We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.

In electromagnetic multisphere-scattering calculations the reexpansion method for seeking a single-field representation of the total scattered field is found impracticable because of severe numerical problems. We present a simple single-field expansion of the total scattered far field based on an asymptotic form of vector translational addition theorems. With this asymptotic expansion of the far field, we derive analytical expressions for the scattering properties of an arbitrary aggregate of spheres. Resulting formulas are free from numerical problems in practical applications. Theoretical predictions from this far-field solution for various aggregates of spheres that we tested agree favorably with laboratory microwave scattering measurements. Some numerical results are presented and compared with experimental data.

Electrochemical reactions, including the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and oxygen reduction reaction (ORR), are important for green and renewable energy conversion and storage systems. [1] However, the sluggish kinetics of these electrochemical reactions seriously affect their energy utilization and output power. Currently, noble metal Pt-based compounds and Ir/Ru-based oxides are used as benchmark catalysts for HER, ORR, and OER. Based on specific interactions between catalytic active sites and intermediate species, each catalyst is used for a certain reaction. However, in many applications, several reactions occur in tandem or in a switchable manner; therefore, different reactions on the same electrode require different catalysts. For instance, both OER and ORR catalysts are required for the redox reaction of gas electrodes in fuel cells and Zn-air batteries (ZABs). Therefore, bi-or even multifunctional catalysts that can promote several reactions have the apparent advantage of simplifying the catalytic electrode design and construction of these essential applications. [2] Furthermore, several catalytic reactions driven by a certain catalyst facilitate the exploration and rationalization of the mutual effects of different reactive intermediates and catalytic active sites, which will further promote the understanding of the reaction kinetics and catalyst design. [1c] However, single precious metals generally cannot simultaneously provide sufficient activities for HER, OER, and ORR. In addition, the high cost, rarity, and low stability limit their industrial applications. Therefore, multifunctional nonprecious catalysts with high activity and excellent stability with respect to several important reactions must be developed. Over the past decades, many substitutable, electroactive materials, such as nanocarbons, phosphides, nitrides, carbides, sulfides, and their composites, have been used as electrocatalysts for different electrochemical reactions. [3] Nitrogen-doped carbon-coated Ni-based nanostructures (Ni@N-C) are of Developing a scalable approach to construct efficient and multifunctional electrodes for the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and oxygen reduction reaction (ORR) is an urgent need for overall water splitting and zinc-air batteries. In this work, a freestanding 3D heterostructure film is synthesized from a Ni-centered metal−organic framework (MOF)/graphene oxide. During the pyrolysis process, 1D carbon nanotubes formed from the MOF link with the 2D reduced graphene oxide sheets to stitch the 3D freestanding film. The results of the experiments and theoretical calculations show that the synergistic effect of the N-doped carbon shell and Ni nanoparticles leads to an optimized film with excellent electrocatalytic activity. Low overpotentials of 95 and 260 mV are merely needed for HER and OER, respectively, to reach a current density of 10 mA cm −2. In addition, a high half-wave potential of 0.875 V is obtained for the ORR, which ...

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