Metallic C₅N monolayer as an efficient catalyst for accelerating redox kinetics of sulfur in lithium–sulfur batteries

Abstract

Lithium–sulfur battery is one of the most promising applicants for the next generation of energy storage devices whose commercial applications are impeded by the key issue of the shuttle effect. To overcome this obstacle, various two-dimensional (2D) carbon-based metal-free compounds have been proposed to serve as anchoring materials for immobilizing soluble lithium polysulfides (LiPs), which however suffer from low electronic conductivity implying unsatisfactory performance for catalyzing sulfur redox. Therefore, we have predicted metallic C₅N monolayers, possessing hexagonal (H) and orthorhombic (O) phases, exhibiting excellent performance for suppressing the shuttle effect. First-principles simulations demonstrate that O-C₅N could serve as a bifunctional anchoring material due to its strong adsorption capability to LiPs and excellent catalytic performance for sulfur redox with active sites from both basal plane and zigzag edges. Furthermore, the rate of Li₂S oxidation over O-C₅N is fast due to the low energy barrier of 0.93 eV for Li₂S decomposition. While for H-C₅N, only N atoms located at the armchair edges can efficiently trap LiPs and boost the formation and dissociation of Li₂S during discharge and charge processes, respectively. The current work opens an avenue of designing 2D metallic carbon-based anchoring materials for lithium–sulfur batteries, which deserves further experimental research efforts.

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1. Introduction

The ever-increasing demand for an energy storage device with a long cycle life, high specific capacity, environmental friendliness and low cost has driven the development of new battery systems. Due to the high theoretical gravimetric energy density of 2600 W h kg⁻¹, which is three to six times higher than that of currently used lithium-ion batteries (LIB), lithium–sulfur (Li–S) batteries have attracted tremendous research attention.^1–4 But there still exists a couple of severe problems remaining unresolved hindering their large-scale commercial applications. For example, the intermediate products of lithium polysulfides (LiPs) generated during the charge–discharge process would dissolve into the electrolyte, which traverses the diaphragm and eventually accumulate on the anode of the battery. Moreover, poor ionic/electronic conductivity of sulfur and the discharge intermediate products (such as Li₂S₂/Li₂S) restrict the rate performance of batteries.^5–8 It has been proposed that the introduction of anchoring materials into the cathode of Li–S batteries could address those obstacles simultaneously due to their enhanced performances in trapping LiPs and accelerating the redox kinetics.⁵ Therefore, searching for ideal anchoring materials is an efficient strategy to overcome such issues, which can help achieve the practical application of Li–S batteries.^9–12 To this end, a large number of two-dimensional (2D) materials have been extensively investigated to alleviate LiPs shuttle due to their high surface volume ratio, which includes metal sulfides,^5,13 graphene,¹⁴ phosphorene,¹⁵ silicone,¹⁶ borophene¹⁷ and MXene.¹⁸

Owing to its advantage of high electrical conductivity, lightweight and mature preparation methods,¹⁹ graphene has been regarded as one of the most promising candidates for anchoring material. However, pristine graphene exhibits poor performance in suppressing the shuttle effect due to weak binding affinity to LiPs.⁵ Therefore, graphene prepared by multiple doping has been investigated for electrodes in Li–S batteries because of more polar adsorption sites and enhanced trapping capability toward LiPs.^20,21 As neighboring elements of carbon, N and B are the two most used elements for doping in order to tailor the intrinsic properties of graphene. The N atoms with higher electronegativity compared to the C atom are considered Lewis-bases in sp² lattice, which strongly interacts with Li atoms in lithium polysulfides.²² However, doping strategy is confronted with the problem of a low density of active sites and inhomogeneous distribution of dopants. Therefore, tremendous research efforts have recently been boosted to explore the anchoring performances of the crystalline phase of carbon-based monolayers, which are either synthesized experimentally or theoretically designed. The trapping capabilities of BN, C₂N, and C₃N₄ toward LiPs are theoretically evaluated based on adsorption energies.²³ A new monolayer of BC₂N has been investigated for anchoring LiPs with and without defects demonstrating its suitability for anchoring material.²⁴ Recently, a novel 2D material, C₄N₄, has been theoretically designed and explored as a sulfur host, which exhibits not only superior performance of adsorbing long-chain LiPs but also fast kinetics of LiPs diffusion.²⁵ Qie reported a C₃B monolayer as an anchoring material for lithium–sulfur batteries, which showed competitive anchoring performance for LiPs.²⁶ Nevertheless, the redox of sulfur has not been extensively investigated on those aforementioned carbon-based metal-free monolayers, which is of paramount importance as well as the entrapment of LiPs. Furthermore, those 2D monolayers suffer from low conductivity due to the existence of an electronic bandgap, which indicates their poor performance for catalyzing the sulfur redox and requires LiPs to diffuse from anchoring materials to the surface of conducting agents for their conversions to Li₂S.²⁷ This means that the transformation from LiPs to Li₂S during the discharge process has to undergo adsorption-diffusion-conversion. Accordingly, it is promising to search for metallic 2D carbon-based anchoring materials, which not only possess strong trapping capability for LiPs but also catalyze effectively the sulfur redox.

Based on their generic family molecular formula of C_xN_y, the 2D carbon nitride family including CN (C₃N₃,²⁸ C₄N₄,²⁵ C₆N₆²⁸), C₂N,²⁹ C₃N,³⁰ C₃N₂,³¹ C₃N₄,³² C₄N,³³ C₄N₃,³⁴ C₅N,³⁵ C₆N₈,³⁶ C₉N₄,³⁷ C₉N₇,³⁷ C₁₀N₃,³⁸ C₁₀N₉³⁹ and C₁₄N₁₂,^40–42 have been theoretically or experimentally designed, which have attracted a lot of research efforts for applications in energy conversion and energy storage.³⁸ Among them, g-C₃N₄,⁴³ C₂N,⁴⁴ C₃N³⁰ and C₄N⁴⁵ monolayers have been experimentally synthesized. Up to date, however, a monolayer with the chemical stoichiometry of C₅N has rarely been reported. Only the prediction of the bulk phase of C₅N was reported whose ground state crystallizes in hexagonal lattice.⁴⁶ Wang et al. designed a C₅N monolayer by simply introducing vacancies in a perfect C₃N monolayer.³⁵ However, other possible structural configurations of 2D C₅N possessing lower energies have not been extensively investigated. Accordingly, to confirm the existence of more energetically stable 2D C₅N appealed to us to perform further investigations.

In this study, we theoretically designed metallic C₅N monolayers with hexagonal and orthorhombic lattices, respectively, via a swarm structural search.⁴⁷ We then extensively investigated the adsorption of LiPs on both the basal plane and edge of C₅N and found that edge sites have stronger binding strength to reaction intermediates of Li–S chemistry. Finally, the redox kinetics of sulfur were extensively investigated by calculating free energy changes of the discharge process and energy barrier of Li₂S decomposition on both phases. Our calculations demonstrate that on the orthorhombic phase of C₅N redox kinetics of Li₂S could be significantly elevated by active sites from the basal plane and edge N atoms, which showed excellent catalytic performance even better than that of single-atom catalysts. While the performance of the hexagonal phase of C₅N for trapping LiPs and catalyzing the redox of Li₂S could only be assigned to the edge atoms.

2. Theoretical approach

We searched the structure by means of a particle swarm optimization (PSO) algorithm, which is implemented in the CALYPSO code.⁴⁷ We discovered a ground state as well as one metastable structure of 2D C₅N by PSO simulation, which requires only chemical composition benefiting from its efficient and multiple algorithms. Each generation consisted of 20 structures, in which 60% of the structures were constructed on the basis of the PSO evolution algorithms, whereas the remaining 40% were randomly generated to avoid premature convergence of structural prediction. The calculation of atomic structure relaxation, electronic structure, and total energy was performed based on the density functional theory (DFT) method, which is integrated with the code of the Vienna Ab initio Simulation Package (VASP).⁴⁸ The projector augmented wave (PAW) has been used to describe the interaction between the ion and electron. Within the generalized gradient approximation, the Perdew–Burke–Ernzerhof form (GGA-PBE) is utilized for describing the exchange–correlation functional.⁴⁹K-Point grids in reciprocal space for all systems corresponding to the simulations of structural relaxation, self-consistent field and the density of states (DOS) are summarized in Tables S1 and S2 in the ESI.†⁵⁰ A vacuum distance of 20 Å was used to avoid interaction between the adjacent layers. The threshold for forces of structural relaxation is 0.03 eV Å⁻¹. A DFT-D3 scheme was employed in order to take the van der Waals (vdW) interactions into account.⁵¹ In order to explore the adsorption performance of C₅N monolayers, we used 3 × 3 × 1 supercell for hexagonal phase and 2 × 4 × 1 supercell for orthorhombic phase, respectively. The equations for calculating the adsorption energy (E_ads) and cohesive energy (E_coh) are labeled as eqn (S1) and (S2), as listed in ESI.†

To investigate the kinetic stability of C₅N monolayers, the phonon dispersion curves were calculated using the PHONOPY program interfaced with the finite displacement method.⁵² To evaluate its thermodynamic stability, the ab initio molecular dynamics (AIMD) simulations with a time step of 3.0 fs lasting for 6 ps under the NVT ensemble were performed using a 3 × 3 × 1 and 2 × 4 × 1 supercell for hexagonal and orthorhombic phases, respectively. The temperature (T = 300 K) was controlled using the Nosé–Hoover thermostat.⁵³ The Gibbs free-energy change (ΔG) for surface-mediated lithiation during the discharge process was computed based on eqn (S3)–(S8) in ESI.†

3. Results and discussion

3.1 Capturing capabilities of the C₅N monolayer for LiPs and S₈ clusters

We utilized the CALYPSO code to identify the ground state of the C₅N monolayer with the hexagonal lattice (H-C₅N, P6̄2m, Z = 1) as well as a metastable state in an orthorhombic structure (O-C₅N, Pmn2₁, Z = 2), which have a tiny total energy difference of 0.134 eV per formula. The complete structural optimization gives rise to the lattice constants of a = b = 4.22 Å for H-C₅N and a = 12.68 Å and b = 2.44 Å for O-C₅N, respectively. As shown in Fig. 1(a) and (d), there exists only one type of honeycomb ring in H-C₅N consisting of five C atoms and one N atom while O-C₅N consists of three types of rings, which combine carbon atoms with 0, 1 and 2 nitrogen atoms, respectively, to form a 6-membered hexagonal ring. That different structural feature is also reflected by atomic charge values of C and N atoms (see Fig. 1(a) and (d)) as well as the C–N/C–C bond length of 1.39 Å/1.40 Å and 1.41 Å/1.44 Å in H-C₅N and O-C₅N, respectively. Note that C atoms bonded to two N atoms in O-C₅N have the largest atomic charge value of 0.76 e.

Fig. 1 The optimized structures and charge distribution of H-C₅N (a) and O-C₅N (d) with the unit cells presented in the blue frames, phonon band structures for H-C₅N (b) and O-C₅N (e) and electronic band structures and DOS for H-C₅N (c) and O-C₅N (f). The numbers on the side of the atoms represent the atomic charge values for H-C₅N (a) and O-C₅N (d).

The dynamical stability is confirmed from phonon dispersion curves, which, as shown in Fig. 1(b) and (e), exhibit no imaginary phonon frequencies for both H-C₅N and O-C₅N. We also explored the thermodynamic stability of H-C₅N and O-C₅N monolayers by performing AIMD simulations, which show that both phases can maintain structural integrity at 300 K (see Fig. S1 and S2, ESI†).

Cyclability and rate performance of the lithium–sulfur battery are strongly correlated with the electron conductivity of cathodes.³⁸ We then explored the electronic properties of C₅N by calculating the electronic band structure and DOS. Fig. 1(c) and (f) clearly show that for both phases valence bands cross the Fermi level implying that they possess metallic states, which facilitate the discharge–charge process of LiPs when used as anchoring materials.

Cohesive energy (E_coh) is widely utilized to evaluate the experimental feasibility of fabrication and the calculated values of E_coh for both H-C₅N and O-C₅N are −7.36 and −7.34 eV, respectively, which possess a very tiny difference of 0.02 eV rendering the possibility that both hexagonal and orthorhombic phases could be simultaneously synthesized. They are slightly higher than that of graphene (−7.95 eV)⁵⁴ but significantly lower than those previously reported for 2D materials of C₄N₄, C₃N, g-CN, g-C₄N₃ and C₂N whose cohesive energies are −7.27,²⁵ −7.07,⁵⁵ −5.71,⁵⁶ −6.7⁵⁷ and −5.59 eV,⁵⁸ respectively. Note that C₃N, g-CN, g-C₄N₃ and C₂N have been experimentally synthesized indicating that our newly predicted H-C₅N and O-C₅N are highly possible to be prepared experimentally. More interestingly, both of our predicted C₅N monolayers are more energetically stable than another 2D C₅N proposed in the previous literature, which was designed by simply introducing double vacancies within 2D C₃N with E_coh = −7.20 eV (see Fig. S3, ESI†).³⁵

We also computed elastic constants of H-C₅N and O-C₅N monolayers, which are summarized in Table 1, together with the results of graphene for comparison.⁵⁷ For H-C₅N, the independent elastic constants are C₁₁ = 371.59 and C₁₂ = 62.66 N m⁻¹, while those for O-C₅N are C₁₁ = 368.83, C₁₂ = 61.25, C₂₂ = 374.53, and C₆₆ = 38.55 N m⁻¹. These results conform to the Born criteria, where C₁₁ > 0, C₆₆ > 0 and C₁₁ > |C₁₂| for H-C₅N and C₆₆ > 0 and C₁₁C₂₂ > C₁₂² for O-C₅N, demonstrating that both phases of C₅N are mechanically stable.^59,60

Table 1 Elastic constants (in units of N m⁻¹) of H-C₅N, O-C₅N and graphene

	H-C5N	O-C5N	Graphene^57
C 11	371.59	368.83	351.71
C 22		374.53
C 12	62.66	61.25	58.63
C 66	154.47	38.55	146.52

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The promising anchoring material in Li–S batteries should have strong interaction intensity with LiPs in particular long-chain clusters of Li₂S₄, Li₂S₆ and Li₂S₈, which is usually evaluated from E_ads based on eqn (S1) shown in ESI.† We tried various adsorption configurations of LiPs on H-C₅N and O-C₅N, of which only those patterns with the lowest E_ads are presented in Fig. 2. In adsorbed systems, the vertical distance between LiPs and substrates, as summarized in Fig. 2, ranges from 2.33 to 3.14 Å on H-C₅N and from 2.01 to 2.41 Å on O-C₅N. When it turns to the case of adsorbed S₈, the distance increases to 3.14 Å on H-C₅N and 3.05 Å on O-C₅N, indicating vdW interaction is a decisive factor for the binding between S₈ cluster and substrates.

Fig. 2 Adsorption configurations and corresponding E_ads of Li₂S, Li₂S₂, Li₂S₄, Li₂S₆, Li₂S₈ and S₈ on H-C₅N (a)–(f) and on O-C₅N (g)–(l), respectively. On H-C₅N, the vertical distances between adsorbates and substrates are depicted, while on O-C₅N the bond length of S–C and Li–C are listed when LiPs form strong chemical bonds with the substrates C₅N.

The E_ads values of LiPs on H-C₅N are in the range of −0.60 to −0.74 eV as listed in Fig. 2, indicating worse trapping capability for LiPs compared to the electrolyte solvent molecule of 1,2-dimethoxyethane (DME). Taking Li₂S₄ as an exaple, its E_ads value on H-C₅N is higher than that on DME by the difference of 0.13 eV,²⁶ leading to the poor performance of the H-C₅N monolayer for inhibiting the shuttle effect. In contrast, the binding strength of all LiPs and O-C₅N is clearly stronger than that of H-C₅N as reflected by their lower E_ads ranging from −0.81 eV to −1.12 eV. Moreover, we believe that O-C₅N could suppress the shuttle effect by immobilizing soluble Li₂S₄ because its E_ads on O-C₅N was calculated to be −0.81 eV, lower than that of −0.80 eV on DME.²⁶ Bader charge analysis shows charge transfers from adsorbed LiPs to O-C₅N, while for the adsorbed S₈, the charge transfer is directed in the reverse direction as summarized in Table S3 (ESI†). In addition, no linear correlation was found between charge transfers and adsorption energy, which might be ascribed to the localized polarization of the O-C₅N monolayer that induces extra electrostatic interactions.²⁶

3.2 Adsorption performance of C₅N edges toward LiPs and S₈ clusters

To extend the anchoring capability toward LiPs, we also investigated the performances of the edges of both phases of C₅N because the enhanced binding affinity has been found in the presence of edge defects in heteroatoms doped graphene.^20,61,62 Therefore, the edge defects are fabricated by cutting both phases of C₅N to nanoribbons along the direction of the zigzag edge or armchair edge. The specific atomic arrangements of N and C in H-C₅N and O-C₅N render a wide variety of nanoribbons with different termination stoichiometries, which in total include 13 kinds of nanoribbons (see Fig. 3 and Fig. S4, S5, ESI†). Among them, three nanoribbons depicted in Fig. 3 are filtered by giving rise to lower E_ads for the long-chain Li₂S₆ clusters than other nanoribbons as illustrated in Table S4 and Fig. S6–S8 (ESI†), which is in the window of −1.72 < E_ads < −1.03 eV. While the rest ten nanoribbons possess a much weaker binding affinity toward Li₂S₆ as reflected by their higher E_ads values (see Table S4, ESI†) as shown in Fig. S4 and S5 (ESI†). Those three nanoribbons depicted in Fig. 3(a)–(c) are named as H-A-C1N1-C2N0 and H-A-C1N1-C1N1 (achieved from H-C₅N with armchair edges) and O-Z-C2N0-C0N2 (achieved from O-C₅N with a zigzag edge). Regarding the names of nanoribbons, hereafter in this study, those cleaved from the hexagonal phase (H-) with armchair/zigzag edges are labeled as H-A/H-Z and otherwise as O-A/O-Z, which are constructed on the basis of the orthorhombic phase. In addition, those names as well contain information on the arrangements of edge atoms. Taking H-A-C1N1-C2N0 as an example, it denotes the nanoribbon with armchair edges derived from H-C₅N with successive edge atoms of one C and one N atom at the left side and two C atoms and zero N atom at the right side of the ribbon, with more details shown in Fig. S4(a) (ESI†). Furthermore, this nomenclature enables us to easily distinguish the adsorption position on nanoribbons. We marked the adsorption site in bold, for instance, H-A-C1N1-C2N0 (shown in Fig. 3(a)) refers to the situation that an adsorbate adsorbs on the left side of the nanoribbon terminated with one C and one N. Note that the C atom exposed at the edge of nanoribbons would be saturated with hydrogen atom while N atoms are not.

Fig. 3 Optimized structures and electronic properties of C₅N nanoribbons. Relaxed configurations of H-A-C1N1-C2N0 (a), H-A-C1N1-C1N1 (b), and O-Z-C2N0-C0N2 (c), with the simulation box illustrated by the blue frames; electrical band structures and DOS of H-A-C1N1-C2N0 (d), H-A-C1N1-C1N1 (e) and O-Z-C2N0-C0N2 (f).

We next briefly explored the structural and electronic properties of those three nanoribbons. They all maintain the conductive nature as confirmed by their band structures and DOS, which have no gaps as illustrated in Fig. 3(d)–(f). Note that O-Z-C2N0-C0N2 has a spin-polarized ground state with the total magnetism of 0.24 μ_B per cell, while it is absent in the other two ribbons.

Next, we explored the performances of edge atoms of C₅N for trapping LiPs and S₈ clusters by calculating E_ads of those clusters on three types of nanoribbons, as shown in Fig. 4 and in Fig. S9–S11 (ESI†). Our DFT calculations demonstrate that edges of H-A-C1N1-C2N0, H-A-C1N1-C1N1 and O-Z-C2N0-C0N2 possess strong chemisorption toward LiPs as shown in Fig. 4, which leads to the chemical bond formed between Li atoms and N atoms. The corresponding E_ads values are lower than −1.02 eV, indicating that the edges of those three nanoribbons qualify to suppress the shuttle effect. In particular, the binding strength between LiPs and O-Z-C2N0-C0N2 (see Fig. 4(c)) was found the strongest, which was due to the most abundant edge N atoms in this structure configuration. The adsorption energies of LiPs on O-Z-C2N0-C0N2 are −3.40, −3.06, −2.79, −1.72, −1.41 and −0.65 eV for Li₂S, Li₂S₂, Li₂S₄, Li₂S₆, Li₂S₈ and S₈, respectively, which are much lower than those on H-A-C1N1-C1N1 and H-A-C1N1-C2N0. These data also demonstrate that O-Z-C2N0-C0N2 does better than graphene nanoribbons on entrapping LiPs (GNR) with corresponding values of E_ads of −0.49, −0.38, −0.36, −0.36 and −0.38 eV.²⁰ Moreover, the anchoring performance of GNR for LiPs could be enhanced by introducing heteroatoms X at the edges of GNR (X-GNR, X = O, N and F), which leads to the E_ads for Li₂S₄ decreasing from −0.36 eV for GNR to −2.56, −2.00 and −1.89 eV for O-GNR, N-GNR and F-GNR, respectively.²⁰ Nevertheless, our calculations clearly demonstrate that O-Z-C2N0-C0N2 could bind LiPs stronger than X-GNR.

Fig. 4 Adsorption configurations and E_ads of LiPs and S₈ clusters H-A-C1N1-C2N0 (a), H-A-C1N1-C1N1 (b), and O-Z-C2N0-C0N2 (c), respectively. (d) Charge redistribution upon the deposition of LiPs and S₈ clusters on O-Z-C2N0-C0N2, the red and yellow regions represent the charge accumulation and depletion, respectively.

Such strong interaction between LiPs and C₅N nanoribbons could be also evidenced from the structural deformation in adsorbed phases of LiPs as summarized in Tables S5–S7 (ESI†). One can clearly see that variations in bond length and bond angle as LiPs are adsorbed on O-Z-C2N0-C0N2 are more pronounced than those on H-A-C1N1-C1N1 and H-A-C1N1-C2N0. The charge density difference was also calculated for the adsorbed systems on O-Z-C2N0-C0N2 to shed light on the interaction intensity between LiPs and S₈ clusters and nanoribbons. As shown in Fig. 4(d), there is a clear charge transfer between adsorbed clusters and nanoribbon. The charge exchange mainly occurs between Li atoms and edge N atoms, indicating a strong chemical bond of Li–N, while the charge around S atoms is found to be reduced due to the adsorption effect. Moreover, the Bader charge analysis was performed to obtain quantitative values of charge transfer between adsorbates and substrate.^63,64 Our calculations demonstrate that the charge transfer from Li₂S, Li₂S₂, Li₂S₄, Li₂S₆, Li₂S₈, and S₈ clusters to O-Z-C2N0-C0N2 nanoribbon by 0.81, 0.99, 0.83, 0.25, 0.23 and 0.01 e, respectively.

3.3 Redox kinetics of sulfur on basal plane and edges of C₅N

In addition to the strong chemisorption of LiPs, the fast reaction kinetics of reverse conversion between S₈ and Li₂S is highly demanded as well as suppressing the shuttle effect and improving the utilization of sulfur. Therefore, we next probed the catalytic performance of O-C₅N and nanoribbons of H-A-C1N1-C1N1, H-A-C1N1-C2N0 and O-Z-C2N0-C0N2 for the redox reaction of Li₂S. The oxidation process of Li₂S was firstly investigated for which the rate of reaction kinetics was evaluated by the energy barrier (E_b) for the breaking of the Li–S bond, which was calculated by the climbing-image nudged elastic band (CI-NEB) method.⁶⁵ The energetically optimal reaction pathways of Li₂S decomposition on those four systems are plotted in Fig. 5(a)–(d), which demonstrate barriers of 0.93, 1.02, 1.61, and 1.58 eV for Li₂S dissociation catalyzed by basal sites of O-C₅N and edges of O-Z-C2N0-C0N2, H-A-C1N1-C1N1 and H-A-C1N1-C2N0, respectively, as shown in Fig. 5(e). Our DFT calculations demonstrate that the rate of Li₂S decomposition is much higher on O-C₅N than those on the edges of O-Z-C2N0-C0N2, H-A-C1N1-C1N1 and H-A-C1N1-C2N0. Interestingly, the catalytic capability of O-C₅N for Li₂S dissociation is even more enhanced than those over single-atom catalysts of VN₄@G and CoN₄@G with E_b values of 1.10⁶⁶ and 1.37 eV,⁶⁷ respectively. Overall, O-C₅N exhibits better catalytic capability for Li₂S decomposition than H-C₅N given the active sites from the basal plane to the edges of nanoribbons.

Fig. 5 The decomposition pathways of Li₂S on O-C₅N (a), O-Z-C2N0-C0N2 (b), H-A-C1N1-C1N1 (c) and H-A-C1N1-C2N0 (d). Energy profiles of Li₂S decomposition (e) and the relative free energy profiles of the transformation from S₈ to Li₂S (f) on the surface of O-C₅N and the three nanoribbons. (insets) The relaxed adsorption configurations of reaction intermediates on H-A-C1N1-C1N1.

Next, the reduction process of sulfur through the opening of the ring structure was extensively investigated, for which we calculated the Gibbs free energy changes corresponding to the discharge process from S₈ to Li₂S accompanied by the generation of gas-phase of Li₂S₂ clusters based on the eqn (S3)–(S8) listed in the ESI.†⁶⁸ The overall free energy change over O-C₅N and the edges of O-Z-C2N0-C0N2, H-A-C1N1-C1N1 and H-A-C1N1-C2N0 are −0.76, −1.46, −0.52 and −0.19 eV, respectively, indicating that the reduction process of sulfur is exothermic. Consistent with previous works, the rate-determining step (RDS) for the conversions from S₈ to Li₂S on those four systems all refer to the reaction from Li₂S₂ to Li₂S, as shown in Fig. 5(f).⁶⁹ The free energy change of RDS (ΔG_RDS) could be considered as a simple descriptor for assessing the performance of catalysts toward sulfur reduction. One can see that the values of ΔG_RDS on those three nanoribbons are 4.53, 4.49 and 4.63 eV, respectively, as shown in Fig. 5(f). Among them, H-A-C1N1-C1N1 exhibits the best catalytic performance for sulfur reduction due to the lowest ΔG_RDS = 4.49 eV. Nevertheless, other systems of O-C₅N, O-Z-C2N0-C0N2 and H-A-C1N1-C2N0 show comparable performance for catalyzing the sulfur reduction due to their similar values of ΔG_RDS as that of H-A-C1N1-C1N1.

Considering the balance between both oxidation and reduction processes, we believe that O-C₅N possesses superior catalytic performance for sulfur chemistry in Li–S batteries. Our calculations have affirmed that active sites from both basal plane and edge (modeled by O-Z-C2N0-C0N2) of O-C₅N exhibit superior catalytic performance for Li₂S oxidation and sulfur reduction, respectively. This is reflected by the low values of energy barrier of Li₂S decomposition and free energy change of RDS, indicating fast kinetics of sulfur redox. While for the case of H-C₅N, the rate of conversion between S₈ and Li₂S could be elevated only by the edge atoms. Overall, nanoflakes of O-C₅N having the zigzag edges would probably serve as good anchoring materials at suppressing the shuttle effect.

4. Conclusions

In summary, we have theoretically predicted two metallic 2D monolayers of C₅N crystallizing in hexagonal (H-C₅N) and orthorhombic phases (O-C₅N), respectively, which are more energetically stable than that proposed in the previous literature. Our calculations demonstrate that O-C₅N could serve as a superior anchoring material for inhibiting the shuttle effect due to its competitive performance for trapping LiPs and accelerating the rate of redox kinetics of sulfur with active sites coming from both basal plane and edges. The LiPs could be strongly chemisorbed onto the basal plane and edges of O-C₅N with the adsorption energies (E_ads) of −0.81 to −3.40 eV, lower than −0.80 eV, indicating stronger binding strength than that on the electrolyte molecule of DME. O-C₅N facilitates both charge and discharge processes as reflected by the energy barrier (E_b) of 0.93 eV for Li₂S decomposition catalyzed by the sites from the basal plane and free energy change of RDS (ΔG_RDS) of 4.53 eV over the zigzag edges, respectively. While, for H-C₅N, only the edge atoms are found to be able to trap LiPs and catalyze the redox of Li₂S with E_ads of −1.02 to −1.81 eV, E_b of 1.57–1.61 eV and ΔG_RDS of 4.49–4.63 eV. These results call for a further experimental synthesis of C₅N for its application as promising anchoring material for Li–S batteries and in particular for other applications of electrochemistry.

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 (Grants No. U1801255, 51972350). The calculations were carried out using supercomputers ‘Tianhe-2’ at NSCC Guangzhou.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1cp04192d

‡ These authors contributed equally.

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