Table 1 Rates, reversibility and the degree of rate control (DRC) of the ten elementary steps of the microkinetic model

From: On the origin of multihole oxygen evolution in haematite photoanodes

Parameters:

C(h+) = 1 ML

C(h+) = 10−2 ML

\({E}_{{{{\rm{diff}}}}}^{{{{\rm{h}}}}}\) = 0.29 eV

Θ(*O1−) = 0.13 ML

Θ(*O1−) = 7.4 × 10−3 ML

 

Eapp = 0.18 eV

Eapp = 0.21 eV

 

\({{{\mathcal{O}}}}\)(C(h+)) = 1.15; 𝒪(Θ(*O1−)) = 3.07 

\({{{\mathcal{O}}}}\)(C(h+)) = 2.94; 𝒪(Θ(*O1−)) = 3.00

Reaction

Rate (s–1)

kb/kf

DRC

Rate (s–1)

kb/kf

DRC

1: *OH + h+ + OH → *O1− + H2O

6.32 × 101

1.48 × 10–1

0.89

1.56 × 10–2

9.81 × 10–1

0.05

2: *O1− + h+ + OH → *OOH

2.00 × 10–1

1.24 × 10–7

0.00

1.95 × 10–7

3.92 × 10–8

0.00

3: *OOH + h+ + OH → *OO + H2O

1.07

8.83 × 10–6

0.02

2.83 × 10–6

6.40 × 10–2

0.00

4: *OO + h+ + OH → O2 + *OH

2.08 × 10–4

9.00 × 10–17

0.00

7.03 × 10–9

1.77 × 10–13

0.00

5: *OO + *O1− + H2O → O2 + 2*OH

2.14 × 101

3.65 × 10–16

0.00

5.20 × 10–3

5.66 × 10–13

0.00

6: 2*O1− + H2O → *OOH + *OH

5.56 × 10–16

5.80 × 10–6

0.00

4.77 × 10–23

2.76 × 10–7

0.00

7: 3*O1− + H2O → *OO + 2*OH

2.16 × 10–9

5.04 × 10–12

0.00

3.92 × 10–14

1.18 × 10–9

0.00

8: 2*O1− + OH → *OOH + *O2−

8.73 × 10–1

4.27 × 10–1

0.00

2.63 × 10–6

9.94 × 10–1

0.00

9: 3*O1− + OH → *OO + *OH + *O2−

2.04 × 101

4.98 × 10–22

0.09

5.19 × 10–3

3.34 × 10–21

0.94

10: *O2− + h+ → *O1−

2.12 × 101

2.39 × 10–3

0.00

5.20 × 10–3

4.12 × 10–1

0.00

  1. The reversibility is expressed as kb/kf, where kf is the forward rate and kb is the backward rate. The activation energy for hole diffusion, \(E^{\mathrm{h}}_{{\mathrm{diff}}}\), was set as 0.29 eV, the experimental bulk value. We report results obtained at two SCL-hole concentrations, C(h+) = 1 and 0.01 ML. Θ(*O1−) is the surface hole coverage, Eapp is the apparent activation energy, 𝒪(C(h+)) is the reaction order with respect to SCL-holes and 𝒪(Θ(*O1−)) is the reaction order with respect to surface holes.