Structural analysis of Graphsene
The conventional lattice of the nanosheet is obtained by repeating 20 carbon atoms in the x-y plane through the two orthogonal lattice vectors of a = 10.07 Å and b = 6.40 Å. The planar carbon density of GrS is calculated to be 0.31 carbon/Å2. Accordingly, Graphsene has a higher density than graphyne family (0.19–0.27 carbon/Å2) and less than graphene (0.38 carbon/Å2 ) and phagraphene (0.37 carbon/Å2) .
The GrS structure features three distinct carbon atoms labeled C1, C2, and C3, as shown in Fig. 1(c). Additionally, five distinguishable C-C covalent bonds fall within the typical range found in previous carbonaceous monolayers (1.38–1.48 Å).
GrS's unique porosity arises from the sharing of 4-, 5-, and 12-carbon rings, contributing a strong anisotropic character to the monolayer. Both armchair and zigzag directions are indicated in the rectangular morphology along the x and y directions, respectively.
The total internal energy of GrS per atom is calculated to be -8.48 eV/atom. This parameter is comparable to α-graphyne (-8.30 eV/atom), β-graphyne (-8.38 eV/atom), phagraphene (-9.03 eV/atom), and biphenylene (-7.55 eV/atom)18, 20. It can be concluded that GrS exhibits superior stability compared to its predecessors. A correlation between atomic density and higher structural stability in two-dimensional carbonaceous nanostructures has been established in previous studies that is confirmed by our results 20. Consequently, GrS can be considered a stable material from a structural standpoint.
Graphsene stability
Assessing the stability of an unknown material from dynamical, mechanical, and thermal perspectives provides insights into its feasibility for synthesis.
The mechanical behavior of a material explains its response to external forces and its ability to resist deformation. To investigate the mechanical stability and elastic behavior of GrS, the second-order elastic stiffness tensor (Cij) was calculated for the orthodromic nanosheet. The mechanical stability of a crystal is confirmed by meeting specific criteria between the Cij elements. The entire evaluated stiffness tensor, as a 6×6 matrix, is provided in Table S1, with all dominant elements determining mechanical stability listed in Table 1. It is evident that for the given parameters, the elastic stability condition proposed by Coudert et al.38, is satisfied: C11C22 – C122 > 0, C44 > 0 and C66 > 0. Thus, GrS fulfills the elastic stability conditions derived from Born elastic criteria, confirming its mechanical stability.
Table 1
The dominant stiffness tensor elements regarding the mechanical stability. The unit of parameters is GPa
C11 | C12 | C21 | C22 | C44 | C66 |
79.51 | 21.08 | 21.08 | 187.36 | 0.145 | 27.58 |
The calculated Cij elements indicate anisotropic behavior of the mechanical property, which is in agreement with different atomic arrangements along the zigzag and armchair directions. To gain a deeper insight into the mechanical characteristics, the orientation dependence of Young’s modulus E(θ) and Poisson’s ratio ν(θ) are computed ,using (S1) and (S2), then are shown in Fig. 2. The polar diagrams of E(θ) and ν(θ) confirm the anisotropic behavior of the mechanical properties of GRS in the x-y plane.
The calculated Young’s modulus along the x-direction (Ex) and y-direction (Ey) are 181.8 and 77.1 GPa, respectively. Accordingly, GrS has a more flexible behavior along the armchair direction than the zigzag one.
Next, the dynamical stability of GrS was verified through phonon dispersion calculations. As the primitive unit cell of GrS deviates from a hexagonal Bravais lattice, more high-symmetry points can be identified in the first Brillouin zone of GrS, as shown in Fig. 3(a). Figure 3 (b) depicts the phonon dispersion of GrS along the specified high-symmetry points. The lack of imaginary frequency in the phonon dispersion confirms the dynamical stability of the proposed nanosheet. The first optical phonon mode appears at a relatively small frequency of 6.92 THz in the acoustic phonon region resulting in low thermal conductivity originated from high level of porosity in GrS.
By employing ab-initio molecular dynamic (AIMD), one can determine a material's characteristics from stability point of view at non-zero temperatures. To study the thermal stability of GrS, AIMD calculations
were performed at 300 K. The calculated free energy profile is plotted in Fig. 4(b). Based on the AIMD results, GrS maintains its original atomic configuration at 300 K. Structural analysis indicates that different geometrical parameters, such as bond length and bonding angles, do not experience significant changes. Due to the dynamical, mechanical and thermal stability, synthetic routes could be utilized for successful fabrication of GrS.
Electronic properties of graphsene
The electronic band structure and total density of states (DOS) of GrS for the rectangular crystal system are presented in Fig. 5. GrS exhibits semiconducting behavior with a small band gap of 20 meV in the HSE06 exchange correlation framework, as depicted in Fig. 5(a). The narrow band gap is observed at the high-symmetry point M. A Dirac-like cone has been obtained at this point with high anisotropy behavior. Accordingly, the Fermi velocity along x-direction is much higher than y-direction. The same phenomena was reported in carbon-based nanosheet with varied carbon-ring sizes39.
The distribution of the valence band maximum (VBM) and conduction band minimum (CBM) is illustrated in Fig. 5(b), with C2 and C3 contributing the most to the frontier electronic states. These carbons, unlike C1, display deviation from ideal sp2 hybridization and their strained nature plays a crucial role in the material's activity. Partial density of states (PDOS) plots for three, indicated in Fig. 5(c), confirms the dominant role of C2 and C3 around Fermi level. Same as previous findings, pz orbitals, ,involved in forming π and π* bonds, mostly contribute to determine electronic properties of in-plane extended carbonaceous materials, as revealed in Fig. 5(c). The orbitals of px, and py actively contribute to the deep bands through the hybridization of σ bonds.
Computed electronic properties in the PBE approach, show several electronic bands crossing the Fermi level, indicating metallicity in GrS, exhibited in figure (S1). In this regard, an observable band gap opening could be recognized at the Γ point after performing hybrid functionals. Here, one can find urgency of incorporating hybrid functionals to predict accurate electronic features of nanomaterials. The electronic localization function (ELF) plot in Fig. 5(d) from the (0 0 1) perspective reveals a strong covalent bond between carbon atoms in GrS.
Electrocatalytic activity of Graphsene
To assess the catalytic potential of Graphsene in the Oxygen Reduction Reaction (ORR), the thermodynamics of the ORR processes were investigated by calculating the ΔG for individual steps along the reaction pathway. In an acidic solution, the electrode reactions concerning ORR processes involves O2 + 4(H++e−) → OOH + 3(H++e−) → O + 2(H++e−) + H2O → OH + (H++e−) + H2O→2H2O, while in alkaline solution that can be expressed as O2 + 2H2O + 4e− → O + *OOH + H2O + OH− + 3e−→ *O + 2OH− + H2O + 2e− → OH + 3OH− + e− → 4OH−. These reactions illustrate the distinct pathways that the ORR follows in acidic and alkaline solutions, highlighting the importance of understanding these variations in catalytic
processes. In acidic conditions, the overall ORR process can be summarized as O2 + 4H+ + 4e− → 2H2O (see Fig. 6). The process initiates with the hydrogenation of the O2 molecule, involving the adsorption of a proton and the transfer of an electron, ultimately forming an *OOH species adsorbed on the graphsene surface.
Our findings reveal that the formation of *OOH on graphsene is energetically favorable, as indicated by a negative free energy change. Specifically, at pH = 0, there is a notably large ΔG of -0.706 eV for the formation of the *OOH species, underscoring the high reactivity of O2 on the proposed nanostructure. It is noteworthy that the carbon atom positioned beneath the adsorbed oxygen atom undergoes a displacement, moving out of the graphsene sheet's plane and toward the oxygen atom.
This displacement leads to a buckling effect of approximately 0.48 Å above the graphsene plane, as illustrated in Fig. 6 for the C20OOH configuration. The primary factor contributing to this out-of-plane buckling of the graphsene sheet is the alteration in its electronic structure. Specifically, the graphsene transitions from a planar, sp2-hybridized configuration to a distorted sp3-hybridized geometry. This transformation results in an increase in adsorption energies. Following the formation of the first H2O molecule, any remaining *O species can undergo further hydrogenation to yield an *OH group. This hydrogenation process is exothermic, with the most negative ΔG value (-0.94 eV) occurring at pH = 0. In the final step, the *OH species can react with the fourth electron/proton pair to produce the second H2O molecule. All these reactions exhibit negative ΔG values for each step, indicating that the ORR process is energetically favorable at zero potential. Ideally, the overall ORR steps should generate 1.23 V per electron to ensure that the free energy change for each elementary step is zero at the equilibrium potential of 1.23 V. Otherwise, an unfavorable overpotential would arise. In the case of graphsene, both the elementary and final steps become endothermic at the equilibrium potential of 1.23 V, suggesting the presence of an overpotential. The step with the largest ΔG value is known as the rate-determining step (RDS) and dictates the value of UL. As depicted in Fig. 6, the RDS is the formation of *OOH (the first electron transfer step) for pH values ranging from 0 to 5. Graphsene exhibits increasing UL values in the order of 0.52 (pH = 0) < 0.58 (pH = 1) < 0.70 (pH = 3) < 0.82 (pH = 5), underscoring its excellent catalytic activity at pH = 5.
In an alkaline condition, the entire reaction process can be succinctly summarized by the equation O2 + 2H2O + 4e− → 4OH−. Within this context, our focus centers on the associative a proton and electron transfer pathway, wherein the adsorbed O2 molecule initially tends to form *OOH and OH− (H2O act as the proton donor). Subsequently, the *OOH species undergoes further dissociation, giving rise to *O and OH−. The *O species then reacts with H+ (from H2O) to produce *OH, which eventually transforms into OH− through
the last electron-transfer step. Similar to the effects observed in acidic conditions, pH exerts a comparable influence, elevating the energy levels of each proton and electron transfer step. As depicted in Fig. 6, at U = 0 V, all reactions at different pH values are exothermic, with the exception of the adsorbed O2 molecule reacting with H2O, which becomes endothermic at pH = 14. When an ideal electrode potential of 0.40 V is applied, both the elementary and final steps become endothermic, indicating the presence of an overpotential. Notably, the reaction between the O2 molecule and H2O is identified as the RDS of the ORR under alkaline conditions, and the energy barrier increases with rising pH values, following the order of -0.52 (pH = 14) < 0.23 (pH = 9) < 0.34 (pH = 11). This observation suggests that ORR in a moderately alkaline environment is more favorable for graphsene. In summary, our findings highlight that graphsene exhibits substantial catalytic activity for the ORR in both acidic and alkaline solution, underscoring its versatility and potential for various electrochemical applications.