From Process to Properties: Correlating Synthesis Conditions and

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From Process to Properties: Correlating Synthesis Conditions and Structural Disorder of Platinum Nanocatalysts Baichuan Sun,* Hector Barron, George Opletal, and Amanda S. Barnard Data61, CSIRO, Door 34 Goods Shed Village Street, Docklands, VIC 3008, Australia

J. Phys. Chem. C Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 11/29/18. For personal use only.

S Supporting Information *

ABSTRACT: Understanding the complicated relationship between various synthetic processing parameters and the functional properties or performance of nanoparticles is one of the goals of computational materials design, and is an ideal problem for materials informatics. In this study, we use machine learning to build predictions of how bulk and surface disorder is controlled by the growth time, atom deposition rate, and temperature, and how they can impact some indicators of the functional properties of platinum nanoparticles used in catalysis, including a range of structural features. We have used an ensemble of 690 unique nanoparticles generated from molecular dynamics trajectories that sample a large variety of different temperature/growth rate combinations, and genetic algorithms providing a prediction accuracy over 85% for all models. We have developed reliable and insightful predictions of structure/property and process/structure relationships (even when the polydispersed structures are almost entirely disordered), but our results suggest that the transcendent process/property relationship requires more detailed descriptors than those traditionally available from conventional computational studies.



INTRODUCTION

of sizes, and a considerable degree of bulk and surface imperfection. Navigating the complicated relationship between various synthetic processing parameters, such as temperature, growth rates (moderated by precursors and surfactants), and time, the final functional properties or performance is one of the goals of computational materials design, particularly in the engineering of nanocatalysts, and is an ideal problem for materials informatics. Among the available methods, machine learning (ML) has been shown to provide insight into complex multistructure correlations that are difficult to identify using conventional computational methods, and are free from some of the assumptions and biases introduced by human researchers. By going one step further and combining conventional simulations, appropriate ML algorithms (such as artificial neural networks and k-means clustering), and a sufficiently large and diverse ensemble of candidate nanostructures, it is possible to identify the set of features that drive performance,30 and the conditions required to deliver the right structures in practice. In this study, we use ML to build predictions of how bulk and surface disorder is related to some synthetic processing conditions, and how it can impact some functional properties of imperfect platinum nanoparticles. We have used an

Although it has been well established that the size, shape, and surface structure of nanoparticles are responsible for their performance in a variety of applications, complete control over the structure remains challenging1−4 due to competition and collaboration between growth kinetics and thermodynamics during synthesis.5−7 Although improvements in controlling the shapes are regularly introduced,8−13 structural imperfection is persistent,14−16 and ideal monodispersed samples remain short-lived or entirely elusive. Many samples contain imperfect shapes, disordered lattices, and defective surfaces. For example, it has been shown that platinum nanoparticles with controlled sizes and shapes, characterized by specific surface areas and in different crystallographic directions, can be used to tune the selectivity and sensitivity of many major catalytic reactions.17,18 Among the methods developed to control these features solution-phase synthesis is highly versatile19−22 and uses the reduction and decomposition of a metal precursor in the presence of a surfactant to engineer the structure of platinum.23−26 Variables contributing to the final structure of individual particles includes the type and concentration of the precursor, the reducing agent and stabilizer, the introduction of seeds or foreign species,27 the impact of twinning and structural defects,28,29 temperature, and time. With so many variables contributing (simultaneously) to the final structure, it is not surprising that samples of platinum nanoparticles typically contain a mixture of shapes, distribution © XXXX American Chemical Society

Received: August 28, 2018 Revised: November 14, 2018

A

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Figure 1. Examples of the type of MD simulation (left) and extracted primary particle (right) present in the ensemble, for T = 100 °C, τ = 2.5 × 10−4 atoms per ns, at three different points along the MD trajectory, where the primary particle measures (a) Rmin = 0.7165 nm and Rmax = 1.8508 nm, (b) Rmin = 0.8977 nm and Rmax = 3.4755 nm, and (c) Rmin = 0.8712 nm and Rmax = 3.7042 nm.

ensemble of 690 unique nanoparticles generated from molecular dynamics (MD) trajectories that sample a large variety of different temperature/growth rate combinations. One of the advantages of applying ML analysis is the ability to assess the impact of each independent feature,31 and so we characterized the ensemble using 25 structural descriptors, three processing parameters, and three indicators of catalytic performance. As we will show, our genetic algorithms (GAs) achieved a prediction accuracy over 85% for all models providing reliable and insightful prediction of structure/ property and process/structure relationships (even when the polydispersed structures are almost entirely disordered), but highlighting the associated process/property relationship

requires more detailed descriptors than those traditionally available from conventional computational studies.



METHODS Data Generation and Characterization. To characterize the atomic structure under different synthesis conditions and growth processes, an existing set of MD simulations were performed using icosahedral crystalline seeds within a large simulation box of 10 nm3. After the insertion of the seed, the growth was initiated by random addition of single Pt atoms and progressed via unguided sintering and coalescence events. This process was repeated for seventy different MD durations, atomic deposition rates, and temperatures to capture the effects of inhomogeneous reaction kinetics and thermal B

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The Journal of Physical Chemistry C fluctuations within a range of values, characteristic of experiments, as described in the Supporting Information. In their raw form, trajectories from MD simulations are not suitable for statistical analysis or machine learning, since structures from temporally adjacent time-steps may or may not be significantly different. Redundant structures, or those that are statistically indistinguishable based on their energy or coordinate geometries, can result in over-representation of certain types of structures and must be eliminated. For this reason, we have cleaned the MD simulations by extracting the primary particles at time steps when they were structurally unique, as shown for three examples along the trajectory generated at T = 100 °C, τ = 2.5 × 10−4 atoms per ns in Figure 1. In this way, an ensemble of 690 unique platinum nanoparticles is created that is suitable for materials informatics. This data set, along with detailed metadata, is freely available online.32 To characterize each of the particles in the ensemble, we can retain some descriptors from the original simulation, including MD duration (time), atomic deposition rate, and temperature, but other properties must be obtained in post-processing. The total number of atoms (NPt), the number of bulk atoms (Nbulk), the number of surface atoms (Nsurf), volume, average radius (Ravg), max/min radii (Rmax and Rmin), radius standard derivation (Rstd), and the radius skewness and kurtosis (Rskew and Rkurt) were calculated for the extracted primary particles. The bulk structure can be further characterized using order parameters to classify the local atomic environment into facecentered cubic (FCC), hexagonal close packed (HCP), icosahedral (ICOS), decahedral (DECA), and other ordered structures (ORD). In cases where the atoms do not conform to one of these local atomic environments, we have classified the structure as disordered (DIS) in the context of a platinum lattice. This method is as described in the Supporting Information. In the case of the surface order and disorder, the surface curvature and packing was classified separately based on the surface coordination and angles. The surface curvature for each surface atom is calculated from the displacement vectors with its first nearest neighbors, and the classification of surface packing (which is defined as the {hkl} facets) combines the particle curvature with the coordination and individual bond angles, as described in the Supporting Information. In addition to this, the prevalence of different types of surface defects can be characterized using the coordination number of the atoms on the surface of each particle in the ensemble, and these have been calculated here using a code previously applied to the classification of surface disorder in gold nanorods33 and platinum nanoparticles.34 The surface coordinate number (SCN) is useful, as it can be used to group types of surface imperfections that have been shown to enhance different catalytic reactions.17,18,35−37 In this classification scheme, three catalytic property indicators, surface defects (sdef), surface microstructures (smic), and surface facets (sfac), are defined by SCNs 1 to 11 by

11

∑ SCNi i=1

where i is the coordinate number. In this study, we have focused on the ratio of sdef, smic, and sfac, that is Sdef =

∑ SCNi i=4

sdef

sdef s = def + smic + sfac Nsurf

(4)

sdef

smic s = mic Nsurf + smic + sfac

(5)

sdef

sfac s = fac Nsurf + smic + sfac

(6)

Smic = Sfac =

Therefore, Sdef, Smic, and Sfac are the coverage ratios of surface atoms in different coordination number ranges. Their absolute values are from 0 to 100%. Some nanoparticles have higher coverage of certain surface atoms whereas others have lower values; this would contribute to different catalysis performance for different nanoparticles.



RESULTS AND DISCUSSION Features of Pt Nanoparticles. As mentioned above, each individual Pt nanoparticle was characterized by its synthesis conditions, and structural and morphological features, as listed in Table 1. All features were standardized. Table 1. Synthesis Conditions and Structural Features of Pt Molecular Dynamics feature abbreviation T τ t Nsurf Nbulk Ntotal volume Rmin Rmax Rdif Ravg Rstd Rskew Rkurt F100 F111 F110 C10 C20 C30 C40 C50 FCC HCP ICOS DECA ORD DIS

(1)

7

smic =

(3)

i=8

3

sdef =

∑ SCNi

sfac =

(2) C

feature Synthesis Conditions temperature atomic deposition rate time (MD simulation duration) Structural Features number of surface atoms number of bulk atoms number of total atoms particle volume minimum radius maximum radius radius difference average radius radius standard derivation radius skewness radius kurtosis fraction of (100) facets fraction of (111) facets fraction of (110) facets fraction of 0−10° curvature fraction of 10−20° curvature fraction of 20−30° curvature fraction of 30−40° curvature fraction of 40−50° curvature face centered cubic population hexagonal close packed population icosahedral population decahedron population other ordered population disordered population DOI: 10.1021/acs.jpcc.8b08386 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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To analyze the synthetic processing conditions, all values of T, τ, and t were taken into account. Here, T covers temperatures of 303, 323, 373, 433, 473, 573, and 673 K; τ ranges from 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.7, 2, 2.25 to 2.50 (×10−4) atoms per ns; and t indexes different frames from the MD trajectory that are statistically different from each other (in nanoseconds). The hierarchical clustering map for the correlation matrix of all structural and processing features is shown in Figure 2. Here, we can see that t, Ntotal, Nsurf, Nbulk, Rmax, and Ravg are correlated, so are F110 and C10, as well as FCC, DIS, and C20. τ impacts Rmin whereas T, DECA, and C30 are independent from almost all other variables. ICOS is excluded because it is constant zero for most of the nanoparticles. In terms of functional property indicators, the histogram of Sdef, Smic, and Sfac for the overall 690 data points is illustrated in Figure 3. It is found that Sdef is independent from Sfac and from Smic, whereas Sfac and Smic are highly correlated with each other with a Pearson coefficient of −97.4%. Structure/Property Relationships. To determine if the property indicators can be predicted based on the structural features, we used genetic programming based on the list provided in Table 1, and found that the prediction performance of the optimized model reaches 89.7% (Figure 4a) and 88.9% (Figure 4b) for training and testing datasets, respectively. This result indicates that the structural features

Figure 2. Hierarchical clustering map of the Pt structural feature correlations.

Figure 3. Standardized histogram and correlation of the property indicators: surface defects (Sdef), Surface Microstructures (Smic), and Surface Facets (Sfac) over the entire Pt dataset. Sfac is correlated with Ravg. D

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Figure 4. Sfac regression results with structural features for (a) training dataset R2 and (b) testing dataset R2, and (c) importance score of each individual structural features.

particles (which has been commonly assumed). This does not exclude the use of size to engineer Pt nanoparticles, but makes for a much more complicated recipe. Previous results reported throughout the literature have made detailed studies of size dependence (of highly crystalline nanoparticles and polyhedral geometries), but lack the details of the structure of the surfaces at each size. It is possible that surface texturing has been playing a role that has been previously overlooked, as some recent studies have shown that significant increases in the catalytic performance are obtained for anisotropic and roughened surfaces.38−43 The topic of size dependence will be revisited in the future with more detailed size-dependent features. Process/Structure Relationships. Given the suggestion from the previous section, the next challenge is to determine if promising structural features, such as C20, can be engineered via the synthesis conditions of t, τ, and T. With these 3 variables, a predictive model was developed using GA, which gave an R2 of 93.7 and 89.7% for the training and testing dataset, respectively, as shown in Figure 5a,b. This confirms that t, τ, and T are strongly correlated with the C20 structural feature (surface roughness), and tuning of the associated structure/property relationship may be possible. In contrast, it was found that the C40 structural feature cannot be predicted accurately by t, τ, and T, suggesting that although roughening can be tuned, the populations of more undercoordinated surface atoms on corners cannot. This can be rationalized when we consider that atoms with a surface curvature of C40 or C50 usually reside at high energy sites such as corners or as adatoms, and are highly mobile at finite (and particular

we have included can be used to predict the property indicators with some degree of confidence, but suggests that a higher prediction performance may be possible if a more detailed or comprehensive list of features or more explicit measures of catalytic performance were available. The optimized model reported from GA was a regularized extreme-random-trees (ExtraTrees) regressor. In practice, treebased models (i.e., ExtraTrees, Random Forests, etc) use bootstrapping or bagging mechanisms to randomly select features and data samples to build trees which reduce potential issues of feature multicollinearity. However, one needs to be cautious when interpreting the feature importance, as highly correlated features can have different important scores from the trees. Therefore strongly corrected features shown in Figure 2 are not mutually compared in the following section. With this caveat in mind, we examined the feature importance reported from the ExtraTrees, as shown in Figure 4c, where we find that the surface curvatures of C20 and C40 are more important than surface curvatures of C10 and C30. This is significant because it means that out-of-plane distortions (C20), which are characteristic of roughened surfaces, and corners (C40) are more strongly associated with property indicators than flat facets (C10) and edges (C30). The results also indicate that the DIS and FCC population is more important than the HCP, DECA, or ORD population, which means more detailed characterization would be desirable in terms of DIS. Most importantly, the size has almost no influence on the property indicators in our study, suggesting that texturing the surface will be far more effective in tuning the catalytic performance than simply growing smaller or larger nanoE

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Figure 5. C20 regression results for (a) training dataset R2 and (b) testing dataset R2, (c) feature importance and (d) correlation between C20 and t.

elevated) temperatures. Atoms with curvatures of C40 or C50 will be subject to surface mass diffusion to sites with lower surface curvature to increase the number of interatomic bonds (such as a step or a kink) and lower the free energy. Together with the feature importance shown in Figure 5c from the tree-based models (searched by GA), we found that t is the most important processing parameter, but not τ because larger particles need longer time to grow. By considering the correlation between C20 and t, as shown in Figure 5d, we found that short growth time leads to higher C20 density, regardless of the size. Temperature, however, is irrelevant beyond catalysing any necessary secondary reactions during synthesis and provides no opportunity for controlling the shape or surface structure. Process/Property Relationships. Although it may be assumed that since process parameters are correlated with certain structural features, and structural features are correlated with property indicators, the process must be related to properties, we find that it is not that straightforward. We attempted to model this transcendent relationship but found that the exact values of the catalytic property indicator Sfac (for example) cannot be predicted accurately by t, τ, and T. In this case, the ML regression models gave poor results for both training (78.2%) and testing (70.7%) data sets. This indicates that more processing parameters are needed to build the predictive models, or more property indicators than these three variables. Alternatively, we studied the selectivity of Sfac under the influence of t, τ, and T by clustering its values into 2 subcategories using k-mean, as shown in Figure 6a. A classifier

was searched by GA that gives an area under curve (AUC) of 97.4% of the receiver operating characteristic (ROC) for test data (Figure 6b), even though the classes are imbalanced in this study. This result suggests that it is possible to predict Sfac classification accurately based on synthetic proceeding conditions, though not the exact value. The relation between Sfac, t, and τ is illustrated as a heat map (Figure 6c), which once again confirmed the significance of t to determine the property indicators. The prediction probability of the ML classifier is shown in Figure 6d. The above workflow was applied to Sdef and Smic as well. It was found that Smic demonstrates a very similar result to Sfac, as suggested by Figure 3b. Sdef, however, cannot be controlled using these synthesis conditions, or predicted by the structural features. More information on the Sdef and Smic results can be found in the Supporting Information.



CONCLUSIONS Following the successful characterization of 690 disordered platinum nanoparticles from trajectories generated using classical MD, we have applied machine learning algorithms to determine the correlation between the synthetic processing conditions, structural features, and indicators of catalytic performance. We achieved a prediction accuracy over 85% for all models, with the exception of process/property relationships, where the number of processing descriptors was insufficient. We found that the formation of roughened Sfac surfaces, where the atomic curvature is between 10 and 20°, could be F

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Figure 6. (a) Sfac clustering into two subclasses based on its value selectivity, (b) receiver operating characteristic (ROC) of the classification results for test data, (c) heat map of Sfac corresponding to the time (t) and atomic deposition rate (τ), and (d) heat map of the output probability of the machine learning classifier.



controlled by modulating the duration of synthesis (or simulation), as this generates more facets with surface coordination numbers of 8, 9, 10, or 11. Similarly, the formation of stepped and kinked Smic surfaces, where the atomic curvature is between 30 and 40°, could also be controlled by the synthesis (or simulation) time, as this generates more facets with surface coordination numbers of 4, 5, 6, or 7. The former is a property indicator for the hydrogen evolution reactions and hydrogen oxidation reactions,44 and the latter is a property indicator for oxygen reduction reactions.45 Surfaces that include adatoms in configurations where the coordination number can be 1, 2, or 3, however, cannot be tuned via these processing parameters. This is significant because it has been well established that CO oxidation is initiated in step sites on (111) terraces and diffuses rapidly to these highlighted undercoordinated sites,46,47 making Sdef an indicator of CO oxidation efficiency. These results establish that by mapping the property indicators to the structural features, and correlating these attributes with synthesis conditions, machine learning models can provide reliable and insightful prediction of structure/ property and process/structure relationships, but the associated process/property relationship requires much more detailed information of the synthesis and processing conditions and catalytic performance to guide the design of more efficient nanoparticles for energy applications. The predictive machine learning modeling workflow presented here is general, and can be applied to any other face-centered cubic metal datasets.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b08386. Details of the generation of the data, bulk and surface characterization of the structures based on order parameters and surface curvature, and machine learning results for Smic and Sdef, along with more information of the machine learning methods, inducing classification and regression trees and genetic algorithm optimization (PDF)



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +61 3 9662 7109. ORCID

Baichuan Sun: 0000-0002-6635-2549 Amanda S. Barnard: 0000-0002-4784-2382 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS Computational resources for this project have been supplied by the Australian National Computing Infrastructure national facility under Grant q27, and Western Australia Pawsey Supercomputing Center Athena project pawsey0238. We gratefully acknowledge the support of NVIDIA Corporation G

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with the donation of the Titan X Pascal GPU used for this research. The characterization of the Pt dataset was supported by Dr Brad Wells.



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