Supplementary Material for

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1 Supplementary Material for Platinum-based nanocages with subnanometer-thick walls and welldefined, controllable facets Lei Zhang, Luke T. Roling, Xue Wang, Madeline Vara, Miaofang Chi, Jingyue Liu, Sang-Il Choi, Jinho Park, Jeffrey A. Herron, Zhaoxiong Xie, Manos Mavrikakis, Younan Xia* This PDF file includes: Materials and Methods Figs. S1 to S8 Tables S1 to S3 Full Reference List *Corresponding author. Published 24 July 2015, Science 349, 412 (2015) DOI: /science.aab0801

2 Materials and Methods Chemicals All chemicals were used as received from Sigma-Aldrich unless specified. These include sodium tetrachloropalladate (Na 2 PdCl 4, 98%), palladium acetylacetonate (Pd(acac) 2, 99%), sodium hexachloroplatinate hexahydrate (Na 2 PtCl 6 6H 2 O, 98%), formaldehyde (HCHO, Fisher Scientific), ascorbic acid (AA, 99%), potassium bromide (KBr, 99%), ethylene glycol (EG, 99%, J. T. Baker), poly(vinyl pyrrolidone) (PVP, MW 55,000), ferric chloride (FeCl 3, 97%), hydrochloric acid (HCl, 37%), ethanol (200 proof, KOPTEC), acetic acid (99.7%), and perchloric acid (HClO 4, 70%, PPT Grade, Veritas). All aqueous solutions were prepared using deionized (DI) water with a resistivity of 18.2 MΩ/cm. Preparation of the 18-nm and 10-nm Pd cubes The Pd cubes with an average edge length of 18 nm (fig. S1, A and B) were synthesized using a previously reported protocol (16). In a typical synthesis, 105 mg of PVP, 60 mg of AA, and 600 mg of KBr were dissolved in 8 ml of DI water, and heated at 80 C in an oil bath under magnetic stirring for 10 min. Subsequently, 57 mg of Na 2 PdCl 4 was dissolved in 3 ml of DI water and then injected into the pre-heated solution with a pipette. The vial was capped and maintained at 80 C for an additional 3 h. The final product was collected by centrifugation, washed three times with DI water, and redispersed in 11 ml of EG at a concentration of 1.68 mg/ml. The Pd cubes with an average edge length of 10 nm were obtained by decreasing the amount of KBr from 600 mg to 300 mg while keeping all other conditions unchanged. The 10-nm Pd cubes were also washed with DI water twice and then re-dispersed in 11 ml of DI water for the preparation of 19-nm Pd octahedra. Preparation of the 19-nm Pd octahedra In a typical synthesis, 105 mg of PVP, 0.1 ml of HCHO, and 0.3 ml of an aqueous suspension (1.8 mg/ml) of the 10-nm Pd cubes were mixed in 8 ml of DI water and then heated at 60 C for 10 min in an oil bath under magnetic stirring. At the same time, 29 mg of Na 2 PdCl 4 was dissolved in 3 ml of DI water and then injected into the pre-heated solution with a pipette. The reaction mixture was capped and maintained at 60 C for 3 h. The final product (fig. S4A) was collected by centrifugation, washed three times with DI water, and re-dispersed in 2 ml of EG at a concentration of 0.83 mg/ml. Preparation of the nanoscale Pd@Pt 4L cubes and Pd@Pt 4-5L octahedra In a standard procedure, 1.0 ml of the 18-nm Pd cubes, 100 mg of AA, 54 mg of KBr, 66.6 mg of PVP, and 12 ml of EG were mixed in a 50-mL three-neck flask and preheated at 110 C for 1 h. The reaction temperature was then quickly ramped to 200 C within 20 min. The Pd@Pt 4L cubes were obtained by injecting 12 ml of a Na 2 PtCl 6 solution in EG (0.25 mg/ml) into the reaction solution at a rate of 4.0 ml/h. After the injection of all the precursor solution, the reaction mixture was kept at 200 o C for another 1 h. The product (fig. S1C) was collected by centrifugation, washed twice with ethanol and three times with DI water, and re-dispersed in 1 ml of DI water. 2

3 For the preparation of 4-5L octahedra, the procedure was the same as for the cubic system except the replacement of the cubic seeds with the octahedral seeds (0.83 mg/ml in concentration). After the solution was ramped to 200 C, 22 ml of a Na 2 PtCl 6 6H 2 O solution in EG (0.10 mg/ml) was injected into the reaction solution at a rate of 4.0 ml/h. The final product (fig. S4B) was collected by centrifugation, washed twice with ethanol and three times with DI water, and re-dispersed in 1 ml of DI water. Preparation of the Pt cubic and octahedral nanocages The Pd cores were etched away from the Pd@Pt 4L cubes using an aqueous solution containing FeCl 3 and HCl (ph=0.55) to generate Pt nanocages. In a standard procedure, 300 mg of KBr, 50 mg of PVP, 30 mg of FeCl 3, 0.18 ml of HCl, and 7 ml of DI water were mixed in a glass vial. The mixture was heated to 100 C in an oil bath under magnetic stirring. Subsequently, 0.2 ml of an aqueous dispersion of Pd@Pt 4L cubes was introduced using a pipette. After 3 h, the product was collected by centrifugation, washed twice with ethanol and three times with water, and then dispersed in DI water for further use. The octahedral cages derived from the Pd@Pt 4-5L octahedra by increasing (relative to the standard procedure) the amount of FeCl 3 and HCl to 40 mg and 0.24 ml, respectively, while the etching was conducted at 100 C for 4 h. To better control the etching of Pd cores, we also titrated a mixture of Pd(acac) 2 and Na 2 PtCl 6 into the reaction solution during the Pt coating process. Depending on the molar ratio between these two precursors, respectively, we could manipulate the density of Pd channels in the Pt shell and thus the etching rate of the Pd core. As demonstrated by the results in Fig. S2, the Pd cores could be more easily etched away at a milder condition even with the incorporation of just 1 mole% of Pd atoms into the Pt shell through a coreduction mechanism. It is critical to use Pd@Pt nl cubes with a proper thickness for the Pt shells in order to generate Pt nanocages without breaking into small pieces. Based on our prior work (12), the number of Pt atomic layers deposited on the surface of Pd cubes could be varied from 1 to 6 by controlling the volume of the Pt precursor solution while keeping the amount of Pd cubes fixed. When the Pd@Pt 2-3L sample (fig. S3A) was subject to standard etching, most of the nanocages (>90%) broke into small fragments. In this case, a much higher density of Pd channels were formed in the Pt shells than the case of Pd@Pt 4L. The resultant nanocages tended to collapse or break into small pieces during etching because of a weak mechanical strength for the ultrathin walls decorated with multiple holes. By switching to a milder etchant with a lower concentration of KBr and FeCl 3 at 80 C, we were able to preserve the nanocages with subnanometer-thick walls (fig. S3, B to D). Structural and compositional analyses TEM images were taken using a Hitachi HT7700 microscope operated at 120 kv. The samples for TEM analysis were prepared by drying a drop of the NCs suspension onto a carbon-coated copper grid. HAADF-STEM and EDS analyses were performed using an aberration-corrected JEOL 2200FS STEM/TEM microscope equipped with a Bruker- AXS SDD detector at 200 kv. The samples for inductively-coupled plasma mass spectroscopy (ICP-MS, NexION 300Q, PerkinElmer) analysis were prepared by 3

4 dissolving the nanocrystals with aqua regia and further diluted with 1% HNO 3 solution to a level of 100 ppb. For the analysis of metal ions in a supernatant, the sample can be directly used after proper dilution with 1% HNO 3 solution. Electrochemical measurements To compare the ORR activities of the Pt cubic and octahedral nanocages, we loaded the same amount of Pt onto the carbon support. Firstly, 0.55 mg nanocages were loaded on 6 mg carbon support (Ketjen Black EC-300J). The carbon-supported catalysts were then dispersed in 10 ml of acetic acid and heated at 60 C for 12 h to clean the surface of the particles, and washed twice with ethanol. After drying, 1.4 mg of the carbon-supported catalyst was re-dispersed in a mixture of 0.5 ml DI water and 0.5 ml isopropanol under ultrasonication for 20 min. Then 20 µl of 5% Nafion was added under ultrasonication for 20 min. Table S1 summarizes the concentrations of Pt, both Pd and Pt, and carbon for the two types of catalysts based on cubic and octahedral nanocages, respectively. Finally, 20 µl of the suspension was deposited on a pre-cleaned glassy carbon rotating disk electrode (RDE, Pine Research Instrumentation) with a geometric of cm 2 and dried in an oven that was pre-set to 50 C. The commercial TKK Pt/C catalyst (46.1 wt% 2.8- nm Pt particles supported on Ketjen Black EC-300J) was used as a reference for benchmarking purpose. 1.1 mg of the commercial catalyst was dispersed in a mixture of 0.5 ml DI water and 0.5 ml isopropanol under ultrasonication for 20 min. 20 µl of 5% Nafion was then added under ultrasonication for 20 min to obtain an ink with a Pt concentration of 0.47 mg/ml (determined by ICP-MS). 10 µl of the ink was deposited on a pre-cleaned RDE with a geometric of cm 2 and dried in an oven that was preset to 50 C. Electrochemical measurements were conducted using a RDE connected to a CHI 600E potentiostat (CH Instruments). A leak-free Ag/AgCl/NaCl (3M) electrode (BASi) was used as the reference. All potentials were converted to values with reference to the reversible hydrogen electrode. The counter electrode was a Pt mesh (1 1 cm 2 ) attached to a Pt wire. The electrolyte was 0.1 M HClO 4 diluted from a 70% stock solution with DI water. The CV curve was recorded at room temperature in a N 2 -saturated 0.1 M HClO 4 solution at a scanning rate of 50 mv/s in the potential range of V RHE. The specific ECSAs were calculated from the charges associated with the desorption of hydrogen in the region of V RHE after double-layer correction by taking a value of 210 (cubic nanocages and commercial Pt/C) or 240 µc/cm 2 (octahedral nanocages) for the desorption of a monolayer of hydrogen from Pt surfaces (29, 30). The ORR activity was measured in the potential range of V RHE in an O 2 -saturated 0.1 M aqueous HClO 4 solution using the RDE method at room temperature with a scanning rate of 10 mv/s (RDE rotating rate of 1,600 rpm). For the accelerated durability test, the CVs and ORR polarization curves were measured after sweeping 5,000 and 10,000 cycles between 0.6 and 1.1 V RHE at a rate of 0.1 V/s in an O 2 -saturated aqueous HClO 4 solution (0.1 M) at room temperature. DFT calculation parameters All DFT calculations were performed using the VASP code (31, 32). Computational parameters were chosen similar to what were used in our recent publications (12-14), 4

5 including a particularly dense k-point mesh required to accurately treat the small differences in calculated energetics between surfaces. Binding energies were verified for convergence to less than 0.01 ev with respect to the computational parameters. For calculating the barrier of a Pd atom diffusing through a Pt membrane, a four-layer Pt(100) slab with a 3 3 surface unit cell was constructed with all atoms relaxed. The interatomic distance between surface atoms was optimized to determine the ideal interatomic distance within each membrane layer. An optimized value of 2.74 Å was calculated, which is shorter than the optimized distance in pure bulk Pt (2.82 Å). Calculations of surface diffusion and substitution barriers were performed in both 3 3 and 2 2 surface unit cells, using k-point meshes of and 8 8 1, respectively. The bulk-optimized lattice constant of Pd (3.96 Å) was used to construct the slab. Four-layer slabs were used, with the top two layers fully relaxed and the bottom two fixed at the bulk-optimized positions. Calculations of bulk diffusion were performed in unit cells, using k-point meshes. The bulk-optimized lattice constant of Pd (3.96 Å) was used to construct bulk Pd and the bulk-optimized lattice constant of Pt (3.99 Å) was used to construct bulk Pt. The calculations for OH binding energy were performed using a 2 2 surface unit cell and a Monkhorst-Pack k-point mesh. Such an accurate k-point mesh was included due to the small differences in binding energies investigated in this work. The nanoscale core-shell cubes and octahedra were modeled with seven layer slabs, with four layers of Pt atop three layers of Pd; the bottom two layers were fixed at the optimized bulk lattice constant of Pd and the top five were allowed to relax. The nanocages were modeled as 6- layer membranes with all atoms relaxed. The topmost and bottommost layers consisted of only Pt atoms. The interatomic distance within layers was optimized; these parameters are shown in Table S2. The binding energy of OH (BE OH ) was calculated as the difference in energy between the total energy of the slab with OH (E total ) and the clean slab energy (E slab ) and gas-phase OH (E OH ): BE OH = E total - E slab - E OH. All geometry optimizations were performed until the Hellman-Feynman forces were less than 0.01 ev/å on each atom. All transition states for diffusion events were calculated until the forces on atoms in each image were less than 0.10 ev/å on each atom. Computational studies of Pt-Pd interdiffusion Diffusion of Pd through Pt membranes The calculations described in this section demonstrate that diffusion of Pd into and through perfectly-formed Pt membranes is not the primary mechanism for Pd-channel formation at the temperature used in our etching experiments. The diffusion of a Pd atom through a four-layer Pt membrane was calculated in three separate stages of calculations: surface to first layer, first layer to second layer, and second layer to third layer. Any subsequent movements of Pd atoms to the other surface 5

6 of the Pt membrane are symmetric to these processes using our simplified membrane model. A schematic illustrating these diffusion processes is shown in Fig. S8. In the first step, we calculated the activation barrier for a Pd atom to move from atop Pt surface into the first surface layer, displacing one surface Pt atom. This process occurred most favorably through the Pd atom pushing one adjoining Pt atom to a nearby hollow site. This step had an activation barrier of 0.82 ev, and was endothermic by 0.28 ev. We also considered three- and four-body rotations for incorporating Pd into the surface, but these were found to have significantly higher barriers (~1.5 ev). It was thermodynamically unfavorable (by 0.16 ev) for the newly formed Pt surface atom to remain bound to the Pd atom in the surface layer, and the barrier for diffusion of the Pt atom away from the Pd-modified surface site is just 0.44 ev. Therefore, we neglected the effects of the surface Pt atom in subsequent stages of diffusion. We then calculated the barrier for the Pd atom to move from the first surface layer to the second surface layer, considering one-to-one atomic swapping and three-body and fourbody rotations. Atomic swapping was found to be very unfavorable kinetically (barrier > 3 ev). The most favorable pathway was found to be a three-body rotation involving the Pd atom and one Pt atom in the first surface layer, and one Pt atom from the second surface layer. The barrier to this step was 1.61 ev, and it was endothermic by 0.04 ev. The final step considered in this analysis was the movement of Pd from the second surface layer to the third surface layer. We note that this movement has symmetric initial and final states in our four-layer membrane model, so it is a thermoneutral process. The most favorable mechanism was a four-fold rotation involving the Pd atom from the second surface layer, two Pt atoms in the third surface layer, and one Pt atom from the fourth surface layer. This process is more activated than either of the two previous steps, having an activation barrier of 2.07 ev. This high barrier stems from the high level of constraint when attempting to rotate atoms deeper in the membrane structure. When moving from the first layer to the second layer, surface atoms are unconstrained by the vacuum region and can relax relatively freely. When Pd moves from the second to third layer, atoms in those layers must push against atoms in the outer layers, which makes the relaxation to accommodate the atomic movements more energetically expensive. The maximum barrier required to be overcome at any stage of this diffusion process is 2.07 ev, which is a very high barrier to overcome at the temperature (100 C) used in our etching experiments. We, here, note that these calculated barriers represent a lower bound on the true barrier for the core-shell system, since an additional constraint will be imposed by the presence of the bulk Pd at the Pt-Pd interface (i.e., on one face of our membrane model). The presence of the bulk Pd prevents full relaxation of the Pt atoms at the Pt-Pd interface, which ultimately will make the outward movement of Pd into the Pt layers more difficult. This simple model is intended to investigate only the feasibility of Pd movement through already-established Pt layers. Since the kinetics of these processes are very unfavorable to those of Pt substitution into a Pd surface (as during the growth process), we can conclude that diffusion of Pd into and through perfectly-formed Pt 6

7 membranes is not the primary mechanism for Pd-channel formation at the temperature used for etching. Surface diffusion As an alternative to Pd diffusion into Pt overlayers, we propose that Pt and Pd are intermixed during the Pt deposition process. To test this hypothesis, we calculated the barrier for Pt diffusion across a Pd(100) surface, performing calculations in 3 3 (0.11 ML coverage by Pt) and 2 2 (0.25 ML) unit cells to give a rough approximation of coverage effects for these processes. We calculated a Pt hopping diffusion barrier, in which Pt moves from one hollow site to an adjacent hollow site by hopping over a bridge site, of 0.99 ev and 1.03 ev in the 3 3 and 2 2 unit cells, respectively. These barriers are relatively high, explaining why a temperature of 200 C is required for the synthesis to facilitate diffusion and thus uniform coating. A summary of these diffusion barriers, along with barriers for diffusion of Pt and Pd atoms through bulk metals, is shown in Table S3. We also calculated the barriers to Pt substitution into the first Pd surface layer, in which a Pt atom in a hollow site replaces one adjacent surface Pd atom, and pushes the Pd atom to a nearby hollow site. The barriers for this process were 0.74 ev in the 3 3 unit cell, and 0.98 ev in the 2 2 unit cell. These barriers are substantially lower than the barrier to Pt hopping across the surface, and should readily occur as Pt overlayers are deposited onto the Pd surface. Further, these processes are exothermic (by 0.38 and 0.41 ev in the 3 3 and 2 2 cells, respectively). We also note that the barrier to substitution seems to increase substantially with the surface coverage by Pt, likely due to the additional constraints imposed by the presence of additional Pt surface atoms. In this way, we anticipate that a substantial fraction of Pd will be removed from the original top surface layer as the first monolayer of Pt is deposited, and end up on the surface of a new Pt-Pd bimetallic surface layer. As the surface becomes more populated with surface adatoms, the substitution of atoms becomes more difficult due to the constraints imposed by those atoms, so the result is ultimately a bimetallic Pt-Pd mixture in the newly-formed adlayer. This process will be repeated as each additional layer of Pt atoms is added, dispersing some amount of Pd in each subsequent adlayer. A detailed understanding of the final Pd composition in each layer is beyond the scope of the current study, as it would require the calculation of many additional DFT parameters for substitution events, surface diffusion events, and interaction (clustering) energies of adatoms. These parameters would be used in combination with stochastic modeling (e.g., kinetic Monte Carlo) to give the most accurate description of the growth process. Growth of contiguous Pd channels in Pt overlayers Our analysis shows that the presence of a Pd channel through the Pt overlayers is a necessary and adequate condition for the etching of Pd to form hollow nanocage structures. We show that Pt and Pd are likely to intermix during the Pt deposition process, which will randomly disperse a fraction of Pd atoms into the adlayers. The probability of forming a Pd channel, composed of adjacent Pd atoms in successive adlayers, at a given point in the shell can be roughly expressed as the product of the probabilities of a Pd nn atom existing in each layer of that region of the shell, i.e., PP =, where P is the ii=1 pp ii 7

8 probability of forming a channel, p i is the probability of finding a Pd atom in layer i, and n is the total number of layers deposited. The effects of increasing shell thickness are therefore twofold: First, as n increases, P decreases since p i is fixed between 0 and 1. Second, a fixed number of Pd atoms, from the top layers of the original Pd seed, is always permuted into the Pt overlayers regardless of the Pt shell thickness. Therefore, increasing n also causes a decrease in p i, since the concentration of Pd atoms will decrease as the number of Pt overlayers increases (p i ~ 1/n). This rough analysis offers a qualitative explanation why 2-layer nanocages might collapse (due to the formation of too many channels) when the standard etching condition was used, while 6-layer nanocages could not be etched completely due to the formation of too few channels (data not shown). Diffusion of Pd and Pt atoms in bulk Pd and bulk Pt We also investigated the diffusion of Pd and Pt atoms through bulk Pd and bulk Pt at vacancy sites. First, one atom in the bulk Pt (or Pd) unit cell was removed, corresponding to a 0.8 mol% concentration of vacancies. The diffusion barrier was calculated by exchanging the positions of the vacancy and a vacancy-adjacent atom. The barriers for these processes were 0.98 ev in bulk Pd and 1.05 ev in bulk Pt. Next, we modified the unit cells by replacing a vacancy-adjacent Pt atom in bulk Pt with a Pd atom (or a vacancy-adjacent Pd atom in bulk Pd with a Pt atom). The diffusion barrier for Pd in bulk Pt at the vacancy site was calculated by exchanging the positions of the vacancy and the vacancy-adjacent Pd atom. Analogously, the diffusion barrier for Pt in bulk Pd at the vacancy site was calculated by exchanging the positions of the vacancy and the vacancyadjacent Pt atom. The barriers for these processes were 0.88 ev and 1.20 ev, respectively. To summarize, we calculated barriers for Pt and Pd diffusion through bulk Pt and Pd lattices at vacancy sites, finding barriers increasing in the order: Pd in bulk Pt (0.88 ev) < Pd in bulk Pd (0.98 ev) < Pt in bulk Pt (1.05 ev) < Pt in bulk Pd (1.20 ev). These barriers are additionally summarized in Table S3. We also calculated the diffusion of Pd and Pt atoms in bulk Pd and bulk Pt without involving vacancy sites. Employing a four-atom rotation mechanism, the barriers calculated were: Pt in bulk Pt (4.48 ev) and Pd in bulk Pd (5.10 ev). These barriers are significantly higher than the vacancy-mediated mechanism, providing clear evidence that vacancies must be involved in these bulk diffusion events. We note that the barriers could decrease by employing even more elaborate diffusion mechanisms, though we do not anticipate that they would decrease near enough to become competitive with vacancymediated diffusion. Calculation of relative ORR activities Previous studies have shown that the ORR specific activity can be improved by weakening the binding energy of adsorbed OH relative to that on Pt through introducing lattice strain effects and/or ligand effects (33-35). We calculate the relative ORR activities from the energetics of OH hydrogenation, which our previous studies have shown to be rate-determining on Pd-Pt core-shell model surfaces (12-14). In our model, we calculated the energetics of adsorbed OH on slabs with four atomic layers of Pt deposited atop Pd (denoted Pt 4L */Pd), representing the nanoscale core-shell cubes 8

9 (denoted Pt 4L */Pd(100)) and octahedra (denoted Pt 4L */Pd(111)). The lattice constant of these slab models was fixed at the value for bulk Pd, which introduces a mild compressive strain into the Pt overlayers because Pd has a slightly smaller lattice constant than Pt. The values for BE OH on these models were then compared with those (BE OH ) calculated on six-layer (100)- and (111)-faceted Pt-Pd bimetallic membranes with all atoms allowed to relax, representing the nanocages derived from the core-shell cubes and octahedra after Pd etching, respectively. Since Pd on the exposed surfaces of the membrane is assumed to be removed during the etching process, the membranes were constructed with the topmost and bottommost layers composed of Pt atoms only. A 3:1 atomic ratio of Pt:Pd atoms (15.3 wt% Pd) was used for the four inner layers of the membranes, which is reasonably close to the experimentally-determined values for the cubic nanocages (6.4 wt% Pd) and octahedral nanocages (9.1 wt% Pd). The interatomic distances between atoms within a layer of these membranes were optimized with all atoms relaxed, since the inner surface of the nanocage is no longer subjected to constraint by the Pd core. The optimized interatomic distances between Pt atoms in each membrane layer for the (100) and (111) surfaces were found to be 2.75 Å and 2.76 Å, respectively, which are considerably smaller than the optimized values for bulk Pd (2.80 Å) and bulk Pt (2.82 Å). These results are consistent with the lattice contraction observed for small Pd-Pt particles by An and Liu (36). This reduced interatomic distance has a destabilizing effect on the adsorbed OH, similar to the effect of compressively strained Pt, weakening BE OH by 0.04 ev on each membrane model for the nanocages relative to the core-shell models (Table S2). We also calculated BE OH on membrane models with a 1:1 atomic ratio of Pt:Pd atoms in the center layers, and found the values to be very similar to those when the 3:1 ratio was used. These results suggest that the destabilization of adsorbed OH and subsequent enhancement in ORR activity is predominantly caused by the shortening of the Pt-Pt interatomic distances in the membrane model. We calculate energetics at 0.9 V RHE, using the computational standard hydrogen electrode model developed by Nørskov et al (37). This model accounts for the effect of cell potential (U) on the free energy change of a reaction (ΔG) as GG = EE + ZZZZZZ TT SS + ee UU, where ΔE is the change in total energy of the reaction, ΔZPE is the change in zeropoint energy corrections, and T is the absolute temperature (298 K, in this study), ΔS is the change in entropy of the reaction, and e is the electron charge. The RHE was chosen as the electrochemical reference, at which the reaction HH 2 2 (HH + + ee ) is in equilibrium at 0 V RHE under standard reaction conditions. We assume that the entropy and zero-point energy corrections are the same for OH on the core-shell structures as on the membrane structures due to the similar adsorption geometries. The relative activities of these surfaces were calculated in accordance with our previous works (12-14) according to an Arrhenius-type expression, in which the activation energy of OH hydrogenation was assumed to be equal to the free energy change of the reaction. The differences in free energy change between the core-shell structures and the nanocages were therefore determined only by differences in binding energies between the surfaces. Therefore, the rate constant k i for OH hydrogenation on surface i relative to the core-shell models was calculated as kk ii = exp ( (BBBB OHii BBEE OHcccccccc ssheeeeee ) ), where BE OH,i is kk B TT the binding energy of OH on the membrane s surface, BE OH,core-shell is the binding energy 9

10 of OH on the core-shell structure, and k B is the Boltzmann constant. Therefore, since OH binds more weakly on the membrane models than on the core-shell models, enhanced activity is found on these surfaces relative to the core-shell models. We note that we do not attempt to quantify the relative activities between the surfaces covered by (100) and (111) facets. As in our previous works, we only compare (100) surfaces and (111) surfaces independently (see Table S2) due to a lack of a precise value for stabilization of OH by adsorbed water on the (100) and (111) surfaces. We calculated the specific activity on the cubic nanocages to be 5.7 times higher than that on the Pt* 4L /Pd(100) nanocube models, and the specific activity to be 5.6 times higher on the octahedral nanocages than on the nanoscale Pt* 4L /Pd(111) octahedra models. The discrepancy between these results and the experimental values of 2.2 and 2.2 times, respectively, can likely be attributed to variations in the elemental composition of the outermost layer on the nanocrystals. 10

11 Fig. S1. TEM images and corresponding size distributions of the Pd cubes, 4L cubes, and Pt cubic nanocages. (A) TEM image and (B) size distribution of the Pd cubes used for the deposition of Pt. (C) TEM image of the 4L cubes and (D) size distribution of the corresponding Pt cubic nanocages. In the histogram, the particle size was defined as an average value of the edge lengths measured along two orthogonal directions of each particle. We counted 100 particles and average edge lengths of 18.2 nm and 20.2 nm were derived for the Pd cubes and Pt cubic cages. 11

12 Fig. S2. TEM images of 4L and 4L cubes and their corresponding products obtained under different etching conditions. (A) TEM image of 4L cubes obtained with the introduction of PtCl 6 2- only (same as in fig. S1C). (B) Pd@(Pt- Pd) 4L cubes obtained with the introduction of a mixture of Pd(acac) 2 and Na 2 PtCl 6 at a molar ratio of 1:99. (C and D) TEM images of products derived from the Pd@Pt 4L and Pd@(Pt-Pd) 4L cubes by reducing (relative to the standard procedure) the amount of KBr, FeCl 3, HCl to 200 mg, 20 mg and 0.12 ml, respectively, while the etching was conducted at 60 C for 5 h. (E and F) TEM images of products derived from the Pd@Pt 4L and Pd@(Pt-Pd) 4L cubes using the standard procedure. The 50 nm scale bar applies to all images. 12

13 Fig. S3. TEM and HAADF-STEM images of 2-3L cubes and the corresponding Pt nanocages. (A) TEM image of 2-3L synthesized using the standard procedure, except that the volume of Na 2 PtCl 6 solution (0.25 mg/ml) added into the reaction system was reduced to 7.0 ml. (B) TEM image of a product derived from the Pd@Pt 2-3L cubes by reducing (relative to the standard procedure) the amount of KBr, FeCl 3, HCl to 50 mg, 10 mg and 0.06 ml, respectively, while the etching was conducted at 80 C for 3 h. (C) HAADF-STEM image taken from one of the nanocages. (D) High-resolution HAADF- STEM image taken from the region indicated by a box in (C), indicating a wall thickness of 4-5 atomic layers (or nm along the [100] direction). 13

14 Fig. S4. TEM images of Pd octahedra and 4-5L octahedra. (A) TEM image of Pd octahedra with an average edge length of 19.4 nm and (B) TEM image of the same batch of Pd octahedra after the deposition of 4-5 atomic layers of Pt shells. 14

15 Fig. S5. TEM and HAADF-STEM images of the Pt octahedral nanocages derived from 2-3L octahedra. (A) TEM image of the Pt nanocages derived from a sample of Pd@Pt 2-3L octahedra using a standard etching procedure. (B) HAADF-STEM image taken from one of the nanocages, indicating a wall thickness of 3-4 atomic layers (or nm along the [111] direction). 15

16 Fig. S6. Electrocatalytic properties of the Pt nanocages benchmarked against a commercial Pt/C catalyst. (A) Cyclic voltammograms and (B) ORR polarization curves of the Pt cubic and octahedral nanocages (shown in Figs. 1 and 3, respectively) in comparison with a commercial Pt/C catalyst (TKK). The current densities were normalized to the geometric area of the RDE (0.196 cm 2 ). (C) Mass and (D) specific activities toward ORR that are presented as kinetic current densities (j k ) normalized to the amounts and ECSAs of Pt, respectively. The color scheme in (B) applies to all other panels. 16

17 Fig. S7. Comparison of the Pt cubic and octahedral nanocages before and after the accelerated durability test. (A and C) TEM images of the cubic nanocages (A) before and (C) after 10,000 cycles of ORR durability test, respectively. (B and D) TEM images of the octahedral nanocages (B) before and (D) after 10,000 cycles of ORR durability test, respectively. 17

18 Fig. S8. Schematic illustration of the pathway for the diffusion of a Pd atom (blue) into a Pt membrane (golden). The numbers indicate the activation barriers for each transition between images. Small arrows in each image indicate the direction of atom movement preferred to reach the next image in sequence. The ejected Pt atom in the top left image can easily diffuse away on the surface, and was neglected in subsequent images. Calculations were performed using a 3 3 surface unit cell. 18

19 Table S1. Summary of material contents in the catalysts. The concentrations of Pt, Pt+Pd, and carbon support for the nanocage-based catalysts developed in this work. The Pt and Pd contents were determined using ICP-MS analysis. Pt + Pd Pt (mg/ml) carbon (mg/ml) (mg/ml) Catalyst based on the cubic nanocages Catalyst based on the octahedral nanocages

20 Table S2. DFT-derived BE OH, relative ORR activities, and Pt-Pt interatomic distances of the Pt nanocages and the corresponding core-shell precursors. The activities are scaled within each facet type. All data are calculated at 0.25 ML OH coverage. BE OH (ev) Relative Activity Intralayer Pt-Pt Distance (Å) Pt 4L */Pd(100) (core-shell cube) Pt*/Pt 3 Pd 1 (100) membrane (cubic nanocage) Pt*/Pt 1 Pd 1 (100) membrane (cubic nanocage) Pt 4L */Pd(111) (core-shell octahedron) Pt*/Pt 3 Pd 1 (111) membrane (octahedral nanocage) Pt*/Pt 1 Pd 1 (111) membrane (octahedral nanocage)

21 Table S3. Summary of diffusion and substitution activation energy barriers. Events occurring on the surface of Pd seeds are shown in the top of the table. Diffusion of atoms through vacancies in bulk metals are given at the bottom of the table. All values are given in ev. Surface diffusion events 2 2 unit cell 3 3 unit cell Pt hopping on Pd(100) Pt substitution into Pd(100) Diffusion through vacancies in bulk Pt bulk Pd bulk Pt atom Pd atom

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