Atomic-Scale Modeling of Particle Size Effects for the Oxygen Reduction Reaction on Pt
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- Tritsaris, G.A., Greeley, J., Rossmeisl, J. et al. Catal Lett (2011) 141: 909. doi:10.1007/s10562-011-0637-8
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We estimate the activity of the oxygen reduction reaction on platinum nanoparticles of sizes of practical importance. The proposed model explicitly accounts for surface irregularities and their effect on the activity of neighboring sites. The model reproduces the experimentally observed trends in both the specific and mass activities for particle sizes in the range between 2 and 30 nm. The mass activity is calculated to be maximized for particles of a diameter between 2 and 4 nm. Our study demonstrates how an atomic-scale description of the surface microstructure is a key component in understanding particle size effects on the activity of catalytic nanoparticles.
KeywordsElectrocatalysisNanoparticlesDFTParticle size effectOxygen electroreductionPlatinum
Several strategies have been employed for enhancing fuel cell (FC) catalysis, including the preparation of cathode catalysts that comprise dispersed nanoparticles of optimum surface-to-volume ratio [1, 2]. In that case, the effect of a particle’s size and shape on the rate of the oxygen reduction reaction (ORR) becomes of primary importance, and the search for efficient and inexpensive catalysts coincides with the optimization of the particle’s geometry. For platinum (Pt), although the existence of a maximum in mass activity versus particle size is now well established [3, 4], efforts to elucidate the origin of such particle size effects are hindered by the lack of models that describe the fine features of catalytic nanoparticles . Traditionally, models of ideal truncated octahedra have been assumed, but the importance of the effect of surface irregularities on the activity has been acknowledged only recently [6–9]. On the application level, the understanding and modeling of particle size effects provide directions for the rational design and synthesis of new and efficient FC catalysts .
Here, we attempt to bring atom-level insight into particle size effects for the ORR on Pt. For that, we construct a model for nanoparticle catalysis which explicitly accounts for the defects present on a particle’s surface as well as their effect on the activity of neighboring sites.
2 Particle Model and Computational Details
Estimating the catalytic activity by averaging as in Eq. 1, assumes that the effect of steps on the activity of the neighboring sites (and vice versa) is negligible. We support this assumption by investigating the effect of adsorbate–adsorbate interactions  on the adsorption free energy of two key ORR intermediates, O and OH . For that analysis, we use model slabs describing fcc(544) surfaces: an fcc(544) surface comprises (111) terraces of nine rows of atoms wide separated by monoatomic steps with the (100) orientation. The wide terrace allows for the calculation of adsorption energies for different distances from the step edge. In this manner, the range of the effect of the step on the nearest active sites was estimated. Total energy calculations were done with the GPAW package , a DFT implementation based on the projector-augmented wave (all electron, frozen core approximation) method ; see Supplementary Material for additional details. For the description of exchange and correlation, the RPBE functional was chosen . Calculated adsorption energies were corrected with zero-point energy and entropic contributions .
3 Results and Discussion
In previous work  we constructed a similar particle model for describing particle size effects on the ORR activity of nanoparticles of different transition metals. One step active site was assumed for every edge atom dissolving. Although trends in specific activity were captured, the maximum in mass activity is not observed (Fig. 4b). Moreover, the removal of low-coordinated atoms from the nanoparticle surface reduces the coordination number of the neighboring sites, which become susceptible to dissolution, too. However, dissolution of the outer atomic rows of the (100) and (111) facets exposes the bulk atomic layers underneath. The ratio of step to facet sites is then reduced. In fact, even better agreement between the proposed model and experiment is possible by assuming less than 100% edge dissolution. In that respect, the previous and proposed models represent two limiting cases.
Furthermore, Eq. 1 cannot describe the significant increase in specific activity observed when extended (111) surfaces are employed . Normalizing to the activity is0,111 of an extended (111) surface, the activities are overestimated (Fig. 4a). However, assuming that the activation energies for the facets of large particles are ~2–3% less than the activation energies for the facets of small particles, the agreement with experiment extends over the range of large diameters.
The geometric model discussed in this work has a simple mathematical form : the population of the active sites is only dependent on the number of atomic shells, which in turn is a function of the diameter of the nanoparticle. However, there is no assumption in the model that limits its applicability to the study of particles with truncated octahedral shape. For example, the use of catalysts that comprise octahedral nanoparticles has been proposed as a route to increased activities . For a model octahedral particle with dissolved edges and corners and a diameter of 30 nm, the activity is calculated to be double the activity of a particle with truncated octahedral shape and the same diameter.
We have demonstrated how the atomic-scale modeling of the surface of nanoparticles can assist in understanding size effects in catalysis. We constructed a model which captures the experimentally observed trends in both the specific and mass oxygen reduction reaction activities on platinum. For fuel cell voltages of practical interest for the reaction (~0.9 V), dissolved edges and corners were shown to have no effect on the activity of adjacent active sites. The ratio between the specific activities of 30 and 2 nm particles was calculated ~4. The mass activity was verified to be maximized for particles of a diameter in the range of 2–4 nm.
CAMD is funded by the Lundbeck Foundation. This work was supported by the Danish Center for Scientific Computing. Work at the Center for Nanoscale Materials at Argonne was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under contract No. DE-AC02-06CH11357.