Structural evolution in the ligand detachment process.
The overall experimental procedure is illustrated in Fig. 1a. Starting with the experimentally resolved 3D atomic structures of ligand-protected Pt NPs in liquid solution19, MD simulations for the ligand detachment process followed by fast thermal annealing were performed for individual Pt NPs with varying sizes (NP1: 2.42 nm, NP2: 2.52 nm, NP3: 2.66 nm, and NP4: 2.92 nm). Tracking of the 3D atomic coordinates was carried out over the whole process to analyse the structural changes. Then, key features of the structures, i.e., the generalized coordination number (GCN)24 and strain, were fed into kinetic Monte Carlo (kMC) simulations of the CO oxidation reaction. Last, the turnover frequency of individual particles was calculated to investigate the per-site activity.
One of the main bottlenecks in simulating the structure-property relation of the ligand detachment process in Pt NPs is a careful evaluation of the structural fluctuations. We addressed the issue by integrating a machine-learning neural network potential (NNP) with first-principles data of atomic energy to enable accurate and fast MD simulations. Various strategies have been applied to efficiently construct the NNP such as data augmentation25 and active learning26. Our strategy is innovative in that it involves efficient construction of first-principles data by incorporating the experimentally reconstructed atomic configurations and defective NPs to describe various local atomic environments (Fig. 1b).
We generated local structural heterogeneity by using structures of experimentally resolved Pt NPs and highly defective Pt NPs at various intermediate steps acquired with first-principles calculations. To estimate the reliability of our approach, we compared the local atomic environments in ideal models and experimentally reconstructed structures (Fig. 1c). The ideal magic-number cuboctahedron consisting of 309 atoms shows only specific atomic environments, represented by the values of the radial (G2) and angular (G4) functions, with duplicated information (essentially core atoms), and this issue is still unresolved even with the addition of model structures. In contrast, the structural heterogeneity in the twenty structures of experimentally reconstructed Pt NPs provides much more densely mapped local configurations, which are fed into the feedforward neural network. Thus, we utilized the accelerated data collection method to make a training set for the NNP. Details of the first-principles data generation and the NNP training and validation results are provided in Supplementary Sections 1 and 2.
The structural evolution of individual Pt NPs during the ligand detachment process and thermal annealing was investigated via MD simulations with the constructed NNP. As shown in Fig. 1d, the total simulation time was 300 ps, in which the initial 100 ps corresponded to the thermal treatment with the ligand detachment process at 773 K, the next 100 ps to the quenching process to 303 K with a quenching speed of 4.7 K per ps, and the final 100 ps to equilibration at 303 K. The total energy of each NP becomes thermodynamically more stable as it undergoes the quenching process. We also observed that the larger the particle size is, the more stable the particle becomes (Fig. S5)27,28. The structural changes in NP3, representatively, show qualitative insights into the reduction of surface adatoms to form close-packed surfaces (Fig. 1d). The lattice parameters and averaged strain after the ligand detachment process indicate that the particle-wise structural heterogeneity decreases as Pt NPs approach the thermodynamic energy minima (Fig. S6a). However, the increase in the error magnitude reflects the flattened distributions of individual coordinates, which presumably signifies the diversified values of individual sites after the thermal treatment.
The temporal changes in the 3D atomic coordinates of NP3 obtained using MD simulations were further investigated. Figure 2a shows the changes in the fractions of the coordination number (CN), which is an index to evaluate the local atomic environments. We divided the atomic local environments into four classes in accordance with the CN29: CN = 12, CN = 10–11, CN = 9 − 7, and CN ≤ 6. Each environment shows different behaviour with elapsed time, especially in the initial stage. The fractions of defective cores or subsurfaces of edges (CN = 10–11) do not fluctuate much, while other sites drastically change in the initial stage. The drastic change in the initial stage is mainly attributed to the ligand being instantly removed at the beginning of the simulation. The fraction of atoms with CN = 12, representing the face-centered cubic (fcc) lattice of the bulk, and that with CN ≤ 6, representing high-Miler-index facets, vertices, edges, or irregular islands of adatoms, decreased, whereas the fraction of atoms with CN = 9 − 7, representing (111) or (110) facets, increased. After the detachment process, the fcc lattice sites gradually recovered during the thermal annealing process. The surface atoms (CN ≤ 9) evolve in a way to minimize the surface energy, forming truncated octahedrons with (111) and (110) facets. The results for other Pt NPs were similar in that the number of surface adatoms initially binding ligands was reduced. The thermodynamic driving force of surface minimization can also be confirmed by the increase in the terrace (111) surface areas (Fig. 2b).
Local atomic arrangements were also analysed by the Voronoi tessellation method30. As shown in Fig. 2c, the distributions of the 25 most abundant Voronoi polyhedra (VPs) before and after the thermal treatments were obtained based on the Voronoi index < n3, n4, n5, n6>, where ni denotes the number of i-edged polygons. Before the treatment, most of the VPs are < 0, 0, 12, 0 > regular icosahedrons along with < 0, 11, 0, 0 > defective icosahedrons and < 0, 9, 0, 1 > polyhedral with multitetragonal surfaces. The major peaks for VPs before the treatment clearly indicate the single crystallinity of NP3. However, the crystallinity significantly decreases after the treatment (e.g., from 287 to 165 counts for < 0, 0, 12, 0>). Additionally, many VPs with low-edged polygons (n3) appear, which indicates defective local atomic configurations. The defect identification by Wigner-Seitz analysis shows that all defects are on the surface (Fig. 2d).
As shown in Fig. 2e, the interatomic distances along the < 111>, < 100>, and < 110 > directions imply that the deviation increases as the atomic site moves away from the core of the NP, which is similar to the results of a previous study19. The distributions before and after the thermal treatment demonstrate that the interatomic distances along the < 111 > and < 110 > directions are rather similar (Fig. 2f). The distribution along the < 100 > direction at 300 ps with two peaks substantiates the surface energy difference among the (111), (110), and (100) surfaces in that adatoms preferentially penetrated into the (100) surface with the least stability and the smallest atomic packing factor. Our structural analyses consistently express the structural rearrangement of Pt NPs to minimize the surface energy induced by thermal energy during the ligand detachment and thermal treatment processes. The core crystallinity is mostly preserved, while surface reconstruction is unavoidable affecting the catalytic performance.
Structure-property relation with thermal treatment.
The chemical reaction energy in a single-component system is largely determined by structural features such as the local atomic coordination environment and strain31,32. Thus, we examined the GCN and atomic strain (Supplementary Section 3) at individual atomic sites of Pt NPs. The thermodynamic driving force for surface energy minimization also induced drastic changes in both GCN and strain (Fig. S7 and S8). Initially, all Pt NPs exhibited structural heterogeneity, especially surface atoms29.
As the simulation time elapses, the density peaks for GCNs in the range of 4 to 6 increase, but those for high GCNs decrease. The increase in the density peaks for lower GCNs during the ligand detachment process implies the formation of, e.g., (110) or higher Miller index, facets along with edges and vertices with GCN values in the range of 5.4 to 6.6, and 5.4 or lower, respectively. The vanishing peaks for very low GCNs indicate the penetration of adatoms into the surface lattice sites. The decrease in peaks for higher GCNs, similar to the CN results, signifies the reduction of core crystallinity, mainly due to the high processing temperature (773 K) of the ligand detachment process. The strain distributions of Pt NPs at the beginning also show the heterogeneity, with less correlation with the size after the process, in which NP2 has the lowest deviation of strain from equilibrium (Fig. S6b). One thing to note is that initially imposed tensile strains were preserved over the process, implying that colloidal methods can be beneficial for catalytic activity through an upshift of the d-band centre energy to enhance the binding affinity33.
The structural features of the atomic sites were further analysed by decoupling the surface and core atoms (Fig. 3). Since catalytic reactions occur at the surface, the structural features of surface atoms are of interest. As shown in Fig. 3a, distinctive surface atom peaks (4.5 to 5 and 5.5 to 6 for edge atoms and high-index facets, respectively) are dominant for all Pt NPs, but the peak intensities vary. The core crystallinity is more preserved for larger-sized NPs, with higher peaks for GCNs in the range of 11 to 12. For all NPs, (111) facet formation (6.6 < GCN < 7.5) is clearly observed based on the colour-coded analysis, but some close- packed facets showed smaller GCNs. This is mainly attributed to the adatoms in the interstitial fcc lattice sites, which induced a void space between the surface and core. In contrast, the strain distributions of surface atoms show no distinctive peaks for all NPs (Fig. 3b). The major strain distributions initially resided in the range of 0 to 2 for all Pt NPs, but surface minimization effects resulted in high strain values (greater than \(\pm\)10 ) after the ligand detachment process. Colour-coded results also represent the predominant tensile strain over the surface atoms.
The change in average bond length was also computed as shown in Fig. S9. Core atoms suffer bond elongation, such as tensile atomic strain, but surface atoms suffer overall bond contraction. This is because the nearest neighbours of surface atoms consist of atoms in the same surface with a higher fraction (0.66) and atoms in the subsurface with a lower fraction (0.33) in general. Overall, the change in the structural features of individual Pt NPs after the ligand detachment process shows distinctive characteristics in that the ensemble of individual sites is magnified in terms of the GCN, while it is reduced in terms of the strain.
Individual site contributions to catalytic activity.
To investigate the ensemble effects of active sites on catalytic reactivity, we constructed microkinetic modelling and performed kMC simulations for CO oxidation in Pt NPs as a prototype catalysis process34,35. Overall reaction energetics were adopted from the previous literature16,36, but strain effects on the adsorption energy were revised by assigning individual atomic strain and site-dependent perturbations. Details of the reaction energetics and the kMC simulation are described in Supplementary Section 4.
Figure 4a shows the Arrhenius-type plot of the temperature-dependent turnover frequency (TOF) for different size Pt NPs. In general, the catalytic activity increases as the particle size increases, which is in accordance with a previous report34. Notably, such behaviour were not seen for modelled NPs35. To understand the peculiar size-dependent activity trend, we computed the fraction of surface atoms with respect to the total number of atoms and the fractions of active and inactive sites with respect to the number of surface atoms (Fig. 4b and Fig. S11). The surface atom fraction decreases with increasing particle size due to the reduction in the surface-to-volume ratio. The ensemble of active sites (TOF > 5·104 s− 1 site− 1) is directly correlated with the activity of the particle, and the low fraction of inactive sites for larger particles indicates less kinetic hindrance. Interestingly, NP2 has a higher TOF than NP3 despite its smaller size.
The activities of ideal NPs (561 and 807 atoms) with similar sizes to NP1 to NP4 were computed. The results show that the NPs with high density peaks for the GCN have higher activity due to the ensemble effects of individual sites (Fig. S12 and Fig. S13). To correlate the results of ideal NPs with those from NP1 to NP4, we compared the deviations in the number of atoms for each NP from that for the ideal NP models with (100) and (111) facets (Fig. S14). NP2 has a marginal deviation (0.01), while NP3 has a much higher deviation (0.10). We speculate that the extent of deviation can be a crucial factor; the closer the number of atoms of an NP is to that of the ideal model, the easier the NP can optimize towards the global minimum for facet formation. To summarize, the catalytic activity of NPs is dominated by the coupled effects of particle size and active site formation, increasing the individual site assembly.
To uncover how much different types of sites contribute to the total activity, we further analysed the TOF of Pt NPs through individual site analysis. First, we evaluated the effects of the GCN, as shown in Fig. 5a. In general, GCNs ranging from 4.8 to 5.5 yield high TOF, which indicates that the edge sites are the most reactive. In addition to the GCN, we considered the strain effect on the TOF of individual sites (Fig. 5b). We plotted the individual sites with TOF > 104 s− 1 site− 1. The active sites were gathered in the region of low GCN (4.8 to 5.5) and tensile strain (5 to 10%). Notably, that the results for ideal model NPs are different (Fig. S15). Ideal model NPs exhibit catalytic activity for GCNs ranging from 4.8 to 5.5 and (111) facets, which is attributed to the kinetic coupling of adsorbates diffusing from the active sites35. However, surface structures are more heterogeneous in real conditions, in which the coupling effects are weakened, and thus the site responsiveness towards the target adsorbates becomes more important.