A measure of active interfaces in supported catalysts for high-temperature reactions

The characterization of the inherent reactivity of the catalyst is critical for the development of an efﬁcient catalytic system for many reactions. Herein, we identify and visualize the active interfaces and quantify the reaction contribution of the individual active site. The analytic methodology suggested in this study enables us to distinguish the importance of individual reaction interfaces depending on the operation conditions (temperature and methane-to-oxygen ratio) and structure of the material (Pt size)


INTRODUCTION
The interplay between oxide supports and supported metal nanoparticles (NPs) is of high significance in the field of heterogeneous catalysis. [1][2][3][4][5] While the role of oxides was oversimplified in the past, evidence suggests that the use of redox-active oxides (such as CeO 2 and ceria) as a support material can dramatically reshape the landscape of multiple high-value catalytic processes. [6][7][8][9][10][11][12][13][14] Often, the augmented catalytic activity is attributed to the synergistic interaction between the metal and the support, as the overall rate of reaction can be much greater than the sum of the rates over the support and the metal individually. 15,16 Therefore, many studies, including CO oxidation and water-gas-shift reactions, have been dedicated to unraveling the roles of such interfaces. [17][18][19][20][21] As such, it is implied that the strong local electronic and structural interactions at metal-support interfaces may improve the inherent catalytic activity of supported metal species. [22][23][24] Other studies have also indicated that such metal-support interactions provide more reactive sites by facilitating interfacemediated reaction paths. 2,8,25,26 Although the aforementioned studies have produced valuable insights regarding the functions of metal-support interfaces, it should be noted that the overall turnover rate may not be entirely determined by the metal-support interface. In other words, the surfaces of metal particles are still likely to be involved in the bigger picture, even when active supports are used. Generally, for supported metal catalysts, the rate of the overall chemical reaction is primarily determined by the elemental steps that The bigger picture Supported catalysts in the form of metal nanoparticles affixed on oxide are at the heart of many chemical industries. However, the information about where the reaction takes place and how much each individual reaction site contributes to the overall rate remains unclear. This work realizes a universal experimental and analysis platform to identify the key reaction sites in a supported catalyst system, which includes the quantification of the turnover rate contribution for individual reaction sites. Thermally robust and geometrically well-defined model catalysts and electron tomography techniques allow three-dimensional visualization of the reaction interfaces, and these data are linked with the catalytic activity and theoretical calculations to quantify the activity of each site. Our work sheds light on the way to explore catalytic pathways and mechanisms for multiple reactions and materials.
occur at either the double-phase boundary (2PB) between the gas and the metal or the triple-phase boundary (3PB) at which the gas, metal, and oxide support phases are simultaneously in contact. Indeed, the extent to which each reaction site contributes to the overall reaction rate likely depends on the type of reaction 27 and/or the catalyst composition. 28,29 Furthermore, the dominant reaction site and pathway, even for the same reaction and material, can vary dynamically according to the temperature, 30 ratio of the reactants, 31,32 and the microstructure of the catalyst (i.e., the size distribution of the supported metal NPs). 33,34 To date, however, few studies have attempted to quantify the competition between these two interfaces. Therefore, it has never been possible to answer the following fundamental questions, which can be a substantial cornerstone in the design of an ideal catalyst: ''Which of the two interfaces of a given catalyst is more active depending on the reaction, temperature, and gas atmosphere?'' and ''How exactly is that interface more important than the other, numerically?'' To this end, two major issues must be resolved-first, the density of each active site (i.e., 2PB and 3PB) should be accurately characterized and controlled; thereafter, the catalytic activity of interest should be monitored carefully in relation to the variant ratio of 2PB and 3PB. In this vein, Cargnello et al. successfully determined how the frequency of atoms at 2PB and 3PB varies with the particle size via imaging of the structures of monodispersed metal nanocrystals dispersed on ceria supports. They reported that the change in the CO oxidation rate according to the particle size coincided with the change in the number of atoms at 3PB, which unambiguously demonstrated that the metal-ceria interface is the only active site for CO oxidation in the measurement condition they studied. 35 Despite the fact that the approach described above represents one of the most triumphant cases of compiling size-activity relationships in heterogeneous catalysis, the temperature window in that study was below the calcination temperature (<573 K), whereas many industrially important chemical reactions proceed at high temperatures (>773 K). Indeed, the coarsening and coalescence of nanosized metal particles are likely to occur at elevated temperatures, 36 posing a particular challenge with regard to maintaining the density of each active site (i.e., the 3PB length and 2PB area per gram of metal used). Methane activation, one of the most treasured reactions for the academy as well as the enterprise, is a typical example of a high-temperature reaction. In particular, this reaction is of interest because specific target applications (i.e., combustion versus reforming) require different operating conditions (i.e., temperatures, types of oxidant, CH 4 -to-oxidant ratios) and the corresponding reaction pathways are therefore expected to vary markedly. Cargnello et al. demonstrated that enhanced metal-support interactions can lead to outstanding methane combustion rates in Pd@CeO 2 subunits. 37 Zhang et al. reported that the interfacial site between Co and CeO 2 is essential for the catalytic reaction during the dry reforming of methane. 38 Previous studies have identified the possibility that the metal-ceria interface may play a role in methane activation; yet, no attempt has been made to quantify the roles of 2PB and 3PB sites individually over a wide range of temperatures and gas atmospheres. Therefore, a novel strategy is essential to overcome the morphological evolution of catalysts at high temperatures and thus to assess the value of each key reaction site, which is much more challenging.
In this study, we present thermally stable and oxide-encapsulated metal catalysts with well-defined geometries and reaction sites. Size-tunable monodisperse Pt NPs surrounded by a gas-permeable ceria shell are selected as a model catalyst. For comparison, silica-encapsulated Pt catalysts are prepared as a reference for inert support. Electron tomography (ET) combined with a three-dimensional (3D) reconstruction method is then utilized to directly observe and quantify the Pt-gas and Pt-CeO 2 -gas interfaces. Based on these corresponding results, we measure how the 2PB and 3PB site densities (per gram of Pt) vary with the particle size and how the catalytic activities for CH 4 oxidation change accordingly. The two reaction sites participate simultaneously in CH 4 oxidation, and the contribution of each reaction site to the overall reaction rate is identified, which is further supported by the theoretical interpretation that corroborates the dual-site reaction pathways for methane oxidation in a ceria-Pt system. Our results suggest a reliable platform to explore catalytically active sites and pathways for various chemical reactions, even at high temperatures.

RESULTS AND DISCUSSION
Monodisperse Pt NPs having four different diameters were prepared through aqueous-based colloidal synthesis using a cationic surfactant. 39 Transmission electron microscopy (TEM) bright-field (BF) images show that the particles are 7.8 G 0.8, 9.1 G 0.5, 11.8 G 1.6, and 19.7 G 1.7 nm in size, respectively ( Figures  1A-1D). Subsequently, the Pt NPs were encapsulated with gas-permeable thin layers of ceria ( Figures 1E-1H) or silica ( Figures 1I-1L) to prevent coalescence at elevated temperatures. The electrostatic interaction between cationic Pt NPs and anionic Ce precursor complex ions helps cerium oxide shell overcoat Pt NPs uniformly, 40 which is manifested in the energy-dispersive spectroscopy (EDS) mapping ( Figure S1). Moreover, scanning electron microscopy (SEM) and TEM BF images at low magnifications confirm that individual Pt NPs are encapsulated in ceria shells ( Figure S2). The CeO 2 crystallites in the outer layer of the core-shell structure were $6 nm in size, corresponding to the calculated value from the X-ray diffraction peaks ( Figure S3). The fabricated Pt@CeO 2 structures were later evenly dispersed on additional high-surface area ceria supports (78 m 2 g À1 ), utilizing the opposite surface charges ( Figures S4 and S5). In a similar manner, Pt@SiO 2 samples were prepared by the hydrolysis and condensation of Si precursors around Pt NPs and the subsequent polymerization of silicates, as has been demonstrated elsewhere. 41,42 For all of the samples, we kept the thickness of the ceria and silica shell constant at $20 and 30 nm, respectively, by adjusting the reaction time so as to eliminate the effects of shell thickness variations on the measured catalytic activities.
These shell configurations demonstrate the capability of effectively inhibiting the structural evolution of the catalysts during high-temperature annealing. Figure 2 shows a series of TEM BF images obtained while annealing a Pt@CeO 2 sample at elevated temperatures (Figures 2A-2D) and at prolonged times ( Figures 2D-2F), demonstrating that the Pt@CeO 2 catalysts maintain their morphology without coarsening of Pt NPs up to 873 K. The as-synthesized Pt NPs showed faceted forms due to different growth rates of Pt NP along <100> and <111> directions, 43 but as the temperature increased, the shape of the Pt NPs became spherical with random orientations ( Figures S6-S8). The ceria shell also retained its porosity without aggregation. Another important factor to consider is that catalysts can undergo structural evolution on the atomic scale, such as single atom (SA) formation, during a high-temperature heat treatment. 18,[44][45][46] In particular, the Pt-CeO 2 system has been reported to favor the atomic-scale dispersion of Pt during oxidative high-temperature calcination. However, we did not observe any noticeable modifications after calcination at 873 K ( Figure S9). Perhaps different catalytic configurations, such as the initial morphology and composition of the catalyst, influenced the process of structural transformation. Similar to Pt@CeO 2 , Pt@silica was also stable up to 873 K while maintaining its core-shell structure ( Figure S6).
Next, we visualized the Pt@CeO 2 catalysts in three dimensions through ET. For 3D reconstruction, samples before and after a heat treatment at 873 K were utilized, and the cubic voxels of all samples had a side length of 1-2 Å . The 3D resolution of the tomogram was calculated based on the Fourier shell correlation (FSC) with a criterion of 0.143 ( Figure S10), showing an average value of 1.28 G 0.19 nm. This value is close to the resolution limit ($1 nm) achievable for a 60 nm object at 1 tilt increments based on the Crowther-Klug criterion. 47 We note that in our study, the core-shell catalysts had a size in the range of 50-60 nm, and the tilt increment for tomography data acquisition was 1 . Each resolution for the nine different samples used in this study is summarized in Table S1. The resolution slightly improved after thermal treatment, likely due to the elimination of the residual organic matter. To quantify the microstructural properties in 3D, including the density of the 2PB and 3PB sites, we applied a semi-automated segmentation routine to the tomograms ( Figure S11). Figure 3A shows the resultant 3D reconstruction image, indicating that the Pt particle is uniformly surrounded by a mesoporous ceria shell, which is  readily accessible to gas molecules. A cross-sectional view of the core-shell catalyst along the z axis also shows pores between 1.6 and 3.7 nm in size inside the ceria shell ( Figure S12). The accuracy of these pore sizes was confirmed by simulated 3D tomography performed with an image resolution similar to that used in this study (Figure S13). Figures 3B and 3C visually identify the 3PB (red line) and 2PB (green phase) sites, respectively. The 3D tomogram results shown in Video S1 display the morphology and the internal structure of the object, a series of core-shell catalysts, improving our structural understanding of the samples. Table S2 presents quantified results showing how each reaction site density normalized to the Pt loading amount depends on the diameter (d) of the Pt NPs. As the particle size decreases, the density of the 2PB and 3PB sites increases, but different tendencies arise according to the value of d. For example, the density of the two sites in the Pt@CeO 2 composites shows power-law exponents of À1.02 G 0.12 and À1.88 G 0.26, respectively, for d ( Figures 3D and 3E). Advanced ET technology has recently begun to be applied to heterogeneous catalytic research, but it has only been used to qualitatively confirm the porous structure, and it is noteworthy that this is ''the first report'' to quantify key reaction sites of nanocomposite catalysts through ET. 48,49 As will be discussed later, the scale relationships between the two reaction site densities with respect to d reflect the respective reaction rates. Before an in-depth discussion of CH 4 activation on the model catalyst system, the validity of the 3D tomography analysis and the reconstruction process must be ensured; hence, we carried out ad hoc CO chemisorption and oxidation analyses with the Pt@CeO 2 catalysts. First, the 2PB site density was directly measured via CO chemical adsorption, taking into account the property by which CO molecules are selectively adsorbed on the Pt surface. Table S3 shows the exposed metal surface area (EMSA) per unit mass of the Pt@CeO 2 catalysts versus d. Thereafter, the 3PB density was reliably deduced by using CO oxidation as a reference reaction. Earlier results demonstrated that the ceria-Pt interface is the dominant reaction site for CO oxidation in the conditions used in this study. 35 Accordingly, the power-law dependence of CO oxidation reactivity on d is expected to reflect that of the 3PB interface in our catalytic system. Indeed, the kinetic results of CO oxidation on the Pt@CeO 2 system are identical to those when the ceria-Pt interface is a dominant reaction site in the Pt/CeO 2 system. Moreover, the core-shell catalyst with a high-3PB density has a higher reaction rate than the supported-Pt catalyst, indicating that the 3PB site is an active site (see details in Figures S14 and S15). Figure S16 shows the changes of the 2PB and 3PB site density levels extracted by additional adsorption and oxidation experiments according to the diameter and with power-law exponents for d of À0.93 G 0.02 and À1.95 G 0.02, respectively. It turns out that the image analyses and experimental supporting results are in good agreement within a standard deviation of 7%. This in combination with the fact that the pore sizes of the ceria shell as judged by tomography are in line with the pore-size distribution obtained via the adsorption experiments clearly demonstrates that our analytic approach is solid. 40 In yet another examination of the  validity, we performed additional tomographic experiments using different equipment, thus further ensuring the precision of the linear regression analysis result. As shown in Figure S17, the newly obtained data did not significantly change the slope of the interface variation with particle size. Nonetheless, considering the resolution of 1.28 nm, the issue may arise that tomography may not yield the exact absolute value of the interface near the resolution limit. In this regard, the slope calculation was simulated by assuming that the standard deviation of the particle size and the interface obtained by tomography corresponds to 50% of the mean value. This describes the situation where the standard deviation would increase when the desired information exists near the resolution limit of the tomogram. The results are shown in Figure S18. We obtained slopes of À1.73 G 0.24 for 3PB and À0.99 G 0.17 for 2PB, which are similar to the measured slope values. Moreover, still, the slope for 2PB and 3PB indicates quite a large difference. Therefore, even if tomography may not yield the absolute values of the interfaces in some cases, we propose that our approach to distinguish each interface is reliable. In sum, this judicious design of a composite catalyst enables the quantification of idealized 2PB and 3PB interfaces for chemical reactions while effectively suppressing the agglomeration of metal cores at high temperatures; this is of key importance when constructing an analytic platform to find the dominant reaction site for a given catalytic reaction.
Next, we evaluated the activity of CH 4 oxidation on oxide-encapsulated Pt NP catalysts as a case study for typical high-temperature reactions. CH 4 oxidation is a fundamental reaction for various industrial applications, such as catalytic combustion, emission control, and hydrogen reforming, 37,50 but the reaction mechanisms within the ceria-Pt system have not yet been fully identified. The kinetic rate data for CH 4 oxidation over ceria-and silica-encapsulated Pt NPs are shown in Figures  4A and S19. First, the Pt@SiO 2 catalysts used as an inert support reference always exhibit a constant reaction rate regardless of the particle size when normalized to 2PB as determined by CO chemisorption ( Figure S19). In contrast, the Pt encapsulated with a reducible CeO 2 support (Pt@CeO 2 ) exhibited directly opposite behavior, as the reaction rate strongly depends on the particle size ( Figure 4A). This implies that, in addition to the Pt surface, another reaction site, plausibly the ceria-Pt interface, acts as a reaction area in the ceria-Pt system. Because the increase in the 3PB density is more pronounced than that of the 2PB density as the size of the Pt dwindles, it is anticipated that the role of the 3PB site is emphasized with tiny Pt NPs. Indeed, as the Pt size decreases, the apparent values of E a gradually decrease from 82.8 to 63.8 kJ mol À1 , signifying that the dominant active site adapts with the catalyst size.
Reaction orders for CH 4 and O 2 will present a clearer understanding of the role of the Pt-ceria interface in CH 4 oxidation reactions. For silica-based catalysts, an increase in the partial pressure of methane (pCH 4 ) accelerates the reaction, whereas an increase in the partial pressure of O 2 (pO 2 ) slows down the reaction, with reaction order values of 0.95 and À0.40, respectively, for CH 4 and O 2 ( Figure S20). These reaction order values are in good agreement with the reported values, meaning that the Langmuir-Hinshelwood-type of reaction path represents the surface reaction between adsorbed CH 4 and O 2 on Pt sites. 51,52 In the ceria-based sample, however, a relatively weak dependence of the reaction rate to pCH 4 and pO 2 was noted, with corresponding reaction orders of 0.55 in CH 4 and À0.19 in O 2 ; thus, it is obvious that methane combustion occurs through a reaction pathway different from that associated with silica-based catalysts. Similarly, a less sensitive dependency of the catalytic activity on the partial pressure of the reactants was observed in the ethane, propane, and butane oxidation reactions on ceria-supported noble metal catalysts. 52 Given the ability of ceria as an oxygen reservoir, these results can be explained by the dual-function mechanism in which the ceria supplies oxygen to the supported metal and the delivered oxygen interacts with methane provided near the Pt-ceria interface. 52,53 The presence of Pt indeed activates lattice oxygen atoms in the vicinity of the ceria surface and reduces the activation energy for the dissociative adsorption of methane. 26,54 Thus, the aforementioned results consistently represent the principal evidence of the active role of Pt-ceria interfacial sites regarding CH 4 oxidation, while their degree of participation may vary with the particle size.
The values of the turnover rate as a function of the catalyst diameter can be considered as more direct and decisive evidence specifying the predominant interface, whereas the plot can be further deconvoluted to quantify the accurate ratio of reaction engagement between 2PB and 3PB. The overall reaction rate comes from ll scaling relationships for CH 4 oxidation, described in the form of a double-logarithmic plot (log TOF versus log d). For the Pt@silica samples, we found that the turnover frequencies (TOFs) for CH 4 oxidation were proportional to d À0.51G0. 36 , which is consistent with the trend of EMSA, which varies with d (EMSA f d À0.54G0.18 ) (Figure S21). This observation corroborates the contention that CH 4 combustion occurs dominantly at the Pt surface sites of the Pt@silica catalysts, which is further supported by the fact that the reaction rate normalized by EMSA is independent of d ( Figure S19). In contrast, the tendency of the change in the TOF in the Pt@ceria samples is not always consistent with the trend of the 2PB site density variation according to the value of d ( Figure 4B); rather, the power-law dependence of d for TOF exists between those of 2PB and 3PB. Therefore, the TOF values of CH 4 oxidation could be fitted using two parallel relationships, as plotted in Figures 4B-4D, showing the TOF value versus d (i.e., TOF f C 1 d À1.02 + C 2 d À1.88 , where C 1 and C 2 are constant). These data fitting results reveal that both active sites concurrently contribute to the methane oxidation reaction and allocate their proportion under the given reaction condition. For example, as shown in Figure 4B and Table S4, when d is 10 nm, the reaction temperature is set to 823 K, and the O 2 /CH 4 ratio of the input gas is 4, it can be found that 2PB and 3PB are almost equally important and partake in the overall reactivity at rates of 45% and 55%, respectively.
Based on these scaling relation results, we can quantify how each interface contributes to the overall TOF value according to the Pt particle size, temperature, and gas composition (ratio between CH 4 and O 2 ). In terms of d, the smaller the particle size, the greater the number of sites at the Pt/ceria interface relative to the surface area of Pt exposed at a given mass, meaning that the overall reactivity of the coreshell catalysts is determined more by an elemental process at 3PB. On the other hand, for larger NPs, 2PB dominates the overall reaction. As shown in Table S4, the role of 3PB increases rapidly from 15% to 90% as the size of Pt decreases from 100 to 1 nm at 823 K with an O 2 /CH 4 ratio of 4. In addition, because the elemental steps in 2PB and 3PB have different activation energies ($100 and $60 kJ mol À1 , respectively), the contribution of each interface varies with the temperature. For example, the 3PB interface plays a more dominant role at the lower temperature of 723 K as compared with the role at 823 K if all other factors (e.g., the feed gas ratio and Pt NP size) are equal (Figures 4B and 4C; Tables S4 and S5).
With smaller Pt particles, as shown in Figures S22 and S23, we can again confirm the rationality of our results, explaining the role of 2PB and 3PB sites. These results indicate that the metal-ceria interface density must be maximized to achieve CH 4 activation at lower temperatures, consistent with earlier findings in the literature. 28,55 In addition to the particle size and temperature effects, the dominant active region also varies with the gas composition introduced. As shown in Figure 4D, if the reaction occurs at an O 2 /CH 4 ratio of 0.0625 (oxygen-lean condition), 2PB contributes entirely to the overall TOF values. In contrast, 3PB dominates the overall catalytic activity at a higher O 2 /CH 4 ratio of 40 (oxygen-rich condition). These reactant-gasdependent catalytic responses arise from the difference in the predominantly adsorbed species on the Pt NPs depending on the O 2 /CH 4 ratio. 56 At higher relative oxygen ratios, more oxygen covers the Pt surface, with intimate Pt-O interactions. The preferred oxygen saturation may suppress CH 4 adsorption on the Pt surface and thus the participation of 2PB accordingly. This reduces the overall activity (Figure S24); however, it makes the participation of 3PB relatively important. Methane oxidation at 2PB, on the other hand, plays an important role during oxygen-lean conditions. Eventually, combining the robust model catalytic system and a quantitative To clarify the mechanistic details pertaining to the roles of 2PB and 3PB, we performed DFT calculations. Two types of structural models are utilized to model CH 4 oxidation on core-shell Pt@CeO 2 comprehensively: a conventional Pt 9 NP on CeO 2 (100) and an inverse Ce 7 O 14 NP on Pt(111). Here, only the energetics from the former system is presented because relatively consistent results were deduced from both systems (refer to supplemental information for additional data pertaining to the latter model). The calculated binding energy, E bind , of CH 4 (À0.44 eV) and O 2 (À2.14 eV) molecules on Pt NPs indicates that the Pt NP preferentially binds to O 2 initially ( Figure S25). Because subsequent dissociation of the Pt-bound O 2 molecule is exothermic with a low E a , we initially saturated the Pt NPs of Pt@CeO 2 models with oxygen ( Figure S25). Later, the O-saturated Pt NP dissociatively adsorbs a CH 4 molecule in the presence of the pre-adsorbed oxygen atoms ( Figures 5A1 and 5B1), initiating the subsequent CH 4 oxidation steps. Although both the Pt-CeO 2 interface (3PB) and the surface Pt (2PB) can bind to CH 4 , 3PB is energetically more preferred ( Figure 5). Moreover, 3PB provides a greater thermodynamic driving force for the sequential dehydrogenation of CH 4 ( Figure 5), suggesting that 3PB is the primary CH 4 activation site at low CH 4 concentrations. Interestingly, both 2PB and 3PB sites show high E a values for the dehydrogenation of CH 4 ( Figures S26 and S27). However, considering that the reaction occurs at a high temperature and that the entropic contribution to the energetics of CH 4 dissociation provides an additional driving force for hydrogen abstraction overall, these E a values will not hinder the reaction. The DFT-estimated subsequent dissociative adsorption of CH 4 and the dehydrogenation of CH 3 * ( Figure 5) show that Pt-bound oxygen atoms, Pt-O*, accept the   Figures 5A7 and 5B7), a large portion of E de can be supplied by the positive (qualitatively) entropic contribution to the Gibbs free energy of H 2 O desorption.
The remaining C of CH 4 was combined with two different oxygen species: Pt-O* (2PB) or lattice oxygen of CeO 2 (3PB), being transformed into Pt-CO* ( Figures  5A5 and 5B5). These two oxygen species concurrently contribute to the overall CO 2 production rate because their E a values of CO 2 formation are nearly identical ( Figures S26 and S27). The comparable E de values of CO 2 from 2PB (0.41 eV) and 3PB (0.55 eV) predict that both are energetically available ( Figures  5A9 and 5B9). Supporting our experimental prediction that Pt@ceria provides at least two active sites for CH 4 oxidation, the DFT calculation results describe the dual-site reaction pathways in a condition in which O 2 covers the Pt surface, similar to the actual environment. Because no notable relative superiority of a specific site was found, the relative ratio of 2PB and 3PB, a direct function of the size of the Pt NPs, steers the dominant reactive species and the pathway for CH 4 oxidation.
In summary, we showcased a generalizable empirical and characterization framework with which to determine the dominant reaction sites in the Pt-CeO 2 system with regard to methane oxidation, a crucial reaction proceeding at elevated temperatures. In contrast to recent reports that narrowly focused on the roles of redox-active supports, we found that the primary reaction sites between 2PB and 3PB vary with extreme sensitivity according to the temperature, gas pressure, and the size of the metal NPs. In particular, empowered by a combination of a theory-based mechanistic study and state-of-the-art experimental synthesis and analysis, we revealed that a larger NP size, an increasing T value, and a decreasing pO 2 value lead to a greater contribution of 2PB to the total methane turnover rate, and vice versa, marking, ''for the first time,'' the development of a quantitative direct relationship between the areal fraction of the reaction sites and the catalytic activity of metal NPs toward high-temperature chemical reactions. The aforementioned strategy may globally guide other metal-catalyst support systems for a variety of industrially important reactions, and the insights gained here present a roadmap with which to find the ''ideal catalyst'' for a specific target condition.

EXPERIMENTAL PROCEDURES
Resource availability Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact, WooChul Jung (wcjung@kaist.ac.kr).

Materials availability
All unique/stable reagents generated in this study are available from the lead contact with a completed materials transfer agreement.

Data and code availability
All data reported in this paper will be shared by the lead contact upon request. This paper does not report original code.

Synthesis of Pt nanoparticles
An aqueous solution of potassium tetrachloroplatinate(II) (10 mM and 5 mL) and alkyltrimethylammonium bromide (C n TAB, n = 12, 14, 16, and 18) (400 mM and 12.5 mL) was added to 29.5 mL of deionized (DI) water while being stirred. The mixture was then heated to 323 K for 20 min. When using the C 18 TAB surfactant, the mixture was heated to 328 K for 25 min due to its greater hydrophobicity. Subsequently, a reduction agent, sodium borohydride (500 mM and 3 mL), was injected into the mixture. Hydrogen gas formed in the flask was released into the fume hood for 20 min using a syringe needle.  Table S3, we prepared an appropriate amount of a Pt@CeO 2 synthetic solution so that the amount of Pt was adjusted to 1 wt % to the total weight of the catalyst. Then, a concentrated ammonia solution (0.38 mL, 28-30 wt %) was added to make the surface of the core-shell structure negative. C 14 TAB (10 mM) was added to the Pt@CeO 2 solution so that the surface charge of the core-shell structure would be positive ( Figure S4; Table S6). Each mixture solution (CeO 2 support and Pt@CeO 2 ) was mixed together with stirring at 300 rpm for 10 min. The resulting solution was centrifuged at 8,000 rpm for 10 min and the precipitate was collected and dried at 353 K overnight. The as-synthesized Pt(1 wt %)@CeO 2 / CeO 2 catalyst was calcined at 623 K for 5 h in air to eliminate the residual organics, such as C n TAB, EDTA, and ethanol, and to lead to the formation of pores in the cerium oxide shell. The wt % of Pt NPs in the final catalysts was reconfirmed by means of an X-ray fluorescence (XRF) analysis. The surface charge of each species was verified via a zeta-potential measurement. The zeta-potential measurement and XRF results are compiled in Tables S6 and S7, respectively.

Preparation of the Pt(1 wt %)/CeO 2 catalysts
A suitable amount of CeO 2 support was dispersed in a basic solution to prepare the surface of CeO 2 to impart a negative charge. We then prepared a proper amount of a colloidal solution consisting of positively charged Pt NPs so as to adjust the amount of Pt to 1 wt % of the total weight of the catalyst (the Pt concentration was verified by ICP-OES and is compiled in Table S3). Each solution (CeO 2 support and Pt NPs) was mixed by stirring at 300 rpm for 10 min. The resulting solution was then centrifuged at 8,000 rpm for 10 min and the precipitate was collected and dried at 353 K overnight. The as-synthesized Pt(1 wt %)/CeO 2 catalyst was calcined at 623 K for 5 h in air. The wt % of the Pt NPs in the final catalysts was confirmed by an XRF analysis (Table S7).
Preparation of the Pt(1 wt %)@silica/silica catalysts A suitable amount of silicon oxide support was dispersed in a basic solution to prepare the surface of silica to have a negative charge. Based on the ICP-OES results shown in Table S3, we prepared an appropriate amount of a positively charged Pt@silica synthetic solution so that the amount of Pt was adjusted to 1 wt % of the total weight of the catalyst. Each solution (silica support and Pt@silica) was mixed while being stirred at 500 rpm for 30 min. Afterward, the mixture was separated into the supernatant liquid and the precipitate. The supernatant liquid was removed, and the precipitate was dried at 353 K overnight. The as-synthesized Pt(1 wt %)@silica/silica catalyst was calcined at 723 K for 3 h in air to remove the residual organics, such as C n TAB, TEOS, and ethanol, leading to the formation of pores in the silica shell.
Preparation of the 2.8 nm-Pt@CeO 2 /CeO 2 catalyst To prepare the Pt NPs (ca. 2.8 nm), 200 mg of platinum(II) acetylacetonate were mixed in 1-octadecene (10 mL) together with oleylamine (OLAM, 1 mL) and oleic acide (OLAC, 1 mL) in a three-neck round bottom flask. The flask with the mixture was connected to the standard Schlenk line. The mixture solution was heated to 393 K in 20 min and flushed at 393 K for 15 min under Ar flow. Next, the solution was left under Ar flowing for 30 min to remove water and other impurities. Subsequently, the solution was further heated to 473 K at a ramping rate of 4 K min À1 . After the reaction at 473 K for 30 min, the mixture solution was cooled down to RT. The stirring rate was kept at 500 rpm during the synthesis procedure. The as-synthesized Pt NPs were separated by centrifugation twice at 8,000 rpm for 10 min. The Pt NPs were dispersed in toluene with 50 mL of OLAM for further use. For the preparation of the 2.8 nm-Pt/CeO 2 , the Pt NPs dispersion was mixed with a solution of CeO 2 dispersed in 40 mL of toluene. The mixture was left stirring at 300 rpm for 10 min. Next, the mixture was separated by centrifugation at 5,000 rpm for 10 min. The precipitates were dried in an oven at 353 K overnight. The as-synthesized 2.8 nm-Pt/ CeO 2 was calcined at 623 K for 5 h in air to remove the remaining organics. To cover the Pt NPs by CeO 2 shell, the 2.8 nm-Pt/CeO 2 powder was immersed in 40 mL of DI water. After then, cerium nitrate hexahydrate (Ce(NO 3 ) 3 $6H 2 O, 1 mM) and hexamethylenetetramine (HMTA, 10 mM) were added into the solution. The mixture was heated to 343 K for 30 min to oxidize cerium precursors on the surface of Pt NPs. The as-synthesized 2.8 nm-Pt@CeO 2 /CeO 2 catalyst was rinsed in DI water, dried in an oven at 353 K overnight, and calcined at 623 K for 5 h.

Catalytic activity tests (CH 4 and CO oxidation)
A fixed-bed micro-reactor with a 4 mm inner diameter was used to measure the catalytic activity of the CH 4 and CO oxidation processes. To create the catalyst bed, 50 mg of a catalyst was mixed with 100 mg of quartz sand, and this was then placed between layers of quartz wool. To ensure that neither mass nor heat transfer limitations affected the measured results, we performed the conversion while changing the flow rate at a constant space velocity, finding that the conversion characteristics remained constant ( Figure S28). The feeds for CH 4 oxidation (composed of 0.5 vol %-CH 4 and 2 vol %-O 2 in an Ar balance) and CO oxidation (composed of 1 vol %-CO and 4 vol %-O 2 in an Ar balance) were passed through the reactor. To investigate the effect of the feed gas ratio, we adjusted the input gas ratio (O 2 /CH 4 ) from 0.0625 (oxygen-lean condition) to 40 (oxygen-rich condition). The total flow rate was 50 mL min À1 for both oxidation reactions. The reaction rate was recorded while increasing the temperature with a ramping rate of 3 K min À1 . For each test, the catalyst was activated in the reaction environment at 873 K for CH 4 oxidation and 573 K for CO oxidation. The gas concentration change was detected with a quadrupole mass spectrometer (Pfeiffer Vacuum GSD320) in real time. The CH 4 and CO conversion ratios (%) were defined as the ratio of the converted reactant to the total input reactant (i.e., CH 4 conversion ratio = 100 3 (mol CH4, inlet À mol CH4, outlet )/mol CH4, inlet ; CO conversion ratio = 100 3 (mol CO, inlet À mol CO, outlet )/mol CO, in ). To rule out the effect of the CeO 2 support itself toward CH 4 oxidation, we subtracted the reaction rate of the CeO 2 support from the overall measured reaction rate so as to determine the reaction rate associated with Pt NPs. The reaction orders for CH 4 and O 2 were determined as follows. For the reaction order of CH 4 , the reaction rate was measured by varying the pCH 4 (from 2 3 10 À3 to 6 3 10 À3 atm) while keeping the pO 2 constant at 5 3 10 À2 atm. In the same way, for the reaction order of O 2 , we determined the reaction rate according to the change in pO 2 (from 1 3 10 À2 to 5 3 10 À2 atm) while keeping the pCH 4 constant at 2 3 10 À3 atm. To investigate the reaction order of CO and O 2 , we measured the reaction rate by changing the partial pressure of carbon monoxide (pCO) (from 1 3 10 À3 to 6 3 10 À3 atm) while holding the pO 2 level at 5 3 10 À2 atm. We also carried out rate measurements according to the pO 2 variation while keeping the pCO level at 1 3 10 À3 atm. Methane gas was detected by the m/z = 15 peak instead of the 16 peak to avoid interference from the fragments ll of CO, CO 2 , H 2 O, and O 2 . The CO gas signal was measured by taking into account the contribution from CO 2 gas via the mass concentration determination (MCD) mode.

Characterization techniques
The morphologies and elemental compositions of the synthesized core-shell catalysts were characterized by means of bright-field TEM and energy-dispersive X-ray spectroscopy (EDX) (JEOL JEM-3010 operating at 300 kV and FEI Talos  Thereafter, the as-prepared sample was mounted in an ultra-high vacuum (UHV) chamber overnight before the image acquisition for tomography to remove residual organics. A pre-heat treatment of the catalyst for ET was carried out using an in situ heating TEM (FEI Tecnai G2 F30 S-Twin). SEM images were acquired using a Hitachi S-4800 device. The Pt NP concentrations in the solutions and the Pt/Ce molar ratios of the core-shell particles were determined by an inductively coupled plasma mass spectrometer (Agilent ICP-OES 720) and an XRF spectrometer (Rigaku ZSX Primus II). For ICP-OES, samples were dissolved in aqua regia and diluted prior to the measurement. The average particle size was calculated by counting more than 200 individual particles. The surface charge of the samples was characterized using a zeta-potential analyzer (Otsukael ELS-Z2). The crystal structure of the samples was identified by powder X-ray diffraction using a Rigaku D/Mas-2500 device with Cu-Ka radiation at 40 kV and 200 mA with a scan rate of 4 per minute from 20 to 60 . CO chemisorption experiments were conducted on a Micromeritics ASAP 2020. The samples were placed in a U-shaped quartz reactor, heated under flowing O 2 (5%) in helium at 723 K for 1 h, reduced in flowing H 2 (5%) in helium at 423 K for 1 h, and then evacuated at 573 K for 4 h. CO chemisorption experiments performed at RT. Nitrogen adsorption/desorption isotherms were carried out at the temperature of liquid nitrogen (77 K) using a Micromeritics Tristar II 3020 instrument to identify the pore-size distribution, pore volume, and total surface area of the samples.

Electron tomography
The tomographic tilt series were acquired in high-angle annular dark-field scanning transmission electron microscopy (HAADF STEM) mode in the angular range of G60 at an increment of 1 at the KAIST Analysis Center for Research Advancement (KARA). Here, we deliberately reduced the electron beam dose with a total screen current of 0.23 nA, which is 10 times lower than the commonly used conditions but sufficient to obtain tomographic images without damaging Pt@CeO 2 . To confirm whether or not there were structural changes by an electron beam, we checked projection images at a 0 before and after the acquisition of the tilt series and identified that structural evolution did not appear during the data collection.
To resolve a linear stage drift at each angle while acquiring the STEM tilt series, we aligned the obtained images using FEI's software package, Inspect 3D, by correlating an individual image with a separate reference image. The cross-correlation function was computed through the Fourier transform of the image. This procedure proceeds with an iterative cross-correlation method to minimize errors in alignment (maximum shift of pixel < À1). The subsequent reconstruction processes were carried out using FEI Inspect 3D. For the reconstruction, the simultaneous iterative reconstruction technique (SIRT) 57  The factor obtained from Equation 1 was 1.55 when a = 60 . For an accurate image analysis and quantification process, the Z direction voxel size of the reconstructed sample was adjusted, taking into account the elongation coefficient. To check the impact of the limited tilt range in this study, we acquired another set of tomographic images in the angular range of G70 at an increment of 1 . Thereafter, we repeated the reconstruction process at 5 intervals from G50 to G70 . From this process, the minimum tilt angle at which information loss by the limited tilt range does not become critical was identified, and that was the angular range of over G 60 , confirming the quantitative interpretation was reliable in this study ( Figure S29).

Segmentation process
In order to quantify the significant morphological features of size-tunable catalysts, a segmentation process of designating each phase (Pt, Ceria, and pore) was utilized in a semi-automated manner. This approach proceeds with the use of a threshold with de-noising and contrast-enhanced filtering. The post-processing has shown its robustness throughout other tomography results. [59][60][61][62][63] To enhance the effect of the post-processing, background areas outside the region of interest (ROI) were removed by a binary mask. Through this process, only the Pt@CeO 2 catalyst remains, with the other pixels set to zero. Then, image de-noising was conducted using an anisotropic diffusion filter. 64 This reduces the noise without diluting the intensity of the edges. Anisotropic diffusion filtering is known as an effective tool for de-noising and edge preservation. [65][66][67] This process is essential to minimize the subjectivity of the analyst, and it can help to clarify the phase distinction after tomography and increase the accuracy of the quantification result. We checked the de-noising and the filtering effect on the quantification in Figure S30. Designation of the phase was performed using the Watershed segmentation algorithm. 68 This algorithm computes the gradient of the voxel and considers it as a 2D or 3D landscape. In order to distinguish each phase from the contour of the Pt NPs more precisely, adaptive histogram equalization filtering was used. 69 This process enhances the contrast between phases and makes it easier to distinguish between the pores and solid phase.

Quantification process
Based on the segmented data, the morphological features of the catalyst, including the particle diameter, 2PB and 3PB, were quantified with an Avizo Fire device (FEI Company). The calculated values are summarized in Table S2. To quantify the diameter of Pt NPs and the EMSA, the phase volume and surface area were calculated by converting the surface of the specific phase voxel into a triangular mesh. This method is a more accurate approach for calculating a 3D surface compared with a voxel counting algorithm. From the quantified surface area and volume of spherical Pt NPs, the particle size can be determined by the Brunauer-Emmett-Teller (BET) formula, D = 6 3 V/S. 70,71 To calculate the 3PB length, the voxels intersected with three ll phases (Pt, ceria, and pore phase) were extracted. The 3PB length was calculated by extracting all voxels in contact with Pt, ceria, and the pore. The extracted voxels were ''skeletonize'' 72 to obtain their length, and the total length was divided by the mass of the Pt particle to yield the 3PB site density.

3D resolution estimation
The spatial resolution of the reconstructed sample was estimated using the FSC with a criterion of 0.143, 73,74 which correlates the reciprocal-space densities of the two sub-tomograms. For this purpose, the tilt series images were separated into two groups based on odd or even numbers of the order of the tilt angles. Each group was independently reconstructed, and their 3D volumes were used to compute the FSC curves as a function of the spatial frequency in the Fourier space. The resolution was determined as the value at which the FSC curve intersected with the preestablished threshold criterion. The resolution estimation process was performed in Matlab using an in-house code.
Simulated 3D tomography Simulated 3D tomograms of the porous structure were prepared as follows. We generated 3D model volumes as ground truths. The size of each 3D model volume was 350 3 350 3 350 voxels with a voxel size of 0.3 nm. Each 3D model volume consists of a big sphere of 60 nm diameter that contains seven pores, with one pore at the origin and the other six symmetrically distributed at positions 6 nm away from the origin. We generated three such 3D model volumes with pore diameters of 1.5, 2.1, and 3.3 nm, respectively. Three tilt series with tilt angles ranging from À60 to 60 with 1 step were generated by taking linear forward-projections from the 3D model volumes. Each tilt series contains 121 projections; whose size was 350 3 350 pixels, with a pixel size of 0.3 nm. To properly simulate the experimental conditions, Poisson noise, random translation errors up to G0.45 nm, and random tilt angle errors up to G0.1 were added to the tilt series. 3D tomograms were reconstructed from the generated tilt series and tilt angles using SIRT algorithm 71 with 30 iterations.
To measure the diameters of pores in the simulated 3D tomogram, we first separated the 3D volume into two parts (the big sphere and pores). To designate each part, a segmentation process similar to that applied to Pt@CeO 2 catalysts was used in an automated manner. Next, the pore size was determined by assuming each pore as a spherical particle, and calculating the diameter can be estimated as D = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 63 volume p 3 q . The resolutions of the simulated 3D tomograms were estimated using the 0.143 criterion of the FSC analysis. 73,74 Density functional theory calculations We modeled the CeO 2 (100) surface using a 3 3 3 supercell with three O-Ce-O triple layers. Quality test results confirmed that two key energy values, the oxygen vacancy formation energy from the 3PB and the oxygen binding energy on the 2PB, were well described using our supercell compared with a larger supercell, (5 3 5). A Pt NP composed of nine atoms was supported on the optimized CeO 2 (100) substrate and repeatedly optimized upon the sequential adsorption of of six oxygen atoms to describe the catalyst structure under the CH 4 oxidation conditions. The bottom ceria triple-layer structure was fixed during all calculations to ensure structural robustness. An inverse Ce 7 O 14 /Pt(111) model was constructed by optimizing a Ce 7 O 14 cluster on a 7 3 7 3 4 Pt(111) slab ( Figure S31). The supplemental information ( Figures S32 and S33) section provides information about the CH 4 oxidation pathways and corresponding energetics calculated from the Ce 7 O 14 /Pt(111) model. We performed spin-polarized DFT calculations using a plane-wave basis with the ll vienna ab-initio simulation package (VASP) code 75 and the Perdew-Burke-Ernzerhof (PBE) functional 76 . The DFT+U 77 scheme with U eff = 5 eV 78 was applied for Ce ions to consider the localized Ce-f orbitals appropriately. The interaction between the ionic core and the valence electrons was described by the projector augmented wave method. 79 Valance electron wave functions were expanded in a plane-wave basis up to an energy cutoff of 400 eV. The Brillouin zone was sampled at the G-point for all calculations. The convergence criteria for the electronic structure and the atomic geometry were 10 À4 eV and 0.03 eV/Å , respectively. We used a Gaussian smearing function with a finite temperature width of 0.05 eV in order to improve the convergence of states near the Fermi level. The location and energy of transition states (TSs) were calculated with the climbing-image nudged-elastic-band method. 80