Integral representation of a solution to the Stokes–Darcy problem

With methods of potential theory, we develop a representation of a solution of the coupled Stokes–Darcy model in a Lipschitz domain for boundary data in H^?1/2. Copyright © 2014 John Wiley & Sons, Ltd.     

On the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer

In this paper, we prove the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer with resolvent parameter , where , and our boundary conditions are nonhomogeneous Neumann on upper boundary and Dirichlet on lower boundary. We want to emphasize that we can choose 0 < ? < π ∕ 2 and γ₀ > 0 arbitrarily, although usual parabolic theorem tells us that we must choose a large γ₀ > 0 for given 0 < ? < π ∕ 2. We also prove the maximal L_p ? L_q regularity theorem of the nonstationary Stokes problem as an application of the ‐boundedness. The key of our approach is to apply several technical lemmas to the exact solution formulas of a resolvent problem. The formulas are obtained through the solutions of the ODEs, in the Fourier space, driven by the partial Fourier transform with respect to tangential space variable . Copyright © 2014 John Wiley & Sons, Ltd.     

Start‐up of electrophoresis of an arbitrarily oriented dielectric cylinder

An analytical study is presented for the transient electrophoretic response of a circular cylindrical particle to the step application of an electric field. The electric double layer adjacent to the particle surface is thin but finite compared with the radius of the particle. The time‐evolving electroosmotic velocity at the outer boundary of the double layer is utilized as a slip condition so that the transient momentum conservation equation for the bulk fluid flow is solved. Explicit formulas for the unsteady electrophoretic velocity of the particle are obtained for both axially and transversely applied electric fields, and can be linearly superimposed for an arbitrarily‐oriented applied field. If the cylindrical particle is neutrally buoyant in the suspending fluid, the transient electrophoretic velocity is independent of the orientation of the particle relative to the applied electric field and will be in the direction of the applied field. If the particle is different in density from the fluid, then the direction of electrophoresis will not coincide with that of the applied field until the steady state is attained. The growth of the electrophoretic mobility with the elapsed time for a cylindrical particle is substantially slower than for a spherical particle.     

Assessing Alkali-Metal Effects in the Structures and Reactivity of Mixed-Ligand Alkyl/Alkoxide Alkali-Metal Magnesiates

Advancing the understanding of using alkali-metal alkoxides as additives to organomagnesium reagents in Mg−Br exchange reactions, a homologous series of mixed-ligand alkyl/alkoxide alkali-metal magnesiates [MMg(CH₂SiMe₃)₂(dmem)]₂ [dmem=2-{[2-(dimethylamino)ethyl]methylamino} ethoxide; M=Li, 1 ; Na, 2 ; (THF)K, 3 ] has been prepared. Structural and spectroscopic studies have established the constitutions of these heteroleptic/heterometallic species, which are retained in arene solution. Evaluation of their reactivity towards 2-bromoanisole has uncovered a marked alkali-metal effect with potassium magnesiate 3 being the most efficient of the three ate reagents. Studies probing the constitution of the exchange product from this reaction suggest that the putative [KMgAr₂(dmem)]₂ (Ar=o-OMe−C₆H₄) intermediate undergoes redistribution into its single metal components [KAr]_n and [MgAr(dmem)]₂ ( 5 ). This process can be circumvented by using a different potassium alkoxide containing an aliphatic chain such as KOR’ (R’=2-ethylhexyl) which undergoes co-complexation with Mg(CH₂SiMe₃) to give [KMg(CH₂SiMe₃)₂(OR’)]₂ ( 7 ). This ate, in turn, reacts quantitatively with 2-bromoanisole furnishing [KMgAr₂(OR’)]₂ ( 9 ) which is stable in solution as a bimetallic compound. Collectively this work highlights the complexity of these alkali-metal mediated Mg−Br exchange reactions, where each reaction component can have a profound effect not only on the success of the reaction; but also the stability of the final metalated intermediates prior to their electrophilic interception.     

“海水提镁”项目式教学设计与实践*

依托广西北海市丰富的海洋资源,创设了“在北海能否建提镁厂”的驱动性总任务,师生合议将任务规划为3个大问题和6个子任务。学生采用信息收集、分类、比较、推理、实验、系统分析等认知策略,最终以ppt的形式进行成果汇报,通过组间评价、核心问题讨论、决策性问题辩论等方式逐步落实项目目标。     

Diffusiophoresis in suspensions of highly charged soft particles

Diffusiophoresis phenomenon of aoft particles suspended in binary electrolyte solutions is explored theoretically in this study based on the spherical cell model, focusing on the chemiphoresis component in absence of diffusion potential. Both the electrostatic and hydrodynamic aspects of the boundary confinement, or steric effect, due to the presence of neighboring particles are examined extensively under various electrokinetic conditions. Significant local extrema are found in mobility profiles expressed as functions of the Debye length in general, synchronized with the strength of the motion-inducing double layer polarization. Moreover, a seemingly peculiar phenomenon is observed that the soft particles may move faster in more concentrated suspensions. The competition between the simultaneous enhancement of the motion-inducing electric driving force and the motion-retarding hydrodynamic drag force from the boundary confinement effect of the neighboring particles is found to be responsible for it. The above findings are also demonstrated experimentally in a very recent study on the diffusiophoretic motion of soft particles through porous collagen hydrogels. The results presented here are useful in various practical applications of soft particles like drug delivery.     

In Situ Grignard Metalation Method for the Synthesis of Hauser Bases

The in situ Grignard Metalation Method (iGMM) is a straightforward one-pot procedure to quickly produce multigram amounts of Hauser bases R₂N-MgBr which are valuable and vastly used metalation reagents and novel electrolytes for magnesium batteries. During addition of bromoethane to a suspension of Mg metal and secondary amine at room temperature in an ethereal solvent, a smooth reaction yields R₂N-MgBr under evolution of ethane within a few hours. A Schlenk equilibrium is operative, interconverting the Hauser bases into their solvated homoleptic congeners Mg(NR₂)₂ and MgBr₂ depending on the solvent. Scope and preconditions are studied, and side reactions limiting the yield have been investigated. DOSY NMR experiments and X-ray crystal structures of characteristic examples clarify aggregation in solution and the solid state.     

C−H Activation of Inert Arenes using a Photochemically Activated Guanidinato-Magnesium(I) Compound

UV irradiation of solutions of a guanidinate coordinated dimagnesium(I) compound, [{(Priso)Mg}₂] 3 (Priso=[(DipN)₂CNPrⁱ₂]⁻, Dip=2,6-diisopropylphenyl), in either benzene, toluene, the three isomers of xylene, or mesitylene, leads to facile activation of an aromatic C−H bond of the solvent in all cases, and formation of aryl/hydride bridged magnesium(II) products, [{(Priso)Mg}₂(μ-H)(μ-Ar)] 4 – 9 . In contrast to similar reactions reported for β-diketiminate coordinated counterparts of 3 , these C−H activations proceed with little regioselectivity, though they are considerably faster. Reaction of 3 with an excess of the pyridine, p-NC₅H₄Bu^t (py^But), gave [(Priso)Mg(py^ButH)(py^But)₂] 10 , presumably via reduction of the pyridine to yield a radical intermediate, [(Priso)Mg(py^But⋅)(py^But)₂] 11 , which then abstracts a proton from the reaction solvent or a reactant. DFT calculations suggest two possible pathways to the observed arene C−H activations. One of these involves photochemical cleavage of the Mg−Mg bond of 3 , generating magnesium(I) doublet radicals, (Priso)Mg⋅. These then doubly reduce the arene substrate to give “Birch-like” products, which subsequently rearrange via C−H activation of the arene. Circumstantial evidence for the photochemical generation of transient magnesium radical species includes the fact that irradiation of a cyclohexane solution of 3 leads to an intramolecular aliphatic C−H activation process and formation of an alkyl-bridged magnesium(II) species, [{Mg(μ-Priso^−H)}₂] 12 . Furthermore, irradiation of a 1 : 1 mixture of 3 and the β-diketiminato dimagnesium(I) compound, [{(^DipNacnac)Mg}₂] (^DipNacnac=[HC(MeCNDip)₂]⁻), effects a “scrambling” reaction, and the near quantitative formation of an unsymmetrical dimagnesium(I) compound, [(Priso)Mg−Mg(^DipNacnac)] 13 . Finally, the EPR spectrum (77 K) of a glassed solution of UV irradiated 3 is dominated by a broad featureless signal, indicating the presence of a doublet radical species.     

分散溶剂对PEMFC催化层中超薄Nafion离聚物质子传导的影响

质子交换膜燃料电池(PEMFC)商业化应用的瓶颈仍然是贵金属催化剂导致的成本问题。然而,目前对于催化层中纳米尺度全氟磺酸离聚物(以Nafion为代表)薄膜中质子传导的问题研究不足,无法完善三相界面的成型规律,进而指导催化层设计。在催化层浆料制备过程中,分散溶剂对Nafion的分散形态有直接影响,可能对催化层成型后附着在催化剂颗粒表面Nafion薄膜的微观结构有潜在影响,进而影响Nafion薄膜的质子传导能力。因此,在本文中利用分子自组装技术模拟催化层离聚物薄膜的聚集过程,于模型基底上制备厚度精确可控的纳米尺度Nafion薄膜,并通过微观测试表征技术探索并建立纳米尺度Nafion离聚物的微观结构模型,阐明分散溶剂对Nafion薄膜微观结构及质子传导的影响。研究发现Nafion薄膜在纳米尺度下的质子电导率比体相膜的质子电导率低一个数量级,使用介电常数较小的醇类溶剂可以使Nafion薄膜形成更有利于质子传导的微观结构,使Nafion薄膜的质子电导率得到提高。相关研究结果为优化PEMFC催化层结构,改善PEMFC催化层中质子传导问题提供给了依据。     

Revealing the Reaction and Fading Mechanism of FeSe2 Cathodes for Rechargeable Magnesium Batteries

Rechargeable Mg batteries (RMBs) are advantageous large-scale energy-storage devices because of the high abundance and high safety, but exploring high-performance cathodes remains the largest difficulty for their development. Compared with oxides and sulfides, selenides show better Mg-storage performance because the weaker interaction with the Mg²⁺ cation favors fast kinetics. Herein, nanorod-like FeSe₂ was synthesized and investigated as a cathode for RMBs. Compared with microspheres and microparticles, nanorods exhibit higher capacity and better rate capability with a smaller particle size. The FeSe₂ nanorods show a high capacity of 191 mAh g⁻¹ at 50 mA g⁻¹ and a good rate performance of 39 mAh g⁻¹ at 1000 mA g⁻¹. Ex situ characterizations demonstrate the Mg²⁺ intercalation mechanism for FeSe₂, and a slight conversion reaction occurs on the surface of the particles. The capacity fading is mainly because of the dissolution of Fe²⁺, which is caused by the reaction between Fe²⁺ and Cl⁻ of the electrolyte during the charge process on the surface of the particles. The surface of FeSe₂ is mainly selenium after long cycling, which may also dissolve in the electrolyte during cycling. The present work develops a new type of Mg²⁺ intercalation cathode for RMBs. More importantly, the fading mechanism revealed herein has considered the specificity of Mg battery electrolyte and would assist a better understanding of selenide cathodes for RMBs.