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. 2025 Feb 28;10(9):9301–9313. doi: 10.1021/acsomega.4c09865

Doping at sp2-Site in Graphene+ Monolayers as High-Capacity Nodal-Line Semimetal Anodes for Na-Ion Batteries: A DFT Study

Surila †,‡, Xiaodong Lv †,‡,*, Shaolong Su †,‡, Bingwen Zhang §, Jian Gong †,‡,∥,*
PMCID: PMC11904845  PMID: 40092820

Abstract

graphic file with name ao4c09865_0011.jpg

Topological semimetals, especially topological semimetallic carbon-based materials, exhibit high electrical conductivity that is resistant to disruptions from defects or impurities, making them ideal alternatives as anode materials for sodium-ion batteries (SIBs). Recently, a novel two-dimensional carbon allotrope known as graphene+ was theoretically proposed [Yu et al., Cell Rep. Phys Sci., 3, 100790 (2022)], and because of its fascinating features, it shows potential for a variety of applications. In this study, we proposed two new two-dimensional carbon-based materials named M2C7 (M = B and Si) monolayers, which can be obtained by doping boron and silicon atoms into graphene+ at sp2-site, and thoroughly investigated their suitability for use as SIB anode materials. We found they exhibit distinctive mechanical and electronic properties, including negative Poisson’s ratios and topological Dirac nodal-line semimetal features, along with excellent dynamic, mechanical, and thermal stability. Particularly noteworthy is that M2C7 (M = B and Si) monolayers show high energy densities for Na adsorption attributed to their elevated storage capacity (2028.65 and 1528.76 mA h g–1), lower barrier energy (0.29 and 0.14 eV), and minimal volumetric variation (1.0% and 0.27%) compared to pristine graphene+ (with values of 1487.70 mA h g–1, 0.16 eV, and 0.30%, respectively). These findings demonstrate the potential of M2C7 monolayers as high-performance SIB anode materials.

1. Introduction

Rapid developments in rechargeable ion batteries, essential parts of energy storage systems, have been fueled by the growing need for sustainable energy on a worldwide scale.1 Lithium-ion batteries (LIBs) have attracted a lot of attention since they have the highest energy density and output voltage of any rechargeable battery. However, their widespread use in portable electronic devices is hampered by safety concerns, financial constraints, and capacity restrictions.2 As a possible replacement for LIBs, sodium ion batteries (SIBs) have attracted a lot of attention once again due to their low cost, natural abundance, and high energy densities.3,4 The electrode materials, an essential component of SIBs, will have a direct influence on battery performance, including capacity, rate capability, and cycle life.5 Anode materials that work well with LIB systems are not suitable for SIBs because of sodium’s larger atomic radius and higher redox potential. However, a lot of research has been done recently on cathode materials with good electrochemical performance for SIBs,6 such as layered transition-metal oxide complexes,7 polyanionic compounds,8 and Prussian blue analogues.9 Therefore, it is crucial to investigate and create appropriate anode materials for SIBs that can hold greater number of Na+ ions while still performing well.

In this context, two-dimensional (2D) materials have attracted a lot of attention due to their rapid carrier motion, high specific surface area, and mechanical flexibility.10−13 Many 2D materials have been intensively studied for use as SIB anode materials,14,22 like transition-metal dichalcogenides (TMDCs),15 transition-metal oxides (TMOs),16−18 transition-metal carbides or nitrides (MXenes),19−21 and carbon-based materials. Among them, 2D carbon materials have gained importance as a research hotspot due to their exceptional electrical and thermal properties, which are essential in the area of rechargeable ion batteries.23 Although inexpensive graphite anodes have been successful commercially, they are not appropriate for SIBs and have a restricted storage capacity of just 372 mA h g–1 in LIBs.24 To date, researchers have explored various 2D carbon materials as potential anode materials for SIBs, such as biphenylene,25 graphether,26 PAI-graphene,27 T-graphene,28,29 Θ-graphene,30 THFS-graphene,31 pentagraphyne,32 xgraphene,33 etc., as they were predicted to exhibit high storage capacities from 670 to 2357.2 mA h g–1. By disrupting graphene’s sp2 conjugated network, Li et al. have produced TQ-graphene, a metallic 2D Janus carbon allotrope that raises the theoretical sodium storage capacity to 2436 mA h g–1.34 A fish-scale-like graphene (FSL-graphene), which was developed by Lv et al. and is made up of a kagome and a honeycomb sublattice, has shown promising performance. It has a very large storage capacity of 3347.1 mA h g–1 and a low diffusion barrier (<0.23 eV).35 Notwithstanding these advancements, the hunt for novel 2D carbon compounds presents a viable avenue for their use in energy storage.

Topological quantum materials (TQMs), such as topological insulators (TIs),36 Dirac semimetals (DSMs),37 Weyl semimetals (WSMs),38 nodal-line semimetals (NLSMs),39 and nodal-surface semimetals (NSSMs)40 have been produced by a variety of disciplines, including material science, condensed matter physics, and solid-state chemistry.41 These materials have been the subject of much research. Due to their inherent high electrical conductivity, which is unaffected by impurities or defects and overcomes the shortcomings of conventional materials, topological semimetal materials (TSMs) in particular have emerged as desirable high-performance anode materials.42 On the one hand, the high intrinsic electrical conductivity facilitates efficient electron transport, enhancing energy storage and discharge capabilities. On the other hand, the robust surface states of TSMs provide a stable platform for metal-ion intercalation and deintercalation, resulting in enhanced cycling stability and capacity retention. The unique characteristic of TSMs makes them promising candidates for improving SIBs’ performance and exploring alternative options for anode materials. Carbon, silicon, and boron are a few examples of three-dimensional (3D) porous semimetallic materials that have been investigated as anodes for SIBs with high cycle stability. However, their specific capacities for anode materials are relatively low, ranging from 160 to 495.9 mA h g–1.43−45 In contrast to 3D TQMs like Si3C (1394 mA h g–1),46 B3S (1662 mA h g–1),47 and B3P (1691 mA h g–1),48 the researchers found that 2D TQMs as anode materials for SIBs demonstrate small-scale area expansion and enhanced specific capacity.

Graphene+, a 2D carbon allotrope with sp2–sp3 hybridization and made up of pentagonal and octagonal carbon rings, was recently proposed by first-principles simulation.49 This novel material retains graphene’s distinctive Dirac properties and exhibits a negative Poisson’s ratio (NPR). Significantly, graphene+, a lightweight 2D material, may have surface furrow pathways that enhance the metal ion storage capacity and ion diffusion rates. According to Yang et al., graphene+ is a top-notch anode material for CIBs because of its remarkable theoretical capacity (1487.7 mA h g–1), low average open circuit voltage (0.51 V), and minimal diffusion barrier (0.21 eV).50 Furthermore, heteroatom doping and defect engineering are prominent as popular and successful techniques for modifying the physical characteristics of material systems51 Many experimental and theoretical studies have explored doping strategies for 2D carbon materials to optimize their characteristics.52 Among these approaches, substituting boron and silicon atoms into carbon matrices is prevalent due to their proximity in the periodic table and comparable sizes.53,54

Therefore, we thoroughly examined the performance of pristine graphene+ and M2C7 (M = B, Si) monolayers as anode materials for SIBs using first-principles calculations. The M2C7 (M = B, Si) monolayers were designed by incorporating heteroatoms boron and silicon into graphene+ systems. Stability was confirmed by using cohesive energy, phonon spectra, and ab initio molecular dynamics (AIMD) simulations. According to our research, graphene+ and Si2C7 monolayers show strong Dirac nodal line semimetallicity, while B2C7 monolayers show metallic properties, indicating superior electrical conductivity as SIB anode materials. Diffusion barriers and theoretical capacities of Na ions on graphene+ and M2C7 (M = B and Si) monolayers are, respectively, 0.16, 0.29, and 0.14 eV, 2028.65, and 1528.76 mA h g–1, according to further calculations. Additionally, the energy density of graphene+ is greatly increased by doping it with B/Si atoms. In addition to proposing a novel carbon-based 2D high-capacity anode material for SIBs, our study offers valuable insights into the design of anode materials for TQMs as potential candidates for SIBs.

2. Computational Methods

All calculations in this work were performed using the Vienna ab initio simulation package (VASP) based on density functional theory.55−57 The electron exchange correlation interaction was selected using the Perdew–Burke–Ernzerhof (PBE) function in the generalized gradient approximation (GGA).58,59 Moreover, the hybrid Heyd–Scuseria–Ernzerhof functional (HSE06)60 was also used to ensure the band structures. The projector-augmented wave method was used to explain the interactions between ion nuclei and valence electrons. The plane-wave basis’ kinetic energy cutoff was 500 eV. Until the force and energy on each atom achieved convergence tolerances of less than 0.02 eV/Å and 10–5 eV, respectively, the geometric optimization was completed. The Grimme semiempirical correction technique (DFT-D2) was used throughout the computation. For the relaxation and electronic structure computations, the Brillouin zone was sampled using the Monkhorst–Pack k-point meshes of 9 × 9 × 1 and 11 × 11 × 1, respectively. To prevent the interlayer effect, an interlayer vacuum layer larger than 20 Å was established.

Phonon spectrum computations were carried out on 2 × 2 × 1 supercells using the Phonopy code’s finite displacement approach.61 With a plane-wave energy cutoff of 600 eV, the convergence requirements for the electronic and ionic minimizations were selected to be 10–8 eV and 10–3 eV Å–1, respectively. A Nose–Hoover thermostat with a period of 5 ps at 300 and 1000 K, respectively, and a time step of 1 fs was used in AIMD simulations in canonical ensemble (NVT) to verify the thermal stability. The lowest energy diffusion paths of Na atoms on the surfaces of graphene+ and M2C7 (M = B and Si) monolayers were searched by the climbing image nudged elastic-band (CI-NEB) method.62 The charge transfer was quantified using the Bader charge analysis.63 With the use of the Bilbao Crystallographic64 Server and the IRVSP algorithm,65 the symmetry of the crystal structure was examined. WANNIER90 software was used to calculate the tight-binding (TB) matrix elements by projecting Bloch states onto maximally localized Wannier functions.66

3. Results and Discussion

3.1. Geometric Configurations and Stabilities

A thorough investigation of the relaxed crystal structure and stability of the graphene+ monolayer was first conducted, as shown in Figure 1a, a square lattice with three distinct kinds of carbon atoms in the unit cell (P4/nmm space group, no. 129). The unit cell’s central sp3-hybridized carbon, designated as C1, is connected by four 5-membered rings. C2 is the designation of four comparable carbon atoms that are connected to the C1 atom. The remaining carbon atoms, C3, are shared by the rings with five and eight members. According to previous studies, the ideal thickness is 1.24 Å and the ideal lattice parameters are a = b = 6.64 Å.43 In this study, we selected sp2-hybridized C2 sites as the positions for doping and B and Si are commonly employed as dopants in graphene+ as shown in Figure S1. The corresponding doping systems are denoted as B2C7 and Si2C7, with their geometric configurations depicted in Figure 1b,c.

Figure 1.

Figure 1

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Top and side views of (a) graphene+, (b) B2C7, and (c) Si2C7 monolayers. The illustration shows three distinct carbon atoms, designated as C1, C2, and C3, represented by the blue, gray, and pink spheres, respectively, while doped boron (B) and nitrogen (N) atoms are shown by the dark green and purple spheres, respectively. The dashed lines in black emphasize the unit cell.

It should be noted that complete substitution with the same dopants at the C2 sites does not disrupt the inherent symmetry of graphene+. Obviously, the dopants induce slight changes in the lattice constants of the new carbides due to variations in the bond lengths between the dopants and their neighboring atoms. The bond lengths dC1–C2 in the pristine graphene+ are 1.56 Å, and the angle ∠θC2–C1–C2 of 99.09° brings a thickness of around 1.24 Å according to our calculations. Although the effective size of the B atom is smaller than that of the C atom, compared with the data of the pristine graphene+, the slightly longer bond lengths dC1–B in B2C7 (1.63 Å) lead to an about 4.8% larger lattice constant. In addition, the large effective size of the Si atom significantly increases the bonds dC1–Si to 1.89 Å, respectively. The increments maintain their thickness at the same level as Si2C7 and further increase the lattice constant of the new silicon carbide to 7.42 Å. To illustrate the differences of their geometric configurations more intuitively, the detailed lattice constant (a and b, Å), height (h, Å), bond lengths (d, Å), and bond angles (∠θ, °) are summarized in Table 1.

Table 1. Lattice Constants (a, in Å), Bond Length (d, in Å), Bond Angle (∠θ, in °), Thickness (h, in Å), Cohesive Energy (Ecoh, in eV per Atom), Formation Energy (Ecoh, in eV per Atom), and Elastic Constants (N/m) of the M2C7 (M = B and Si) Monolayers in Comparison to Pristine Graphene+.

system a H d ∠θ Ecoh Eform C11 C12 C66
graphene+ this work 6.64 1.24 1.56 99.09 –8.57 –4.77 140.54 55.69 118.69
doped B2C7 6.96 0.92 1.63 94.60 –8.08 –3.48 122.62 48.15 79.39
  Si2C7 7.42 1.70 1.89 101.51 –7.70 –2.59 96.11 49.26 66.97
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To verify the stability of M2C7 monolayers, systematic studies of their thermodynamic, dynamic, thermal, and mechanical stabilities were carried out. Initially, their cohesive energy was calculated to assess thermodynamic stability, and this may be approximated as follows:

3.1. 1

where Etotal, EM, and EC are the total energies of M2C7 (M = B and Si) monolayers and isolated B and Si atoms, respectively, and n/m is the number of M/C atoms in the unit cell. A more negative Ecoh of the materials indicates a higher thermodynamic stability. According to our calculations at the PBE level, the obtained Ecoh values of M2C7 (M = B and Si) monolayers are −8.08 and −7.70 eV/atom, respectively. Similar to the earlier work, we computed an Ecoh of −8.57 eV/atom for the pure graphene+.43 At the same theoretical level, these values are slightly smaller than those of tetrahaxcarbon (−8.38 eV/atom),67 Tubene (−8.90 eV/atom),68 penta-octa-graphene (−8.60 eV/atom),69 and even the experimentally synthesized graphdiyne (−8.46 eV/atom)70 and β-graphdiyne (−8.31 eV/atom).71 At the same time, the formation energy for the M2C7 (M = B and Si) monolayers are further calculated with the following equation: Eform = (Etot – nMEM – ncEc)/(M = B and Si), where Etot is the total energy of the M2C7 monolayers and EM and Ec are the energies per atom in the bulk phase, respectively. The numbers of M and C atoms in the unit cell are denoted by nM and nc, respectively. Exothermic processes are indicated by the obtained negative formation energies for the M2C7 monolayers (Table 1), ensuring that the experimental synthesis of M2C7 monolayers is feasible.

To verify the dynamical stability of M2C7 (M = B and Si) monolayers, the phonon dispersion curves were verified as depicted in Figure 2a–c, no negative imaginary frequency exists in the Brillouin zone indicating that they are dynamically stable. The maximum frequencies of M2C7 (M = B and Si) are estimated to be around 1370.79 and 1471.64 cm–1 at the Γ point, respectively. These are much higher than those of the MoS2 monolayer (473 cm–1)72 and black phosphorene (450 cm–1),73 but lower than those of graphene+ monolayer (1514.09 cm–1), suggests the strong binding properties than MoS2 and black phosphorene in M2C7 monolayers.

Figure 2.

Figure 2

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(a–c) Phonon dispersion and (d–f) phonon density states of the graphene+, B2C7, and Si2C7 monolayers, respectively.

AIMD modeling was used to assess the thermal stability of M2C7 (M = B and Si) monolayers at 300 and 1000 K, respectively, in a 3 × 3 × 1 supercell of 108 atoms. Figure S2 illustrates how the M2C7 (M = B and Si) monolayer framework may preserve structural integrity (for more than 10 ps at 300 K, Figure S3) during 5000 fs simulation durations with a time step of 1 fs. Their thermal stability above room temperature is confirmed by the absence of chemical bond breakage and structural repair.

Using the finite distortion approach, the independent elastic constant of M2C7 (M = B and Si) monolayers was calculated in order to further evaluate their mechanical stability.74Table 1 displays the computed results, which completely meet the Born–Huang requirements:75 (C11C22–C122 > 0 and C66 > 0). The M2C7 (M = B and Si) monolayers are, hence, mechanically stable as well. These findings imply that under certain experimental circumstances, the M2C7 (M = B and Si) monolayers have a high synthetic potential.

To further understand the stabilizing mechanism and bonding nature, we further investigated the electron localization function (ELF) to look at the electron distributions in real space. ELF values of zero (blue) generally indicate a location with low electron density, whereas ELF values of 1.0 (red) and 0.5 (green) reflect perfect localization and the free electron-gas, respectively. According to Figure S4, the red regions in the middle of the B/Si–C connection indicate that strong covalent bonds have formed and that there is a lot of electron aggregation between them. The existence of covalent bonds gives them excellent structural stability.

3.2. Mechanical Properties

The mechanical characteristics of M2C7 (M = B and Si) monolayers were further investigated in terms of calculating Young’s modulus Y(θ) and Poisson’s ratio υ(θ) using the following equation, which was based on the elastic constant:

3.2. 2
3.2. 3

where A = (C11C22–C212)/C66–2C12 and B = C11 + C12-(C11C22–C212)/C66. Y(θ) and v(θ) polar diagrams of the M2C7 (M = B and Si) monolayers are shown in Figure 3. The 2D polar representation curve clearly indicates that Young’s modulus of M2C7 (M = B and Si) monolayers are highly anisotropic. The values of Y(θ) of M2C7 (M = B and Si) monolayers increase from a minimum value of 103.71/70.86 N/m along the x/y direction to a maximum value of 164.56/139.41 N/m along the 45° direction. Note that the doping boron and silicon atom systems are significantly more flexible compared with the pristine graphene+ monolayer from a minimum value along the x/y direction (118.48 N/m) to a maximum value (214.85) along the 45° direction. These values are comparable to those of MoS2 (122 N/m)67 and silicene (61.7 N/m)76 but much lower than those of well-known 2D materials, such as graphene (341.60 N/m)77 and hexagonal h-BN (271 N/m),78 indicating that the M2C7 (M = B and Si) monolayers are softer than graphene and h-BN monolayers. Curiously, Figure 3d illustrates that the NPR phenomena are also visible in the pure graphene+ monolayer. To shed light on the origin of the mechanical properties of NPR, we analyzed the variations of thickness (h) in the graphene+ monolayer under uniaxial strains in the range of −4.5%–4.5% along the x-axial direction, and the increase of distance d between C1 and C2 atoms along the c direction leads to the mechanical behavior of NPR (Figures S5 and S6). The softer and auxetic behaviors are favorable advantages for the application of anode material.33

Figure 3.

Figure 3

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Calculated orientation-dependent Young’s modulus Y(θ) and Poisson’s ratio ν(θ) for (a,d) graphene+, (b,e) B2C7, and (c,f) Si2C7 monolayers.

3.3. Electronic Properties

After confirming the structural stabilities of M2C7 (M = B and Si) monolayers, we turned to investigate their electronic properties. The orbit-projected energy band structures and projected density of states (PDOS) are presented in Figures 4 and S7. We found the highest valence band (HVB) and lowest conduction band (LCB) of graphene+ and Si2C7 monolayers exhibit two linear dispersion Dirac cone at the Fermi energy level, respectively, and cross along the Γ–X and M−Γ high symmetry directions (denoted as N1, N2, N3, and N4), showing semimetallicity characters, and the electrons at the Dirac cone are mainly contributed by C_py+pz orbitals which is in agreement with the previous report.43 As seen in Figure 4a–c, the B2C7 monolayer, on the other hand, exhibits metallicity due to the Fermi energy level crossing the valence band and the C_py+pz orbitals providing the majority of the electrons near the Fermi energy level. The degree of freedom of spin may be disregarded in virgin graphene+ and Si2C7 monolayers, where the SOC-induced band gaps at N1/N2 and N3/N4 are only 1.71/1.52 and 1.90/2.20 meV, respectively, due to the relatively weak SOC in lightweight carbon and silicon elements (Figure S8). To verify the findings, we used the HSE06 functional as shown in Figure S9 to recalculate the band structures of graphene+ and Si2C7 monolayers. The retention of the semimetallic feature at the HSE06 level demonstrates the resilience of the Dirac linear dispersion characteristic.

Figure 4.

Figure 4

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Orbital projection electronic band structure of (a) graphene+, (b) B2C7, and (c) Si2C7 monolayers without including SOC. (d–g) Orbital projections near (d) N1, (e) N2, (f) N3, and (g) N4. DT4 and DT5 represent irreducible representations of the intersection bands near the nodes N1/N2 and N3/N4, respectively.

The 3D band structures of graphene+ and Si2C7 monolayers have been computed and displayed in Figure 5a,d to better illustrate the linear dispersion in reciprocal space. In the 3D BZ, the intersection of HVB and LCB results in a Fermi surface that resembles a lotus root. Instead of forming many degenerate node points, the crossing points create a nodal line. To shed light on the distribution features of the Dirac nodes across the BZ, we also constructed a TB model based on the maximum local Wannier function, as shown in Figure 5b,e, the nodal-line features are more easily understood in the color map of the energy differential between the HVB and LCB (Figure 5c,f). Thus, time-reversal and spatial inversion symmetries make graphene+ and Si2C7 monolayers a novel class of topological Dirac NLSMs.

Figure 5.

Figure 5

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(a,d) HVB and LCB’s 3D band structure for the graphene+ and Si2C7 monolayer, (b,e) band structures determined using the PBE functional and the TB model, and (c,f) the band gap contour plot between the LCB and the HVB.

As is known, the band crossing of most topological semimetals comes from band inversion, we can see that from Γ → N1 point, the energy of the pz state is lower than that of the py state, while from N1→ Χ point, the energy ordering between the pz and py state is changed and the energy band reversal occurs. For the Si2C7 monolayer, comparable orbital projection characteristics also show up close to the N2 point and N3/ N4 point. Along with the intersection of the HVB and LCB, their energy ordering exchanges, leading to the so-called band inversion. To understand the presence of band inversion, we further study the irreducible representation of the symmetry using the IRVSP code. The findings show that HVB and LCB along the high symmetry Γ–X lines for graphene+ and Si2C7 monolayers have distinct symmetric representations but belong to the same point group (D4h). Our conclusion that Si2C7 and graphene+ monolayers are topological Dirac NLSMs is further supported by Figure 4d–g. Two different irreducible representations, DT4 and DT5, are represented by the HVB and LCB along the high symmetry path Γ–X, respectively. These representations are essential components of the topological semimetals. Similar band crossings occur along the M−Γ high symmetry directions.

The Fermi velocity, which is often used to assess the carrier mobility, is another crucial characteristic of Dirac materials. The Fermi velocity of a Dirac cone may be obtained by fitting its linear energy band, which is described as υF = dE(k)/dk. PBE functional fits produced graphene+ values of 7.0 × 105 m/s and Si2C7 monolayer value of 5.0 × 105 m/s, respectively. These values are in the same magnitude compared with the Fermi velocity of graphene (9.42× 105 m/s),79 g-SiC3 (6.0 × 105 m/s),80 silicene (5.42 × 105 m/s),81 and germanene (5.3 × 10 5 m/s).82

3.4. Adsorption and Diffusion Properties for SIBs

Previous studies indicate that carbon-based 2D materials have potential as anode materials for SIBs because to their wide availability and low cost.36 Furthermore, because of their exceptional electrical conductivity, high Fermi velocity, and excellent stability, M2C7 monolayers provide ideal anode materials for SIBs.

To do this, we investigated in detail the adsorptions, diffusion behavior, specific capacity, open circuit voltage, and volume change of Na atoms throughout the Na ion insertion process in M2C7 monolayers. We also thoroughly examined the sodium storage ability in the pure graphene+ monolayer for comparison’s sake. Initially, to avoid interaction between nearby Na atoms, the adsorption sites for a single Na atom on the surface of M2C7 monolayers were investigated by using a 2 × 2 × 1 supercell. The adsorption energies (Eads) of a single Na atom on these monolayers are as follows:

3.4. 4

where ENa is the energy per Na atom in bulk sodium metal and Etotal and Esubs are the energies of graphene+/M2C7 (M = B and Si) monolayers with and without the adsorbed Na atoms, respectively. Our definition states that a more favorable exothermic interaction between M2C7 (M = B, Si) monolayers and the Na atom is indicated by a larger negative adsorption energy.

Based on the lattice symmetry, 13 representative sites are considered, as shown in Figure 1a–c. After conducting full optimizations, we identified four stable adsorption sites: H1, H2, T1, and T2, respectively. Notably, other Na atoms at different adsorption sites shifted toward these four sites during the relaxation process. Our findings showed that, the energetically most favorable adsorption site for the Na atom on the B2C7 monolayer is H1 with an adsorption energy (Eads) of −2.07 eV. On the other hand, the T1 site has Eads values of −2.04 eV, which is in accordance with Na on the pure graphene+ monolayer, which has Eads values of −1.99 eV. These sites are the preferred adsorption sites for Na on Si2C7 monolayers. Additionally, H1 (H2) sites are as the second most favorable adsorption sites for Na on Si2C7 (graphene+ and B2C7) monolayers as shown in Figure 6. These findings align with previous reports on recent report of Ca adsorption on the graphene+ monolayer.50 Meanwhile, the highly negative adsorption energies indicate that the adsorption processes of Na on the graphene+ and M2C7 (M = B, Si) monolayers are exothermic spontaneous reactions.

Figure 6.

Figure 6

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Adsorption energies of a single Na atom on the graphene+ and M2C7 (M = B and Si) monolayers at the four examined adsorption sites T1, T2, H1,and H2, respectively.

Figure 7a–c presents the fully optimized structures for the Na-adsorbed graphene+, B2C7, and Si2C7 monolayers at the energetically preferred adsorption site T1, H1, and T1, respectively. We found that the adsorption height (h) i.e., the vertical distance between the top-layer atoms and Na atom is 2.02, 1.10, and 3.22 Å for Na-adsorbed graphene+ and M2C7 (M = B and Si) monolayers, respectively. Obviously, the adsorption height (h) increased with the atomic number increasing from B to Si; however, the bond length (dNa–C/B) and adsorption energy (Eads) are inversely proportional to the atomic radii.

Figure 7.

Figure 7

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(a–c) Na-adsorption configurations that are the most stable from the top and side views. (d–f) The charge density varies for the most stable Na-adsorption topologies of graphene+ and M2C7 (M = B and Si) monolayers. Blue and yellow spots indicate electron accumulation and depletion; the iso-surface level is 0.002 e A–3.

To further understand the adsorption of Na on the graphene+ and M2C7 (M = B and Si) monolayers, we also use the following formula to analyze the charge density difference for a single Na atom adsorbed at the stable adsorption sites:

3.4. 5

where ρtotal and ρ– donate the total electron densities of the graphene+/M2C7 (M = B and Si) monolayers with and without Na atoms, respectively, and ρNa is the total electron density of the Na atom. In Figure 7d–f, the charge density graphs for the Na-adsorbed graphene+/Si2C7 monolayer at the T1 site and the Na-adsorbed B2C7 monolayer at the H1 sites are shown from the top and side perspectives. Between the Na atom and the graphene+/Si2C7 monolayers is where electron accumulation (yellow) occurs, and surrounding the Na atom is where electron depletion (blue) occurs. This implies that the Na atom transfers electrons to the graphene+/Si2C7 monolayers. This is because the Na atoms have a lower electronegativity (0.93) than the C (2.55), B (2.04), and Si (1.90) atoms. Furthermore, the charge transfer can be investigated by Bader charge analysis, and it is found that the Na atom transferred its entire valence electrons (0.91/0.88/0.77 e–, respectively) to the graphene+/M2C7 monolayers (M = B and Si), leading to a strong ionic interaction between them. The presence of hybridization between the Na atom and graphene+/M2C7 (M = B and Si) monolayers may be further examined from the PDOS of Na-adsorbed graphene+/M2C7 (M = B and Si) monolayers, as seen in Figure S10. It is encouraging that graphene+/M2C7 (M = B, Si) monolayers retain their metallic nature after Na adsorption. As a result, the pristine and Na-adsorbed doped graphene+ monolayers’ metallicity confers a highly desired property for their use as SIB anodes.

The rapid charge and discharge processes of SIBs correlate closely with the Na-ion diffusion velocity, which can be obtained by investigating the diffusion energy barrier of Na ions on the graphene+ and M2C7 (M = B and Si) monolayers. Hence, it is necessary to estimate the diffusion behavior of the Na atom on the surface of graphene+ and M2C7 (M = B and Si) monolayers. For graphene+ and Si2C7 monolayers, the diffusion behavior of Na atoms between the two most stable adsorption sites next to one another is shown in Figure 8a,c,e. Path 1 (T1 → H1 → T1), Path 2 (T1 → T1/T2 → T1), and Path 3 (T1 → H2 → T1) are the three probable pathways for such diffusion in graphene+ and Si2C7 monolayers, as shown by the green, blue, and pink arrows. For the B2C7 monolayer, three possible diffusion paths with neighboring energetically most favorable adsorption sites (site H1): Path 1 (H1 → T1 → H1), Path 2 (H1 → H2 → H1), and Path 3 (H1 → T2 → H1), as marked by green, blue, and pink arrows, respectively. Figure 8b,d,f shows the energy profiles for Na diffusion across graphene+ and M2C7 (M = B and Si) monolayers over the investigated diffusion paths. It is evident that the Na ion diffusion from one adsorption site T1 to another neighboring adsorption site T1 with an energy barrier of 0.16/0.14 eV along Path 1, 0.25/0.33 eV along Path 2, and 0.32/0.33 eV along Path 3 for graphene+/Si2C7 monolayers, respectively. The diffusion energy barriers of the Na ion for the B2Si7 monolayer are 0.31, 0.40, and 0.30 eV along Path 1, Path 2, and Path 3 directions, respectively. It should be noted that Path 3 has the lowest diffusion energy barrier for B2C7 monolayers, whereas Path 1 has the lowest for graphene+ and Si2C7 monolayers. As an anode of SIBs, these barriers are close to those in T-graphene (0.41 eV)28 and Θ-graphene (0.39 eV)30 and have significant advantage over commercial electrodes TiO2 (0.45–0.65 eV).83 Hence, they have potential applications in large-grid-scale energy storage devices.

Figure 8.

Figure 8

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(a,c,e) Diffusion pathways and (b,d,f) energy profiles of Na diffusing on the graphene+, B2C7, and Si2C7 monolayers, respectively.

Although electrolytes are crucial in regulating SIB performance, the majority of earlier theoretical research has concentrated on evaluating the performance of anode materials in vacuum.84 To delve deeper into the stability and sodium ionic transport properties of the graphene+ and M2C7 material in electrolytes, we specifically focused on the influence of the DMC (dimethyl carbonate) electrolyte on sodium ion adsorption and diffusion in graphene+ and M2C7 monolayer materials. The electrolytes that are mostly taken into consideration in this research include ethylene carbonate (EC), propylene carbonate (PC), butylene carbonate (BC), vinylene carbonate (VC), dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), and diethyl carbonate (DEC).85Figure S11 illustrates that, from an energy point of view, the conduction band minimum (CBM) energies of the monolayers are all lower than the LUMO energies of the seven widely used electrolytes. This suggests that the electrons in the monolayers do not leap to the electrolytes’ LUMO. This characteristic effectively prevents electrons from being directly injected from the anode material M2C7 into the electrolyte during charging or discharging, thereby significantly reducing the risk of deactivation of the M2C7 anode material. Additionally, using the DMC electrolyte as an example, we thoroughly examined how the dielectric constant affects the adsorption energy and diffusion energy barrier. Our computations for the widely used electrolyte solvent dimethyl carbonate (DMC) show that as DMC is added, the adsorption energy progressively rises, but the energy barriers for each diffusion channel tend to fall. This finding suggests that the electrolyte solvent DMC promotes the adsorption and migration of sodium ions on the surfaces of graphene+ and M2C7 materials. Above research indicated that the electrolyte solvent DMC is advantageous for the adsorption and migration of Na ions on the surface of graphene+ and M2C7.

3.5. Theoretical Storage Capacity and Average Open-Circuit Voltage

In practical applications, the theoretical storage capacity (C) and average open-circuit voltage (OCV) are two important indicators for evaluating high-performance anode materials. We then explored the maximum storage capacity and average open-circuit voltage of Na-adsorbed graphene+ and M2C7 monolayers. To estimate the maximum possible storage of Na atoms, we calculated the average adsorption energies (Eave), which is defined as:

3.5. 6

where x is the chemical content of adsorbed Na atoms per unit cell, while Etotal, Esubs, and ENa are the total energies of Na-adsorbed graphene+/M2C7 (M = B and Si) monolayers, the pristine graphene+/M2C7 monolayers, and the energy per Na atom in bulk sodium metal, respectively. In general, Eave decreases gradually as the number of Na atoms increases, ideally, if Eave is less than 0 eV/atom, anode material may be able to continue adsorbing Na atoms. In the meanwhile, the following formula was used to determine the matching maximal theoretical capacity of Na atoms:

3.5. 7

where F is the Faraday constant (26,801 mA h mol–1), Msubs is the molar mass of graphene+ and M2C7 (M = B and Si) monolayers, and xmax represents the maximum adsorption concentration of Na atoms on the graphene+ and M2C7 (M = B and Si) monolayers.

We progressively introduced the Na atoms one by one to the graphene+ and M2C7 (M = B and Si) (M = B and Si) monolayer surfaces to simulate the battery charging process. The first layer of Na interaction for graphene+/B2C7/Si2C7 monolayers takes place at the T1/H1/T1 sites, respectively; after the most stable adsorption places are completely occupied, the subsequently adsorbed Na atoms form a second and a third layer. Additionally, we computed the formation energy (Ef), which is defined as follows, for different sodium concentrations on the graphene+ and M2C7 (M = B and Si) monolayers to identify the most stable configurations for each concentration:

3.5. 8

where Etotal, Esubs, and ENa are total energy of with/without Na-adsorbed graphene+/M2C7 (M = B and Si) monolayers and the energy per atom in the bulk metal Na, respectively, and x refers to the chemical content of adsorbed Na atoms on the graphene+ and M2C7 (M = B and Si) monolayers. The formation energies of the configurations under study lie on the solid line of the convex energy hull, as shown in Figure S12. This suggests that the compounds are formed spontaneously and that the configurations are thermodynamically stable with a negative formation energy.

Here, the 2 × 2 × 1 supercell is presented as an example to illustrate the successive adsorption of Na atoms on the graphene+ monolayer (18 atoms in a unit cell). Attaching a Na atom at site T1 on one surface of graphene+ results in a low-limit chemical formula Na0.25C18. Our calculations show that Na atoms tend to bond to both surfaces of the graphene+ monolayer when occupying the T1 site (see in Figures S13–S15). After all the T1 site of two surfaces are occupied, Na atoms started to occupy the H2 sites in the second Na atom layer, and the T1 sites in the third Na atom layer. Thus, the several possible configurations with both surfaces exposed to Na atoms were carefully considered for NaxC18 systems with higher x values (x = 0.25, 0.5, 0.75, 1, 2, 4, 6, 8, 10, and 12), and the most stable configurations for each concentration are shown in Figure 9a–h. The same approach was used to construct NaxB2C7 and NaxSi2C7 systems (Figures S16–S21), and the most stable configurations of NaxB2C7 and NaxSi2C7 are displayed in Figures S22 and S23, respectively.

Figure 9.

Figure 9

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Top and side views of the most stable structures with different Na concentrations in the graphene+ monolayer. (a) Na0.5C18; (b) Na0.75C18; (c) NaC18; (d) Na2C18 (e) Na4C18; (f) Na6C18; (g) Na8C18; and (h) Na12C18. (i) Average adsorption energy and (j) OCV with the increase of Na content on the graphene+ and M2C7 (M = B and Si) monolayers.

The average adsorption energy varies with the increasing Na (x) concentration, as seen in Figure 9i. Because of the Coulomb contact between Na atoms, there is a general tendency that the average adsorption energies for Na drop as the Na content x increases. For the B2C7/Si2C7 monolayer, the first Na-adsorption layer is formed by placing Na at the most favorable sites (H1/T1) on both sides with an Eave of −0.46/–0.53 eV (the composite is Na2B2C7/Na2Si2C7), suggesting the feasibility of adsorbing the second Na layer. The Eave of the second Na layer with Na adsorbing is −0.15/–0.43 eV and the corresponding configurations are Na4B2C7 and Na4Si2C7. The Eave for the third Na layer configurations of Na6B2C7/Na6Si2C7 is −0.097/–0.12 eV, respectively. When adding the fourth layer on both sides, the Eave is −0.052/–0.11 eV, and the composites are Na8B2C7 and Na8Si2C7. However, for the graphene+ monolayer, attaching the Na atom at favorable sites (T1) on both sides of the graphene+ monolayer forms a first layer with an Eave of −0.77 eV, the chemical formula is Na4C18. The Eave of the second layer with Na atoms locating at site H1 is −0.09 eV and the corresponding chemical formula is Na8C18. The third Na layer with Na atom adsorption at site T1 on both sides has an Eave of −0.04 eV with the chemical formula Na12C18. As Na12C18, Na8B2C7, and Na8Si2C7 represent the highest Na storage capacities for graphene+, B2C7, and Si2C7 monolayers, we can easily deduce the corresponding maximum storage capacities are 1487.70 mA h g–1, 2028.65 mA h g–1, and 1528.76 mA h g–1, respectively, which are higher than those of many currently reported carbon-based anode materials for SIBs, such as Θ-graphene (1275.1 mA h g–1),30 xgraphene (1302.0 mA h g–1),33 Hd-graphene (1116.7 mA h g–1),86 biphenylene (1075.4 mA h g–1),25 α-graphene (1395.89 mA h g–1),87 twin-graphene (496.2 mA h g–1),88 SiC2 (1203 mA h g–1),89 Si2C4 (514.3 mA h g–1),90 SiC3 (686 mA h g–1),91 BC3(582.63 mA h g–1),92 and many more as shown in Figure 10, which ensures excellent mobility of ions across monolayers. Above results indicate they have potential as ultrafast diffusion and high storage capacity anode materials for SIBs.

Figure 10.

Figure 10

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Comparison of storage capacity and diffusion energy barrier of graphene+ and M2C7 (M = B and Si) with previously reported typical 2D anode materials for SIBs.

The average OCV for Na intercalation on graphene+ and M2C7 (M = B and Si) monolayers was further investigated. As the charge/discharge processes of graphene+ and M2C7 (M = B and Si) follow the common half-cell reaction vs Na/Na+, when the volume and entropy effects are both neglected, the OCV for Na intercalation in graphene+ and M2C7 (M = B and Si) monolayers can be derived from the average adsorption energy (Eave) as:

3.5. 9

where n is the number of valence electron (n = 1 for Na), the voltage profiles as a function of the Na concentration (x) as shown in Figure 9j, which decreases from 0.16 to 0.04 V for graphene+ and from 0.25 to 0.05 V for B2C7; while for Si2C7, the OCV value increases from 0.41 to 0.43 V and then decreases from 0.43 to 0.11 V. The corresponding average OCVs are 0.09, 0.14, and 0.27 V for graphene+, Si2C7, and B2C7, respectively, which are lower than commercial anode material TiO2 (1.80 V),79 and meet the requirement of a suitable anode working potential below 1.0 V.93 The results of low OCVs suggest that graphene+ and M2C7 materials have potential applications as anode materials for SIBs.

Last but not least, the potential cluster formation brought on by the sodiation process that might result in battery failure is another crucial element to take into account in SIBs. Therefore, it is crucial to thoroughly examine whether, at such a high concentration of Na adsorption, the Na atoms will cluster on the graphene+ and M2C7 (M = C, B, Si) surfaces. At 300 K for 5 ps, the thermal stabilities of Na12C18, Na8B2C7, and Na8Si2C7 were examined using AIMD simulations (refer to Figure S24).

After 5 ps simulations, the Na12C18, Na8B2C7, and Na8Si2C7 structures do not exhibit substantial deformation, suggesting that they exhibit high stability throughout the sodiation process at room temperature. In addition, there are negligible volume changes caused by the sodiation process, resulting in a slight volume change of less than 0.3%, 1.0%, and 0.27%, which indicate that graphene+ and M2C7 (M = B and Si) monolayers can accommodate Na ions reversibly and are favorable for battery applications.

4. Conclusions

In conclusion, using first-principles calculations, pristine graphene+ and doped graphene+ named M2C7 (M = B and Si) monolayers are systematically investigated as anode materials for SIBs. The AIMD simulations, phonon dispersion curves, and elastic constants indicate their thermal, dynamical, and mechanical stability, respectively. More interestingly, we found that graphene+ and Si2C7 possess Dirac NLSM characters based on the analysis of the crystalline symmetries in irreducible representation, and the B2C7 monolayer exhibits metallic properties. In addition, the graphene+ and M2C7 (M = B and Si) monolayers possess a high reversible capacity of 1487.70, 2028.65, and 1528.76 mA h g–1, a low diffusion energy barrier of 0.16, 0.14, and 0.29 eV, and a small volume change of 0.3%–1.0% as anode materials for SIBs. Our work provides a systematic study of using topological nodal-line carbon as the anode material, shedding light on the development of next-generation SIB anodes.

It is observed that 2D anode materials offer exceptional potential as primary materials for SIBs in large-scale energy storage systems. However, the technology for producing SIBs is still in its early stages. Current theoretical descriptors may be used to determine or estimate the ground-state structure, adsorption sites, diffusion barriers, and capacity of 2D materials. Nonetheless, one of the pressing needs is to establish effective descriptors to assess the practicality of the generated materials. For instance, although electrode materials work within an electrolyte, current calculations are done in a vacuum. Furthermore, the material’s chemical composition has a big impact on its properties. Furthermore, the majority of 2D materials now on the market are not beneficial for out-of-plane ion migration because their pores are not sufficiently broad. If further 2D materials with low in-plane and out-of-plane metal ion migration barriers can be developed and subsequently used, their efficacy as electrode materials for SIBs will be significantly increased. In conclusion, it is impossible to ignore the difficulties involved in using 2D materials in SIB anodes. However, we are confident that through persistent efforts and innovation, we will overcome these challenges and propel the development of SIB technology.94,95

Acknowledgments

This work was funded by the Inner Mongolia Autonomous Region’s Higher Education Scientific Research Project (no. NJZY21564), the Inner Mongolia Autonomous Region Natural Science Foundation’s Key Project Funding (no. 2023ZD27), and the High Level Introduction of Talent Research Start-up Fund (no. 5909002405).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c09865.

  • Phonon dispersion curves of B and Si atom doping in the C1 and C3 sites; final structures (side view) of Si2C7, B2C7, and graphene+ monolayers using a 10 ps AIMD simulation at 300 K and a 5 ps AIMD simulation at 300 and 1000 K; (001) slices of graphene+, B2C7, and Si2C7 monolayers’ ELF maps; half-NPR’s geometric progression; structural properties of graphene+ with uniaxial strain varying from −4.5% to 4.5%; PDOS and band structures for Si2C7, B2C7, and virgin graphene+ monolayers; electrical band structures of graphene+ and Si2C7 monolayers, including SOC; band structures of graphene+, B2C7, and Si2C7 monolayers based on the HSE06 functional; PDOS of graphene+, Na-adsorbed Si2C7, and B2C7 monolayers; formation energies (Ef); optimized configurations and corresponding average adsorption energies for different concentrations of Na-adsorbed M2C7; CBM and LUMO energies, adsorption energies, and diffusion energy barriers of Na on graphene+, B2C7, and Si2C7 monolayers with and without solvent; andfinal structures of the Na-intercalated M2C7 monolayers through a 5 ps AIMD simulation at 300 K (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao4c09865_si_001.pdf (1.9MB, pdf)

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