Expanding and Reducing Complexity in Materials Science Models with Relevance in Catalysis and Energy

Shape-Dependent Single-Electron Levels for Au Nanoparticles

The shape of metal nanoparticles has a crucial role in their performance in heterogeneous catalysis as well as photocatalysis. We propose a method of determining the shape of nanoparticles based on measurements of single-electron quantum levels. We first consider nanoparticles in two shapes of high symmetry: cube and sphere. We then focus on Au nanoparticles in three characteristic shapes that can be found in metal/inorganic or metal/organic compounds routinely used in catalysis and photocatalysis. We describe the methodology we use to solve the Schrödinger equation for arbitrary nanoparticle shape. The method gives results that agree well with analytical solutions for the high-symmetry shapes. When we apply our method in realistic gold nanoparticle models, which are obtained from Wulff construction based on first principles calculations, the single-electron levels and their density of states exhibit distinct shape-dependent features. Results for clean-surface nanoparticles are closer to those for cubic particles, while CO-covered nanoparticles have energy levels close to those of a sphere. Thiolate-covered nanoparticles with multifaceted polyhedral shape have distinct levels that are in between those for sphere and cube. We discuss how shape-dependent electronic structure features could be identified in experiments and thus guide catalyst design.

Shape Evolution of Metal Nanoparticles in Water Vapor Environment

The structures of the metal nanoparticles are crucial for their catalytic activities. How to understand and even control the shape evolution of nanoparticles under reaction condition is a big challenge in heterogeneous catalysis. It has been proved that many reactive gases hold the capability of changing the structures and properties of metal nanoparticles. One interesting question is whether water vapor, such a ubiquitous environment, could induce the shape evolution of metal nanoparticles. So far this question has not received enough attention yet. In this work, we developed a model based on the density functional theory, the Wulff construction, and the Langmuir adsorption isotherm to explore the shape of metal nanoparticle at given temperature and water vapor pressure. By this model, we show clearly that water vapor could notably increase the fraction of (110) facets and decrease that of (111) facets for 3-8 nm Cu nanoparticles, which is perfectly consistent with the experimental observations. Further investigations indicate the water vapor has different effects on the different metal species (Cu, Au, Pt, and Pd). This work not only helps to understand the water vapor effect on the structures of metal nanoparticles but also proposes a simple but effective model to predict the shape of nanoparticles in certain environment.

Nanoparticle shapes by using Wulff constructions and first-principles calculations

BACKGROUND

The majority of complex and advanced materials contain nanoparticles. The properties of these materials depend crucially on the size and shape of these nanoparticles. Wulff construction offers a simple method of predicting the equilibrium shape of nanoparticles given the surface energies of the material.

RESULTS

We review the mathematical formulation and the main applications of Wulff construction during the last two decades. We then focus to three recent extensions: active sites of metal nanoparticles for heterogeneous catalysis, ligand-protected nanoparticles generated as colloidal suspensions and nanoparticles of complex metal hydrides for hydrogen storage.

CONCLUSION

Wulff construction, in particular when linked to first-principles calculations, is a powerful tool for the analysis and prediction of the shapes of nanoparticles and tailor the properties of shape-inducing species.