the anchoring material via multi-element synergy engineering. It provides significant insight into the effective regulation of the electrochemical reactions of Li₂S.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 11904084, 22208088 and U2004212), the Henan Center for Outstanding Overseas Scientists (No. GZS202300), and the China Postdoctoral Science Foundation (2021M690933). The simulations are performed on resources provided by the High Performance Computing Center of Henan Normal University.

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Footnote

† Electronic supplementary information (ESI) available: A detailed description of models and computational methods; the AIMD simulations at a temperature of 500 K of the TiC(001) surface (Fig. S1); the total and partial density of states of TMC (001) surfaces (Fig. S2); the structures of S₈ and LiPSs and the optimized adsorption structures of Li₂S₈, Li₂S₆, and Li₂S₄ with organic molecules (Fig. S3); the optimized adsorption structures of S₈ and LiPSs on TMC (001) surfaces (Fig. S4–8); the charge density difference (CDD) of S₈ and LiPSs on TMC (001) surfaces (Fig. S9–13); the total and projected density of states of S₈ and LiPSs on the TMC (001) surfaces (Fig. S14–18); the minimum energy path of Li₂S decomposition on TMC surfaces (Fig. S19); the structure information of TMCs and LiPSs before and after the adsorption interaction (Tables S1–11); the comparison of the adsorption energy for the LiPSs on the HfC(001) surface with or without the DFT+U method (Table S12); the binding energies of Li₂S₈, Li₂S₆ and Li₂S₄ with organic molecules (Table S13); the charge transfer (Δq, in e) of S or Li atoms in the S₈ or LiPSs adsorbed on TMCs (Table S14); the detailed test data of Li-ions adsorbed on the (001) surfaces of TMCs (Table S15). See DOI: https://doi.org/10.1039/d3nr04298g

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