Abstract: Three-dimensional (3D) shapes of particles are characterized from a two-dimensional (2D) image of the particles that is obtained using TEM. The 3D shape characterization method includes the steps of obtaining a 2D image of a batch of nanoparticles, determining 2D shapes of the nanoparticles from the 2D image, and deriving six distributions, each of which corresponds to a 2D shape and a 3D shape associated with the 2D shape. The first size distribution is derived from the nanoparticles having the 2D triangle shape. The second and third size distributions are derived from the nanoparticles having the 2D tetragon shape. The fourth, fifth and sixth size distributions are derived from the nanoparticles having the 2D round shape. Based on these six size distributions, three size distributions, each of which corresponds to one of three 3D shape classes, are estimated.

Abstract: The catalytic efficiency of supported catalysts containing metal nanoparticles is strongly related to the chemical softness at the surfaces of such nanoparticles. Supported catalysts containing platinum nanoparticles having average surface softness values (expressed in scaled units ranging from 0 to 1) between 0.07198 and 0.09247 exhibit high catalytic efficiency. The catalytic efficiency of such platinum nanoparticles for CO oxidation, expressed as the turn-over frequency (TOF), was observed to be on or above 0.03062 s?1. The supported catalysts containing platinum nanoparticles with tighter average surface softness ranges exhibit even higher catalytic efficiencies. The TOF for CO oxidation of platinum nanoparticles having average surface softness values between 0.08031 and 0.08679 was observed to be on or above 0.06554 s?1.

Abstract: The catalytic efficiency of supported catalysts containing metal nanoparticles is strongly related to the chemical softness at the surfaces of such nanoparticles. The chemical softness of a nanoparticle is obtained using results from Density Functional Theory modeling, an extended version of Embedded Atom Method modeling, and continuum modeling based on size and shape of the nanoparticle. A metal nanoparticle of a certain size and shape is first modeled using the extended EAM and EAM parameters that have been validated with results from DFT modeling, to obtain atomic energy densities at each atom location. The chemical softness value at each atom location is then calculated from the atomic energy densities and various parameters that are derived based on results from DFT modeling. The surface chemical softness value is derived from the local chemical softness values based on the geometry and atomistic structure of the metal nanoparticle.

Abstract: The size distributions corresponding to the three-dimensional (3D) shapes of particles are estimated from a 3D-to-2D projection matrix and a two-dimensional (2D) image of the particles that is obtained using TEM. Two different methods to generate a 3D-to-2D projection matrix are described. The first method determines the matrix coefficients assuming equal probability for all high-symmetry projections. The second method employs a large set of 3D-to-2D projection matrices with randomly generated coefficients satisfying the high-symmetry projection constraint. The second method is a general method to determine 3D-to-2D projection matrices based on the assumption that certain high-symmetry projections are present for the system under investigation.