Size-Dependence of the Electrochemical Activity of Platinum Particles in the 1 to 2 Nanometer Range

: Monodisperse Pt nanoparticles supported on carbon (Pt/C) were prepared via an impregnation method. By changing the concentration of the platinum precursor in the initial reagent mixture, the average particle size ( d ) could be controlled to within a narrow range of less than 2 nm. The specific activity ( SA ) of these materials, when applied to the oxygen reduction reaction (ORR), increased rapidly with d in the range below 1.8 nm, with a maximum SA at d = 1.3 nm. This value is approximately four times that of a commercial Pt/CB catalyst. The electrochemical active area, ECAA (electrochemical surface area ( ECSA )/specific surface area ( SSA ) × 100), decreased drastically from 100% with decreases in d below 1.3 nm. In this study, we present a correlation between SA and ECAA as a means of determining the appropriate d for polymer electrolyte fuel cells (PEFCs) and propose an optimal size.


Introduction
Polymer electrolyte fuel cells (PEFCs), which typically incorporate platinum nanoparticles as catalysts, may serve as next-generation primary power sources for vehicles and residences.To allow for large-scale commercialization of this technology, it will be critical to reduce the amount of platinum used in PEFCs due to cost and supply constraints.In particular, the overvoltage of the cathode (at which the oxygen reduction reaction (ORR) proceeds) is higher than that of the anode (at which the hydrogen oxidation reaction (HOR) proceeds) and so requires a large amount of platinum.The most effective approach to minimizing the Pt loading in PEFCs is to increase the electrochemical surface area (ECSA).Therefore, the average particle sizes (d) of Pt catalysts have been gradually reduced to the nanometer range.Currently, d values can be as small as 2-5 nm.As an example, a commercial Pt/C catalyst (TEC10E50E, TKK) that is often used as a standard for comparison has an ECSA of ca. 100 m 2 g −1 .The catalytic performance of aggregates of atoms (referred to as clusters) has also been investigated [1][2][3][4].However, many studies of cluster-type catalysts have shown that the ECSA is considerably lower than the specific surface area (SSA) predicted from particle geometry.As a result, ORR activity values are also lower than expected.These effects are attributed to the different chemical properties of Pt clusters size (atomic scale) compared with Pt nanoparticles (with sizes from approximately 2 nm) or the bulk metal.Here, we propose a new definition of the real electrochemical active area, ECAA (i.e., ECSA/SSA × 100), which is an important factor in evaluating d and ORR activity.
Another important factor affecting ORR activity is the so-called particle size effect, which has been investigated in studies of Pt catalysts.Some researchers have reported an increase in activity as the particle size is reduced.This occurs because the area occupied by highly active sites on which the ORR occurs is determined by particle size [5][6][7][8][9][10].Even so, it has also been proposed that activity should be constant regardless of particle size [11][12][13][14] or even decrease with decreasing particle size [15][16][17].At present, there is no clear consensus on this matter.One reason is that most discussion focus only on the relationship between the ORR mass activity (MA) and/or specific activity (SA) and d.For example, as reported by Shao et al. [16], ORR activity has been associated with specific crystal planes on the particle surface that vary with particle size.There are also reports that changes in interparticle distance with particle size is an important factor in improving ORR activity, as suggested by Inaba et al. [17].However, the MA is the product of the SA and ECSA (MA (A g −1 ) = SA (A m −2 ) × ECSA (m 2 g −1 )), and the value of ECSA (i.e., ECAA) has no small effect on MA.Therefore, we believe that the most important factor for ORR activity is the ECAA value, which has not received much attention.
Thus, it was suggested that the synergistic effect of ECAA and SA could be used to determine the particle size for maximization of catalytic capacity in a very narrow particle size range.One obstacle to evaluating this hypothesis is a current lack of methods for the synthesis of highly uniform platinum particles having sizes of less than 2 nm.
The present work developed a method for preparing Pt/C catalysts with precisely controlled particle sizes (denote as Pt dnm /C).This process involves dissolving a predetermined amount of platinum chloride in alcohol together with carbon acting as a support.In this study, several Pt dnm /C catalysts having particle sizes of less than 2 nm were prepared, and the relationship between d, ECAA and ORR activity (MA and SA) was investigated in detail to identify the optimum d.

Preparation of Pt dnm /C Catalysts
Typical conditions and properties of prepared catalysts (Pt dnm /C) are summarized in Table 1.Hydrogen hexachloroplatinate (IV) hexahydrate (H 2 PtCl 6 •6H 2 O) was dissolved in ethanol.To control the d, the H 2 PtCl 6 •6H 2 O concentration was varied from 4.6 to 47.9 mmol L −1 with the amount of solvent (EtOH).To avoid the possibility of Pt particles entering the pores and affecting the ECSA in high-surface-area microporous carbon, such as Ketjen Black (800 m 2 g −1 ) [18], graphitized carbon black (C, 150 m 2 g −1 , Tanaka Kikinzoku Kogyo, Tokyo, Japan) was added as a support material and mixed into the mortar.The mixture was stirred while the materials were warmed using a heat gun until the ethanol was almost evaporated.The powders obtained were then completely dried under vacuum at 60 • C for 30 min.Finally, they were heat-treated in an Ar atmosphere at 200 • C for 2 h in a furnace.The heat treatment temperatures were determined experimentally.Figure S1 in the Supporting Information (SI) shows TEM images of Pt dnm /C heat-treated at different temperatures.The aggregation of Pt occurs at temperatures above 300 • C. Therefore, the optimal heat treatment temperature in this study was set at 200 • C. The loading amount of the Pt on the C was quantified from the weight loss by combustion of C at 800 • C in air.The Pt dnm /C powders before and after electrochemical assessments were observed using transmission electron microscopy (TEM, Hitachi H-9500, Hitachi High-Tech Japan, acceleration voltage = 200 kV) and scanning transmission electron microscopy (STEM, Hitachi HD-2700, Hitachi High-Tech Japan acceleration voltage = 200 kV) to determine the d value, the distribution of d values and the fine structure of the Pt particles.

Electrochemical Analyses
Electrochemical evaluations were performed on five of the prepared catalysts.Catalyst inks were prepared by mixing 2 mg of catalyst powder with 2 mL of ethanol, followed by ultrasonication for 10 s.A ca.20 µL quantity of this ink was then pipetted onto a carbon disk electrode having a diameter of 5 mm to form a thin catalyst layer.Following this, 2 µL of 0.2 wt% Nafion solution was dropped onto the catalyst layer, after which the sample was dried in air at 60 • C for 30 min.The amounts of Pt attached on the carbon disk of each electrode are summarized in Table 2.All of the electrochemical trials were performed with a rotating disk electrode system (RRDE-3A, ALS Co., Ltd., Tokyo, Japan) together with a gastight water-jacketed Pyrex glass cell.A Pt wire and a reversible hydrogen electrode (RHE) were used as the counter and reference electrodes, respectively.Cyclic voltammetry (CV) data were acquired from 0.05 to 1.2 V at a scan rate of 50 mV s −1 in a 0.1 M HClO 4 solution deaerated with Ar at 30 • C. The ECSA of each specimen was estimated from the electrical charge associated with the hydrogen desorption wave, ∆Q H , in the CV data, with a value of ∆Q H = 210 µC cm −2 expected for smooth polycrystalline Pt [19,20].Hydrodynamic linear sweep voltammetry (LSV) data for the ORR were recorded from 0.3 to 1.0 V at a scan rate of 10 mV s −1 employing the same electrolyte solution as used in the CV experiments but saturated with O 2 . 1 Nafion-coated Pt dnm /C. 2 Amount of Pt attached on the carbon disk substrate. 3Specific surface area calculated by Equation (3). 4 Electrochemical surface area. 5Electrochemical active area [=(ECSA/SSA) × 100].

Characterization of Catalysts
Figure 1 presents TEM images and particle size distribution histograms for the five different Pt dnm /C powders prepared with 4.6, 11.8, 23.4,24.0, and 47.9 mmol L −1 H 2 PtCl 6 •6H 2 O concentrations.The d values and standard deviations of these Pt dnm /C were 1.1 ± 0.2, 1.2 ± 0.2, 1.3 ± 0.2, 1.4 ± 0.2, and 1.8 ± 0.2 nm, respectively.For comparison, the TEM image and the particle size distribution histogram for a commercial Pt/C (TEC10EA20E, 20 wt% Pt dispersed on the same graphitized carbon black support as that of our Pt dnm /C) in Figure S2 in the SI.It was found that the Pt particles in our Pt dnm /C are very uniformly dispersed on the C support, and their size distribution is fairly narrow.The d values increased approximately in proportion to the increases in H 2 PtCl 6 •6H 2 O concentration, as demonstrated in Figure 2. A conceptual diagram of the platinum particle formation process is shown in Figure S3 in the SI.The homogeneous mixing of platinum salts and carbon in the ethanol solvent results in the uniform formation of platinum nuclei on defects in the carbon.These nuclei grow to any size depending on the concentration of platinum salts, as shown in Figures 1 and 2. As an example, the results of the microstructural analysis of the Pt 1.4nm /C are provided in Figure 3. Figure 3B shows the electron diffraction (ED) pattern of the region selected in Figure 3A.This pattern could be assigned to the (111), ( 220

CV Measurements
Figure 4 shows the CV data in the region corresponding to the hydrogen desorption wave together with the full range data (inset).Prior studies with well-defined Pt(hkl) single-crystal electrodes have provided an improved understanding of the properties of each lattice plane [7,[21][22][23][24].On the basis of these previous results, it is possible to discuss the significance of the change in the shape of the hydrogen desorption wave in Figure 4.
Here, the peaks in the lower potential region (around 0.1 V) correspond to hydrogen adsorption and desorption at the structure with the lower Miller index (110) (i.e., the step-

CV Measurements
Figure 4 shows the CV data in the region corresponding to the hydrogen desorption wave together with the full range data (inset).Prior studies with well-defined Pt(hkl) single-crystal electrodes have provided an improved understanding of the properties of each lattice plane [7,[21][22][23][24].On the basis of these previous results, it is possible to discuss the significance of the change in the shape of the hydrogen desorption wave in Figure 4.
Here, the peaks in the lower potential region (around 0.1 V) correspond to hydrogen adsorption and desorption at the structure with the lower Miller index (110) (i.e., the step-like site) [23,24].The peaks at 0.2 V include a contribution from the strong adsorption of hydrogen on the steps of the (100) structure [24].On the other hand, it is difficult to identify the hydrogen waves associated with the (111) structure on Pt nanoparticles because the potential region exhibiting hydrogen waves in the (111) structure overlaps with the potential region of the polycrystalline structure [24,25].With decreases in particle size, the shoulder peak at low potential increased in intensity, whereas the (110)/(100) peak intensity ratio reached a maximum in the case of the Pt 1.1nm /C catalyst.
model for the Pt1.4nm/C powder.

CV Measurements
Figure 4 shows the CV data in the region corresponding to the hydrogen desorption wave together with the full range data (inset).Prior studies with well-defined Pt(hkl) single-crystal electrodes have provided an improved understanding of the properties of each lattice plane [7,[21][22][23][24].On the basis of these previous results, it is possible to discuss the significance of the change in the shape of the hydrogen desorption wave in Figure 4.
Here, the peaks in the lower potential region (around 0.1 V) correspond to hydrogen adsorption and desorption at the structure with the lower Miller index (110) (i.e., the steplike site) [23,24].The peaks at 0.2 V include a contribution from the strong adsorption of hydrogen on the steps of the (100) structure [24].On the other hand, it is difficult to identify the hydrogen waves associated with the (111) structure on Pt nanoparticles because the potential region exhibiting hydrogen waves in the (111) structure overlaps with the potential region of the polycrystalline structure [24,25].With decreases in particle size, the shoulder peak at low potential increased in intensity, whereas the (110)/(100) peak intensity ratio reached a maximum in the case of the Pt1.1nm/C catalyst.Assuming a cuboctahedral shape for the Pt 1.1nm particles, the number of atoms, N atom = 55, contained in a Pt 1.1nm particle with L = 3 layers can be calculated using the following equations [26,27]: and where a Pt is the lattice constant of the Pt (a Pt = 0.392 nm).The present cuboctahedral model for platinum, which can comprise any number of layers, is provided in Figure 5.It is evident that, as L decreases (i.e., as d decreases), the proportion of the surface occupied by the (100) and (111) planes decreases.At L = 3, the majority of the Pt 1.1nm /C surface is expected to consist of (110) planes.
where aPt is the lattice constant of the Pt (aPt = 0.392 nm).The present cuboctahedral model for platinum, which can comprise any number of layers, is provided in Figure 5.It is evident that, as L decreases (i.e., as d decreases), the proportion of the surface occupied by the (100) and (111) planes decreases.At L = 3, the majority of the Pt1.1nm/C surface is expected to consist of (110) planes.The SSA values were calculated as follows: where ρ and r are the density of Pt (ρ = 21.5 g cm -3 ) and the radius of the particle, respectively.These values, along with the ECSA data, are summarized in Table 2.The ECSA values for the Pt1.8nm/C and Pt1.4nm/C were 176 and 195 m 2 g -1 , respectively, which were close to the SSA values calculated by assuming a spherical shape for the Pt particles.These results indicate that the ECAA was nearly 100%, as shown in Table 2.However, the ECAA values decreased in the case of particles having sizes of less than d = 1.3 nm due to a decrease in the ECSA values.This electrochemical inactivation, which occurred with decreasing particle size, has also been observed in theoretical studies [29,30].The hydrogen adsorption energy of Pt particles consisting of 147 atoms (corresponding to a diameter of 1.6 nm) was found to be almost the same as that of the bulk metal but increased for 55 atoms (corresponding to a diameter of 1.1 nm) [30].Thus, the adsorption energy of hydrogen atoms gradually increased with decreases in particle size [29,30].Thus, Pt1.1nm/C likely did not adsorb the expected amount of hydrogen on its surface.

ORR Activities
The LSV data and Koutecky-Levich plots (I -1 vs. ω -1/2 ) generated at 0.85 V and 0.90 V using electrodes made with four different Ptdnm/C specimens coated in Nafion are shown The SSA values were calculated as follows: where ρ and r are the density of Pt (ρ = 21.5 g cm −3 ) and the radius of the particle, respectively.These values, along with the ECSA data, are summarized in Table 2.The ECSA values for the Pt 1.8nm /C and Pt 1.4nm /C were 176 and 195 m 2 g −1 , respectively, which were close to the SSA values calculated by assuming a spherical shape for the Pt particles.
These results indicate that the ECAA was nearly 100%, as shown in Table 2.However, the ECAA values decreased in the case of particles having sizes of less than d = 1.3 nm due to a decrease in the ECSA values.This electrochemical inactivation, which occurred with decreasing particle size, has also been observed in theoretical studies [29,30].The hydrogen adsorption energy of Pt particles consisting of 147 atoms (corresponding to a diameter of 1.6 nm) was found to be almost the same as that of the bulk metal but increased for 55 atoms (corresponding to a diameter of 1.1 nm) [30].Thus, the adsorption energy of hydrogen atoms gradually increased with decreases in particle size [29,30].Thus, Pt 1.1nm /C likely did not adsorb the expected amount of hydrogen on its surface.

ORR Activities
The LSV data and Koutecky-Levich plots (I −1 vs. ω −1/2 ) generated at 0.85 V and 0.90 V using electrodes made with four different Pt dnm /C specimens coated in Nafion are shown in Figure 6.In each case, a linear relationship with a constant slope was obtained for the plots.The kinetically controlled currents (I) were calculated by extrapolating these relationships to ω = 0.The kinetically controlled SA and the MA for each catalyst were calculated based on the ECSA determined from the CV results and the mass of Pt initially loaded (m Pt ), respectively, as follows: Figures 7 and 8 show the changes in SA and MA associated with the ORR at 0.85 V and 0.90 V, respectively, as a function of d.As shown in Figure 7, the SA value of the Pt 1.8nm /C catalyst was 1.2 mA cm −2 , which was similar to that of a standard commercial Pt/CB catalyst (TEC10E50E, Tanaka Kikinzoku Kogyo, d = 2.5 nm).It can be assumed that there would be no change in SA at particle sizes greater than 1.8 nm.In fact, the particle size range obtained in the present work was consistent with the ranges in prior studies that found no particle size effect.As an example, Yano et al. demonstrated no change in SA in the size range above 2 nm [14].In contrast, the SA values increased rapidly when the particle size dropped below 1.8 nm, reaching a maximum at 1.3 nm (SA = 4.8 mA cm −2 , approximately four times the value for a standard Pt/CB material) and then decreasing rapidly.The MA values exhibited trends much the same as those shown by the SA values (Figure 7B).As can be seen from Figure 8, the variations in SA and MA at 0.90 V also showed very similar trends.However, the SA values were lower than those of the standard Pt/CB.One possible cause is the effect of surface oxidation of Pt.The formation of oxide species on a Pt surface at 0.90 V during ORR has been demonstrated via X-ray photoelectron spectroscopy combined with an electrochemical cell (EC-XPS) research [31].Another possible cause is that the local coordination number and/or distance of Pt is different between our catalyst and the standard catalyst, which affects the oxidation state and electronic state of the Pt surface [32].The details are currently under investigation using the in situ X-ray absorption fine structure (XAFS) technique and will be reported separately as part of the clarification of the activity mechanism.
Surfaces 2024, 7, FOR PEER REVIEW 7 in Figure 6.In each case, a linear relationship with a constant slope was obtained for the plots.The kinetically controlled currents (I) were calculated by extrapolating these relationships to ω = 0.The kinetically controlled SA and the MA for each catalyst were calculated based on the ECSA determined from the CV results and the mass of Pt initially loaded (mPt), respectively, as follows: Figures 7 and 8 show the changes in SA and MA associated with the ORR at 0.85 V and 0.90 V, respectively, as a function of d.As shown in Figure 7, the SA value of the Pt1.8nm/C catalyst was 1.2 mA cm -2 , which was similar to that of a standard commercial Pt/CB catalyst (TEC10E50E, Tanaka Kikinzoku Kogyo, d = 2.5 nm).It can be assumed that there would be no change in SA at particle sizes greater than 1.8 nm.In fact, the particle size range obtained in the present work was consistent with the ranges in prior studies that found no particle size effect.As an example, Yano et al. demonstrated no change in SA in the size range above 2 nm [14].In contrast, the SA values increased rapidly when the particle size dropped below 1.8 nm, reaching a maximum at 1.3 nm (SA = 4.8 mA cm - photoelectron spectroscopy combined with an electrochemical cell (EC-XPS) research [31].Another possible cause is that the local coordination number and/or distance of Pt is different between our catalyst and the standard catalyst, which affects the oxidation state and electronic state of the Pt surface [32].The details are currently under investigation using the in situ X-ray absorption fine structure (XAFS) technique and will be reported separately as part of the clarification of the activity mechanism.Here, we discuss why the ORR activity shows a maximum around d = 1.3 nm.Prior research concerning well-defined single-crystal Pt electrodes has confirmed that ORR activity increases with changes in the crystal plane in the order of (111) << (100) < (110) [7,33].In addition, the proportion of (110) planes (edges + corners) on the surface of the particles increased as the d decreased (Figure 5).Therefore, the present results showing increased ORR activity on going from a d of 1.8 to 1.3 nm are consistent with the crystallographic data.Even so, this effect related to the proportion of (110) planes on the surface cannot be applied to the Pt1.1nm specimen.This is due to the increased proportion photoelectron spectroscopy combined with an electrochemical cell (EC-XPS) research [31].Another possible cause is that the local coordination number and/or distance of Pt is different between our catalyst and the standard catalyst, which affects the oxidation state and electronic state of the Pt surface [32].The details are currently under investigation using the in situ X-ray absorption fine structure (XAFS) technique and will be reported separately as part of the clarification of the activity mechanism.Here, we discuss why the ORR activity shows a maximum around d = 1.3 nm.Prior research concerning well-defined single-crystal Pt electrodes has confirmed that ORR activity increases with changes in the crystal plane in the order of (111) << (100) < (110) [7,33].In addition, the proportion of (110) planes (edges + corners) on the surface of the particles increased as the d decreased (Figure 5).Therefore, the present results showing increased ORR activity on going from a d of 1.8 to 1.3 nm are consistent with the crystallographic data.Even so, this effect related to the proportion of (110) planes on the surface cannot be applied to the Pt1.1nm specimen.This is due to the increased proportion Here, we discuss why the ORR activity shows a maximum around d = 1.3 nm.Prior research concerning well-defined single-crystal Pt electrodes has confirmed that ORR activity increases with changes in the crystal plane in the order of (111) << (100) < (110) [7,33].In addition, the proportion of (110) planes (edges + corners) on the surface of the particles increased as the d decreased (Figure 5).Therefore, the present results showing increased ORR activity on going from a d of 1.8 to 1.3 nm are consistent with the crystallographic data.Even so, this effect related to the proportion of (110) planes on the surface cannot be applied to the Pt 1.1nm specimen.This is due to the increased proportion of corners with relatively low ORR activity between the two types of platinum (i.e., edges and corners) in the (110) surface [34].
This work attempted to explain why the SA values decreased at d smaller than 1.3 nm.An important point to consider here is the relationship between ECAA and SA.The data indicate that the d value associated with the maximum SA coincided with the value at which ECAA began to decrease (Table 1 and Figure 4).As noted, the value of ECAA was affected by the hydrogen adsorption energy.The adsorption energy of oxygen on particle surfaces smaller than 1.3 nm may also have been different from that on larger particles, leading to a decrease in activity.Because MA is defined as SA × ECSA, both these variables will have a synergistic effect on MA.In the present study, maxima of both ORR activity and ECAA and minima of d values were found in a very narrow particle size range (approximately 1-2 nm).
Figure1presents TEM images and particle size distribution histograms for the five different Pt dnm /C powders prepared with 4.6, 11.8, 23.4,24.0, and 47.9 mmol L −1 H 2 PtCl 6 •6H 2 O concentrations.The d values and standard deviations of these Pt dnm /C were 1.1 ± 0.2, 1.2 ± 0.2, 1.3 ± 0.2, 1.4 ± 0.2, and 1.8 ± 0.2 nm, respectively.For comparison, the TEM image and the particle size distribution histogram for a commercial Pt/C (TEC10EA20E, 20 wt% Pt dispersed on the same graphitized carbon black support as that of our Pt dnm /C) in FigureS2in the SI.It was found that the Pt particles in our Pt dnm /C are very uniformly dispersed on the C support, and their size distribution is fairly narrow.The d values increased approximately in proportion to the increases in H 2 PtCl 6 •6H 2 O concentration, as demonstrated in Figure2.A conceptual diagram of the platinum particle formation process is shown in FigureS3in the SI.The homogeneous mixing of platinum salts and carbon in the ethanol solvent results in the uniform formation of platinum nuclei on defects in the carbon.These nuclei grow to any size depending on the concentration of platinum salts, as shown in Figures1 and 2. As an example, the results of the microstructural analysis of the Pt 1.4nm /C are provided in Figure3.Figure3Bshows the electron diffraction (ED) pattern of the region selected in Figure3A.This pattern could be assigned to the (111), (220) and (420) planes of a face-centered cubic structure.The high-resolution STEM (HR-STEM) image presented in Figure3Calso demonstrates that the inter-lattice distance in the front-facing plane was 2.21 Å, corresponding to the (111) plane distance.The orientation of the (111) plane and the angle of the particle contour indicate that these particles had a cuboctahedron geometry, as shown in the diagram in Figure3D.As a result, this work assessed the Pt particles based on a cuboctahedral model.

Figure 1 .
Figure 1.TEM images (low and high magnification) and particle size distribution histograms for pristine Ptdnm/C powders having d values of (A) 1.8, (B) 1.4, (C) 1.3, (D) 1.2, and (E) 1.1 nm.The particle size distribution histograms were measured visually with a ruler and determined for 300 particles in randomly selected multiple images.

Figure 2 .
Figure 2. The relationship between the concentration of the Pt precursor compound ([H2PtCl6•6H2O]) and d.

Figure 1 .
Figure 1.TEM images (low and high magnification) and particle size distribution histograms for pristine Pt dnm /C powders having d values of (A) 1.8, (B) 1.4, (C) 1.3, (D) 1.2, and (E) 1.1 nm.The particle size distribution histograms were measured visually with a ruler and determined for 300 particles in randomly selected multiple images.

Figure 1 .
Figure 1.TEM images (low and high magnification) and particle size distribution histograms for pristine Ptdnm/C powders having d values of (A) 1.8, (B) 1.4, (C) 1.3, (D) 1.2, and (E) 1.1 nm.The particle size distribution histograms were measured visually with a ruler and determined for 300 particles in randomly selected multiple images.

Figure 2 .
Figure 2. The relationship between the concentration of the Pt precursor compound ([H2PtCl6•6H2O]) and d.

Figure 3 .
Figure 3. (A) TEM image, (B) ED pattern, (C) HR-STEM image and (D) diagram of the cuboctahedral model for the Pt 1.4nm /C powder.

Figure 4 .
Figure 4. Cyclic voltammograms obtained from Nafion-coated Ptdnm/C electrodes in Ar-purged 0.1 M HClO4 solutions at 30 °C with a potential scan rate of 50 mV s -1 .

Figure 4 .
Figure 4. Cyclic voltammograms obtained from Nafion-coated Pt dnm /C electrodes in Ar-purged 0.1 M HClO 4 solutions at 30 • C with a potential scan rate of 50 mV s −1 .

Figure 5 .
Figure 5.A diagram of the cuboctahedral models used for the Pt particles with various L values.* Fraction of (110) plane and (111) + (100) planes plane on the surface of Pt particles[28].

Figure 5 .
Figure 5.A diagram of the cuboctahedral models used for the Pt particles with various L values.* Fraction of (110) plane and (111) + (100) planes plane on the surface of Pt particles[28].

Figure 7 .
Figure 7. Particle size-dependence of kinetically controlled (A) specific activity (SA) and (B) mass activity (MA) during the ORR on Nafion-coated Ptdnm/C (d = 1.1, 1.2, 1.3, 1.4, and 1.8 nm) electrodes in 0.1 M HClO4 solutions at 30 °C.The square symbols indicate value for a standard commercial Pt/C catalyst (d = 2.5 ± 0.4 nm).All data were acquired with a working electrode potential of 0.85 V.

Figure 8 .
Figure 8. Particle size-dependence of kinetically controlled (A) specific activity (SA) and (B) mass activity (MA) during the ORR on Nafion-coated Ptdnm/C (d = 1.1, 1.2, 1.3, 1.4, and 1.8 nm) electrodes in 0.1 M HClO4 solutions at 30 °C.The square symbols indicate value for a standard commercial Pt/C catalyst (d = 2.5 ± 0.4 nm).All data were acquired with a working electrode potential of 0.90 V.

Figure 7 .
Figure 7. Particle size-dependence of kinetically controlled (A) specific activity (SA) and (B) mass activity (MA) during the ORR on Nafion-coated Pt dnm /C (d = 1.1, 1.2, 1.3, 1.4, and 1.8 nm) electrodes in 0.1 M HClO 4 solutions at 30 • C. The square symbols indicate value for a standard commercial Pt/C catalyst (d = 2.5 ± 0.4 nm).All data were acquired with a working electrode potential of 0.85 V.

Figure 7 .
Figure 7. Particle size-dependence of kinetically controlled (A) specific activity (SA) and (B) mass activity (MA) during the ORR on Nafion-coated Ptdnm/C (d = 1.1, 1.2, 1.3, 1.4, and 1.8 nm) electrodes in 0.1 M HClO4 solutions at 30 °C.The square symbols indicate value for a standard commercial Pt/C catalyst (d = 2.5 ± 0.4 nm).All data were acquired with a working electrode potential of 0.85 V.

Figure 8 .
Figure 8. Particle size-dependence of kinetically controlled (A) specific activity (SA) and (B) mass activity (MA) during the ORR on Nafion-coated Ptdnm/C (d = 1.1, 1.2, 1.3, 1.4, and 1.8 nm) electrodes in 0.1 M HClO4 solutions at 30 °C.The square symbols indicate value for a standard commercial Pt/C catalyst (d = 2.5 ± 0.4 nm).All data were acquired with a working electrode potential of 0.90 V.

Figure 8 .
Figure 8. Particle size-dependence of kinetically controlled (A) specific activity (SA) and (B) mass activity (MA) during the ORR on Nafion-coated Pt dnm /C (d = 1.1, 1.2, 1.3, 1.4, and 1.8 nm) electrodes in 0.1 M HClO 4 solutions at 30 • C. The square symbols indicate value for a standard commercial Pt/C catalyst (d = 2.5 ± 0.4 nm).All data were acquired with a working electrode potential of 0.90 V.

Table 1 .
Preparation conditions of Pt dnm /C catalysts.