Communication—Hydrogen Peroxide Reduction in Aqueous Electrolytes: Influence of a Heterogeneous Decomposition Step

A mechanistic model is herein presented for the reduction of H2O2(aq) in aqueous electrolytes on a rotating disk electrode that considers the possible heterogeneous dismutation of H2O2(aq). A theoretical analysis of this model predicts Koutecky-Levich plots that deviate from linearity at high rotation rates depending on the relative values of the rates constants of the processes involved, in agreement with the behavior found for a variety of electrode materials. © The Author(s) 2016. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.0211608jes] All rights reserved.


Theoretical
The mechanistic pathways for H 2 O 2 (aq) reduction to be considered herein (see Scheme 1) 9,10 assumes that none of the species involved displays any affinity for the electrode surface, i.e. the possible role of adsorbed reaction intermediates is fully neglected. As shown in the scheme, H 2 O 2 (aq) present in a region immediately adjacent to the electrode surface, denoted as H 2 O 2 * (aq), can be reduced via a twoelectron process to yield water, i.e. 2e − + H 2 O 2 → 2H 2 O. In addition, H 2 O 2 * (aq) can undergo a surface-catalyzed disproportionation generating water and O 2 (aq), i.e. 2H 2 O 2 → 2H 2 O + O 2 , which, in turn, can be reduced, regenerating H 2 O 2 * (aq) via a two-electron process, i.e. 2e − + O 2 → H 2 O 2 , or producing water via a four-electron reaction, i.e. 4e − + O 2 → 2H 2 O. Also specified in the scheme are the rate constants associated with each of processes involved, as well as the mass transport contributions, denoted as (D/δ) j , j = H 2 O 2 (aq) and O 2 (aq), where D j is the diffusion coefficient of species j, δ = 1.61(D 2 ω −3 ν) 1/6 , the diffusion boundary layer thickness, ν, the kinematic viscosity of the solution, and the superscript ∞ refers to the bulk concentration. On this basis, and assuming all of the reactions are first order in the reactant, as assumed originally by Bagotskii et al., 9 The current density, i, will be given by the sum of the three electrochemical processes in Scheme 1, i.e.
where F is Faraday's constant. Substituting Eqs. 3 and 4 into Eq. 5, the reciprocal current density can be expressed as: As expected, for k d = 0, i.e. no H 2 O 2 * (aq) dismutation, Eq. 6 will reduce to a conventional Koutecky-Levich (KL) expression for the two-electron reduction of H 2 O 2 (aq) proceeding at a rate proportional to k 3 : Scheme 1. Reaction pathways for the reduction of H 2 O 2 (aq) considered in this work, where k 1 is rate constant for the reduction of oxygen to water, k 2 and k 3 are the rate constants for the reduction of solution phase oxygen, O 2 (aq), to solution phase peroxide, H 2 O 2 (aq), and water, respectively, k d is the first-order rate constant for the catalytic disproportionation of H 2 O 2 (aq), and δ j is the diffusion boundary layer thickness for species j = H 2 O 2 (aq) and O 2 (aq). The symbols * and ∞ represent the region immediately adjacent to the electrode surface and bulk, respectively. We recognize that one or more steps in the mechanism, that involve the transfer of multiple electrons, may be more complex, and, thus, that the first order rate constants would be of a global character.

Furthermore, as k d reaches values much larger than
, Eq. 6 can be expressed as: In this specific case, a KL plot will also be linear with exactly the same slope as that in Eq. 7 and an intercept inversely proportional to the sum of the rates constants for O 2 (aq) reduction to peroxide and water, i.e. k 1 and k 2 , respectively.

Results and Discussion
Insight into the effect of k d on the shape of the KL plots was obtained using, as a means of illustration, values for the electrochemical rate constants similar to those reported by Muthukrishnan et al. 11 for a pyrolyzed Fe-containing carbonaceous material derived from mixtures of fine particles of polyimide and tris(acetylacetonato) iron(III) recorded at a potential E ≈ 0.6 V vs. RHE (as specified in the legend in Panel A, Fig. 1; cf. to bend upward as ω increased approaching the limit predicted by Eq. 7 for k d → 0 (see gray dashed line).
A more detailed mathematical analysis of Eq. 6 reveals that the bending direction of the KL plots or, equivalently, the sign of their first derivative with respect to ω −1/2 in the limit as ω→∞, is governed by the difference between the limiting values of the reciprocal current densities in Eqs. 7 and 8, which can be conveniently expressed in terms of a dimensionless parameter γ, defined as: 2k 3 [9] In particular, In other words (and ignoring the rather small differences in the values of D H 2 O 2 and D O 2 ), if the rates of oxygen reduction, regardless of the mechanism involved, are larger than the corresponding rates of peroxide reduction, γ would be positive, whereas should the opposite be the case, γ would be negative. The latter is illustrated in Panel B, Fig. 1, for the set of (fictitious) parameters specified in the legend for which γ is the same as in Panel A, but of opposite sign.
In yet another paper, Amirfakhri et al. examined the reduction of H 2 O 2 (aq) on metal-free nitrogen-doped graphene nanoflake electrodes in unbuffered 0.1 M Na 2 SO 4 aqueous solutions and found KL plots bending downward 1 (see scattered symbols in Fig. 2 below), where the solid lines are linear fits to the data in the original paper). As indicated, the experimental data displays a curvature which according to our analysis, is consistent with a rate for peroxide reduction that exceeds that of oxygen reduction, i.e. γ < 0. Assuming, for simplicity, a value of k 1 = 0, i.e. total neglect of a four-electron reduction of oxygen to water, a potential independent two-electron reduction of oxygen to peroxide, and a constant value of k d , the best fits to the data based on our model (see Eq. 5; solid lines in Fig. 2), yielded values of k 2 = 0.0016 cm/s, and k d = 0.25 cm/s, which reproduce the curvature observed in the experimental results for all rotation rates, except perhaps the lowest one for the most negative voltage. It should be emphasized that for large ω our model provides a much better fit than their linear analogue (dotted lines in Fig. 2).
Also included in this report 1 was a thorough theoretical analysis of mechanistic aspects of H 2 O 2 (aq) reduction using a similar approach to that employed in this work yielding expressions (cf. Eqs. 13 and 14 in Ref. 1) equivalent to those in Eq. 6. However, the model considered therein assumed that the O 2 generated from H 2 O 2 (aq) dismutation remained adsorbed on the surface undergoing a subsequent irreversible desorption, which led them to conclude that KL plots would always be linear, a fact that is not supported by their own measurements. These contradictory results stem from their neglect of the mass transport contribution associated with the O 2 (aq) and thus its dependence on ω.

Summary
The theoretical analysis herein presented has shown that the curvature of Koutecky-Levich plots observed for the reduction of H 2 O 2 (aq) in aqueous electrolytes reported in the literature can be accounted for by including the heterogeneous dismutation of H 2 O 2 (aq), whereby the direction of the bending depends critically on the values of the rates of the processes involved. On this basis, caution must be exercised when forcing a linear fit to such plots, as the slope and intercept could not be interpreted in the conventional way, and thus yield unreliable values for the rate constants for H 2 O 2 (aq) reduction. One possible means of avoiding this problem is by measuring the rate constant for the heterogeneous dismutation of H 2 O 2 (aq) under the same identical conditions as those employed in the electrochemical experiments and include those in the mechanistic analysis.
The diffusion coefficients of peroxide, D H 2 O 2 , and oxygen, D O 2 , were accidentally interchanged when calculating the data shown in ported in the original paper and, as such, do not affect the conclusions drawn from the analysis provided therein. Note that Fig.  2 was obtained using the correct diffusion coefficients for the species in question and therefore was not compromised by the error noted.