First-principles study of peroxides effects on β₁₂-borophene cathode for efficient lithium and sodium oxygen batteries

Abstract

The shift to clean energy is crucial in mitigating the harmful effects of fossil fuels on the environment. Nevertheless, as we embrace clean energy sources, particularly solar and wind energies, high-energy-density storage devices like lithium and sodium-oxygen batteries are essential. However, challenges such as the irreversibility of lithium and sodium peroxides and their non-conductivity nature on the cathode electrode hinder practical use. 2D materials, particularly {\beta }_{12}-borophene, show promise in addressing these challenges. In this study, we used density functional theory to thoroughly investigate the adsorption mechanisms of alkali-metal peroxides and their impact on the electronic properties of the {\beta }_{12}-borophene. Our results revealed adsorption energies of −3.71 and −3.54 eV for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, respectively, showing that the adsorbed peroxides are stable and unlikely to decompose into the electrolyte. The calculated Gibbs free energy changes that revealed low overpotentials of 1.03 V for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 1.61 V for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2. Moreover, even with increased concentrations of peroxides on the surface, {\beta }_{12}-borophene retained its ability to adsorb additional peroxides, achieving theoretical voltages of 2.60 V for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 2.04 V for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2. Notably, the metallic nature of {\beta }_{12} remained stable despite the adsorption of peroxides, evidenced by an increase in electronic states around the Fermi level and the overlap of the valence and conduction bands. Furthermore, thermal stability analysis at 300 K confirmed that the structure of {\beta }_{12}-borophene remained intact, reinforcing its suitability as a cathode at standard temperature of the battery. The low diffusion energy barriers of 1.04 and 0.92 eV were obtained for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, respectively, suggesting a high rate of peroxides migration on the substrate surface. The dissociation energy barriers for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 were found to be minimal at 1.86 and 1.69 eV, respectively, indicating the catalytic effects and enhancing electrochemical processes. Our findings suggest that {\beta }_{12}-borophene can be a potential cathode electrode for the next-generation lithium and sodium-oxygen batteries.

Graphical abstract

Keywords

β ₁₂-borophene / density functional theory / lithium and sodium oxygen batteries / diffusion energy barrier / peroxides

1 Introduction

The significant use of fossil fuels is undeniably contributing to the production of toxic gases such as carbon dioxide (\mathrm{C}{\mathrm{O}}_2), which is directly responsible for the challenges facing global food security due to climate change [1]. The devastating impact of these gases is particularly evident in the struggles of farmers who rely on rain-fed agriculture. Alterations in rainfall patterns have unequivocally led to widespread floods and droughts in numerous parts of the world, posing an undeniable threat to food security [2-4]. The shift from fossil fuels to clean energy sources like wind and solar energy is a vital step in tackling today’s climate change challenges [5, 6]. One crucial aspect of this transition is the storage of energy generated from wind and solar sources. In that regard, the energy density of storage systems, especially batteries, plays a key role in effectively harnessing clean energy. Among the various types of batteries, alkali-metal ion batteries, such as lithium-ion batteries (LIBs), are known for their high energy density [7, 8]. Consequently, they have become the most widely used energy storage systems in modern technologies, including electric vehicles and portable devices [9, 10]. However, with technological advancements, it has become increasingly evident that LIBs have limitations in satisfying growing energy demands. Thus, efforts are currently being made to enhance the energy and power densities of various alkali-metal and other metal batteries, including sodium-ion [11, 12], potassium-ion [13, 14], and magnesium-ion [15-17] batteries. These alternatives are gaining attention due to their favorable characteristics, such as lighter weight, abundant element availability, and similarities in electrochemical processes to state-of-the-art lithium-ion batteries (LIBs). Researchers are actively testing, investigating, and tailoring a range of materials as potential electrodes since the choice of electrode is critical in determining a battery’s energy density [18-21]. Additionally, alkali-metal oxygen-based batteries, particularly those using lithium and sodium, present a promising energy storage solution due to their high specific capacities. Their cost-effective mechanisms utilize ambient air, making them a compelling alternative to traditional alkali-metal-ion batteries. Notably, oxygen is one of the most abundant elements on Earth and serves as the primary active material in the porous cathode of these systems [22-25].

Despite their potential for high specific capacity and cost-effectiveness, the practical realization of alkali-metal oxygen batteries faces challenges, including the electrochemical irreversibility of formed peroxides (discharge products) and the poor conductivity of cathode electrodes caused by these non-conducting discharge products [26]. In response to the challenges mentioned earlier, extensive studies are currently being conducted to identify potential electrode materials. One particularly promising material is graphene, which was discovered in the early 2000s by Novesolov et al. [27]. Building on this success, various techniques are now being employed to exfoliate and synthesize graphene [28-30]. Graphene has garnered significant attention for its potential applications in various electronic systems, particularly in energy storage technologies such as lithium and sodium air batteries [31-34], for sensing toxic gases [35, 36], and water splitting technology [37, 38].

Based on the achievements of graphene, researchers are currently exploring other 2D materials such as silicene [39, 40], germanene [41], phosphorene [42, 43], and Mxene [44, 45], which demonstrate significant potential for similar applications. Furthermore, the impressive accomplishment of isolating and producing 2D boron materials (borophenes) by Mannix et al. [46] has ignited extensive research into their potential uses in electronics. This is due to their exceptional metallic, mechanical, optical, dynamic, and thermodynamic properties. These materials are poised to revolutionize various systems, particularly in the realm of energy storage. With 2D boron polymorphs such as {\beta }_{12} and {\chi }_3-borophene, the remarkable stability and potential electronic applications specifically for {\beta }_{12}-borophene have been demonstrated through first-principles calculations [47, 48]. It has shown promise as a cathode electrode material for enhancing electrochemical processes in the lithium-superoxide based battery [49], a gas sensor for capturing toxic gases [50], and a cathode electrode in lithium−sulfur batteries [51]. Despite numerous reports on the electronic applications of {\beta }_{12}-borophene. However, there is scarce information on its potential to improve oxygen reduction reactions (ORRs) and serve as an electrode in lithium and sodium-oxygen batteries (LOB and SOBs). This exceptional 2D material could be the ideal candidate for addressing the challenges of irreversibility in electrochemical processes and the insulation of cathode electrodes [26], because of its excellent metallic and other properties necessary for electrode materials [52, 48].

In this study, we used density functional theory to explore the adsorption mechanisms of peroxides and their catalytic influence on {\beta }_{12}-borophene as a cathode material, aiming to enhance the efficiency of lithium and sodium oxygen batteries. We started our investigations by systematically optimizing the configurations of lithium and sodium peroxides on {\beta }_{12}-borophene. After establishing the stable configurations, we gradually increased the concentrations of the peroxides and examined the resulting variations in adsorption energies and voltages. Subsequently, we calculated charge density distributions to analyze the charge transfer dynamics between the peroxides and the substrate. Additionally, we evaluated the density of states (DOS) to confirm the metallic characteristics both before and after the adsorption of the peroxides. To assess the structural integrity of the system, we utilized ab initio molecular dynamics (AIMD) to investigate its thermal stability following the adsorption. We also characterized the diffusion and decomposition energy barriers associated with the peroxides. Finally, we compared our findings to previously reported results concerning the behavior of peroxides on other two-dimensional materials, offering a comprehensive view of the potential of {\beta }_{12}-borophene as a cathode in battery applications.

2 Computational methods

In this study, all the first-principles density functional theory (DFT) calculations were performed using quantum ESPRESSO [53, 54]. By adopting spin-polarised generalized gradient approximation (GGA) [55, 56] within the functional of Perdew−Burke−Ernzerhof (PBE) [57, 58], the exchange and correlation energy of interacting electrons were treated. Using the projector augmented wave (PAW) potential [59], core electrons for the system were described. After the convergence tests, a kinetic energy cut-off of 50 Ry was set to solve Kohn−Sham equations, with a plane-wave basis set. Upon adopting the Monkhorst-pack scheme, we sampled k-points of 13 × 9 × 1 within the Brillouin zone [62, 63]. Systems optimization was achieved until all the positions of atoms had converged within an energy difference of {10}^{-6} eV, and Hellman−Feynman force convergence was set to {10}^{-7} eV/Å. For the smearing of electrons, we used the Methfessel and Paxton (MP) occupational function [64]. To account for the van der Waals interactions arising from the presence of lithium and sodium peroxides on the {\beta }_{12}-borophene surface, we implemented the DFT-D3 correction according to the Grimme scheme [65]. To mitigate the effects of periodic images of the {\beta }_{12}-borophene supercell, which is of size 3 × 2 and consists of 30 boron atoms, we incorporated a vacuum space of 15 Å in the z-direction. For calculating the adsorption energy of the peroxides, we used the following equation:

(1)\begin{array}{rl}& E_{adsorption}\\ & =\frac{E_{(peroxide+{\beta }_{12}\text{-}borophene)}-E_{{\beta }_{12}\text{-}borophene}-n{E}_{peroxide}}{n}.\end{array}

In this equation, E_{(peroxide+{\beta }_{12}\text{-}borophene)} refers to the total energy of the complex system, E_{{\beta }_{12}\text{-}borophene} represents the total energy of {\beta }_{12}-borophene without the peroxides, E_{peroxide} signifies the total energy of the free peroxides, and n represents the number of adsorbed peroxides. We also analyzed the charge density distributions using the following equation:

(2)\begin{array}{rl}& {\rho }_{charge\text{-}density}\\ & ={\rho }_{complex\text{-}system}-{\rho }_{free\text{-}substrate}-{\rho }_{free\text{-}peroxide}.\end{array}

In this case, {\rho }_{complex\text{-}system} is the charge density for {\beta }_{12}-borophene with the peroxide, {\rho }_{free\text{-}substrate} corresponds to the charge density of the free {\beta }_{12}-borophene, and {\rho }_{free\text{-}peroxide} is the charge density of the free peroxide. The atomic positions for the free {\beta }_{12}-borophene and the free peroxide were kept consistent with those in the complex system [66].

3 Results and discussion

3.1 Optimized crystal structure of {\beta }_{12}-borophene and the complex systems

After carefully re-optimizing and evaluating the pristine {\beta }_{12}-borophene obtained from our previous work [49]; with lattice parameters in agreement with previously DFT work [67-69], we critically identified diverse sites and tested them by adsorbing the peroxides. For \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 system as shown in Fig.1(a)−(c); site 1, oxygen atoms are positioned parallel to the bridge, and lithium atoms face the hollow. At site 2, oxygen atoms face the hollow, and the lithium atoms face the bonded boron atoms, and at site 3, the oxygen atoms are perpendicular to the bridge between the hollows with the lithium atoms facing the hollows. For \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 system as shown in Fig.1(d)−(f), we have three distinct sites. At site 1, the oxygen atoms are parallel to the bridge, and the sodium atoms are facing the hollow. At site 2, the oxygen atoms face the hollow, and the sodium atoms face the bonded boron atoms. At site 3, the oxygen atoms are perpendicular to the bridge, separating the hollows, and the sodium atoms are facing the hollows.

Following effective optimizations, we observed that the configurations at site-1 were strongly adsorbed onto the substrate confirmed by formed covalent bonds. Site-2 configurations showed lower adsorption than the configuration at site-1 because the peroxides moved slightly away from the substrate. Meanwhile, site-3 configurations exhibited strong adsorption as the peroxides bonded with the boron atoms. Notably, the calculated adsorption energies revealed that site-1 configurations for both Li and Na systems displayed the most negative adsorption energy as shown in Tab.1. This suggests that the configurations at this site are the most stable compared to others. Consequently, they were utilized for characterizations to acquire the properties of the {\beta }_{12}-borophene before and after adsorbing the peroxides.

3.2 Gibbs free energies during the formation of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene

During the discharging process in batteries, oxygen reduction reactions (ORRs) occur, leading to the formation of discharge products such as superoxides and peroxides on the surface of the electrode. The reactions can be summarized by the following mechanisms [70, 71]:

(3)\begin{array}{rl}& \mathrm{S}\mathrm{u}\mathrm{b}+{\mathrm{M}}^{+}+{\mathrm{e}}^{-}+{\mathrm{O}}_2\to \mathrm{M}{\mathrm{O}}_2@\mathrm{S}\mathrm{u}\mathrm{b},\\ & \mathrm{M}{\mathrm{O}}_2+{\mathrm{M}}^{+}+{\mathrm{e}}^{-}\to {\mathrm{M}}_2{\mathrm{O}}_2@\mathrm{S}\mathrm{u}\mathrm{b}.\end{array}

Here, M = Li or Na and Sub represents the substrate ({\beta }_{12}-borophene) where the discharge products are adsorbed.

Furthermore, the rate of formation of discharge products is heavily influenced by the catalytic properties of the cathode electrode. In our analysis, we calculated the Gibbs free energy changes to gauge this effect, as it provides critical insights into the underlying electrochemical processes. Working within the framework of density functional theory, we regarded the theoretical Gibbs free energy changes as equivalent to the change in adsorption energy, \mathrm{\Delta } E_{ad}, of the adsorbed discharge products, given that the contributions from pressure, entropy, and volume effects are negligible at 300 K [72, 73]. In the context of electrochemical processes, multiple potentials must be accounted for to efficiently define both discharging and charging behaviors. These include the charging potential (U_{\mathrm{c}}), discharge potential (U_{\mathrm{d}\mathrm{c}}), equilibrium potential (U_{\mathrm{e}\mathrm{q}}), and overpotential (\eta). The equilibrium potential (U_{\mathrm{e}\mathrm{q}}) represents the voltage necessary to keep the total change in Gibbs free energy at zero throughout the oxygen reduction reactions (ORRs) and oxygen evolution reactions (OERs). Consequently, U_{\mathrm{d}\mathrm{c}} and U_{\mathrm{c}} denote the minimum and maximum voltages required to ensure monotonic reduction of Gibbs free energy during these processes [71, 72, 74]. To proceed with calculating these potentials, we first obtained the Gibbs free energy values, as illustrated in Fig.2. From this data, we can derive the equilibrium potential for the reactions using the following expression [74]:

(4)V_{eq}={\displaystyle \frac{\mathrm{\Delta }G}{ze}}.

Here, z represents number of electrons transferred during the reactions.

After the calculations, the Gibbs free energy changes associated with the formation of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 were determined to be 0.12 and 0.3 eV, respectively (Fig.2). These relatively low values imply that the formation of these peroxides is thermodynamically favorable on {\beta }_{12}-borophene. Since oxygen evolution reactions (OERs) are essentially the reverse of oxygen reduction reactions (ORRs), we calculated their overpotentials using the equations: {\eta }_{ORR}=V_{eq}-V_{dc} and {\eta }_{OER}=V_c-V_{eq}.

From our analysis, we found that for the formation of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2, the discharge and charge potentials were 2.60 and 3.63 V, respectively, resulting in an overpotential of 1.03 V. For \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, the discharge and charge potentials were 2.06 and 3.67 V, yielding an overpotential of 1.61 V. The moderate discharge and charge potentials, combined with the low overpotentials, suggest a faster rate of electrochemical processes, which can be attributed to the catalytic effects of {\beta }_{12}-borophene. Thus, our findings demonstrate that {\beta }_{12}-borophene significantly enhances the reaction kinetics for the oxygen reduction reactions that lead to peroxide formation.

3.3 Variation in binding and potential of {\beta }_{12}-borophene adsorbed with \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2

Upon identification of the most stable configurations in the systems as mentioned in the previous Section 3.1, we proceeded to increase the concentrations of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 gradually [Fig.3(a)−(c) and Fig.4(a)−(c)] until all the energetically stable sites were completely occupied on both sides of the surfaces, as depicted in Fig.3(d) and Fig.4(d). Subsequently, we investigated variations in voltages and average adsorption energies. This exploration is crucial as it provides valuable insights into the adsorption efficiency, lattice alterations and the extent of the energy and power densities of the battery.

As mentioned earlier in Section 3.2, that the pressure, entropy and volume effects are negligible. The varying potentials were calculated using the following equation:

(5)V(n_1,n_2)=-{\displaystyle \frac{\mathrm{\Delta }{E}_{av\text{-}ads}}{ne}}.

The V(n_1,n_2) is the potential (theoretical) at changing peroxides concentration (n=n_1-n_2), and E_{av\text{-}ads} stands for the average adsorption energy.

The results revealed that for the system of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2, there was a linear decrease in average adsorption energies and voltage as the concentration of peroxides increased [Fig.3(e)]. Similarly, we observed a comparable trend for the system of \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 [Fig.4(e)]. These findings strongly suggest the existence of repulsive forces among the adsorbed peroxides, significantly influencing the average adsorption energies and the potential of {\beta }_{12}-borophene. Notably, as the number of adsorbates increased on the surface, the lattice changed from being flat to wrinkled. However, the material maintained its structural integrity, as evidenced by the remaining potential. The significant remaining voltages, 2.60 and 2.06 V for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, respectively, suggest that it can continue to adsorb additional peroxides until stability is attained. This resilience indicates the potential of {\beta }_{12} borophene to effectively accommodate various discharge products while maintaining the performance, further establishing its suitability as a cathode for lithium and sodium oxygen batteries.

3.4 Charge density distributions in the systems of {\beta }_{12}-borophene adsorbed with \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2

To enhance our understanding of the electronic interaction between the substrate and adsorbate, we performed charge density distribution calculations following the optimization of the pristine and the complex systems of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene as depicted in Fig.5. According to our findings, complex charge distributions were observed. For the \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene, it was revealed that charge accumulated (yellow) towards the substrate, with no visible charge near the lithium ions, indicating significant charge transfer towards the substrate from the adsorbate. Examination of the charge between the oxygen atoms and the substrate showed both accumulation and depletion occurring simultaneously. This can be attributed to the formation of covalent bonds between the oxygen and boron atoms, confirming the sharing of charge, as depicted in Fig.5(a). In the case of \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, we observed similar charge density distribution mechanisms as in the case of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2, with a distinct difference of small iso-surfaces reflecting the charge accumulation towards the substrate [Fig.5(b)]. This difference can be attributed to the high electronegativity of sodium compared to lithium. These observations of charge transfer provide strong evidence that there are electronic interactions between the peroxides and the {\beta }_{12}-borophene.

3.5 Metallic characteristic of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene

The metallic characteristic of an electrode is crucial for the efficiency of a battery. An effective electrode should retain its metallic properties throughout the charging and discharging processes.

This stability is particularly important when the electrode adsorbs non-conductive lithium and sodium oxide peroxides during electrochemical reactions, as these interactions can potentially alter the materials electronic properties. Therefore, we analyzed the metallic characteristics of {\beta }_{12}-borophene both before and after the adsorption of these peroxides. Our investigation aimed to check if the electrode material maintain its conductive nature after adsorbing insulating adsorbates. This was achieved by calculating the DOS and bands structures as shown in Fig.6. The results indicate that the pristine {\beta }_{12}-borophene is highly metallic because the valency and conduction bands overlap [Fig.6(a)] with a high concentration of electronic states along the Fermi level, mostly dominated by the boron p orbitals ({\mathrm{B}}_{\mathrm{p}}). Upon introducing single molecules of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 [Fig.6(b)] and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 [Fig.6(c)] on the surface, the decrease in the concentration of the electronic states along the Fermi level was observed in both systems, but still, the valency and conduction bands remained overlapping, showing that the metallic properties are being preserved. Furthermore, after increasing the concentration of the peroxides, \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 [Fig.6(d)] and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 [Fig.6(e)], the findings indicated the increased electronic states along the Fermi level and high hybridization contributed mainly by the {\mathrm{O}}_{\mathrm{p}}. This shows that the electronic conductivity of the {\beta }_{12}-borophene is enhanced after increasing the concentrations of the peroxides.

Additionally, to gain a deeper understanding of how peroxides influence the energy levels within the electronic structure of {\beta }_{12}-borophene, we calculated the band structures for both the pristine material and peroxides after the adsorption, as shown in Fig.7. Our analysis indicated that the band structure for a single lithium peroxide adsorbed on {\beta }_{12}-borophene [Fig.7(b)] showed only minimal changes in the energy bands levels compared to the pristine configuration [Fig.7(a)]. This minor alteration is primarily attributed to the transfer of electrons from the single lithium peroxides to the substrate. A similar trend was observed with the adsorption of a single sodium peroxide, as shown in Fig.7(c). However, upon the introduction of multiple lithium peroxides, we detected a significant upward shift in the Fermi level within the electronic structure [Fig.7(d)], which highlights the substantial charge transfer from the peroxides into the {\beta }_{12}-borophene system. Likewise, for multiple sodium peroxides, this charge transfer resulted in a comparable upward shift of the Fermi level, as seen in Fig.7(e). Notably, even with an increased density of adsorbed electrons, the Fermi level remains positioned within the overlapping conduction and valence bands. This observation reinforces the retention of metallic properties, a crucial characteristic for materials intended for cathode electrode applications.

3.6 Thermal stability of {\beta }_{12}-borophene absorbed with \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2

Given that battery operation often involves significant temperature fluctuations, evaluating the performance of electrodes under elevated temperatures is crucial. To address this, we conducted a rigorous investigation of thermal stability using ab-initio molecular dynamics (AIMD) within an NPT ensemble, employing a Langevin thermostat for a 20 ps simulation at 300 K, a typical operational temperature for batteries.

The results were compelling: the {\beta }_{12}-borophene material, when adsorbed with \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2, demonstrated remarkable integrity, with the bonds between boron atoms remaining resolutely intact. While some deformation of the adsorbate together with the substrate was observed, the system maintained structural cohesion, as illustrated in Fig.8(a). A similar assessment confirmed the thermal stability of the {\beta }_{12}-borophene after adsorbing \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, with the surface integrity preserved despite noticeable alterations in flatness [Fig.8(b)]. Overall, our findings revealed that even when the systems are subjected to heating up to 300 K, they remained stable (Fig.8). This stability underscores {\beta }_{12}-borophene significant potential to withstand temperature fluctuations, positioning it as a formidable candidate for cathode applications in LOB and SOB.

3.7 Diffusion of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene

During discharging process in batteries, oxidation occurs at the anode, leading to the production and migration of Li and Na ions toward the cathode through the electrolyte. The oxygen diffusing into the battery via the porous cathode combines with the ions to form lithium and sodium peroxides as the discharge products [22, 75, 76]. Once the discharge products are formed, they rapidly diffuse across the surface to locate the most stable sites. The diffusion rate of the products is directly influenced by the energy barrier of the material used as an electrode. Our calculations precisely determined the energy barrier of the {\beta }_{12}-borophene against the Li₂O₂ and Na₂O₂ using the nudged elastic band scheme [77, 78].

After a careful analysis of the structure symmetry, we identified the diffusion paths between the most stable sites to be across the hexagon of boron atoms (Fig.9). It is important to emphasize that the Li₂O₂ and Na₂O₂ are anticipated to transition between corresponding stable sites as depicted in Fig.9a and Fig.9b. Consequently, the energy barrier represents the resistance that the peroxides must overcome as they diffuse across the surface. Our findings demonstrated low energy barriers of 1.04 eV for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 0.92 eV for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 systems as shown in Fig.9(c). This signifies rapid flow or diffusion across the surface of the {\beta }_{12}-borophene, effectively preventing clustering at the surface and substantially increasing the rate of the charging process.

3.8 Decomposition of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene

During the charging process, both \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 [Fig.10(a)] and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 [Fig.10(b)] break down into individual \mathrm{L}\mathrm{i}, \mathrm{N}\mathrm{a}, and {\mathrm{O}}_2 species, i.e., \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2\to2\mathrm{L}{\mathrm{i}}^{+} + {\mathrm{O}}_2 + 2{\mathrm{e}}^{-} and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2\to2\mathrm{N}{\mathrm{a}}^{+} + {\mathrm{O}}_2 + 2{\mathrm{e}}^{-} [75, 76]. The Li and Na ions migrate back to the anode, while the {\mathrm{O}}_2 diffuses back into the ambient environment. Therefore, we calculated the energies required for splitting the peroxides to assess the electrocatalytic impact of {\beta }_{12}-borophene. This was accomplished using the NEB scheme [77, 78], following the same approach used to calculate the diffusion energy barrier in the previous section. The results demonstrated that the decomposition energies of 1.86 eV for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 1.69 eV for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 are relatively low [Fig.10(c)]. Notably, a lower decomposition energy leads to an increased charging process rate, which can extend the cycle life of the battery [79]. This suggests that {\beta }_{12}-borophene catalyzes the Li₂O₂ and Na₂O₂, as its decomposition energies are lower than the adsorption energies recorded in Tab.1. These findings are consistent with those observed for alkali-metal polysulfides on \mathrm{W}\mathrm{S}{\mathrm{e}}_2 [79] and graphene-based substrates [80]. We can conclude that {\beta }_{12}-borophene not only contributes to strong peroxide adsorption but also enhances the rate of decomposition of Li and Na-O bonds, which helps inhibit the loss of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 during battery operation.

3.9 Comparisons with other cathodes adsorbed with \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2

As previously highlighted, a variety of materials have been extensively researched for their excellent electronic properties and their potential as cathode electrodes in lithium and sodium oxygen batteries. This line of research is crucial for enhancing battery performance, with the goal of exceeding the energy and power densities of traditional fossil fuels. In this section, we summarized how some electronic properties of several candidates for cathode materials are significantly affected by their interactions with peroxides, also presented a comparative analysis of the previous and current findings, as shown in Tab.2. Our review highlighted that the electronic properties of {\beta }_{12}-borophene closely resemble those of other two-dimensional materials and, in many cases, even surpass materials such as \mathrm{N}{\mathrm{b}}_2{\mathrm{O}}_5, \mathrm{M}\mathrm{o}{\mathrm{O}}_3, and \mathrm{H}-{\mathrm{M}\mathrm{n}\mathrm{O}}_2. This is particularly evident in the open circuit voltages (OCVs) obtained (Tab.2), which are critical for determining specific capacity and ultimately impacting the energy and power densities for energy storage systems. The remarkable combination of properties exhibited by {\beta }_{12}-borophene not only emphasizes its advantages but also firmly positions it as an outstanding candidate for cathode materials in next-generation LOB and SOB.

4 Conclusions

In conclusion, we used DFT to investigate the adsorption mechanisms of \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 on {\beta }_{12}-borophene and assess their impact on its electronic properties. The results demonstrated a robust anchoring of the peroxides to the surface, with adsorption energies of −3.71 and −3.54 eV for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, respectively; indicating a low likelihood of decomposition into the electrolyte during the discharging process. The calculated Gibbs free energy changes revealed low overpotentials of 1.03 V for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 1.61 V for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2. Moreover, even with increased concentrations of peroxides on the surface, {\beta }_{12}-borophene retained its ability to adsorb additional peroxides, achieving theoretical voltages of 2.60 V for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 2.04 V for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2. Notably, the metallic nature of {\beta }_{12} remained stable despite the adsorption of peroxides, evidenced by an increase in electronic states around the Fermi level and the overlap of the valence and conduction bands. Furthermore, thermal stability analysis at 300 K confirmed that the structure of {\beta }_{12}-borophene remained intact, reinforcing its suitability as a cathode material at standard temperature of the battery. Additionally, low diffusion energy barriers of 1.04 eV for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 0.92 eV for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2 suggest rapid diffusion of the peroxides across the surface, which enhances the kinetics of charging and discharging processes. The low dissociation energy barriers of 1.86 eV for \mathrm{L}{\mathrm{i}}_2{\mathrm{O}}_2 and 1.69 eV for \mathrm{N}{\mathrm{a}}_2{\mathrm{O}}_2, highlight the catalytic effects of {\beta }_{12}-borophene on the peroxides; leading to inhibiting loss of the peroxides and enhancing electrochemical processes. Our research indicates that {\beta }_{12}-borophene has the potential to address the non-conductivity of the cathode and irreversibility of the electrochemical processes, making it a promising material for next-generation LOB and SOB. While this study has demonstrated the adsorption of Li₂O₂ and Na₂O₂ on {\beta }_{12}-borophene and its influence on electronic properties, we strongly recommend future research to investigate the complex interplay between peroxides and solvents on {\beta }_{12}-borophene. Investigating the adsorption energy of Li₂O₂ and Na₂O₂ in the presence of solvents, alongside evaluating their thermal stability through AIMD, could yield critical insights. Unraveling how solvents function as electrolytes can significantly enhance our understanding of the adsorption behavior of peroxides.

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