Results and Discussion

Chapter 5. Kinetic Insights for Oxygen Reduction Activity in Metal-Free Carbon

5.3 Results and Discussion

To obtain a kinetic understanding of the ORR on the ISW defect, which was predicted to be able to activate metal-free carbon nanomaterials, the activation energies required for the elementary step of the ORR were investigated. The adsorption of O2 was considered as the first step of the ORR. The

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energetics of O2 molecules and the ISW defects were computed by changing the distance between the oxygen in the O2 molecule and the carbon of the active site. To identify the stable spin state of the O2

adsorbate, we optimized the first step with a fixed spin state. Note that the singlet, doublet, and triplet pin states were considered. In Figure 5.1, from the local energy minimum, chemisorption and physisorption could be identified at O-C distances of approximately 1.5 and 2.9 Å, respectively. When the O2 molecule was chemisorbed onto the ISW defect, the doublet spin state was more stable than the singlet and triplet states, indicating that O2 molecules required the charge transfer from the substrate during the adsorption. In other words, the transferred charges stabilized the O2 adsorbate. Mulliken population analysis estimated the charge that was transferred from the substrate to the adsorbtae at 0.53 e. Meanwhile, the triplet spin state of the O2 molecule was stable in the gas phase. An activation energy of 0.22 eV was required for this transition of the spin state during adsorption. This value was comparable with the 0.29 eV observed in nitrogen-doped CNT surfaces. The reaction energy was for the adsorption was 0.02 eV.

Figure 5.1 The activation and reaction energies during O2 adsorption on ISW defect as a function of the distance from the surface. The considered distance is from 1.4 to 5.0 Å. Three different spin states are fixed during the geometry optimization.

After the adsorption of the O2 molecules, the reaction intermediate of OOH^* could be formed via 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0 0.2 0.4 0.6 0.8

R e la ti v e e n e rg y ( e V )

Distance from the active site (Å)

Singlet Triplet Doublet

Phy sisorption

5.0 Å

0.1 Å

1.4 Å

Chemisorption

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a single proton/electron transfer. It was confirmed that a proton presents in the solvated H3O⁺ was spontaneously transferred to the O2 adsorbate, forming OOH^*. The work function of the surface was 6.04 eV before the transfer of the proton occurred, implying that the reaction of O2* + H⁺ + e^- → OOH^* is expected to be spontaneous below the electrode potential of 1.64 V. Note that to evaluate the work function of the reactant, the O-H distances of hydronium were fixed during the geometry optimization, limiting the proton transfer. As the ORR can operate at under 0.9 V, the adsorbed O2 was immediately reduced to OOH^* on the ISW defect. After the formation of the reaction intermediate OOH^*, the reaction proceeds via a two-electron or four-electron pathway. To elucidate the reaction pathway, we can compare the activation energy for the formation of H2O2 with the reaction intermediate of O^*. The potential-dependent activation energy was calculated within the charge-extrapolation scheme (Figure 5.2). The activation energy for the two-electron pathway was always higher than that of the four-electron pathway. Thus, it was expected that the ISW defect could act as an active site for application in fuel cells. The reduction of O^* that followed the reduction of the reaction intermediate of OOH^* to O^* was also rapid with a low activation energy (< 0.2 eV under ORR operating condition). Since the transition state required for the reduction of O^* was close to the reactant, where the symmetry factor was almost 0 (Table 5.1), the activation energy was not significantly changed by varying the electrode potential.

The following step of reducing OH^* required a relatively large energy barrier, indicating that the rate- determining step could be the formation of H2O.

Figure 5.2 The potential-dependent activation energy for elementary step of ORR. The considered

4.4 4.8 5.2 5.6

0.0 0.2 0.4 0.6 0.8

E

a

( e V )

F (eV)

OOH* + H⁺ + e^- ®H₂O₂ OOH* + H⁺ + e^- ®H₂O + O*

O* + H⁺ + e^- ®OH*

OH* + H⁺ + e^- ®H₂O

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Table 5.1 Symmetry factor (β) for elementary step of ORR. Since the O2 adsorbate is reduced spontaneously on ISW defect, the corresponding symmetry factor is not estimated.

β

OOH^* + H⁺ + e^- → H2O2 0.47

OOH^* + H⁺ + e^- → H2O + O^* 0.25

O^* + H⁺ + e^- → OH^* 0.08

OH^* + H⁺ + e^- → H2O 0.43

As a result, the full free energy diagram could be described, including the activation energies in Figure 5.3. During the electrochemical reaction, the water near the electrode was reorganized, inducing an additional energy barrier. Thus, the water reorganization energy was added to the activation energy for all the steps in the electrochemical reaction. The value was taken from the results on the Pt surface²⁴. In the ISW defect, the rate-determining step was evaluated as the formation of H2O. Notably, the competing reaction step of the formation of OOH^* required an activation energy of 0.35 eV. The activation energy of the corresponding step (i.e., 0.64 eV) was comparable to that of Pt at an electrode potential of 0.9 V. Thus, the reaction rate for the overall ORR on the ISW defect was expected to be optimal for ORR. In addition, the selectivity for the ORR was quantitatively estimated by calculating the faradaic efficiency²⁵.

 = ^

^





× 100% (5.9)

where δG refers to the difference of activation energy at constant potential. kB and T represent the Boltzmann constant and temperature. As shown in Figure 5.4, the selectivity towards the four-electron pathway was almost 100%, while the formation of H2O2 increased as the electrode potential decreased.

This was caused by the difference in the symmetry factors of the two reaction pathways. The symmetry

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factor of the four-electron pathway was 0.25, while that of the two-electron pathway was 0.47 (Table 5.1). Thus, the change in the activation energy of the two-electron pathway was relatively larger as a function of the electrode potential than the four-electron pathway. In conclusion, the presence of an ISW defect activates the graphene basal plane, rendering it applicable for use in the proton exchange membrane fuel cell.

Figure 5.3 Free energy diagram for ORR on ISW defect at the electrode potential of 0.9 V vs. RHE.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5

D G

Reaction coordinate

2 e

^-

4 e

^-

O

₂

O

₂^*

OOH

^*

H

₂

O

₂

O

^*

OH

^*

H

₂

O

U = 0.9 V vs. RHE

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Figure 5.4 Schematic of competitive reaction in ORR and computed faradaic efficiency for four- electron pathway of ORR as a function of electrode potential.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

99.85 99.90 99.95 100.00

F a ra d a ic e ff ic ie n c y ( % )

U

_RHE

(V)

0 1 2 3

D G ( e V )

Reaction coordinate

4e

^-

2e

^-

OOH*

O*

H

₂

O

₂

*

eU_RHE

aeU_RHE beU_RHE

1 100%

1

^B

G k T

f

e

-d

= ´

+

Boltzmann distribution

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