Catalysis Letters

, Volume 141, Issue 7, pp 909–913

Atomic-Scale Modeling of Particle Size Effects for the Oxygen Reduction Reaction on Pt


    • Center for Atomic-scale Materials Design, Department of PhysicsTechnical University of Denmark
    • Center for Interface Science and CatalysisSLAC National Accelerator Laboratory
  • J. Greeley
    • Center for Nanoscale MaterialsArgonne National Laboratory
  • J. Rossmeisl
    • Center for Atomic-scale Materials Design, Department of PhysicsTechnical University of Denmark
  • J. K. Nørskov
    • Center for Interface Science and CatalysisSLAC National Accelerator Laboratory
    • Department of Chemical EngineeringStanford University

DOI: 10.1007/s10562-011-0637-8

Cite this article as:
Tritsaris, G.A., Greeley, J., Rossmeisl, J. et al. Catal Lett (2011) 141: 909. doi:10.1007/s10562-011-0637-8


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.

Graphical Abstract


ElectrocatalysisNanoparticlesDFTParticle size effectOxygen electroreductionPlatinum

1 Introduction

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 [5]. 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 [69]. 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 [10].

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

Particles of truncated octahedra were modeled as Wulff constructions of (100) and (111) facets (Fig. 1) using a ratio between the respective surface free energies of \( \gamma_{100} /\gamma_{111} = 1.189 \). The ratio was calculated on the basis of the density functional theory (DFT) surface energies reported in the study of Vitos et al. [11]. The diameter dPt of each particle was calculated as the average distance between every two opposite facets. Given that the dissolution potential and the coordination number of dissolving atoms are correlated [12], every atom on the particle surface facets was considered to be an active site with the exception of the edge and corner atoms, which are expected to dissolve in solution at low potentials. A step was assumed to be created at each of the adjacent facets. Recent advances in electron microscopy have allowed for the direct observation of the atomic structure of the surface of nanoparticles [13, 14], supporting the presence of defects in the form that our particle model assumes. We ignored the effect of the support on the morphology of the particle [15], and we assumed no surface restructuring during the reaction. The specific activity is for the ORR was calculated using the expression
Fig. 1

Model particle with truncated octahedral shape with dissolved edges and corners. Differently colored atoms correspond to active sites of different activity for the oxygen reduction reaction

$$ i_{\text{s}} \left( {d_{\text{Pt}} } \right) = i_{\text{s}}^{ 0} \sum\limits_{i} {n_{\text{i}} \left( {d_{\text{Pt}} } \right)e^{{ - \beta \Updelta G_{\text{i}} }} } $$
with 1/β = 26 meV, and is0 a prefactor. The sum runs over the three different types of active sites present on the particle surface, i.e. (100), (111) and step sites (Fig. 1). Equation 1 shows the dependence of the activity on the coverage n and the ORR activation energy ΔG of each type of active sites. Figure 2 illustrates the dependence of the coverages n on the particle diameter dPt. For the activation energies ΔG (a measure of activity), the values 0.10, 0.12 and 0.72 eV were used for the (100), (111) and step sites respectively, adapted from Greeley et al. [16] at a FC voltage of 0.9 V. The value for the step site corresponds to that of a (211) surface, which is used as a model for low-coordinated sites. Greeley et al. [16] offers an extended discussion on the structure sensitivity of the ORR kinetics on (100), (111) and (211) surfaces of transition metals. In this work, we focus on the geometric effect. The relationship between specific and mass activity is established using im = isAPt, where APt is the particle surface area, calculated as APt = 6/(ρPt x dPt) with ρPt the Pt density.
Fig. 2

Fractional population n of the (100), (111) and step surface sites of the particle model of Fig. 1 versus diameter dPt

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 [17] on the adsorption free energy of two key ORR intermediates, O and OH [18]. 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 [19], a DFT implementation based on the projector-augmented wave (all electron, frozen core approximation) method [20]; see Supplementary Material for additional details. For the description of exchange and correlation, the RPBE functional was chosen [21]. Calculated adsorption energies were corrected with zero-point energy and entropic contributions [18].

3 Results and Discussion

Figure 3a demonstrates how the adsorption free energy of O and OH changes with respect to the distance from a non-occupied step. Both bind strongly on the step, a situation attributed to the low-coordination of the step atoms as suggested by the d-band model [17]. Step active sites are thus expected to become occupied first. The effect of the step is local: both of the adsorption energies quickly converge to the corresponding terrace values already at a distance of one atomic row. The effect of a step that is half-occupied by either O or OH on the adsorption free energy of the same adsorbate bound at different distances from the step is shown in Fig. 3b. For each separation, the difference in adsorption energy for a half and a non-occupied step is plotted. Both adsorbates become destabilized when bound on a step or on the first adjacent atomic row when the step is already half-occupied, but no such effect is observed for greater separations. For FC voltages of practical interest for the ORR (~0.9 V), the expected surface coverage is ~1/3 of a monolayer [22]. At this coverage, the ORR intermediates are embedded in a half-dissociated water layer [23] with every two intermediate species separated by water molecules. Given that the step becomes occupied before any other site, the next atomic row occupied by ORR intermediate species is the second, on which the step has no effect. That step active sites are poisoned by strongly bound ORR intermediates is also suggested by the high ORR activation energy calculated for (211) surfaces [16], and by experiments [7, 24]. The activation energies for the (100) and (111) sites are almost equal. Both are significantly lower the activation energy for the step sites. Because of the exponential dependence of the particle activity on the activation energies (see Eq. 1), defects give rise to effectively inactive sites. However, they are found to have no effect on the activity of the adjacent facets.
Fig. 3

a Adsorption free energy of two oxygen reduction reaction intermediates, O and OH, for different separations from a step. The energies are given with respect to the gas-phase energies of H2O and H2. The step is expected to become occupied before any other active site. b Difference in the adsorption free energy of O, and OH, between a half-occupied step with the same adsorbate and a non-occupied step. The effect of the step is shown not to extend further than one neighboring row of atoms

After excluding communication between steps and facets, we proceed to estimate the catalytic activity. In Fig. 4, the calculated trends in specific activities is and mass activities im for the ORR are plotted against the particle surface area APt for a set of particles with sizes of practical importance (dPt = 2–30 nm). The activities for Pt-black (APt = ~5 m2/gPt) and Pt/C catalysts (APt > 35 m2/gPt) at 0.9 V and 60 °C determined via RDE-measurements in O2--saturated 0.1 M HClO4 are also shown in Fig. 4, taken from the work of Gasteiger et al. [1]. Both theoretically and experimentally determined activities are shown normalized with respect to the activity i0,p of the smallest particle of each set. Figure 4 shows that the proposed model captures the experimentally observed trends in both the specific and mass activities. The ratio between the specific activities of the 30 and 2 nm particles is calculated ~4. The maximum in mass activity is reproduced, found for APt = 70-110 m2/gPt (dPt = 2–4 nm).
Fig. 4

a Specific activities is -and b mass activities im for the oxygen reduction reaction on platinum versus particle surface area APt. All activities are shown normalized with respect to the activity i0,p of the smallest particle of each data set. The specific activities calculated with the proposed model are also shown normalized to the activity of a fcc(111) surface is0,111. The dashed lines serve as a guide to the eye for the experimental data points (readable on both scales). The proposed model (diamonds) captures the experimental trends (squares, see also Fig. 8 in Gasteiger et al. [1]) with a maximum in mass activity observed for APt = 70–110 m2/gPt

In previous work [16] 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.

In the work of Lee et al. [24] the fraction of atoms associated with step surfaces was reported to be less than ~25% for ~2 nm nanoparticles. Our model assumes a fraction between 40 and 80% for the step sites for particles of dPt = 2–4 nm (Fig. 2). The extent to which the assumed coverage of surface sites compensates for the effect of processes that the model does not explicitly describe merits further investigation. For example, for small nanoparticles in particular, induced strain by either the support or the high surface curvature [15] could affect the energetics of the surface facets and, therefore, the catalytic activity of the particle [25]. The introduction of ORR activation energies that are size-dependent could help in better separating the geometric from the electronic effect that may be relevant to a specific range of diameters [15, 26]. Eq. 1 may be refined as
$$ i_{\text{s}} \left( {d_{\text{Pt}} } \right) = i_{\text{s}}^{ 0} \sum\limits_{i} {n_{\text{i}} \left( {d_{\text{Pt}} } \right)e^{{ - \beta \,\Updelta G_{\text{i}} \left( {d_{\text{Pt}} } \right)}} } $$

Furthermore, Eq. 1 cannot describe the significant increase in specific activity observed when extended (111) surfaces are employed [1]. 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 [27]: 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 [2]. 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.

4 Conclusion

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.

Supplementary material

10562_2011_637_MOESM1_ESM.doc (286 kb)
Supplementary material 1 (DOC 286 kb)

Copyright information

© Springer Science+Business Media, LLC 2011