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We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain. 

We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.

 

Elastomers generally possess low Young's modulus and high failure strain, which are widely used in soft robots and intelligent actuators. However, elastomers generally lack diverse functionalities, such as stimulated shape morphing, and a general strategy to implement these functionalities into elastomers is still challenging. Here, a microfluidic 3D droplet printing platform is developed to design composite elastomers architected with arrays of functional droplets. Functional droplets with controlled size, composition, position, and pattern are designed and implemented in the composite elastomers, imparting functional performances to the systems. The composited elastomers are sensitive to stimuli, such as solvent, temperature, and light, and are able to demonstrate multishape (bow‐ and S‐shaped), multimode (gradual and sudden), and multistep (one‐ and two‐step) deformations. Based on the unique properties of droplet‐embedded composite elastomers, a variety of stimuli‐responsive systems are developed, including designable numbers, biomimetic flowers, and soft robots, and a series of functional performances are achieved, presenting a facile platform to impart diverse functionalities into composite elastomers by microfluidic 3D droplet printing.

 

Oxidation is a corrosion reaction where the corroded metal forms an oxide. Prevention of oxidation at the nanoscale is critically important to retain the physicochemical properties of metal nanoparticles. In this work, we studied the stability of polyethylene glycol (PEG) coated copper nanoparticles (PEGylated CuNPs) against oxidation. The freshly-prepared PEGylated CuNPs mainly consist of metallic Cu which are quite stable in air although their surfaces are typically covered with a few monolayers of cuprous oxide. However, they are quickly oxidized in water due to the presence of protons that facilitate oxidation of the cuprous oxide to cupric oxide. PEG with carboxylic acid terminus could slightly delay the oxidation process compared to that with thiol terminus. It was found that a solvent with reducing power such as ethanol could greatly enhance the stability of PEGylated CuNPs by preventing further oxidation of the cuprous oxide to cupric oxide and thus retain the optical properties of CuNPs. The reducing environment also assists the galvanic replacement of these PEGylated CuNPs to form hollow nanoshells; however, they consist of ultra-small particle assemblies due to the co-reduction of gold precursor during the replacement reaction. As a result, these nanoshells do not exhibit strong optical properties in the near-infrared region. This study highlights the importance of solvent effects on PEGylated nonprecious metal nanoparticles against oxidation corrosion and its applications in preserving physicochemical properties of metallic nanostructures. 

Single particle electrochemical oxidation of polyvinylpyrrolidone-capped silver nanoparticles at a microdisk electrode is investigated as a function of particle shape (spheres, cubes, and plates) in potassium nitrate and potassium hydroxide solutions. In potassium nitrate, extreme anodic potentials (≥1500 mV vs Ag/AgCl (3 M KCl)) are necessary to achieve oxidation, while lower anodic potentials are required in potassium hydroxide (≥900 mV vs Ag/AgCl (saturated KCl)). Upon oxidation, silver oxide is formed, readily catalyzing water oxidation, producing a spike-step current response. The spike duration for each particle is used to probe effects of particle shape on the oxidation mechanism, and is substantially shorter in nitrate solution at the large overpotentials than in hydroxide solution. The integration of current spikes indicates oxidation to a mixed-valence complex. In both electrolytes, the rate of silver oxidation strongly depends on silver content of the nanoparticles, rather than the shape-dependent variable–surface area. The step height, which reflects rate of water oxidation, also tracks the silver content more so than shape. The reactivity of less-protected citrate-capped particles toward silver oxidation is also compared with that of the polymer-capped particles under these anodic conditions in the nitrate and hydroxide solutions.