Solution‐processable colorless polyimides derived from hydrogenated pyromellitic dianhydride with controlled steric structure

This work presents novel colorless polyimides (PIs) derived from 1R,2S,4S,5R‐cyclohexanetetracarboxylic dianhydride (H″‐PMDA). Isomer effects were also discussed by comparing with PI systems derived from conventional hydrogenated pyromellitic dianhydride, that is, 1S,2R,4S,5R‐cyclohexanetetracarboxylic dianhydride (H‐PMDA). H″‐PMDA was much more reactive with various diamines than H‐PMDA, and the former led to PI precursors with much higher molecular weights. The results can be explained from the quite different steric structures of these isomers. The thermally imidized H″‐PMDA‐based films were colorless regardless of diamines because of inhibited charge‐transfer interaction. In particular, the H″‐PMDA/4,4′‐oxydianiline system simultaneously achieved a very high T_g exceeding 300 °C, high toughness (elongation at break > 70%), and good solution processability. In contrast, the H‐PMDA‐based counterparts were essentially insoluble. The outstanding solubility of the former probably results from disturbed chain stacking by its nonplanar steric structure. An advantage of chemical imidization process is also proposed. In some cases, a copolymerization approach with an aromatic tetracarboxylic dianhydride was effective to improve the thermal expansion property. The results suggest that the H″‐PMDA‐based PI systems can be promising candidates for novel high‐temperature plastic substrate materials in electronic paper displays. A potential application as optical compensation film materials in liquid crystal displays (LCD) is also proposed in this work. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Why Matter Occupies so Large a Volume？

The paper represents a rigorous treatment of the underlying quantum theory, not just in words but providing the underlying technical details, as to why matter occupies so large a volume and its intimate connection with the Pauli exclusion principle, as more and more matter is put together, as well as of the contraction or shrinkage of ＂bosonic matter＂, upon collapse, for which the Panli exclusion is abolished. From the derived explicit bounds of integrals of powers of the particle number densities, explicit bounds on probabilities of the occurrences of the events just described are extracted. These probabilities lead one to infer the change of the ＂size＂ or extension of such matter, upon expansion or contraction, respectively, as their content is increased.     

Acid-Catalyzed E-Ring Expansion and Isomerization of 3-Acetylbetulin: Synthesis of Cytotoxic Anhydrobetulin Saponins

22(17 → 28)abeo-Lupene derivatives 5a and 6a were obtained after the acid-catalyzed E-ring expansion of 3-acetylbetulin (1a). Glycosylation of these dehydrated triterpenoids using Schmidt's trichloroacetimidate sugar donors in the presence of trimethylsilyl trifluoromethanesulfonate (TMSOTf) provided the new anhydrobetulin saponins 7b–7e in which the terminal olefin C-20(29) isomerizes to form a C-19 tetrasubstituted alkene. The preliminary cytotoxic evaluation revealed that saponins 7b–7d exhibited a moderate cytotoxic activity against A549, DLD-1, and WS1 human cell lines with IC₅₀ ranging from 22 to 49 μM.     

基于耦合声场建模的膨胀腔消声器声学性能分析及试验

针对圆柱形膨胀腔消声器三维建模及声学性能分析问题, 提出一种基于切比雪夫变分原理的耦合声场建模方法, 建立三维圆柱形膨胀腔消声器理论模型并搭建试验台架, 传递损失试验结果验证了理论模型的准确性. 将膨胀腔消声器内部声场分解为多个子声场, 基于子声场间压力与质点振速连续性条件, 推导声场耦合变分公式, 构建子声场拉格朗日泛函. 将子声场声压函数展开为切比雪夫-傅里叶级数形式, 通过瑞利-里兹法求解膨胀腔消声器频率、声压响应及传递损失. 计算并对比分析扩张比、扩张腔长度、进出口管偏置对膨胀腔消声器消声性能的影响. 结果表明: 扩张比增大会有效提高消声器在低频段的消声性能, 进出口管的偏置对消声器消声性能影响很小.     

Lattice Boltzmann method for the fractional sub‐diffusion equation

A lattice Boltzmann model for the fractional sub‐diffusion equation is presented. By using the Chapman–Enskog expansion and the multiscale time expansion, several higher‐order moments of equilibrium distribution functions and a series of partial differential equations in different time scales are obtained. Furthermore, the modified partial differential equation of the fractional sub‐diffusion equation with the second‐order truncation error is obtained. In the numerical simulations, comparisons between numerical results of the lattice Boltzmann models and exact solutions are given. The numerical results agree well with the classical ones. Copyright © 2015 John Wiley & Sons, Ltd.     

Isobaric expansion coefficient and isothermal compressibility for a finite-size ideal Fermi gas system

Due to quantum size effects (QSEs), the isobaric thermal expansion coefficient and isothermal compressibility well defined for macroscopic systems are invalid for finite-size systems. The two parameters are redefined and calculated for a finite-size ideal Fermi gas confined in a rectangular container. It is found that the isobaric thermal expansion coefficient and isothermal compressibility are generally anisotropic, i.e., they are generally different in different directions. Moreover, it is found the thermal expansion coefficient may be negative in some directions under the condition that the pressures in all directions are kept constant.     

A Facile Route to Backbone‐Tethered N‐Heterocyclic Carbene (NHC) Ligands via NHC to aNHC Rearrangement in NHC Silicon Halide Adducts

The reaction of 1,3‐diisopropylimidazolin‐2‐ylidene (iPr₂Im) with diphenyldichlorosilane (Ph₂SiCl₂) leads to the adduct (iPr₂Im)SiCl₂Ph₂ 1 . Prolonged heating of isolated 1 at 66 °C in THF affords the backbone‐tethered bis(imidazolium) salt [(^aHiPr₂Im)₂SiPh₂]²⁺ 2 Cl^? 2 (“^a” denotes “abnormal” coordination of the NHC), which can be synthesized in high yields in one step starting from two equivalents of iPr₂Im and Ph₂SiCl₂. Imidazolium salt 2 can be deprotonated in THF at room temperature using sodium hydride as a base and catalytic amounts of sodium tert‐butoxide to give the stable N‐heterocyclic dicarbene (^aiPr₂Im)₂SiPh₂ 3 , in which two NHCs are backbone‐tethered with a SiPh₂ group. This easy‐to‐synthesize dicarbene 3 can be used as a novel ligand type in transition metal chemistry for the preparation of dinuclear NHC complexes, as exemplified by the synthesis of the homodinuclear copper(I) complex [{^a(ClCu?iPr₂Im)}₂SiPh₂] 4 .     

N‐Heterocyclic Silylenes in Boron Chemistry: Facile Formation of Silylboranes and Silaborinines

Reaction of a N‐heterocyclic silylene (NHSi) with PhBX₂ (X=Cl, Br) readily afforded six‐membered silaborinines through an insertion/ring expansion sequence. Increasing the sterics of the borane from phenyl to duryl enabled the selective generation and isolation of the highly colored silylborane intermediates. Theoretical studies on the mechanism and energetics of the silaborinine formation were fully consistent with the experimental observations.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.