Theoretical investigation of the ORR on boron–silicon nanotubes (B–SiNTs) as acceptable catalysts in fuel cells

Abstract

Here, the potential of boron doped silicon nanotubes (7, 0) as ORR catalysts is examined. Acceptable paths for the ORR on studied catalysts are examined through DFT. The optimum mechanism of the ORR on the surface of B₂–SiNT (7, 0) is shown. The ORR on the surface of B₂–SiNTs (7, 0) can continue through LH and ER mechanisms. The calculated beginning voltage for the ORR on B₂–SiNTs (7, 0) is 0.37 V and it is smaller than the beginning voltage (0.45 V) for platinum-based catalysts. In the acidic solution the beginning voltage for the oxygen reduction process can be evaluated to be 0.97 V, which corresponds to 0.37 V as a minimum overvoltage for the ORR. The B₂–SiNTs (7, 0) are suggested as an ORR catalyst in acidic environments.

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1. Introduction

Fuel cells as energy machines are important due to their low contamination and great efficiency. The ORR rate in electrodes of cells is slow, therefore the ORR can be evaluated as a significant reason to increase the full cell efficiency.^1–4 Platinum-compounds have been used as catalysis in the ORR but platinum-compounds have low ability to endure CO.^5–9

The potential of various compounds was investigated to find and propose effective catalysts for the ORR. Nanostructures and doped nanostructures with high ability for CO endurance can be used as suitable replacements for platinum-compounds.^10–15 The B-nanostructures are acceptable catalysts for the ORR in alkaline conditions and mechanisms of action of B-doped nanostructures in acidic position are not clear.^16–23

The nanostructures due to their electrical conductivity and thermal conductivity can be used to product the transistors and non-volatile memory devices.^24–28 The electrical conductivity of doped carbon/silicon nanotubes indicated that the adoption of carbon/silicon nanotubes (with various atoms such as B, N, O and some metals) increased their electrical conductivity, significantly. These findings improved the application of carbon/silicon nanotubes in nano-electronic devices and novel catalyst to ORR.^29–38 Results demonstrated that the adoption of carbon/silicon nanotubes increased their electrical conductivity and enhanced the ORR efficiency.^39–48

Wang et al.⁴⁹ demonstrated that boron-doped graphene nanoribbons are suitable catalyst to ORR catalyst. Xiao et al.⁵⁰ proved that the layered silicon–carbon nano sheets represented the high activity in ORR without CO poisoning. Xia and Zhang et al.^51,52 investigated the mechanisms of ORR of fuel cells in acidic environment on graphene cathodes. Stevenson et al.⁵³ proved in ORR the O₂ in a 2-electron path is reduced to form OOH on carbon nanotubes. Hu and Xiong et al.^54,55 confirmed that nitrogen and boron-doped nanostructures as ORR catalysts have low price, great durability and excellent potential. Zhao and Wei et al.^56,57 confirmed the doping of carbon nanotubes have vital roles on performance of ORR. Ferrighi et al.⁵⁸ demonstrated that boron atoms of nano-sheets increase the reactions of oxygen with graphene.

In current study, ORR on B-doped silicon nanotube (7, 0) as acceptable catalysts is examined to find possible mechanisms to ORR on B₂–SiNT (7, 0) and to suggest high activity nano-catalysts to ORR.

2. Computational details

In this study the silicon nanotube (length and diameter are 1 and 0.475 nm) is modeled and their open elements are saturated with hydrogen atoms to elude border effects. The geometries of nanotubes and studied molecules (such as OOH, OH, H₂O and CO) are optimized by M06-2X/6-311G+ (2d, 2p) in GAMESS package.^59–72 The consistent field is investigated by 10⁻⁶ Hartree as convergence value. Vibrational frequencies of nanotubes and molecules by M06-2X/6-311G+ (2d, 2p) are calculated.

In the density functional, M06 functionals are extremely parameterized proximate exchange functionals theory and they are supported on generalized gradient approximation (meta-GGA). These functionals are used for traditional quantum chemistry, solid-state physics calculations and thermodynamic values of reactions.^73–82 M06-2X as the most accurate functional of Minnesota functional is a Global hybrid functional with 54% HF exchange and it is the ascendancy constructor within the 06 functionals for thermochemistry, kinetics and various chemical interactions.^73–82 The M06-2X functional as hybrid meta exchange–correlation functionals present 32 empirically improved factors within the exchange–correlation functional.^83–87

The energy and Gibbs free energy (G = E₀ + ZPE + ΔH + RT − TS) values of nanotubes are calculated. The E₀ and ZPE are electronic energy and zero-point energy and T is 298.15 K.^59–72 Adoption energy (E_doped) and Gibbs free energy adoption (G_doped) of B atoms in SiNT (7, 0) are calculated:

E_doped = E(B–SiNT) − E(SiNT) − E(B) (1)

G_doped = G(B–SiNT) − G(SiNT) − G(B) (2)

E_doped = E(B₂–SiNT) − E(SiNT) − 2E(B) (3)

G_doped = G(B₂–SiNT) − G(SiNT) − 2G(B) (4)

E(B–SiNT (7, 0)) and E(B₂–SiNT (7, 0)) are energies of B–SiNT (7, 0) and B₂–SiNT (7, 0).

Energy adsorption (ΔE_ad) and Gibbs free energy adsorption (ΔG_ad) of molecules (such as OOH, OH, H₂O and CO) on surfaces of studied nanotubes (SiNT, B–SiNT, B–B–SiNT and B₂–SiNT) are calculated:

ΔE_ad = E(molecule–nanotube) − E(nanotube) − E(molecule) (5)

ΔG_ad = G(molecule–nanotube) − G(nanotube) − G(molecule) (6)

E(molecule–nanotube) and G(molecule–nanotube) are E and G of molecules–nanotubes. G(nanotube) and G(molecule) are G of nanotubes and molecules. E(nanotube) and G(molecule) are energy and G of nanotubes and molecules. Natural bond orbital charges (q) and gap energy (E_HLG) complexes are calculated^59–72 and transition state, reaction energy (ΔE_r) and activation barrier energy (ΔE_a) are examined by LST/QST method and M06-2X.⁶⁴

Activation energy (ΔE_a = E_TS − E_IS) is difference of energy between transition (E_TS) and initial (E_IS) studied complexes. In this study, the reaction energy (ΔE_a = E_FS − E_IS) is difference of energy between final (E_FS) and initial (E_IS) studied complexes.^88–95 The ΔG of ORR on B₂–SiNT (7, 0) in according to standard hydrogen electrode was evaluated through ΔG = ΔE + ΔZPE − TΔS + ΔG_U + ΔG_pH (obtained data were reported in Fig. 5).^96–104 ΔG_pH (ΔG_pH = kT ln 10 × pH) is modification of proton Gibbs free energy and ΔG_U = − neU. The n, e and U are electrons, first charge and electrode potential. The U is requested potential and overvoltage is η = U₀ − U.^49–58 Conductor like screening method is used to estimate water environment (dielectric constant is 78.54).^59–72

3. Results and discussion

3.1. Molecule adsorptions on nanotube

In this section, the B adoption of SiNT (7, 0) were investigated and then interactions of B–SiNT (7, 0) structures with O₂, OOH, OH, H₂O and CO molecules were investigated. The one Si atom of the SiNT (7, 0) was replaced with one B atom and the B–SiNT (7, 0) was produced (Fig. 1). Also the two Si atoms of the SiNT (7, 0) in two difference positions were replaced with two B atoms and B–B–SiNT (7, 0) and B₂–SiNT (7, 0) structures were produced (Fig. 1). Structures of SiNT, B–SiNT, B–B–SiNT, B₂–SiNT, O₂, OH, H₂O, H₂O₂ and CO are presented in Fig. 1. The adoption energy (E_doped), adoption free Gibbs energy (G_doped) and bond lengths of B–Si of B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) were reported in Fig. 1. In the B–SiNT (7, 0) the B atom was connected with three neighboring silicon atoms and the E_doped and G_doped were −2.18 and −2.10 eV and average of bonds of B–Si in B–SiNT (7, 0) is 1.95 Å. In the B–B–SiNT (7, 0) the B atoms are connected with four neighboring silicon atoms and the E_doped and G_doped are −2.23 and −2.14 eV and average of bonds of B–Si in B–B–SiNT (7, 0) is 1.93 Å. In the B₂–SiNT (7, 0) the B atoms are connected with six neighboring silicon atoms and the E_doped and G_doped values are −2.28 and −2.17 eV and average of bonds of B–Si in B₂–SiNT (7, 0) are 1.92 Å.

Fig. 1 The initial structures of SiNT, B–SiNT, B–B–SiNT and B₂–SiNT and O₂, OH, H₂O, H₂O₂ and CO molecules.

The q and E_HLG of SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) are stated in Table 1. E_HLG of SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) are 1.84, 1.75, 1.68 and 1.64 eV. The q of B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) are 0.58, 0.69 and 0.73|e|. The |E_doped|, |G_doped| and q values of B₂–SiNT (7, 0) are higher than B–SiNT (7, 0) and B–B–SiNT (7, 0). Results showed that the E_HLG value of B₂–SiNT (7, 0) is lower than corresponding values on surfaces of B–SiNT (7, 0) and B–B–SiNT (7, 0). Therefore, it can be concluded that the B₂–SiNT (7, 0) is the most stable than B–SiNT (7, 0) and B–B–SiNT (7, 0) from thermodynamic view point. The B atoms in B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) structures are advantageous to adsorption of O₂ molecule and these B atoms are active positions of B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) as catalyst for ORR. Therefore, B atoms are essential location to adsorption of O₂ molecule and B atoms can be considered as initiator of first ORR step.

Table 1 Charge transfer (q) (in |e|) and HOMO–LUMO band gap (E_HLG) (in eV) of studied complexes

Complex	q	E HLG	Complex	q	E HLG	Complex	q	E HLG	Complex	q	E HLG
SiNT	—-	1.84	B–SiNT	0.58	1.75	B–B–SiNT	0.69	1.68	B2–SiNT	0.73	1.64
2a	0.36	1.69	2b	0.47	1.61	2c	0.59	1.52	2d	0.64	1.48
2e	0.29	1.75	2f	0.39	1.68	2g	0.51	1.59	2h	0.58	1.55
2i	0.32	1.72	2j	0.43	1.64	2k	0.54	1.56	2l	0.61	1.52
2m	0.49	1.35	2n	0.62	1.23	2o	0.73	1.17	2p	0.82	1.14
3a	0.41	1.54	3b	0.51	1.45	3c	0.65	1.38	3d	0.73	1.25
3e	0.59	1.14	3f	0.81	1.05	3g	0.84	0.99	3h	0.91	0.95
3m	0.11	1.80	3n	0.14	1.70	3o	0.19	1.62	3p	0.21	1.60
3q	0.08	1.82	3r	0.12	1.72	3s	0.15	1.64	3t	0.18	1.63

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Therefore, O₂ adsorption on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) were investigated. The possible positions of SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) to O₂ adsorption including top position B atom and bridge positions of B–Si, B–B and Si–Si bonds were examined in Fig. 2. The B–O, O–O and Si–O in SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) with O₂ are presented in Fig. 2 (2a–2l structures). The ΔE_ad and ΔG_ad of O₂ on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) are displayed in Table 2. |ΔG_ad| of O₂ on B–SiNT, B–B–SiNT and B₂–SiNT are greater than SiNT (7, 0). The |ΔE_ad| and |ΔG_ad| of O₂ on B₂–SiNT (7, 0) are greater than B–SiNT (7, 0), B–B–SiNT (7, 0). The bridge position of B–B in B₂–SiNT (7, 0) is stable than top position B in B₂–SiNT (7, 0) to O₂ adsorption.

Fig. 2 Complexes of the SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) with O₂ and OH molecules.

Table 2 The ΔE_ad (in eV) and ΔG_ad (in eV) values of studied complexes

Complex	ΔEad	ΔGad	Complex	ΔEad	ΔGad	Complex	ΔEad	ΔGad	Complex	ΔEad	ΔGad
2a	−0.41	−0.36	2b	−0.61	−0.54	2c	−0.84	−0.79	2d	−0.88	−0.81
2e	−0.39	−0.33	2f	−0.42	−0.38	2g	−0.55	−0.51	2h	−0.61	−0.55
2i	−0.27	−0.24	2j	−0.64	−0.61	2k	−0.69	−0.64	2l	−0.73	−0.68
2m	−2.07	−1.97	2n	−2.23	−2.15	2o	−2.31	−2.21	2p	−2.39	−2.28
3a	−0.87	−0.81	3b	−1.06	−0.99	3c	−1.11	−1.03	3d	−1.17	−1.12
3e	−3.11	−2.97	3f	−3.59	−3.45	3g	−3.67	−3.56	3h	−3.79	−3.67
3i	−2.24	−2.13	3j	−2.25	−2.15	3k	−2.27	−2.17	3l	−2.31	−2.21
3m	−0.15	−0.10	3n	−0.18	−0.13	3o	−0.20	−0.15	3p	−0.24	−0.19
3q	−0.09	−0.05	3r	−0.10	−0.07	3s	−0.11	−0.08	3t	−0.14	−0.12

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Wang, Xiao and Xia et al.^49–51 calculated the O₂ adsorption on surfaces of boron-doped graphene nanoribbon, silicon–carbon nano sheets and B and N doped-graphene by theoretical methods, respectively (results reported in Table 4). The ΔE_ad of O₂ on B-doped graphene, silicon–carbon nano-sheets and N-doped graphene are −0.62, −0.53 and −0.60 eV. Therefore ΔE_ad value (−0.61 eV) of O₂ on B₂–SiNT (7, 0) in present study is similar to corresponding values of O₂ on various nanostructures were calculated in previous theoretical works.^49–51

Table 3 The ΔE_a and ΔE_r for ORR on B₂–SiNT (7, 0)

Path	Studied reaction steps	ΔEa (eV)	ΔEr (eV)
1	O2 + B2–SiNT (7, 0) → B2–SiNT (7, 0)–*O2	—	−0.68
1	B2–SiNT (7, 0)–*O2 + H^+ + e^− → B2–SiNT (7, 0)–*OOH	0.00	−1.07
1	B2–SiNT (7, 0)–*OOH + H^+ + e^− → B2–SiNT (7, 0)–*O + H2O	0.18	−2.75
1	B2–SiNT (7, 0)–*O + H^+ + e^− → B2–SiNT (7, 0)–*OH	0.37	−1.57
1	B2–SiNT (7, 0)–*OH + H^+ + e^− → B2–SiNT (7, 0)* + H2O	0.07	−1.34
2	O2 + B2–SiNT (7, 0) → B2–SiNT (7, 0)–*O2	—	−0.68
2	B2–SiNT (7, 0)–*O2 + H^+ + e^− → B2–SiNT (7, 0)–*OOH	0.00	−1.07
2	B2–SiNT (7, 0)–*OOH + H^+ + e^− → *OH–B2–SiNT (7, 0)–*OH	0.24	−2.97
2	*OH–B2–SiNT (7, 0)–*OH + H^+ + e^− → B2–SiNT (7, 0)–*OH + H2O	0.35	−1.20
2	B2–SiNT (7, 0)–*OH + H^+ + e^− → B2–SiNT (7, 0)* + H2O	0.07	−1.34

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Table 4 The ΔE_ad (in eV) values of O₂, O, OH and OOH on B-doped graphene, silicon–carbon nano-sheets and N-doped graphene^65–67 and B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) in this study

Catalysts/species	B-doped graphene^49	Si–C nano-sheet^50	N-doped graphene^51	B–SiNT (7, 0)	B–B–SiNT (7, 0)	B2–SiNT (7, 0)
O2	−0.62	−0.53	−0.60	−0.69	−0.84	−0.88
O	−3.74	−4.11	−3.55	−3.59	−3.67	−3.79
OH	−2.38	−2.87	−2.41	−2.23	−2.31	−2.39
OOH	−1.12	−1.18	−1.06	−1.06	−1.11	−1.17

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The charge transfer (q) and HOMO–LUMO band gap (E_HLG) of the complexes of SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) with O₂ molecule are displayed in Table 1. The E_HLG values of O₂ adsorption on B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) are lower than SiNT (7, 0). The E_HLG values of O₂ adsorption on B₂–SiNT (7, 0) are lower than B–SiNT (7, 0), B–B–SiNT (7, 0). The bridge position of B–B in B₂–SiNT (7, 0) has higher q and lower E_HLG than top position B in B₂–SiNT (7, 0) to O₂ adsorption. Complex of B₂–SiNT (7, 0) with O₂ molecule (2d structure) is the most stable than other complexes of B–SiNT (7, 0) and B–B–SiNT (7, 0) with O₂ molecule from thermodynamic view point. It can be concluded that O₂ adsorbed on B₂–SiNT (7, 0) in figure 2d significantly and there are suitable interactions between the O₂ molecule and B₂–SiNT (7, 0) and the adsorption of O₂ molecules on studied surfaces are chemical adsorption processes.

In this study the interactions of important intermediates such as O, H, OOH, OH, H₂O and CO molecules with SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) surfaces in process of ORR were investigated (Fig. 2 and 3). The bonds of Si–O of SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) with molecules are stated. E_HLG, q, ΔE_ad, ΔG_ad of molecules on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) are reported in Tables 1 and 2. OOH and OH intermediates can be adsorb on B site of B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0). The O intermediate has tendency to adsorb on B–Si and B–B bridge positions of B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0). It can be concluded that the complexes of B₂–SiNT (7, 0) with O, H, OOH, OH and H₂O molecules are stable than SiNT (7, 0), B–SiNT (7, 0) and B–B–SiNT (7, 0).

Fig. 3 Complexes of the SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) with O and H atoms, OOH, H₂O and CO molecules.

Wang, Xiao and Xia et al.^49–51 calculated the O, OH and OOH adsorption on surfaces of boron-doped graphene nanoribbon, silicon–carbon nano sheets and B and N doped-graphene by theoretical methods, respectively (results reported in Table 4). ΔE_ad of O on B-doped graphene, silicon–carbon nano-sheets and N-doped graphene were −3.74, −4.11 and −3.55 eV. ΔE_ad of OH on boron-doped graphene, silicon–carbon nano-sheets and N-doped graphene were −2.38, −2.87 and −2.41 eV. ΔE_ad of OOH on B-doped graphene, silicon–carbon nano-sheets and N-doped graphene are −1.12, −1.18 and −1.06 eV. ΔE_ad values of O, OH and OOH (−1.17, −2.39 and −1.17 eV) on B₂–SiNT (7, 0) in present study are similar to corresponding values of O, OH and OOH on various nanostructures were calculated in previous theoretical works.^49–51

The H₂O molecule favored to adsorb on above ring position of SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) and the average of ΔE_ad and ΔG_ad values are −0.19 and −0.14 eV. The average of q and E_HLG values for adsorption of H₂O molecule on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) surface is 0.16|e| and 1.68 eV. H₂O molecule can be adsorbed on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) surfaces as physical adsorption processes.

In process of ORR the CO can occupy the positions of catalysts and the performance of ORR is reduced and efficiency of catalyst decreases sharply. Previous works showed that reactions between CO molecule and surface of platinum nano-catalyst was powerful (ΔE_ad is −1.90 eV) and CO poisoning was happen.^20,66 The average of ΔE_ad and ΔG_ad of CO on SiNT, B–SiNT, B–B–SiNT and B₂–SiNT surfaces are −0.11 and −0.08 eV. The average of q and E_HLG values for adsorption of CO on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) surface is 0.13|e| and 1.70 eV. The CO molecule can be adsorbed on SiNT (7, 0), B–SiNT (7, 0), B–B–SiNT (7, 0) and B₂–SiNT (7, 0) surfaces as physical adsorption processes. It can be concluded that B₂–SiNT (7, 0) as acceptable catalyst can be endurance to CO poisoning and it can solve the major problem of platinum nano-catalysts.

Wang, Xiao and Xia et al.^49–51 calculated the H₂O and CO adsorption on surfaces of boron-doped graphene nanoribbon, silicon–carbon nano sheets and B and N doped-graphene. The ΔE_ad of H₂O on surfaces of B-doped graphene, silicon–carbon nano-sheets and N-doped graphene were −0.24, −0.18 and −0.08 eV. The ΔE_ad of CO on surfaces of B-doped graphene, silicon–carbon nano-sheets and N-doped graphene were −0.17, −0.07 and −0.12 eV. The ΔE_ad of H₂O and CO (−0.24 and −0.14 eV) on B₂–SiNT (7, 0) in present study are similar to corresponding values of H₂O and CO on various nanostructures were calculated in previous theoretical works.^49–51

3.2. B₂–SiNT (7, 0) as catalyst to ORR

Nano-catalysts processed the chemical reactions through the ER and LH paths. The paths for ORR via B₂–SiNT (7, 0) as acceptable catalyst through the LH and ER mechanisms were investigated. As start, O₂ adsorption is investigated via O₂ dissociation or hydrogenation of O₂ to create B₂–SiNT (7, 0)–*OOH. Firstly, the O₂ dissociation process can be defined as B₂–SiNT (7, 0)–*O₂ → *O–B₂–SiNT (7, 0)–*O. The dissociated O atoms were elected to link on B–Si position and activation barrier energy is 0.96 eV (figures 2a (IS), 2b (TS) and 2c (FS)). Secondary, adsorbed O₂ can interact via H atom to create B₂–SiNT (7, 0)–*OOH as follow: B₂–SiNT (7, 0)–*O₂ + H⁺ + e⁻ → B₂–SiNT (7, 0)–*OOH, this process has no any activation barrier energy.

The OOH adsorption on of B₂–SiNT (7, 0) has higher ΔE_ad than O₂ca. 0.29 eV and also O₂ dissociation on surface of B₂–SiNT (7, 0) has high activation barrier energy. H atom is added into Si in B₂–SiNT (7, 0)–*OOH and H atom reacted via B₂–SiNT (7, 0)–*OOH. Then the B₂–SiNT (7, 0)–*OOH dissociated to *O–B₂–SiNT (7, 0)–*OH (figures 2d (IS), 2e (TS) and 2f (FS)), due to great activation barrier energy (1.31 eV) this process is impossible. The creation of B₂–SiNT (7, 0)–*OOH in ORR on B₂–SiNT (7, 0) is suitable than dissociation of O₂ molecule.

The ORR is done through the B₂–SiNT–*OOH intermediate as follows:

B₂–SiNT–*OOH → B₂–SiNT–*O + H₂O (7)

B₂–SiNT–*OOH → *OH–B₂–SiNT–*OH (8)

B₂–SiNT–*OOH → B₂–SiNT + H₂O₂ →*OH–B₂–SiNT–*OH (9)

In path 1, B₂–SiNT (7, 0)–*OOH intermediate was decreased to H₂O molecule and B₂–SiNT (7, 0)–*O (ΔE_a = 0.18 eV). In this process, O–O is fragmented and the first H₂O molecule is created (figures 2g (IS), 2h (TS) and 2i (FS)). Then two hydrogenation stages were done and B₂–SiNT (7, 0)–*OH (figures 2j (IS), 2k (TS) and 2l (FS)) and the second H₂O molecule was created (figures 2m (IS), 2n (TS) and 2o (FS)). The activation barrier energies of these two hydrogenation processes are 0.37 and 0.07 eV, respectively.

In path 2, H atom is linked to O and *OH–B₂–SiNT (7, 0)–*OH is created and activation barrier energy is 0.24 eV (figures 2p (IS), 2q (TS) and 2r (FS)). Then, *OH–B₂–SiNT (7, 0)–*OH linked to H atom and the first H₂O molecule is created and activation barrier energy of this stage is 0.35 eV (figures 2s (IS), 2t (TS) and 2u (FS)). In the end stage of path 2, the B₂–SiNT (7, 0)–*OH is hydrogenated and in this step the second H₂O molecule is separated.

In the path 3, the B₂–SiNT (7, 0)–*OOH is hydrogenated and the H₂O₂ molecule and B₂–SiNT (7, 0) catalyst are created and activation barrier is 0.31 eV (figures 2v (IS), 2w (TS1), 2x (MS), 2y (TS2) and 2z (FS)). The H₂O₂ molecule creation is a mediated state (MS) on surface of B₂–SiNT (7, 0) and it cannot effect on potential of the B₂–SiNT (7, 0), significantly. In next stage of path 3, separated H₂O₂ dissociated into *OH–B₂–SiNT (7, 0)–*OH structure and therefore H₂O₂ dissociation has activation barrier energy about 0.82 eV. The ORR via path 3 continued via two hydrogenation stage as presented in path 1 in Fig. 4 (figures 4s (IS), 4t (TS) and 4u (FS)) and path 2 in Fig. 4 (figures 4m (IS), 4n (TS) and 4o (FS)).

Fig. 4 The intermediates of ORR and relative energies: (1) B₂–SiNT (7, 0)–*O₂ → *O–B₂–SiNT (7, 0)–*O; (2) B₂–SiNT (7, 0)–*OOH → *O–B₂–SiNT (7, 0)–*OH; (3) B₂–SiNT (7, 0)–*OOH → B₂–SiNT (7, 0)–*O + H₂O; (4) B₂–SiNT (7, 0)–*O → B₂–SiNT (7, 0)–*OH; (5) B₂–SiNT (7, 0)–*OH → B₂–SiNT (7, 0)–* + H₂O; (6) B₂–SiNT (7, 0)–*OOH → *OH–B₂–SiNT (7, 0)–*OH; (7) *OH–B₂–SiNT (7, 0)–*OH → *OH–B₂–SiNT (7, 0) + H₂O; (8) B₂–SiNT (7, 0)–*OOH → B₂–SiNT (7, 0) + H₂O₂ →*OH–B₂–SiNT (7, 0)–*OH.

The parameters of two acceptable paths about reduction of B₂–SiNT (7, 0)–*OOH structure are stated in Table 3. In path 1, rate-determining stage (ΔE_a = 0.37 eV) on B₂–SiNT (7, 0) surface is creation of B₂–SiNT (7, 0)–*OH. In path 2, creation of B₂–SiNT (7, 0)–*OH structure and H₂O molecule is rate-determining stage (ΔE_a = 0.35 eV). In path 2, creation of *OH–B₂–SiNT (7, 0)–*OH has higher ΔE_a than formation of B₂–SiNT (7, 0)–*O + H₂O in path 1 ca. 0.06 eV and so path 1 can be considered as optimal pathway to ORR.

The over-potential of ORR on Pt-based compounds and graphene are 0.44 and 0.45 V.^49–59 The experimental researchers investigated the onset-potential for the ORR performed on several catalysts^105–110 and results are stated in Table 5. The G of ORR steps are stated in Fig. 5. The level of the final produce (B₂–SiNT (7, 0)–* + 2H₂O) is considered as reference step and ORR steps in U = 0 V is downhill. Reaction steps become downward that U is decreased to 0.97 V and beginning voltage for ORR is 0.97 V. The B₂–SiNT (7, 0) is suggested as suitable ORR catalyst.

Table 5 The onset-potential (in eV) values for the ORR performed on several catalysts^105–110

Catalyst	Onset potential	Catalyst	Onset potential	Catalyst	Onset potential
Pd/CNT^105	0.764	Pd–Ni^107	1.105	PdNi^109	1.040
Pd/MWCNT^105	1.014	PtCo/C^107	0.836	Pd^109	0.901
Pd–Ni(3 : 1)/C^106	1.005	Pd–Fe/C^108	0.865	Pd–Cu^110	1.001
Pd2Co/C^106	0.735	Pd/C^108	0.920	Pt/C^110	0.900

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Fig. 5 The G values for ORR on B₂–SiNT (7, 0).

4. Conclusions

Performances of boron–silicon nanotube (7, 0) as novel catalyst to ORR are investigated. The ORR on surface of B₂–SiNT can be continued through LH and ER mechanisms. The rate-determining stage (ΔE_a = 0.35 eV) for ORR on B₂–SiNT (7, 0) surface is creation of B₂–SiNT (7, 0)–*OH structure. The calculated beginning voltage to ORR on surface of the B₂–SiNT (7, 0) is 0.37 V. In the acidic solution the beginning voltage to oxygen reduction process can be evaluated to 0.97 V. Results indicated that the B₂–SiNT (7, 0) is suggested as catalyst to ORR with suitable efficiency.

Conflicts of interest

There are no conflicts to declare.

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