Navier–Stokes equations with regularity in one directional derivative of the pressure

This paper concerns the 3D Navier‐Stokes equations and prove an almost Serrin‐type regularity criterion in terms of one directional derivative of the pressure. Copyright © 2014 John Wiley & Sons, Ltd.     

2,5‐Difluorenyl‐Substituted Siloles for the Fabrication of High‐Performance Yellow Organic Light‐Emitting Diodes

2,3,4,5‐Tetraarylsiloles are a class of important luminogenic materials with efficient solid‐state emission and excellent electron‐transport capacity. However, those exhibiting outstanding electroluminescence properties are still rare. In this work, bulky 9,9‐dimethylfluorenyl, 9,9‐diphenylfluorenyl, and 9,9′‐spirobifluorenyl substituents were introduced into the 2,5‐positions of silole rings. The resulting 2,5‐difluorenyl‐substituted siloles are thermally stable and have low‐lying LUMO energy levels. Crystallographic analysis revealed that intramolecular π–π interactions are prone to form between 9,9′‐spirobifluorene units and phenyl rings at the 3,4‐positions of the silole ring. In the solution state, these new siloles show weak blue and green emission bands, arising from the fluorenyl groups and silole rings with a certain extension of π conjugation, respectively. With increasing substituent volume, intramolecular rotation is decreased, and thus the emissions of the present siloles gradually improved and they showed higher fluorescence quantum yields (Φ_F=2.5–5.4 %) than 2,3,4,5‐tetraphenylsiloles. They are highly emissive in solid films, with dominant green to yellow emissions and good solid‐state Φ_F values (75–88 %). Efficient organic light‐emitting diodes were fabricated by adopting them as host emitters and gave high luminance, current efficiency, and power efficiency of up to 44 100 cd m^?2, 18.3 cd A^?1, and 15.7 lm W^?1, respectively. Notably, a maximum external quantum efficiency of 5.5 % was achieved in an optimized device.     

Achieving Efficient Multichannel Conductance in Through‐Space Conjugated Single‐Molecule Parallel Circuits

Constructing single‐molecule parallel circuits with multiple conduction channels is an effective strategy to improve the conductance of a single molecular junction, but rarely reported. We present a novel through‐space conjugated single‐molecule parallel circuit (f‐4Ph‐4SMe) comprised of a pair of closely parallelly aligned p‐quaterphenyl chains tethered by a vinyl bridge and end‐capped with four SMe anchoring groups. Scanning‐tunneling‐microscopy‐based break junction (STM‐BJ) and transmission calculations demonstrate that f‐4Ph‐4SMe holds multiple conductance states owing to different contact configurations. When four SMe groups are in contact with two electrodes at the same time, the through‐bond and through‐space conduction channels work synergistically, resulting in a conductance much larger than those of analogous molecules with two SMe groups or the sum of two p‐quaterphenyl chains. The system is an ideal model for understanding electron transport through parallel π‐stacked molecular systems and may serve as a key component for integrated molecular circuits with controllable conductance.     

Full emission color tuning in luminogens constructed from tetraphenylethene, benzo-2,1,3-thiadiazole and thiophene building blocks

Full color luminogens are constructed from tetraphenylethene, benzo-2,1,3-thiadiazole and thiophene building blocks. OLED fabricated using one of the luminogens exhibits orange-red electroluminescence with high luminance and efficiencies of 8330 cd m(-2), 6.1 cd A(-1) and 3.1%, respectively.     

Formation of superhydrophobic microspheres of poly(vinylidene fluoride- hexafluoropropylene)/graphene composite via gelation

We report on the spontaneous formation of superhydrophobic poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP)/graphene composite microspheres with uniform size via gelation. When the suspension of PVDF-HFP/graphene (0.25 wt. % with respect to PVDF-HFP) in DMF adsorbs water vapor, it changes to a hybrid gel. A dried porous gel is obtained after solvent exchange and freeze drying. Morphology characterization shows that this hybrid gel is composed of PVDF-HFP/graphene microspheres with a diameter of 8-10 μm. In contrast, PVDF-HFP solution gives rise to a cellular microstructure following the same experimental procedures. We further elucidate the formation mechanism on the basis of the characterization by freeze fracture transmission electron microscopy, X-ray diffraction, and differential scanning calorimetry characterizations. Furthermore, contact angle measurements of water on PVDF-HFP/graphene indicates that the hydrophobic nature of PVDF-HFP combined with the micro/nanoscale hierarchical texture creates a superhydrophobic surface. Such superhydrophobic microspheres may have potential applications as water-repellent catalyst-supporting materials.     

Palladium nanoparticles encapsulated in a metal-organic framework as efficient heterogeneous catalysts for direct C2 arylation of indoles

Highly dispersed palladium nanoparticles (Pd NPs) encapsulated in the mesoporous cages of the metal-organic framework (MOF) MIL-101(Cr) have been prepared by using the wetness impregnation method. The Pd NPs were characterized by powder X-ray diffraction (PXRD), N(2) adsorption, transmission electron microscopy, inductively coupled plasma atomic emission spectroscopy (ICP-AES), and X-ray photoelectron spectroscopy (XPS). The particles size ((2.6±0.5) nm) of the obtained Pd NPs was in good agreement with the cage diameters (2.9 and 3.4 nm) of the MOF. The resulting Pd/MIL-101(Cr) catalyst exhibited extremely high catalytic activities in the direct C2 arylation of substituted indoles by using only 0.1 mol% of the Pd catalyst. Moreover, the catalyst is easily recoverable and can be reused several times without leaching into solution and loss of activity. The combination of the highly dispersible Pd NPs within the accessible mesoporous cages and the favorable adsorption of the aryl halides on MIL-101 are suspected to be the main reasons for the observed high activities of the Pd/MIL-101(Cr) catalyst in the direct C2 arylation of indoles.     

Two New Regularity Criteria for the 3D Navier-Stokes Equations via Two Entries of the Velocity Gradient Tensor

We consider the Cauchy problem for the incompressible Navier-Stokes equations in R ³, and provide two new regularity criteria involving only two entries of the Jacobian matrix of the velocity field.     

Red Emissive Biocompatible Nanoparticles from Tetraphenylethene‐Decorated BODIPY Luminogens for Two‐Photon Excited Fluorescence Cellular Imaging and Mouse Brain Blood Vascular Visualization

BODIPY (4,4‐difluoro‐4‐bora‐3a,4a‐diaza‐s‐indacene) is an emissive chromophore in solutions but suffers from fluorescence quenching when aggregated due to its flat molecular conformation and small Stokes shift. To create aggregate‐state emissive BODIPY luminogens, tetraphenylethene (TPE), which is a popular luminogen with intriguing aggregation‐induced emission (AIE) characteristic, is introduced as periphery to a methylated BODIPY core. Three TPE‐BODIPY adducts are synthesized and characterized, and their photophysical properties and electronic structures are investigated. The incorporation of AIE‐active TPE units alleviates aggregation‐caused quenching of BODIPY core, furnishing emissive nanoparticles based on TPE‐BODIPY adducts. Significantly, the two‐photon absorption (TPA) and two‐photon excited fluorescence (TPEF) properties are improved as more TPE units are attached. The luminogens with 3TPE units (3TPE‐BODIPY) shows the strongest TPA and TPEF in the wavelength range of 750–830 nm, with cross‐section values of 264 and 116 GM at 810 nm, respectively. Red emissive nanoparticles with a Stokes shift of 60 nm and a fluorescence quantum yield of 16% are attained by encapsulating 3TPE‐BODIPY with 1,2‐sistearoyl‐sn‐glycero‐3‐phosphoethanolamine‐N‐[methoxy(polyethylene glycol)‐2000]. The nanoparticles are biocompatible and function well in TPEF cellular imaging and mouse brain blood vascular visualization.     

An Osgood type regularity criterion for the liquid crystal flows

In this paper, we prove an Osgood type regularity criterion for the model of liquid crystals, which says that the condition $$\sup_{2 \leq q< \infty} \int \nolimits_0^T \frac{\| \bar{S}_{q} \nabla {\bf u}(t)\|_{L^\infty}}{q \, {\rm \ln} \, q} {\rm d} t<\infty$$ implies the smoothness of the solution. Here, ${{\bar S_q=\sum\nolimits_{k=-q}^q \dot {\triangle}_k}}$ with ${\dot{\triangle}_k}$ being the frequency localization operator.     

Red Light-Emitting Thermally-Activated Delayed Fluorescence of Naphthalimide-Phenoxazine Electron Donor-Acceptor Dyad: Time-Resolved Optical and Magnetic Spectroscopic Studies

We prepared an orthogonal compact electron-donor (phenoxazine, PXZ)-acceptor (naphthalimide, NI) dyad ( NI-PXZ ), to study the photophysics of the thermally-activated delayed fluorescence (TADF), which has a luminescence lifetime of 16.4 ns (99.2 %)/17.0 μs (0.80 %). A weak charge transfer (CT) absorption band was observed for the dyad, indicating non-negligible electronic coupling between the donor and acceptor at the ground state. Femtosecond transient absorption spectroscopy shows a fast charge separation (CS) (ca. 2.02∼2.72 ps), the majority of the singlet CS state is short-lived, especially in polar solvents (τ_CR = 10.3 ps in acetonitrile, vs. 1.83 ns in toluene, 7.81 ns in n-hexane). Nanosecond transient absorption spectroscopy detects a long-lived transient species in n-hexane, which is with a mixed triplet local excited state (³LE) and charge separated state (³CS), the lifetime is 15.4 μs. In polar solvents, such as tetrahydrofuran and acetonitrile, a neat ³CS state was observed, whose lifetimes are 226 ns and 142 ns, respectively. Time-resolved electron paramagnetic resonance (TREPR) spectra indicate the existence of strongly spin exchanged ³LE/³CT states, with the effective zero field splitting (ZFS) |D| and |E| parameters of 1484 MHz and 109 MHz, respectively, much smaller than that of the native ³NI state (2475 and 135 MHz). It is rare but solid experimental evidence that a closely-lying ³LE state is crucial for occurrence of TADF and this ³LE state is an essential intermediate state to facilitate reverse intersystem crossing in TADF systems.