Building up Strain in One Step: Synthesis of an Edge-Fused Double Silacyclobutene from an Extensively Trichlorosilylated Butadiene Dianion

The exhaustive trichlorosilylation of hexachloro-1,3-butadiene was achieved in one step by using a mixture of Si₂Cl₆ and [nBu₄N]Cl (7:2 equiv) as the silylation reagent. The corresponding butadiene dianion salt [nBu₄N]₂[ 1 ] was isolated in 36 % yield after recrystallization. The negative charges of [ 1 ]²⁻ are mainly delocalized across its two carbanionic (Cl₃Si)₂C termini (α-effect of silicon) such that the central bond possesses largely C=C double-bond character. Upon treatment with 4 equiv of HCl, [ 1 ]²⁻ is converted into neutral 1,2,3,4-tetrakis(trichlorosilyl)but-2-ene, 3 . The Cl⁻ acceptor AlCl₃, induces a twofold ring-closure reaction of [ 1 ]²⁻ to form a six-membered bicycle 4 in which two silacyclobutene rings are fused along a shared C=C double bond (84 %). Compound 4 , which was structurally characterized by X-ray crystallography, undergoes partial ring opening to a monocyclic silacyclobutene 2 in the presence of HCl, but is thermally stable up to at least 180 °C.     

Friction and tribochemical reactions occurring at shearing interfaces of nanothin silver films on various substrates

The tribological and tribochemical properties of 5-10 nm thick Ag films sliding on various metal and inorganic substrates were measured using a surface forces apparatus coupled with ex situ x-ray photoelectron spectroscopy. We observed enhanced chemical reactivity in the sheared regions compared to the unsheared regions, which we attribute to significant frictional heating in agreement with two recent simulations. It is also found that the initial topography (roughness) of the films plays a significant role in determining the friction, wear, and tribochemical reactions. The larger the surface roughness, the larger are the friction coefficients. Initially smooth surfaces, forming large continuous junctions, create large wear debris particles; whereas initially rough surfaces, forming many small junctions, create many small particles. Even though initially smooth surfaces are chemically less reactive than initially rough surfaces, they are tribochemically more reactive, forming two to three times more oxides of silver during shearing than under static conditions and organometals of silver that under normal (static) conditions do not form. The chemical reactions observed cannot be explained without including the tribological processes, such as the local stresses, temperature rises, and type of wear produced by the shearing surfaces.     

Building up Strain in One Step: Synthesis of an Edge‐Fused Double Silacyclobutene from an Extensively Trichlorosilylated Butadiene Dianion

The exhaustive trichlorosilylation of hexachloro‐1,3‐butadiene was achieved in one step by using a mixture of Si₂Cl₆ and [nBu₄N]Cl (7:2 equiv) as the silylation reagent. The corresponding butadiene dianion salt [nBu₄N]₂[ 1 ] was isolated in 36 % yield after recrystallization. The negative charges of [ 1 ]^2? are mainly delocalized across its two carbanionic (Cl₃Si)₂C termini (α‐effect of silicon) such that the central bond possesses largely C=C double‐bond character. Upon treatment with 4 equiv of HCl, [ 1 ]^2? is converted into neutral 1,2,3,4‐tetrakis(trichlorosilyl)but‐2‐ene, 3 . The Cl^? acceptor AlCl₃, induces a twofold ring‐closure reaction of [ 1 ]^2? to form a six‐membered bicycle 4 in which two silacyclobutene rings are fused along a shared C=C double bond (84 %). Compound 4 , which was structurally characterized by X‐ray crystallography, undergoes partial ring opening to a monocyclic silacyclobutene 2 in the presence of HCl, but is thermally stable up to at least 180 °C.     

A pericyclic cascade to the stereocontrolled synthesis of 9-cis-retinoids

A domino reaction that is pericyclic in nature is thought to be triggered upon treatment of alkenynol 10 with arylsulfenyl chlorides. The process comprises an ordered sequence of sigmatropic rearrangements: a reversible [2,3]-allyl sulfenate to allyl sulfoxide shift, followed by a [2,3]-propargyl sulfenate to allenyl sulfoxide rearrangement, and last a stereodifferentiating [1,5]-sigmatropic hydrogen migration leading to polyene 13. The occurrence of the C7 to C11 hydrogen migration has been demonstrated by labeling experiments. The double diastereoselection of the [1,5]-sigmatropic hydrogen shift to afford a single isomer of the final polyene 13 is thought to arise from a combination of the electronic effect of the sulfoxide at one terminus, and the steric effect imparted by the bulky trimethylcyclohexenyl substituent at the other terminus. The overall process thus constitutes a stereoselective synthesis of an E,Z,Z-triene fragment from an alkenynol and, in particular, a retinoid with the 7E,9Z,11Z,13E configuration on the conjugated polyenic side chain. Application of this method to the synthesis of retinoids, including labeled analogues, is straightforward.     

碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。     

Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.     

Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

On regularity of block triangular fuzzy matrices

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.     

Calorimetric studies on an anhydride‐cured epoxy resin from diglycidyl ether of bisphenol‐A and diglycidyl ether of poly(propylene glycol). I. Onset of diffusion control during isothermal polymerization

Calorimetric studies on a series of anhydride‐cured epoxy resins, in which the epoxy oligomer is a mixture of diglycidyl ether of bisphenol‐A (DGEBA) and diglycidyl ether of poly(propylene glycol) (DGEPPG) in different mole ratios, were carried out. DGEPPG is a flexible epoxy oligomer that was used to tune glass transition temperature for the fully reacted epoxy resin. Conversion versus time curves for the systems with different DGEBA/DGEPPG mole ratios (not including the neat DGEPPG system) were found to overlap with each other in mass‐controlled reaction regime, indicating similar reactivities of epoxy groups in both epoxy oligomers. Onset of diffusion‐controlled reaction regime for different systems was estimated by fitting the conversion versus time data using a phenomenological kinetic equation, as well as from direct comparison of the conversion versus time curves. For the systems (i.e., 0, 10, and 30% DGEPPG) that vitrify during reaction, the crossover from mass‐controlled to diffusion‐controlled reaction occurs close to the onset of the vitrification, where T_g is about 25–30 K below the reaction temperature. For the system (i.e., 50% DGEPPG system) that does not vitrify during the reaction, such crossover still occurs when the T_g of the mixture reaches a value about 25 K below the reaction temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2155–2165, 2008     

Structure‐Property Relationships for Model Heterocyclic Polymer Networks: Effect of Monomer Functionality

The effect of initial monomer functionality on the final properties of densely cross‐linked heterocyclic polymer networks (HPN) was evaluated from comparative studies of the viscoelastic behavior and enthalpy relaxation in the glass transition range of polyisocyanurates prepared from a bifunctional monomer D (1,6‐hexamethylene diisocyanate, HDI) and a trifunctional monomer T (the isocyanurate of HDI). Quantitative analysis of these data suggested that an HPN prepared from the monomer T was chemically more heterogeneous and possessed a lower effective network density (presumably, as a result of a lower mobility of the initial monomer T compared to monomer D).