$$L^2_f$$ L f 2 -harmonic 1-forms on smooth metric measure spaces with positive $$\lambda _1(\Delta _f)$$ λ 1 ( Δ f )

In this paper, we study vanishing and splitting results on a complete smooth metric measure space \((M^n,g,\mathrm {e}^{-f}\mathrm {d}v)\) with various negative m-Bakry-Émery Ricci curvature lower bounds in terms of the first eigenvalue \(\lambda _1(\Delta _f)\) of the weighted Laplacian \(\Delta _f\), i.e., \(\mathrm {Ric}_{m,n}\ge -a\lambda _1(\Delta _f)-b\) for \(0<a\le \dfrac{m}{m-1}, b\ge 0\). In particular, we consider three main cases for different a and b with or without conditions on \(\lambda _1(\Delta _f)\). These results are extensions of Dung and Vieira, and weighted generalizations of Li-Wang, Dung-Sung, and Vieira.

     

Viscoelastic properties of ultrathin polycarbonate films by liquid dewetting

A liquid dewetting method for the determination of the viscoelastic properties of ultrathin polymer films has been extended to study thickness effects on the properties of ultrathin polycarbonate (PC) films. PC films with film thicknesses ranging from 4 to 299 nm were placed on glycerol at temperatures from below the macroscopic glass transition temperature (T_g) to above it with the dewetting responses being monitored. It is found that the isothermal creep results for films of the same thickness, but dewetted at different temperatures can be superposed into one master curve, which is consistent with the fact of PC being a thermorheologically simple material. Furthermore, the results show that the T_g of PC thin films is thickness dependent, but the dependence is weaker than the results for freely standing films and similar to literature data for PC films supported on rigid substrates. It was also found that the rubbery plateau region for the PC films stiffens dramatically, but still less than what has been observed for freely standing polycarbonate films. The rubbery stiffening is discussed in terms of a recently reported model that relates macroscopic segmental dynamics with the stiffening. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1559–1566     

Hitherto-Unexplored Photodynamic Therapy of Ag2S and Enhanced Regulation Based on Polydopamine In Vitro and Vivo

Given their superior penetration depths, photosensitizers with longer absorption wavelengths present broader application prospects in photodynamic therapy (PDT). Herein, Ag₂S quantum dots were discovered, for the first time, to be capable of killing tumor cells through the photodynamic route by near-infrared light irradiation, which means relatively less excitation of the probe compared with traditional photosensitizers absorbing short wavelengths. On modification with polydopamine (PDA), PDA-Ag₂S was obtained, which showed outstanding capacity for inducing reactive oxygen species (increased by 1.69 times). With the addition of PDA, Ag₂S had more opportunities to react with surrounding O₂, which was demonstrated by typical triplet electron spin resonance (ESR) analysis. Furthermore, the PDT effects of Ag₂S and PDA-Ag₂S achieved at longer wavelengths were almost identical to the effects produced at 660 nm, which was proved by studies in vitro. PDA-Ag₂S showed distinctly better therapeutic effects than Ag₂S in experiments in vivo, which further validated the enhanced regulatory effect of PDA. Altogether, a new photosensitizer with longer absorption wavelength was developed by using the hitherto-unexplored photodynamic function of Ag₂S quantum dots, which extended and enhanced the regulatory effect originating from PDA.     

Space-Confined Atomic Clusters Catalyze Superassembly of Silicon Nanodots within Carbon Frameworks for Use in Lithium-Ion Batteries

Incorporating nanoscale Si into a carbon matrix with high dispersity is desirable for the preparation of lithium-ion batteries (LIBs) but remains challenging. A space-confined catalytic strategy is proposed for direct superassembly of Si nanodots within a carbon (Si NDs⊂C) framework by copyrolysis of triphenyltin hydride (TPT) and diphenylsilane (DPS), where Sn atomic clusters created from TPT pyrolysis serve as the catalyst for DPS pyrolysis and Si catalytic growth. The use of Sn atomic cluster catalysts alters the reaction pathway to avoid SiC generation and enable formation of Si NDs with reduced dimensions. A typical Si NDs⊂C framework demonstrates a remarkable comprehensive performance comparable to other Si-based high-performance half LIBs, and higher energy densities compared to commercial full LIBs, as a consequence of the high dispersity of Si NDs with low lithiation stress. Supported by mechanic simulations, this study paves the way for construction of Si/C composites suitable for applications in future energy technologies.     

Sandwich-like Catalyst–Carbon–Catalyst Trilayer Structure as a Compact 2D Host for Highly Stable Lithium–Sulfur Batteries

Herein, we propose the construction of a sandwich-structured host filled with continuous 2D catalysis–conduction interfaces. This MoN-C-MoN trilayer architecture causes the strong conformal adsorption of S/Li₂S_x and its high-efficiency conversion on the two-sided nitride polar surfaces, which are supplied with high-flux electron transfer from the buried carbon interlayer. The 3D self-assembly of these 2D sandwich structures further reinforces the interconnection of conductive and catalytic networks. The maximized exposure of adsorptive/catalytic planes endows the MoN-C@S electrode with excellent cycling stability and high rate performance even under high S loading and low host surface area. The high conductivity of this trilayer texture does not compromise the capacity retention after the S content is increased. Such a job-synergistic mode between catalytic and conductive functions guarantees the homogeneous deposition of S/Li₂S_x, and avoids thick and devitalized accumulation (electrode passivation) even after high-rate and long-term cycling.     

Transition-Metal Catalysis of Triene 6π Electrocyclization: The π-Complexation Strategy Realized

Triene 6π electrocyclization, wherein a conjugated triene undergoes a concerted stereospecific cycloisomerization to a cyclohexadiene, is a reaction of great historical and practical significance. In order to circumvent limitations imposed by the normally harsh reaction conditions, chemists have long sought to develop catalytic variants based upon the activating power of metal–alkene coordination. Herein, we demonstrate the first successful implementation of such a strategy by utilizing [(C₅H₅)Ru(NCMe)₃]PF₆ as a precatalyst for the disrotatory 6π electrocyclization of highly substituted trienes that are resistant to thermal cyclization. Mechanistic and computational studies implicate hexahapto transition-metal coordination as responsible for lowering the energetic barrier to ring closure. This work establishes a foundation for the development of new catalysts for stereoselective electrocyclizations.     

Fabricating Dual-Atom Iron Catalysts for Efficient Oxygen Evolution Reaction: A Heteroatom Modulator Approach

Understanding the thermal aggregation behavior of metal atoms is important for the synthesis of supported metal clusters. Here, derived from a metal–organic framework encapsulating a trinuclear Fe^III₂Fe^II complex (denoted as Fe₃) within the channels, a well-defined nitrogen-doped carbon layer is fabricated as an ideal support for stabilizing the generated iron nanoclusters. Atomic replacement of Fe^II by other metal(II) ions (e.g., Zn^II/Co^II) via synthesizing isostructural trinuclear-complex precursors (Fe₂Zn/Fe₂Co), namely the “heteroatom modulator approach”, is inhibiting the aggregation of Fe atoms toward nanoclusters with formation of a stable iron dimer in an optimal metal–nitrogen moiety, clearly identified by direct transmission electron microscopy and X-ray absorption fine structure analysis. The supported iron dimer, serving as cooperative metal–metal site, acts as efficient oxygen evolution catalyst. Our findings offer an atomic insight to guide the future design of ultrasmall metal clusters bearing outstanding catalytic capabilities.     

Anti-Markovnikov Hydroamination of Racemic Allylic Alcohols to Access Chiral γ-Amino Alcohols

A ruthenium-catalyzed formal anti-Markovnikov hydroamination of allylic alcohols for the synthesis of chiral γ-amino alcohols is presented. Proceeding via an asymmetric hydrogen-borrowing process, the catalysis allows racemic secondary allylic alcohols to react with various amines, affording enantiomerically enriched chiral γ-amino alcohols with broad substrate scope and excellent enantioselectivities (68 examples, up to >99 % ee).     

Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Direct visualization of the nanoscopic three‐phase structure and stiffness of NBR/PVC blends by AFM nanomechanical mapping

The PeakForce Quantitative Nanomechanical Mapping based on atomic force microscope (AFM) is employed to first visualize and then quantify the elastic properties of a model nitrile rubber/poly(vinyl chloride) (NBR/PVC) blend at the nanoscale. This method allows us to consistently observe the changes in mechanical properties of each phase in polymer blends. Beyond measuring and discriminating elastic modulus and adhesion forces of each phase, we tune the AFM tips and the peak force parameters in order to reliably image samples. In view of viscoelastic difference in each phase, a three‐phase coexistence of an unmixed NBR phase, the mixed phase, and PVC microcrystallites is directly visualized in NBR/PVC blends. The nanomechanical investigation is also capable of recognizing the crosslinked rubber phase in cured rubber. The contribution of the mixed phase was quantified and it was found that the mechanical properties of blends are mainly determined by the homogeneity and stiffness of the mixed phase. This study furthers our understanding the structure–mechanical property relationship of thermoplastic elastomers, which is important for their potential design and applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 662–669