Size-, Shape-, and Composition-Dependent Model for Metal Nanoparticle Stability Prediction

Abstract

Although tremendous applications for metal nanoparticles have been found in modern technologies, the understanding of their stability as related to morphology (size and shape) and chemical ordering (e.g., in bimetallics) remains limited. First-principles methods such as density functional theory (DFT) are capable of capturing accurate nanoalloy energetics; however, they are limited to very small nanoparticle sizes (<2 nm in diameter) due to their computational cost. Herein, we propose a bond-centric (BC) model able to capture cohesive energy trends over a range of monometallic and bimetallic nanoparticles and mixing behavior (excess energy) of nanoalloys, in great agreement with DFT calculations. We apply the BC model to screen the energetics of a recently reported 23 196-atom FePt nanoalloys ( Yang et al. Nature 2017 , 542 , 75 - 79 ), offering insights into both segregation and bulk-chemical ordering behavior. Because the BC model utilizes tabulated data (diatomic bond energies and bulk cohesive energies) and structural information on nanoparticles (coordination numbers), it can be applied to calculate the energetics of any nanoparticle morphology and chemical composition, thus significantly accelerating nanoalloy design.

Predicting Metal–Support Interactions in Oxide-Supported Single-Atom Catalysts

“…Finally, we apply the Square-Root Bond (SRB) cutting model [59][60] to introduce a hypothetical cohesive energy of metal nanoparticles. We plot the hypothetical cohesive energy versus the DFT calculated metal adsorption energy.…”

“…In addition to the DFTcalculated parameters, we also investigate coordination numbers (using the Van der Waals radii reported in Table S5). We also use a "hypothetical cohesive energy" (CEhyp) described in the SRB cutting model to predict metal nanoparticle energetics in SACs [59][60] . This is given in Equation 3-1,…”

Recent Advanced Materials for Electrochemical and Photoelectrochemical Synthesis of Ammonia from Dinitrogen: One Step Closer to a Sustainable Energy Future

“…Compared with conventional bulk catalysts, nanomaterials embrace a broad spectrum of tunable physical and chemical properties including high surface to volume ratio and abundant active sites, rendering them immense potential for a wide range of catalytic reactions . Nanocatalysts are highly designable because their surface structures and electronic properties are very sensitive to particle size and morphology . In this section, we will review these advanced nanomaterials grouped into four categories based on the number of dimensions that is not confined to nanoscale range (<100 nm): 0D NPs including nanospheres and nanocubes, 1D nanorods, nanowires, and nanospikes, 2D nanosheets/films and nanobelts, and 3D nanostructures such as the hybrid nanocomposites.…”

“…[82][83][84][85] Nanocatalysts are highly designable because their surface structures and electronic properties are very sensitive to particle size and morphology. [82,86,87] In this section, we will review these advanced nanomaterials grouped into four categories based on the number of dimensions that is not confined to nanoscale range (<100 nm): [88] 0D NPs including nanospheres and nanocubes, 1D nanorods, nanowires, and nanospikes, 2D nanosheets/films and nanobelts, and 3D nanostructures such as the hybrid nanocomposites. In addition, the sub-nanoscale materials including the emerging single-atom catalysts as the transition between molecular and heterogeneous catalysts, will also be covered and discussed as a sub-category of 0D materials.…”

Machine learning corrected alchemical perturbation density functional theory for catalysis applications

“…However, even relatively efficient methods such as DFT are too computationally costly to systematically model many different adsorbates at different coverages on different facets and compositions of hypothetical alloys. There have been efforts to address such points by developing approximate models such as cluster expansions, [4][5][6] coordination number models, [7][8][9] as well as an assortment of machine learning (ML) models [10][11][12][13][14][15][16] that all can be trained from quantum mechanics calculations but leveraged to make predictions on systems outside of the training set.…”