Mechanisms of direct hydrogen peroxide synthesis on

PCCP PAPER

Cite this: Phys. Chem. Chem. Phys., 2017, 19, 9007

Mechanisms of direct hydrogen peroxide synthesis on silicon and phosphorus dual-doped graphene: a DFT-D study† Shuo Li,a Zhansheng Lu,*ab Yi Zhang,a Dongwei Mac and Zongxian Yangad Hydrogen peroxide (H2O2) is an important chemical commodity, with demand growing significantly in chemical synthesis due to its green characteristics. The mechanisms of the direct synthesis of hydrogen peroxide (DSHP) on metal-free silicon and phosphorus dual-doped graphene (Si–P–G) catalyst, based on a dispersion-corrected density functional theory (DFT-D) method, are systematically investigated. The most stable Si–P–G catalyst is presented, with the local region of dopants shown to play an impor-

Received 20th December 2016, Accepted 6th March 2017

tant role in the adsorption and reduction of oxygen. A two-electron pathway is probable for DSHP

DOI: 10.1039/c6cp08668c

rate-limiting step, with a small barrier energy of 0.66 eV, and the potential energy surface is downhill by

on Si–P–G according to kinetic and thermodynamic analyses. The hydrogenation of O2 to OOH is the Gibbs free energy calculations. All results indicate that Si–P–G is a novel catalyst with high activity and

rsc.li/pccp

good selectivity for DSHP.

1. Introduction Hydrogen peroxide (H2O2) is among the 100 most important chemicals worldwide,1 and is a highly efficient and green oxidant because of its high active oxygen content and production of H2O as the only byproduct.2,3 H2O2 is categorized into commercial H2O2, high-purity H2O2, and concentrated H2O2. In recent years, commercial H2O2 has seen wide applications in the field of chemical synthesis, such as in the epoxidation of propylene to propylene oxide, oxidation of cyclohexanone amine to cyclohexanone oxime, and the desulfurization of gasoline and diesel.4–9 In H2O2 production, the direct synthesis of hydrogen peroxide (DSHP) from H2 and O2 is a typical green and atom economical chemical reaction in noble metal catalysis and fuel cells, among others.10 DSHP using the fuel cell method, including an anode, electrolyte membrane, and cathode, has been reported by Yamanaka et al. in 1990.11 Therein, the twoelectron reduction of O2 resulted in H2O2 production, while the four-electron reduction formed H2O as a side product. To improve H2O2 productivity, the preparation of highly active electrode catalytic materials and synergy with selective a

College of Physics and Materials Science, Henan Normal University, Xinxiang 453007, China. E-mail: [email protected] b State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, P. R. China c School of Physics, Anyang Normal University, Anyang 455000, China d Collaborative Innovation Center of Nano Functional Materials and Applications, Kaifeng, China † Electronic supplementary information (ESI) available. See DOI: 10.1039/c6cp08668c

This journal is © the Owner Societies 2017

electrocatalysis should be studied to achieve higher H2O2 concentrations and increased extracted power. Various methods with different catalytic materials have been considered to improve H2O2 selectivity.12–15 Noble metals are involved in both noble metals catalysis and fuel cell methods. However, as traditional catalysts, noble metals incur some problems, including high cost, poor durability, inactivation by CO poisoning, and low selectivity. Therefore, much effort has been dedicated to designing new low-cost catalysts with high selectivities.10,14,16,17 Interestingly, metal-free catalysts, such as graphene doped with nitrogen,18,19 boron,20 phosphorus,21,22 sulfur,23,24 and silicon,25 have shown efficient catalytic activity and long-term stability, both experimentally and theoretically, in proton exchange membrane fuel cells. Furthermore, graphene catalysts dual-doped with nitrogen and boron,26 sulfur and nitrogen,27 phosphorus and nitrogen,28,29 and others30,31 were found to be efficient in the oxygen reduction reaction (ORR), giving final products of H2O or H2O2, depending on whether a four-electron or two-electron pathway occurred. Herein, we report that using silicon and phosphorus as dual dopants efficiently tuned the activity and selectivity of graphene. When Si and P were dual-doped into defective graphene, the presence of abundant regulatable geometries and electron redistributions could be investigated with efficient catalytic activity for DSHP. The revealed structure of metal-free Si and P dual-doped graphene (Si–P–G) showed that dual-doped graphene can tune activity and selectivity for the efficient catalysis of DSHP. In our current calculations, we first investigated the structure of Si–P–G, with the most stable configurations shown

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Fig. 1 (a) The most stable configurations of Si and P dual-doped graphene (Si–P–G), the SiPC3 moiety, is marked with a blue dotted box and the bond length is marked in red. Gray, yellow, and pink spheres represent C, Si, and P atoms, respectively. (b) Formation energies of Si–P–G (black line, mP = mP atom; blue line, mP = mP4) and divacancy (SiC4, red line). Zero point energy is marked with a blue dotted line. (c) Final Si–P–G structure from molecular dynamics simulation at 1000 K.

in Fig. 1a. Subsequently, we identified the active center and presented two overall mechanisms based on earlier reports,32,33 indicating that the ORR process occurred with a combination of four-electron and two-electron pathways. Moreover, we showed that H2O2 was favored as the final product, according to transition state calculations for kinetic processes and Gibbs free energy for thermodynamic analysis. Our results showed that Si–P–G is a novel catalyst for DSHP.

2. Computational details All calculations were performed within dispersion-corrected density functional theory (DFT-D) computations, as implemented using DMol3 code embedded in Materials Studio. Generalized gradient approximation (GGA) with a Perdew–Burke–Ernzerhof (PBE) functional was employed, using the DFT semi-core pseudopotential34 with long-range dispersion correction based on the Grimme approach to accurately describe van der Waals bonds.35 Double numerical plus polarization (DNP) was specified as the atomic orbital basis set. The k-points were generated automatically using the Monkhorst–Pack method.36 K-points of 5 5 1 were used for structure relaxation, while denser meshes of 15 15 1 are used to calculate the density of states (DOS). Mulliken charge analysis was used to determine charge transfer. Convergence tolerances of the geometry optimization were set to 105 Ha (1 Ha = 27.21 eV) for the energy, 0.002 Ha Å1 for the maximum force, and 0.005 Å for the maximum displacement. The electronic SCF tolerance was set to 106 Ha. A smearing of 0.005 Ha was applied to the orbital occupation to achieve accurate electronic convergence. The transition state (TS) was obtained using LST/QST tools in DMol3 code. Moreover, the transition states were confirmed to have only one imaginary frequency. First-principles molecular dynamics was performed with a single k point at G to sample the Brillouin zone. A time step of 1 fs was used and the temperature was controlled by velocity scaling in each step. Further details of the DMol3 code can be found elsewhere.35,37 The original graphene was modeled as a 4 4 1 graphene supercell with the coordinated structures separated by a vacuum layer of 15 Å, which was found to be enough for the ORR. The adsorption energy (Ead) is defined as Ead = Eadsorbate + Esubstrate Eadsorbate/substrate

9008 | Phys. Chem. Chem. Phys., 2017, 19, 9007--9015

(1)

where Eadsorbate, Esubstrate, and Eadsorbate/substrate are the total energies of the free adsorbate, the corresponding substrate, and the substrate with the adsorbate, respectively. Using this definition, a positive value indicates an exothermic adsorption. The same periodic box dimensions and same level of calculations were used to obtain all the above energy values. The Gibbs free energy of the ORR intermediates can be calculated using the approach developed by Nørskov et al.38 In the present study, the change in free energy for the elemental step was defined as DG = DE + DZPE + TDS, where DE is the reaction energy based on DFT-D calculations, DZPE is the zero point energy, T is the temperature (298.5 K), and DS is the change in entropy. The ZPE and S of the ORR intermediates were calculated based on vibrational frequencies. The standard hydrogen electrode was set as the reference potential. The free energy of 1/2H2 can be used instead of that of (H+ + e). The free energy of H2O was calculated in the gas phase at 298.5 K and the free energy of O2 was obtained from the reaction O2 + 2H2 = 2H2O, for which the free energy change was 4.92 eV.39 A conductor-like screening model (COSMO) was used to simulate a H2O solvent environment throughout the thermodynamic process. COSMO is a continuum model in which the solute molecule forms a cavity within the dielectric continuum of permittivity.40 The DMol3/COSMO method was generalized to the periodic boundary cases, and deviation of this COSMO approximation from the exact solution was small. The dielectric constant was set to 78.54 for H2O solvent.

3. Results and discussion 3.1

Si–P–G structure

There were three main types of doped graphene structure: (i) Si and P doped into a monovacancy, respectively; (ii) Si doped into a divacancy and P doped into a monovacancy; and (iii) P doped into a divacancy and Si doped into a monovacancy. Larger defects were not considered. For all type (i) structures, it was found that Si and P preferred to be close to each other in a distortion structure, as shown in Fig. S1 in the ESI.† We also found that the most stable Si and P dual-doped structure, with Si and P close to each other, was unstable in oxygen-containing environments. Upon O2 adsorption, the P atom was withdrawn by the O2, forming a PO2 moiety


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on P and Si codoped graphene, resulting in the dual doping structure being crushed, as presented in Fig. S2 in the ESI.† It was suggested that P-coordinated Si-doped monovacancy graphene was not stable in the oxygen environment. For all type (ii) and (iii) structures, we mainly considered the total energy, because the same number of atoms were present in each structure. Different Si and P dual-doped graphene substrates, named ortho, meta-I, meta-II, para, and same lattice, were considered. Therefore, there were 10 possible configurations of Si and P dual-doped graphene with dopants introduced into the graphene framework, with their relative energies shown in Fig. S3 in the ESI.† The most stable Si and P dual-doped graphene was marked ‘‘Si–P–G’’ (corresponding to surface 1 in Fig. S3, ESI†) following investigation of the ORR. The structure of Si–P–G was deformed because the P atoms slightly protruded from the surface. In the next section, the stability of Si–P–G was investigated in depth. 3.1.1 Si–P–G stability. The selected structure of Si–P–G is presented in Fig. 1a, with an Si–P bond length of 2.27 Å and three Si–C bonds lengths of 1.95 Å, 1.81 Å, and 1.86 Å, respectively. For the designed Si–P–G material, we first considered whether Si–P–G was easily formed. Therefore, we calculated the formation energies (Ef) of the Si and P dual-doped graphene, given by Ef = Etotal(m, n) Etotal(0, 0) mmSi nmP + (m 0 + n)mC

(2)

where m is the number of Si atoms, n is the number of P atoms, and m 0 is the number of the C atoms substituted by Si atoms. Etotal(m, n) is the total energy of the supercell with the defect complex, and Etotal(0, 0) is the total energy of pristine graphene.

mSi, mP and mC are the chemical potentials of Si, P, and C reservoirs, respectively. mC was calculated as in graphene. For the chemical potentials of Si and P, which were tunable during experiments, one limit was set at the states of mSi and mP for the Si bulk of 64 atoms and the P4 cluster (white phosphorus is pure and readily available41), while the other was set for single atoms of Si and P, respectively. The most important problem was determining the range of chemical potential. The chemical potential of Si bulk and P4 cluster are shown in Fig. 1b. The formation energy of Si–P–G was 5.10 eV and that of Si-doped divacancy graphene (marked as ‘‘SiC4’’) was 4.72 eV. However, following an increased mP, the Ef of Si–P–G became below 0 eV, indicating that the designed Si–P–G substrate could be easily synthesized in terms of thermodynamics. To further confirm the stability of the selected Si–P–G structure, first-principles molecular dynamics calculations were performed, which found that Si–P–G could even be stable for 2 ps at 1000 K, with some distortion over time. The snapshot of the final Si–P–G structure from molecular dynamics calculations at high temperature is displayed in Fig. 1c. 3.1.2 Electronic properties of Si–P–G. We investigated the electronic properties of the Si–P–G structure to determine its potential catalytic activity. As presented in Fig. 2a, atomic Si and P were positively charged by 1.03 |e| and 0.21 |e|, respectively, while the SiPC3 moieties is negatively charged by 0.01 |e|. The total density of states (TDOS) of Si–P–G and the partial density of states (PDOS) of Si, P and SiPC3 moieties are presented in Fig. 2b. Compared with the 2p states of Si, P, and SiPC3 moieties, many peaks were at the same energy level, indicating hybridization between the 2p states of Si, P, and C,

Fig. 2 (a) Relaxed Si–P–G structure and selected atomic charges (in blue). (b) Total density of states (TDOS) for Si–P–G and pure graphene, and partial density of states (PDOS) for Si, P, and SiPC3 moieties. The Fermi level (Ef) is defined as zero (red dotted line). (c) Color map of Fukui function plot of Si–P–G (electrophilic, blue; nucleophilic, red).



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and the covalent properties of the SiPC3 moieties. Furthermore, unlike pure graphene, a peak emerged in the gap area of Si–P–G, indicating that charge transfer between various ORR-involved species and Si–P–G was favorable, and implying that Si–P–G had efficient catalytic activity. The electrophilic and nucleophilic Fukui function plot of Si–P–G confirmed that the P and Si atoms exhibited strong electrophilic (blue) and nucleophilic (red) properties (Fig. 2c), respectively, indicating good electron transfer for the ORR. 3.2

Adsorption of various species involved in ORR on Si–P–G

We examined various adsorption sites to determine the most stable configuration for each adsorbate. The most stable configurations of the various ORR-involved species on Si–P–G, including O2, OOH, O, H, OH, H2O, and HOOH, are presented in Fig. 3, and their corresponding adsorption properties are summarized in Table 1. We first investigated the adsorption characteristics of O2, because adsorbed O2 (denoted as O2* here and as ‘‘*’’ subsequently, representing the reactant bonded with the substrate) is a prerequisite of the two-electron and four-electron pathways. O2 molecules preferred to anchor at Si and P sites, with Ead values of 0.43 eV and 0.74 eV, respectively. For the end-on configuration at the Si site, the O–O and O–Si bond lengths were 1.34 Å and 1.81 Å, respectively (Fig. 3a). Upon O2 adsorption, O2* was negatively charged by 0.43 |e|, and compared with clean Si–P–G, Si and P atoms were more positively charged by 0.23 |e| and 0.10 |e|, respectively. The charge transfer of C atoms

PCCP Table 1 Compiled corresponding adsorption sites, adsorption energy (Ead in eV), and Mulliken charges (Dq in e). Geometric and energetic parameters of reaction intermediates, as identified in the stable state. Positive values indicate an exothermic adsorption with the definition

Reaction intermediates Configurations Ead Fig. Fig. Fig. Fig. Fig. Fig. Fig.

3a 3b 3c 3d 3e 3f 3g

O2(Si) O2(P) O+O O H OH O + OH

Fig. 3h Fig. 3i

H2O O2 + H

Fig. 3j Fig. 3k

OOH HOOH

0.43 0.74 5.83 5.94 2.41 3.80 4.87(O); 2.73(OH) 0.44 0.66(O2); 2.33(H) 1.71 0.27

Dq Dq (adsorption) (Si)

Dq (P)

0.43 0.23 0.10 0.66 0.02 0.63 0.55; 0.70 0.34 1.02 0.69 0.32 0.53 0.20 0.03 0.03 0.34 0.25 0.01 0.55(O); 0.24 0.50 0.41(OH) 0.28 0.11 0.08 0.68(O2); 0.02 0.65 0.24(H) 0.29 0.03 0.40 0.01 0.03 0.07

in these systems is negligible. For the side-on configuration at the P site (Fig. 3b), the O–O bond length was 1.58 Å and two P–O bond lengths were 1.63 Å and 1.71 Å. O2* was negatively charged by 0.66 |e|, and the two O atoms of the O2 molecule were negatively charged by 0.32 |e| and 0.34 |e|. Compared with clean Si–P–G, the P atom was more positively charged by 0.63 |e|. Therefore, the main charge transfer was from the SiPC3 moiety area, which was believed to act as the active center for ORR. The most stable adsorption configuration of the two O atoms (dissociative species from O2) is presented in Fig. 3c.

Fig. 3 Top views and side views of relaxed atomic structures for various ORR chemical species adsorbed on Si–P–G: (a) O2(Si), (b) Op(Si), (c) O + O, (d) O, (e) H, (f) OH, (g) O + OH, (h) H2O, (i) O2 + H, (j) OOH, and (k) HOOH. Gray, yellow, pink, red, and white spheres represent C, Si, P, O, and H atoms, respectively. Red numbers are distances between atoms (in Å).



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The two O atoms were adsorbed on the P site and located atop the Si–P bond, forming a P–O bond length of 1.49 Å and P–O and Si–O bond lengths of 1.61 Å and 1.70 Å, respectively. The two O* atoms were negatively charged by 0.55 |e| and 0.70 |e|. In the intermediate products, the most stable adsorption configuration of an O atom is presented in Fig. 3d. O* was located atop the Si–P bond with a large Ead of 5.94 eV, forming a Si–O bond length of 1.72 Å and P–O bond length of 1.64 Å, respectively. O* was negatively charged by 0.69 |e|. Atomic H was preferably adsorbed on the C site (neighboring the Si dopant) with an Ead of 2.41 eV and C–H bond length of 1.12 Å (Fig. 3e). Atomic H was positively charged by 0.20 |e|, confirming that H* could be used as H+ in the calculations. As important intermediates in the ORR, OH species were preferably adsorbed on the Si site with an Ead of 3.80 eV, forming a Si–O bond length of 1.69 Å (Fig. 3f). OH* was negatively charged by 0.44 |e|. The coadsorption of O and OH was an important intermediate product, where O and OH were adsorbed on the P and Si sites, forming a P–O bond length of 1.52 Å and Si–O bond length of 1.68 Å, respectively (Fig. 3g). The O* and the OH* is negatively charged by 0.55 |e| and 0.41 |e|, respectively. As the four-electron product, H2O was weakly adsorbed on the Si–P–G with a small Ead of 0.44 eV (Fig. 3h), together with a negligible charge transfer between H2O and the substrate, indicating that the interaction between H2O and the Si–P–G substrate was rather weak, and that H2O would be easily released as the final ORR product. For the precursor of OOH*, the co-adsorption configuration of O2 and H was investigated. For end-on O2* on the Si site, H* adsorbed on the C site neighboring O2* with an O–O bond length of 1.34 Å and C–H bond length of 1.11 Å (Fig. 3i). H* was positively charged by 0.23 |e|, and the O2 molecules were negatively charged by 0.47 |e|. Adsorbed OOH on the P site was negatively charged by 0.29 |e| with an O–OH bond length of 1.50 Å (Fig. 3j) and Ead of 1.71 eV.

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As the final product of DSHP, HOOH was weakly adsorbed on Si–P–G, with a small Ead of 0.27 eV (Fig. 3k), and showed negligible charge transfer between HOOH and the Si–P–G substrate, indicating that the interaction between HOOH and the Si–P–G substrate was rather weak, and that HOOH could be easily released as the final DSHP product.

3.3

Chemical behavior in various reaction pathways

3.3.1 Four-electron pathway to form H2O. There are two possible reaction pathways for adsorbed O2: hydrogenation into OOH* species or dissociation into two O* atoms. The O2 dissociation process on Si–P–G from the end-on configuration on the Si site is presented in Fig. 4. Firstly, the O2 molecule was easily adsorbed on the Si site by the end-on configuration. Subsequently, the most stable adsorption of O2 atop the Si–P bond formed from end-on adsorption of O2 on Si with a barrier energy (Eb) (TS1) of 0.32 eV and an exothermic reaction energy of 0.38 eV (see stage-1 in Fig. 4). Then, O2 dissociated into two O* with an Eb (TS2) of 0.001 eV and large exothermic reaction energy of 4.39 eV, for which this process can be assumed to be spontaneous. The above process is marked as ‘‘stage-2’’ in Fig. 4. In contrast, for sideon adsorption of O 2 on the P site, adsorbed O2 directly dissociated to two O* through its Eb (TS3) with dissociation of the O–O bond. This process was exothermic by 4.68 eV and had a small Eb of 0.19 eV. The configuration of the final product of two O* was the same as that in stage-1: one O atom is adsorbed on bridge site of the Si–P bond and another is adsorbed on P site. The process above is marked as ‘‘stage-3’’ in Fig. 4. Next, the hydrogenation of atomic O* was considered. H* was preferably adsorbed on the C site, first forming OH* through hydrogenation of O* on the P site with an Eb (TS4) of 1.34 eV and exothermic reaction energy of 0.20 eV. The above process is marked as ‘‘stage-4’’ in Fig. 4. As presented in stage-1 to stage-4, the reaction following stage-4 did not need to be considered, due to the large Eb (1.34 eV) of the first hydrogenation.

Fig. 4 Dissociation of O2 from Si site (stage-1 and stage-2) and P site (stage-3) adsorption configurations, and the hydrogenation of atomic O (stage-4). Transition states (TS) are marked by a dashed rectangular box, and corresponding barrier energies (Eb) and reaction energies (D E, change in total energy between products and reactants) are presented below each TS.



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Fig. 5 All four-electron pathways. Stage-5: hydrogenation of adsorbed O2 on the P site and the formation and subsequent dissociation of OOH* species. Stage-6: hydrogenation of O* on the P site. Stage-7 and stage-8: formation of two H2O molecules on Si–P–G.

For the hydrogenation of O2* on the P site, H* was preferably adsorbed on C site (Fig. 5), while OOH was formed from the hydrogenation of O2 on the P site with an Eb (TS5) of 0.66 eV and exothermic reaction energy of 0.94 eV. Subsequently, O–O bond scission in OOH* produced an O* atom on the P site and an OH* species on the Si site with an Eb (TS6) of 0.30 eV and a large exothermic reaction energy of 3.02 eV. The formed OH* underwent torsion easily to the most stable states with an Eb (TS7) of 0.18 eV and exothermic reaction energy of 0.15 eV. This process is marked as ‘‘stage-5’’ in Fig. 5. Following the formation of O* + OH* species, there were two possible pathways for further hydrogenation: O* hydrogenation or OH* hydrogenation into OH* + OH* or O* + H2O, respectively. We found that the configuration of O* + H2O was not stable, and would spontaneously convert into the coadsorbed configuration of two OH*. Therefore, we focused on the process of hydrogenation of O* + OH* that would result in the coadsorbed configuration of two OH* with an Eb (TS8) of 0.38 eV and exothermic reaction energy of 0.62 eV, as shown in stage-6 in Fig. 5. Following the formation of two OH* species, and with H* adsorbed on the C site, the first H2O molecule was formed by the hydrogenation of OH* with an Eb (TS9) of 0.58 eV and exothermic reaction energy of 0.51 eV, as shown in stage-7 in Fig. 5. As the final product of the ORR process, H2O would be released easily due to the weak interaction between water and the substrate. Upon release of the (first) H2O molecule, the OH* species adsorbed on the P site would undergo further hydrogenation to a second H2O molecule, with an Eb (TS10) of 0.59 eV and a small exothermic reaction energy of 0.04 eV, as shown in stage-8 in Fig. 5. Again, the formed H2O would be released easily due to the weak interaction between water and the substrate, resulting in recovery of Si–P–G.


In summary, in the kinetic process, the rate-limiting step of the four-electron pathway was O2 hydrogenation to OOH*, with an Eb 0.66 eV, and all stages were exothermic. 3.3.2 Two-electron pathway to form HOOH. As discussed above, the OOH species was formed from the hydrogenation of O2 on P the site (stage-5 in Fig. 5). Following the OOH species formation, the final product of DSHP, HOOH, was formed from the further hydrogenation of OOH* with an Eb (TS11) of 0.04 eV and exothermic reaction energy of 0.32 eV, as shown in stage-9 in Fig. 6. As the final product of DSHP, HOOH can be further dissociated or hydrogenated. HOOH dissociation resulted in two OH* species with an Eb (TS12) of 0.98 eV and exothermic reaction energy of 4.23 eV, as shown in stage-10 in Fig. 6. The hydrogenation of HOOH resulted in OH* + H2O with an Eb (TS13) of 1.15 eV and exothermic reaction energy of 4.10 eV, as shown in stage-11 in Fig. 6. Therefore, both Eb values of further dissociation or hydrogenation were larger than their corresponding Ead values, indicating that HOOH molecules would be released rather than undergo further dissociation or hydrogenation. In summary, in the kinetic process, the rate-limiting step of the two-electron pathway was O2 hydrogenation to OOH* with an Eb 0.66 eV, and all stages were exothermic. The side reactions of HOOH dissociation and hydrogenation were inhibited by large Eb values (0.98 and 1.15 eV). 3.4

Effect of temperature on HOOH formation

As mentioned above, in the kinetic process, the rate-limiting steps of the four-electron and two-electron pathways were both O2 hydrogenation (0.66 eV). However, the barriers of dissociation and hydrogenation of OOH* into O* + OH* and HOOH, respectively, were slightly different. To further define the product selectivity, we performed a thermodynamic analysis to determine the preferred pathway.


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Fig. 6 All two-electron pathways. HOOH formation from the hydrogenation of OOH is shown in stage-9, while the dissociation and hydrogenation of HOOH are shown in stage-10 and stage-11, respectively.

Table 2 Rate constant (k) for the rate-determining steps of OOH dissociation and HOOH formation on Si–P–G at different temperatures

Rate constant k/s1 Elementary reaction OOH* - O* + OH* OOH* + H* - HOOH

273 K

298 K 7

1.68 10 1.04 1012

5.33 107 1.31 1012

3.4.1 Rate constants of OOH dissociation and HOOH formation. The Eb values for OOH* dissociation and HOOH formation on Si–P–G (0.30 and 0.04 eV, respectively) were small, showing that these reactions could occur at room temperature. The working temperatures of the DSHP process were 273 K and 298 K from the principles of noble metal catalysis and fuel cells,10 respectively. Therefore, we investigated the rate constant of OOH* dissociation and HOOH formation using harmonic transition state theory42–44 (TST) to probe the role of temperature during the DSHP process. kB T qTS Ea (3) exp k¼ h qR KB T where kB is the Boltzmann constant, h is the Planck constant, T is the absolute temperature, and qTS and qR are the vibrational partition functions for the TS and reactant in the elementary reaction, respectively. For the partition function, q, vibrational degrees of freedom were only considered in the surface reaction, and were calculated in the harmonic model, 1 q ¼ vibrations Q hn i 1 exp kB T i¼1

(4)

where vi is the vibrational frequency. At the experimental temperature of DSHP, the rate constants for these key steps were calculated at 273 K and 298 K, respectively. The results are listed in Table 2. Notably, the rate constant of HOOH formation increased with increasing temperature on Si–P–G and the rate constant of OOH dissociation


was always smaller than that of HOOH formation, indicating that Si–P–G would exhibit better catalytic activity for the DSHP. The results of rate constant were in line with our kinetic results. 3.4.2 Gibbs free energy. Using the kinetic process barrier energy calculations, we summarized the main stages and favorable pathways (blue lines) for ORR in Fig. 7a. It was found that OOH* hydrogenation in the two-electron pathway was easier than OOH* dissociation in the four-electron pathway (0.04 eV vs. 0.30 eV). Thermodynamic analysis of Gibbs free energy considered the temperature effect at 298.5 K and the solvent effect using the COSMO method as the working environment. According to the computed free energy diagram, the favorable reduction steps of the four-electron pathway and two-electron pathway are presented in Fig. 7b. In the four-electron pathway, all reduction steps, except the two OH reductions, were downhill at 0 potential, as shown in Fig. 7b. The reduction steps for transforming OH into H2O had positive DG values of 0.27 eV and 0.34 eV, respectively. Formation of the second H2O was the thermodynamic ratedetermining step. However, in the two-electron pathway, all reduction steps were downhill at 0 potential, indicating that HOOH was successfully produced in thermodynamic calculations. Therefore, the DSHP process with a two-electron pathway was the most plausible for the ORR on Si–P–G. Table 3 summarizes some popular catalysts for DSHP and their properties in the preferable reaction pathways, and the lowest reaction barriers for H2O2 decomposition to 2OH. According to transition state calculations, the Si–P–G was more active in H2O2 formation than most noble metal catalysts. Compared with other catalysts, the decomposition of formed H2O2 on Si–P–G was difficult. The current DFT calculations showed that metal-free Si–P–G could promote the DSHP, and that its catalytic activity seemed comparable to those of standard metal catalysts. This study sheds light on the promising future role of graphene-based catalysts in the DSHP.


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Fig. 7 (a) Proposed ORR reaction mechanisms on Si–P–G. The most favorable reaction pathway is expressed as a blue line. Activation and reaction energies (in eV) are given in parentheses in the form ‘‘(Eb, D E)’’. (b) Free energy diagram of ORR along the four-electron and two-electron pathways on Si–P–G. Subscript ‘‘ads’’ represents adsorption on Si–P–G.

Table 3 Best reaction pathways and their corresponding rate-limiting step reaction barriers for DSHP on various catalysts. Lowest reaction barriers occurred for H2O2 decomposition into 2OH

Mechanism

Rate-limiting steps (eV)

Reaction barriers (HOOH* - 2OH*) (eV)

Au12 Pd(111)46

OOH* + H* - HOOH* O2* + H* - OOH*

Au@Pd(111)46 Pd(111)47 Pd(100)47 Pd(110)47 Si–P–G

O2* + H* - OOH* O2* + H* - OOH* O2* + H* - OOH* OOH* + H* - HOOH* O2* + H* - OOH*

0.47 0.92 0.82 0.85 0.58 0.67 1.05 0.66

0.18 0.03 0.09 0.23 0.30 0.07 0.10 0.98

Models 45

4. Conclusions Calculations were performed to investigate the detailed kinetic and thermodynamic behaviors of the ORR in the DSHP process on Si–P–G. From calculations of various Si and P dual-doped graphene structures, we found that the most stable Si–P–G configuration and electronic structure indicated efficient catalytic activity. O2 molecules preferred to anchor on or near the Si and P dopants, implying that SiPC3 moieties were the active center. The best pathway for DSHP on Si–P–G was identified, involving two steps for the direct hydrogenation of O2 on the P site. In the kinetic process, the rate-determining steps were O2 hydrogenation to OOH* (0.66 eV) and the two-electron pathway for HOOH formation was exothermic. In the thermodynamic analysis, the four-electron pathway was inhibited in Gibbs free


energy analysis. The rate constant of OOH dissociation was always smaller than that of HOOH formation, indicating that Si–P–G would exhibit good catalytic activity in the DSHP. Therefore, Si–P–G, as a metal-free catalyst, was expected to catalyze the reduction of O2 via a two-electron pathway in the DSHP.

Acknowledgements This work was supported by the National Natural Science Foundation of China [Grant No. 51401078, 11474086 and U1504108], the Program for Science & Technology Innovation Talents in Universities of Henan Province [Grant No. 15HASTIT016], the Foundation for the Key Young Teachers of Henan Province and Key Technology Research and Development Program of Henan Province


PCCP

[Grant No. 152102210083 and 142102210455], and the Science Foundation for the Excellent Youth Scholars of Henan Normal University [Grant No. 14YQ005]. This work was also supported by the High Performance Computing Center of Henan Normal University.

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