Active site model for CO adlayer electrooxidation on nanoparticle catalysts

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Abstract

We present a two-state model for CO electrooxidation on catalyst nanoparticles. It exploits the active site concepts in order to describe the effects of the heterogeneous surface structure on the catalytic activity of nanoparticle systems. In this approach, the apparent reactivity results from the interplay between kinetic processes that occur on active sites and surface transport of adsorbed reactants from inactive towards active sites. It is demonstrated that this model is a generalization of well-known mean field (MF) and nucleation and growth models. Kinetic Monte Carlo (kMC) simulations specifically developed for this problem were employed for establishing the relevance of the different model parameters for the shape of chronoamperometric and linear sweep current transients. In the limit of fast COad surface mobility, the corresponding MF approximation with active sites and its analytical solutions for limiting cases are presented. The comparison of the general kMC solution with the MF approximation reveals major applicability limits of the MF approach for heterogeneous surface models. Although the current work concentrates on the specific case of COad adlayer electrooxidation, the model is readily applicable for other reactions where surface heterogeneity is likely to play an important role.

Introduction

In recent years, the interest in understanding the factors that determine the electrocatalytic activity of metal nanoparticles has increased tremendously [1]. Highly dispersed supported nanoparticle catalysts of Pt or Pt alloys are widely used in the catalyst layers of polymer electrolyte fuel cells (PEFC) [2]. It is, however, far from being understood how the size of these particles affects their electrochemical activity. Obviously, a reduction in particle size improves the surface-to-volume ratio of the number of catalyst atoms. Since only surface atoms could be potentially active, this has a direct impact on catalyst utilization, a key target in fuel cell development. Yet, the relation between particle size and activity is highly non-trivial, since the size of the particles also affects electronic and geometric properties at their surface [1]. A better understanding of the relationships between particle size, heterogeneous surface structure and activity, including those surface phenomena, could be critical in view of the design of highly performing catalyst layers. A concomitantly achieved reduction in catalyst loading could take down decisive hurdles for the advancement of fuel cell technology.

All relevant electrochemical reactions in PEFC have shown sensitivity to surface structure of the catalyst [3]. The abundances of the different surface sites (facets, edges and corners) are closely related to the size of the nanoparticles [4]. Therefore, structural dependencies inevitably translate into particle size effects [5], which have been observed to exhibit diverging trends for different relevant reactions. Whereas oxygen reduction on Pt shows a maximum in mass activity for a particle diameter of ∼3 nm [6], [7], the mass activity for hydrogen reduction on Pd particles increases significantly upon reduction of the Pd cluster size [8]. On the other hand, for methanol oxidation, a notable drop in mass activity has been found in experiments for particle sizes smaller than ∼5 nm [9], [10].

The influence of the particle size and surface morphology on the catalytic activity of nanoparticle systems is particularly pronounced for reactions involving COad. COad electrooxidation is the most thoroughly studied model reaction in electrochemistry. This reaction is of vital practical relevance for PEFCs due to the possible poisoning of the anode catalyst by strongly adsorbed COad. The latter problem arises if the hydrogen-rich reactant gas supplied at the fuel cell anode contains traces of CO as a by-product of the reforming of hydrocarbons. COad can also be formed as a strongly adsorbed intermediate in methanol electrooxidation.

For COad electrooxidation, a drop in mass activity has been observed for decreasing particle size [11], [12], [13], [14], [15]. The maximum oxidation rate in potential step measurements decreases by a factor of ∼5 when the nanoparticle diameter drops from >5 nm to 2 nm. As pointed out by Zhdanov et al. [16], [17], the modulation of the electric field around nanoparticles should rather enhance the net rate constant on nanoparticles in comparison to a flat surface.

A vast number of studies have been undertaken in order to elucidate the effects of particle size and morphology for COad electrooxidation, exploring the favourable catalyst surface morphology and the pertinent reaction mechanisms [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]. Studies on well-defined single crystalline surfaces indicate that COad electrooxidation is predominantly activated at step sites and that COad surface mobility is not a limiting process [25], [26]. However, recent detailed studies suggest that these findings can hardly be transferred to nanoparticle systems. Maillard et al. concluded that significant restrictions in COad surface diffusivity arise on the smallest Pt nanoparticles [11]. Zhdanov et al. analyzed the relevance of surface diffusion on the overall kinetics of CO electrooxidation as observed in stripping voltammetry using a MF approach [28]. Their results demonstrate that the reaction kinetics are significantly affected by interfacet diffusion of COad.

As of today, the extent and the detailed mechanism of morphological effects on nanoparticles are poorly understood. However, even for pure metal catalysts, there is convincing evidence that local variations in activity on the catalyst surface are substantial. Sufficiently strong variations in activity of catalyst surface atoms imply that only a fraction of sites constitute active sites, whereas the remaining surface atoms should be deemed “inactive” [11], [29]. This distinction becomes more lucid on alloyed catalysts, which employ the bifunctional mechanism [30]. For COad electrooxidation on PtRu alloy catalysts, the Ru atoms on the surface constitute the active sites since they promote the rate-determining step of OHad formation via water splitting [22], [31], whereas the Pt surface atoms represent the inactive sites which merely act as a reservoir for adsorbed COad. The distinct components of the alloy, thus, promote different reactions [17], [22].

Evidently, the abundance and distribution of preferred reaction sites on the surface plays a major role in determining the reactivity of a catalyst. Pertinent models for electrocatalytic reactions on nanoparticle surfaces should, thus, incorporate their surface morphology. In the present work, we explore a heterogeneous surface model for COad electrooxidation on Pt nanoparticles. It exploits the so-called active site concept to distinguish between active and inactive sites. This model, thus, implies that the difference in activity of different surface sites is the driving factor of the particle size effect.

As will be demonstrated, the model generalizes existing approaches for catalyst reactivity that are based on homogeneous surface models. In [32], this model was applied to extract kinetic data from chronoamperometric measurements of CO monolayer oxidation on nanoparticles. The present paper focuses on the fundamental properties of this two-state model. We explore the basic limitations inherent in a mean field (MF) approximation of two-state models for heterogeneous surfaces, and discuss simple analytical solutions for the kinetics of COad monolayer oxidation upon a potential step for large particles at potentials above the OH equilibrium potential. Furthermore, the general solution of the two-state model is extended to treat problems with time-dependent rate constants, allowing simulations of linear sweep voltammograms.

Section snippets

Model of surface structure and relevant reaction steps

The major objective of this work is to rationalize the effects of the surface heterogeneity on the net CO electrooxidation reaction rate. In our approach, we utilize a simple two-state model, in which the catalyst surface is partitioned in electrocatalytically active sites and inactive sites. The latter merely act as reservoir for COad. The model, thus, accounts for the strong experimental and theoretical indications that CO electrooxidation occurs predominantly at only a fraction of surface

General solution using kinetic Monte Carlo simulations

The solution of the general model, Eqs. (1.1), (1.2), (1.3), (1.4), that includes details of the heterogeneous surface structure and the effects of finite CO surface mobility, requires stochastic methods. Kinetic Monte Carlo Simulations (kMC) provide the appropriate means for this type of problem. Such simulations proceed in real time and they permit the straightforward inclusion of time-dependent transition rates. The kMC method has found increasing use in the field of electrochemical

Mean field approximation for fast surface diffusion

When CO surface diffusion is much faster than the electrochemical reaction rates, i.e. in the limit kd  ∞, positions of individual adsorbates become irrelevant. In this case, it is sufficient to specify the surface configuration at a specific time in terms of effective surface coverages. This so-called mean field (MF) approximation greatly reduces the problem of solving a system of non-linear ordinary differential equations. Its state variables are the surface coverages of COad on inactive

Results

We will analyze the resulting kinetics of the active site model mainly in terms of chronoamperometric transients. Thereby, we have a method at hand that allows for a detailed analysis of the kinetics at a fixed electrode potential. Furthermore, a great amount of experimental potential step data are available for analysis [11], [15], [25], [26]. We believe that in the vicinity of the onset potential for CO electrooxidation, the analysis of the electrode kinetics by chronoamperometric transients

Conclusions

Surface morphology has been shown to be crucial for the overall reactivity of a multitude of electrocatalytic reactions. The present study focuses on the relevant case of COad electrooxidation on nanoparticle catalysts. We have presented a simple two state approach to incorporate non-uniform reaction rate distributions on heterogeneous nanoparticle surfaces. In this model, which builds on the well-established reaction mechanism by Gilman [34], the COad removal reaction is limited to active

Acknowledgements

We thank Dr. Elena Savinova and Dr. Frédéric Maillard as well as David Breton and Joanna Kocylo for their substantial contributions to this work. We acknowledge financial support from a Provincial Research Fellowship of the BC Innovation Council. B.A. acknowledges the support by the Swiss National Science Foundation.

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