Estimation,dependence and stability of solutions of an iterative equation

Aequationes mathematicae - In this paper we study estimation, continuous dependence and Hyers–Ulam stability for continuous solutions of a second order iterative equation. First we give an...     

Athermal and Soft Multi-Nanopatterning of Azopolymers: Phototunable Mechanical Properties

Imprinting nanopatterns on flexible substrates has diverse applications in advanced fabrication. However, the traditional thermal nanoimprint lithography (T-NIL) often causes shrinkage upon cooling. Here, a simple yet versatile method is introduced to fabricate multiple nanopatterns on a flexible substrate coated with an azopolymer by combining athermal nanoimprint lithography (AT-NIL) and photolithography. The azopolymer has various mechanical properties upon photoirradiation: 1) phototunable glass-transition temperatures (T_g) and concomitantly photoinduced switch from glassy plastic to viscoplastic polymer; 2) prominent modulation of viscoplasticity under light illumination at different wavelengths. Regionally selective multiple nanopatterns are conveniently fabricated, presenting angle-dependent structural color images on poly(ethylene terephthalate) (PET) substrates. The flexible, athermal and multiple nanopatterning method has the potential for on-demand fabrication of complex nanopatterns.     

Single‐Walled Carbon Nanotubes in Highly Viscous Media: A Comparison between the Dispersive Agents [BMIM][BF4], L121, and Triton X‐100

Dispersions of single‐walled carbon nanotubes (SWNTs) have been prepared by using the room‐temperature ionic liquid [BMIM][BF₄] (1‐butyl‐3‐methylimidazolium tetrafluoroborate), the triblock copolymer Pluronic L121 [poly(ethylene oxide)₅‐poly(propylene oxide)₆₈‐poly(ethylene oxide)₅] and the non‐ionic surfactant Triton X‐100 (TX100) in the pure state. The size of the SWNTs aggregates and the dispersion degree in the three viscous systems depend on the sonication time, as highlighted by UV/Vis/NIR spectroscopy and optical microscopy analysis. A nonlinear increase in conductivity can be observed as a function of the SWNTs loading, as suggested by electrochemical impedance spectroscopy. The generation of a three‐dimensional network of SWNTs showing a viscoelastic gel‐like behavior above a critical percolation concentration has been found at 25 °C in all the investigated systems by oscillatory rheology measurements.     

Reply to the Comment on “Realization of Lewis Basic Sodium Anion in the NaBH3− Cluster”

We reply to the comment by S. Pan and G. Frenking who challenged our interpretation of the Na^?:→BH₃ dative bond in the recently synthesized NaBH₃^? cluster. Our conclusion remains the same as that in our original paper ( https://doi.org/10.1002/anie.201907089 and https://doi.org/10.1002/ange.201907089 ). This conclusion is additionally supported by the energetic pathways and NBO charges calculated at UCCSD and CASMP2(4,4) levels of theory. We also discussed the suitability of the Laplacian of electron density (QTAIM) and Adaptive Natural Density Partitioning (AdNDP) method for bond type assignment. It seems that AdNDP yields more sensible results. This discussion reveals that the complex realm of bonding is full of semantic inconsistencies, and we invite experimentalists and theoreticians to elaborate this topic and find solutions incorporating different views on the dative bond.     

Precisely Controlled Multidimensional Covalent Frameworks: Polymerization of Supramolecular Colloids

Rapid and selective removal of micropollutants from water is important for the reuse of water resources. Despite hollow frameworks with specific functionalized porous walls for the selective adsorption based on a series of interactions, tailoring a stable shape of nanometer- and micrometer-sized architectures for the removal of specific pollutants remains a challenge. Here, exactly controlled sheets, tubes, and spherical frameworks were presented from the crosslinking of supramolecular colloids in polar solvents. The frameworks strongly depended on the architecture of original supramolecular colloids. As the entropy of colloids increased, the initial laminar framework rolled up into hollow tubules, and then further curled into hollow spheres. These shape-persistent frameworks showed unprecedented selectivity as well as specific recognition for the shape of pollutants, thus contributing to efficient pollutant separation.     

Synergistic N-Heterocyclic Carbene/Palladium-Catalyzed Umpolung 1,4-Addition of Aryl Iodides to Enals

An umpolung 1,4-addition of aryl iodides to enals promoted by cooperative (terpy)Pd/NHC catalysis was developed that generates various bioactive β,β-diaryl propanoate derivatives. This system is not only the first reported palladium-catalyzed arylation of NHC-bound homoenolates but also expands the scope of NHC-induced umpolung transformations. A diverse array of functional groups such as esters, nitriles, alcohols, and heterocycles are tolerated under the mild conditions. This method also circumvents the use of moisture-sensitive organometallic reagents.     

In-situ preparation and electrochromic properties of TiO2/PTPA-HTAN core-shell nanocomposite film

A new star-shaped structure conjugated microporous polymers, poly (2,8,14-tri[4-diphenyl-benzene]-hexaazatrinaphthylene) (PTPA-HATN), was designed and in-situ electrochemically polymerized on the surfaces of FTO electrodes with a directional alignment TiO₂ nanorod array to obtain TiO₂/PTPA-HATN core-shell nanocomposite films. Compared with the PTPA-HATN film, the TiO₂/PTPA-HATN composite film exhibits higher optical contrast and faster response time, with contrast of 57% at 783 nm, coloring time of 3.62 s and discoloring time of 2.55 s (43%, 4.63 s and 4.77 s for PTPA-HATN film, respectively). After 400 cycles, the contrast of nanocomposite film decreased by 28%, while the PTPA-HATN film basically lost its electrochromic properties. A simple three-layer EC prototype device based on TiO₂/PTPA-HATN nanocomposite film constructed with hydrogel electrolyte clearly shows color changes at different voltages. On the one hand, the formation of core-shell porous nanostructure of TiO₂/PTPA-HATN composite film provides a larger ion doping/de-doping interface, shortening the average diffusion length of ions. On the other hand, the large indented polymer-nanorods contact interface makes it difficult for the polymer to detach from the electrode, thus significantly improving the cyclic stability of the composite film.