Biphenylene Nanotube: A Promising Anode Material for Sodium‐Ion Batteries

The properties of pristine and boron‐doped biphenylene nanotubes (BPNT and BBPNT, respectively) as anode materials for sodium storage are studied using density functional theory (DFT). To this end, the electronic properties, adsorption energy, diffusion energy barrier, open‐circuit voltage (OCV), and theoretical capacity are evaluated. The density of states calculations indicate that BPNT and BBPNT with zero band gap have a metallic character, which is critical for electron transferring in electrode materials. The calculation of adsorption energies suggests that the inside of the tube has better adsorption than the outside. Also, doping with boron improves the adsorption inside and outside the nanotube. Sodium ion sees three ways to penetrate from the outside to the inside of the tube. Calculations illustrate that the bigger ring with eight atoms with a 7.08 eV energy barrier, compared to the other cavities, is more appropriate for diffusion. This energy decreases to 5.84 eV after boron doping. The OCV profile of BBPNT confirms that this structure is in the acceptable voltage range for sodium‐ion batteries (SIBs). Finally, this work obtains a theoretical capacity of 403.82 mAh g−1 (without sodium clustering) for BBPNT, which confirms the potential of this structure for use in SIBs.


Introduction
The world is changed. The progress of human civilization, pollutants, limitation of fossil fuel resources, and undesirable climate changes due to fossil fuel usage, have revealed our critical requirement for green and renewable energy resources. [1,2] Electrical energy storage (EES) technologies play a vital role in storing energy from renewable sources such as water, wind, solar energy, etc., to clean electrical energy. [3] Lithium-ion batteries (LIBs) are one of the best EESs for grid-level energy storage. [4] Also, due to their high capacity and good cycle www.advmatinterfaces.de 1075.37 mAh g −1 make it a fantastic anode for SIBs. Recently a three-dimensional BP was designed by Obeid et al. as an anode electrode for SIBs using computational approaches. [34] This three-dimensional BP is an appropriate electrode material for sodium storage with a high capacity of 956 mAh g −1 , suitable average potential, insignificant volume expansion, and low diffusion energy barrier. Hydrogen storage, [35,36] gas sensors, [30,37,38] catalysts for electrochemical oxygen reduction reaction (ORR), [39] and hydrogen evolution reaction (HER) [40] are other attractive applications of BP. The electronic and optical properties of BP and modified BP were also studied by many scientists [31,41,42] which shows the importance of this structure in different scientific fields.
BP can have a tubular structure in two configurations, armchair, and zigzag. Their properties were studied by many researchers. [31,43] Similar to 2D BP, both 1D tubular structures have metallic properties. [31] Herein, for the first time we investigate the pristine armchair biphenylene nanotube (BPNT) and doped structure (BBPNT) as anode electrode material for SIBs by DFT calculations. For this purpose, we evaluate the electronic properties of structures, adsorption energies of sodium atoms, and diffusion energy barrier of sodium ions. Also, the cohesive energy, theoretical capacity and open-circuit voltage (OCV) are investigated.

Computational Details
The DFT framework with the plane-wave self-consistent field theory (PWSCF), [44] implemented in the QUANTUM ESPRESSO package, [45] was used for all our calculations. We operated from a revised generalized gradient approximation functional (PBEsol) [46] to treat electronic exchange-correlation energy. All calculations have been carried out by the ultrasoft pseudopotential. [47] Kohn−Sham wave functions were limited via an optimized kinetic energy cutoff of 100 Rydberg. An optimized Monkhorst−Pack [48] grid of 1 × 1 × 10 was used to integrate into the Brillouin zone. The semiempirical Grimme's technic [49,50] was adapted to define weak van der walls interactions between sodium and host structure in adsorption and diffusion mechanisms. Firstly, we made an initial 72 atomic nanotube with a radius of about 8.68 Å and length of 6.04 Å, in the direction of the c vector, and the vacuum space was considered 25 Å in both a and b vector directions to avoid interaction of nanotube with itself images in periodic calculations. This structure has three types of pores, including four, six, and eight-membered rings. The BBPNT was made by substituting one boron atom instead of a carbon atom at the common point of three pores. Figure 1 shows the boron-doped structure and three types of adsorption cavities. Note that, boron atom can replace in two different positions. The first one is common between three rings and the other one is common between 6and 8-atomic ring. The optimized structures are represented in Figure S1 (Supporting Information). The changes in the bond length of the bonds and lattice parameters after doping are listed in Table 1. As shown boron doping did not change the lattice constant.
The adsorption energy of the host structure is defined as  Bond 1 is the common bond between adjacent 4-and 8-atomic rings; b) Bond 2 is the common bond between adjacent 6-and 8-atomic rings.

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where E ad , E complex , E Bp, and n are adsorption energy, the energy of the sodiated structure, host structure, and the number of adsorbed Na atoms, respectively. E Na is the energy of a single sodium atom placed in the center of a cubic box with dimensions of 20 Å. The cohesive energy of adsorbed structures was calculated by the following equation to evaluate the stability of structures.
where E coh , E complex , E C , m and n are the cohesive energy, the energy of complex, the energy of a single carbon atom, and the total number of carbon atoms, respectively. The energy and number of added heteroatoms must be added to Equation (2). The climbing image nudged elastic band (CI-NEB) method [51,52] was applied to calculate the activation energy barrier of sodium ion migration. This method is based on finding paths with minimum energy between two different stable adsorption sites.

Electronic Properties
The electronic behavior of the structure is an important criterion to consider as electrode material for SIBs. Because of the electron transfer on the electrode, an anode material should have a high electron conductivity. Herein we obtained the density of states (DOS) plots of pristine BPNT and BBPNT. As shown in Figure 2, both BPNT and BBPNT have metallic attributes due to the lack of gap in the Fermi level.
The electronic behavior of BPNT is compatible with previous work [31] (there has been no research on BBPNT until now). Therefore, by boron doping, the structure has been maintained in the metallic state. Just the Fermi energy shifts toward the lower energies (from −2.81 eV for BPNT to −2.97 eV for BBPNT) due to the substitution of a boron atom instead of a carbon atom (in 72 atomic structure) which causes to reduce one electron from the closed-shell structure of BPNT. Both BPNT and BBPNT have electronic states at the Fermi level that lead to the electrochemical activity of these two structures. So, regarding electronic properties, both BPNT and BBPNT with high electron conductivity are suitable structures for SIBs.

Adsorption Energy of Sodium on BPNT and BBPNT
The ability of a structure to absorb and store an adsorbent atom is determined by adsorption energy. Herein, three positions on pristine and doped structures were considered to calculate the adsorption energies. These three sites are named A, B, and C for 8-, 6-and 4-atomic rings, respectively. (See Figure 1). Table 1 shows the results of adsorption energies for different sites of BPNT and BBPNT. A lower energy value represents stronger adsorption.
As shown, the sodium atom in BPNT tends to adsorb on the larger ring (A site) with more favorable energy than other sites. Arrange the absorption energies as follows A > B > C. Calculations of adsorption energy on A, B, and C sites of BBPNT show that sodium absorbs more strongly on BBPNT than BPNT. The difference in adsorption energy in different sites and two different structures arises mainly from two reasons. I) Different radiuses of pores, as a ring with a large radius provides a low steric hindrance for sodium adsorption in comparison with small rings, II) the tendency of the electron transferring from sodium atom to the host structure in the adsorption process. Sodium's tendency for electron transferring increases by reducing the electron charge density of adsorption site and therefore adsorption energy improves; therefore, the larger cavity provides the better adsorption energy. This arrangement of sodium adsorption energy was also confirmed in previous studies on BP nanosheets. [34] Such a trend is also www.advmatinterfaces.de obtained by Ferguson et al. [29] for lithium adsorption. Just there is a slight discrepancy with The results of Han et al. [33] on pure BP nanosheets is a slight discrepancy with the above reports, where the calculated adsorption energy of sodium on the 4-atomic ring is a little more than the 6-atomic ring.
The presence of a boron atom creates an electron-less hole in the BBPNT. So, as shown in Figure 3, the electron charge density is low at the boron-doped site. The adsorption energies of sodium inside BPNT are stronger than outer equal sites ( Table 2). This stronger absorption could be because of the internal curvature of the nanotube, which causes sodium to experience the adsorption effect of neighbor pores. Figure 4 illustrates the projected density of states (PDOS) plots of some adsorptions for a better understanding of the adsorption mechanism. These figures show that due to the electron transferring from the sodium electron donator to the host electron acceptor, with the ionization of sodium in the adsorption process, the sharp peak of sodium's s orbital shifts to higher energies (conduction band). More shift to conduction bond indicates more ionization of sodium. Note that the single sodium peak is located precisely at the Fermi level. [53] As shown, sodium ionization in the A site is more than B site in doped and nondoped structures ( Figure 4A,B), which were in line with the adsorption energies. Figure 4C shows a more ionization level for inside adsorption than outside one, and Figure 4D indicates that sodium is further ionized in borondoped structure compared with pure form. Here, the effect of electron deficiency of structure is seen due to the presence of a boron atom. The effect of pore size and boron doping on the adsorption energies agrees with our previous works and other research. [53][54][55] The ionization of sodium is critical in a researchable battery. Because the adsorption of atoms on the anode must be reversible and a noncovalent interaction (the electrostatic interaction between sodium with a positive partial charge and host with a negative partial charge) provides it. Also, to illustrate the dependence of adsorption to distance from the boron atom (Figure 5), we calculated the adsorption energy of three positions on the outside of the tube, away from the rings containing boron as listed in Table 3. It clearly shows that the absorption energy decreases for all three positions when moving away from the doped site.  As mentioned, the steric effects can also affect the absorption process. We have investigated the impact of aluminum doping on sodium adsorption outside aluminum-doped BPNT (AlBPNT). The calculations indicate the adsorption energies of −1.99 eV and −1.93 eV for the A site and B site, respectively, which are lower than the adsorption energies of the same sites in BPNT and BBPNT. Two views of electron density for AlBPNT are shown in Figure S2, Supporting Information.

Sodium Ion Diffusion
Mobility and diffusion of ions on the host structure affect the rate of charge/discharge, which is an essential parameter in the performance of rechargeable batteries. [54] By knowing and controlling this parameter, we can determine the applicability of a structure as an anode material for sodium storage. Herein, the CI-NEB method was used to calculate the energy barrier of sodium ion movement in different paths of pristine and doped structures. One of these paths (path 1) is the case that sodium ion diffuses from the outside to the inside of the nanotube via the center of an A pore. In the other one (path 2) ion moves from the top of the 8-atomic ring (A site) and passes the top of the carbon-carbon bond, and reaches to 6-atomic ring (B site). These ways are investigated in pristine and boron-doped structures. Figure 6 indicates these paths and related energy barriers.
As shown, the boron-doping decreases energy barrier in path 1 (Figure 6A), which agrees with previous works on boron doping effects. [53] This energy barrier reduction is because of one less electron of boron atom and low atomic radius in comparison with carbon atoms, based on the descriptions given in the absorption energies, generates a favorable path for sodium ion migration. More accurately, the boron atom affects the migration of ions via two factors. I) low radius, which decreases the steric effects, II) an electron less hole making. In the case    of path 2, this decrease is not observed, and the experienced energy barrier of sodium from BPNT is less than BBPNT. This is because of more stability of the A site's adsorption in BBPNT than BPNT (see Table 1). A low diffusion energy barrier of sodium ion from 8-to 6-atomic pore is in concurrence with Han et al. work on pure BP nanosheet. [33] The energy barrier of path 2 was also calculated for the AlBPNT structure for more evaluation from steric effects. As shown in Figure 7, despite the one less electron in the valence band of aluminum (see electron charge density in Figure S2, Supporting Information), the big radius of Al causes a steric effect and higher energy barrier (4.05 eV) than pristine and boron-doped structure ( Figure 6) for sodium ion diffusion.
Also, it is essential to say that, due to the large radius of sodium, the B and C sites cannot pass sodium ions from themselves. As shown for the B site in Figure S3 (Supporting Information), this diffusion can destroy the structure. Therefore, these two are wrong paths.

Theoretical Capacity and Open-Circuit Voltage of BBPNT
The maximum theoretical capacity and OCV are two essential properties of an electrode material that must be evaluated. To calculate the theoretical capacity, firstly, we added a sodium atom in a position with the highest absorption energy (inside of A site). The following sodium atoms were added by observing the distance from each other and better absorption location. Note that the adsorption process continues until the adsorption energy reaches a more positive value of sodium clustering energy (the clustering energy of sodium is −1.13 eV). The optimized adsorbed structure in different sodium concentrations and related adsorption energies are shown in Figure 8.
The capacity of 403.82 mAh g −1 has been achieved, for 13 sodium atoms, by the following equation where F is the Faraday constant, n is the number of transferred electrons (this number equals the number of adsorbed sodium ions), and M is the molecular mass of the absorbent (BBPNT). This capacity is more than the capacity of many other types of nanotubes, such as reduced graphene oxide/carbon nanotube (rGO/CNT) with a capacity of 166 mAh g −1 , [56] bamboolike carbon nanotube-carbon nanotube with a capacity of 177.9 mAh g −1 , [57] coaxial carbon nanotube supported TiO 2 @ MoO 2 @Carbon core shell with a capacity of 175 mAh g −1 , [58] carbon-coated MoS 2 /N-doped carbon nanotubes with a capacity of 348 mAh g −1 , [59] and the structures with other morphologies such as spherical Br-doped Na 3 V 2 (PO 4 )2F 3 /C with a capacity of 116.1 mAh g −1 [60] and bronze-type VO 2 with a capacity of 218 mAh g −1 , [61] etc.
To compare, we evaluated the theoretical capacity of pure BPNT. Similar to BBPNT, BPNT adsorbs 13 sodium atoms with an average adsorption energy of −1.82 eV. The theoretical capacity of this number of adsorbed atoms on BPNT is 402.92 mAh g −1 Since the charge/discharge process in rechargeable batteries follows the common half-cell reaction versus Na/Na + (i.e., BBPNT + x Na + + xe − ↔Na x BBPNT) we have computed the OCV for sodium adsorption on BBPNT (see Figure 9). Our calculations indicate an average OCV of 0.315 V, which is in the appropriate voltage range for SIBs (0.2-1 V). [62] So, BBPNT is a promising structure to be used as an anode electrode in SIBs.

Cohesive Energy
The cohesive energy was calculated for different sodium concentrations to evaluate the stability of adsorbed structures. The results are listed in Table 4. It can be seen that the stability of the tube is not lost after boron doping. Also, the strength of structures is well preserved after the adsorption of 13 sodium atoms.

Conclusion
DFT was applied to investigate the BP and boron-doped BP nanotube as anode material for sodium-ion batteries. Investigation of electronic properties indicated that these structures have a metallic character which is critical for electrode material. Evaluation of adsorption mechanisms illustrated the physical characteristics (and reversibility) of the interaction. This reversibility  is critical for using material as anode electrodes in secondary batteries. We calculated the energy barrier of sodium ion migration on the structures. The results showed that diffusion in the boron atom presence is almost better than the pristine structure. According to the adsorption and energy barriers, we continued the calculations on BBPNT. The cohesive energy calculations represented that with the adsorption of sodium and increasing its concentration, the stability of structures is not lost. The estimate of OCV represented that this structure is in the voltage range for SIBs. Finally, the theoretical capacity of 402.92 mAh g −1 for BPNT and 403.82 mAh g −1 for BBPNT confirmed the suitability of these materials as anode materials for SIBs.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.