Silk has outstanding mechanical properties and biocompatibility. It has been used to fabricate traditional textiles for thousands of years and can be produced in large scale. Silk materials are potentially attractive in modern textile electronics. However, silk is not electrically conductive, thus limiting its applications in electronics. Moreover, regenerated silk is generally rigid and brittle, which hinder post processing. Here we report the fabrication of conductive silk wire in which carbon nanotube (CNT) yarns are wrapped with fluffy and flexible silk nanofiber films. The silk nanofiber film was prepared by electrospinning and then wrapped around a rotating CNT yarn in situ. The obtained silk-sheathed CNT (CNT@Silk) wire has an insulating sheath, which protects the body against electrical shock. In addition, the fabricated wires exhibit a high electrical conductivity (3.1 × 104 S/m), good mechanical strength (16 cN/tex), excellent flexibility, and high durability. More importantly, the wires have an extremely low density (2.0–7.8 × 104 g/m3), which is 2 orders of magnitude lower than that of the traditional metal wire (for example, Cu). Moreover, the wires display a good resistance to humidity, and a simple post treatment can make the wires splash-resistant, thereby expanding its applications. On the basis of these features, we demonstrate the use of the lightweight CNT@Silk wires in smart clothes, including electrochromism and near-field communication.

The construction of multi‐heteroatom‐doped metal‐free carbon with a reversibly oxygen‐involving electrocatalytic performance is highly desirable for rechargeable metal‐air batteries. However, the conventional approach for doping heteroatoms into the carbon matrix remains a huge challenge owing to multistep postdoping procedures. Here, a self‐templated carbonization strategy to prepare a nitrogen, phosphorus, and fluorine tri‐doped carbon nanosphere (NPF‐CNS) is developed, during which a heteroatom‐enriched covalent triazine polymer serves as a “self‐doping” precursor with C, N, P, and F elements simultaneously, avoiding the tedious and inefficient postdoping procedures. Introducing F enhances the electronic structure and surface wettability of the as‐obtained catalyst, beneficial to improve the electrocatalytic performance. The optimized NPF‐CNS catalyst exhibits a superb electrocatalytic oxygen reduction reaction (ORR) activity, long‐term durability in pH‐universal conditions as well as outstanding oxygen evolution reaction (OER) performance in an alkaline electrolyte. These superior ORR/OER bifunctional electrocatalytic activities are attributed to the predesigned heteroatom catalytic active sites and high specific surface areas of NPF‐CNS. As a demonstration, a zinc‐air battery using the NPF‐CNS cathode displays a high peak power density of 144 mW cm−2 and great stability during 385 discharging/charging cycles, surpassing that of the commercial Pt/C catalyst.

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Herein, novel conductive composite hydrogels are developed with high stretchability, ultra-softness, excellent conductivity, and good self-healing ability. The hydrogels are formed in the water/glycerol binary solvent system, in which the polyaniline nanoparticles (PANI-NPs) are incorporated into the poly(poly(ethylene glycol) methacrylate-co-acrylic acid) (P(PEG-co-AA)) scaffolds via the dynamically electrostatic interactions and hydrogen bonds. The PANI-NPs serve as conductive fillers to assign conductivity to the hydrogel, while the enhanced interfacial interactions between the PANI-NPs and P(PEG-co-AA) matrix endow the hydrogel with high stretchability (>1000%), low modulus (≈6 kPa), excellent elasticity (η = 0.07, energy loss coefficient at 500% strain), and fast self-healing ability (93.3% after 10 mins). Particularly, the desirable anti-freezing property is achieved by introducing a binary solvent system. The composite hydrogel-based sensors are proposed, with the states-independent properties, low detection limit (0.5% strain and 25 Pa), highly linear dependence, and excellent anti-fatigue performance (>1000 cycles). In addition, during the practical wearable sensing tests, various external stimulus and human motions can be detected, including speaking, writing, joint movement, or even small water droplets, indicating the potential applications for the next generation of epidermal sensors.

Abstract. In this paper, we consider the following problem involving fractional Laplacian operator:where Ω is a smooth bounded domain in. We show that for any sequence of solutions u n of (1) corresponding to ε n ∈ [0, 2 * α − 2), satisfying u n H ≤ C in the Sobolev space H defined in (1.2), u n converges strongly in H provided that N > 6α and λ > 0. An application of this compactness result is that problem (1) possesses infinitely many solutions under the same assumptions.

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To meet various practical requirements and enhance human experience, hydrogels possessing multifunctionality are of great significance for flexible wearable sensors. Herein, a novel strategy has been developed to fabricate nanocomposite hydrogels with a combination of excellent stretchability, rapid recoverability, self-healing, and outstanding adhesiveness. The PAAc/SiO2-g-PAAm nanocomposite hydrogels were facilely prepared through the polymerization of acrylic acid (AAc) using SiO2-g-polyacrylamide core–shell hybrid nanoparticles (SiO2-g-PAAm) as the dynamic cross-linking center. The densely dynamic hydrogen bonds between PAAc matrices and grafted PAAm chains could reversibly be destructed and reconstructed to dissipate a large amount of energy. Due to this unique feature, the formulated hydrogels showed a wide spectrum of desirable properties, including skin-mimetic modulus, excellent stretchability (1600%), exceptional self-healing properties (96.5% at ambient temperature), and fast recoverability. The sensors fabricated with the prepared hydrogels exhibited a high detection sensitivity in the strain range from 50% to 500% with a gauge factor value of 5.86, rapid response time, and good antifatigue performance. Depending on the outstanding adhesiveness, this sensor could attach to different substrates to release the real-time motion monitoring. In the practical wearable sensing test, various human motions, including tiny-scaled swallowing, laughing, and speaking, as well as large-scaled wrist, elbow, and knee movements during basketball shooting, could be sensed. These demonstrations heralded the potential application of our sensor in accurate and long-term human motion monitoring.

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