Dembowski-Ostrom型完全非线性函数构造的线性码权分布

Dembowski-Ostrom型完全非线性函数是目前最主要的完全非线性函数类,已发现的完全非线性函数中只有一种不属于Dembowski-Ostrom型.为此,该文首先给出Dembowski-Ostrom型完全非线性函数的定义,将已有的线性码构造推广到这一类型函数上.进而给出此类函数构造的线性码的码字与有限域上非退化二次型之间的关系,并得到相应二次型的原像分布的一些性质.通过有限域上的二次型以及指数和理论,用统一的方法完全确定了基于所有Dembowski-Ostrom型完全非线性函数构造的两类线性码的权分布.

Ethylene Polymerization and Ethylene/Hexene Copolymerization with Vanadium(III) Catalysts Bearing Heteroatom-Containing Salicylaldiminato Ligands

A series of novel vanadium(III) complexes hearing heteroatoill-containing group-substituted salicylaldiminato ligands [RN=CH(ArO)]VCl2(THF)(2) (Ar = C6H4, R = C3H2NS, 2a; C7H4NS, 2c; C7H5N2, 2d; Ar = C(6)H(2)tBu(2) (2,4), R = C3H2NS, 2b) have been synthesized and characterized. Structure of complex 2c was further confirmed by X-ray crystallographic analysis. The complexes were investigated as the catalysts for ethylene polymerization in the presence of Et2AlCl. Complexes 2a-d exhibited high catalytic activities (up to 22.8 kg polyethylene/mmolv h bar), and affording polymer with unimodal molecular weight distributions at 25-70 degrees C in the first 5-min polymerization, whereas produced bimodal molecular weight distribution polymers at 70 degrees C when polymerization time prolonged to 30 min. The catalyst structure plays an important role in controlling the molecular weight and molecular weight distribution of the resultant polymers produced in 30 min polymerization. In addition, ethylene/hexene copolymerizations with catalysts 2a-d were also explored in the presence of Et2AlCl, which leads to the high molecular weight and unimodal distributions copolymers with high comonomer incorporation.

SYNTHESIS AND CHARACTERIZATION OF HYPERBRANCHED VINYL POLYMERS FROM RAFT POLYMERIZATION OF AN ASYMMETRIC DIVINYL MONOMER

Hyperbranched vinyl polymers were prepared by reversible addition-fragmentation chain transfer ( RAFT) polymerization of a styrenic asymmetric divinyl monomer. This was achieved by using cumyl dithiobenzoate or S-dodecyl-S'-(alpha,alpha'-dimethyl-alpha ''-acetic acid) trithiocarbonate as the chain transfer agent, 1,1'-azobis(cyclohexanecarbonitrile) or thermal initiation as a source of radicals. Cross-linking was inhibited by a rapid RAFT-based equilibrium between active propagation chains and dormant species, and thus a hyperbranched polymer with a monomer conversion as high as 80% was obtained. The hyperbranched structure and properties of the resultant polymers were characterized by a combination of H-1-NMR spectroscopy and a triple detection size exclusion chromatography (TRI-SEC). The hyperbranched vinyl polymer has a broad molecular weight distributions and a low Mark-Houwink exponent alpha value compared with the linear counterpart.

Soluble neodymium chloride 2-ethylhexanol complex as a highly active catalyst for controlled isoprene polymerization

Soluble NdCl3 center dot 3EHOH (2-ethyl hexanol) in hexane combined with AlEt3 is highly active for isoprene polymerization in hexane. The NdCl3 center dot 3EHOH/AlEt3 has higher activity than the typical binary catalyst NdCl3 center dot 3(i)PrOH (isopropanol)/AlEt3 and ternary catalyst NdV3 (neodymium versatate)/AlEt2Cl/Al(i-Bu)(2)H. The molecular weight of polyisoprenes can be controlled by variation of [Nd], [Al]/[Nd] ratio and polymerization temperature and time. The NdCl3 center dot 3EHOH/AlEt3 catalyst polymerized isoprene to afford products featuring high cis-1,4 stereospecificity (ca. 96%), high molecular weight (ca. 10(5)) and relatively narr ow molecular weight distributions (M-w/M-n = 2.0-2.8) simultaneously. More importantly, some living polymerization characteristics were demonstrated: (a) absence of chain termination; (b) linear correlation between M-n and polymer yield; (c) increment of molecular weight in the 'seeding' polymerization. Though some deviation from the typical living polymerization such as molecular weight distribution is not narrow enough and the line of M-n and polymer yield does not extrapolate to zero, controlled polymerization with the current catalyst can still be concluded.

Enolic Schiff-base aluminum complexes and their application in lactide polymerization

A series of NNOO-tetradentate enolic Schiff-base ligands were prepared where ligand L-1 = bis(benzoylacetone)propane-1,2-diimine, L-2 = bis(acetylacetone)-propane-1,2-diimine, L-3 = bis-(acetylacetone)cyclohexane-1,2-diimine. Their further reaction with aluminum tris(ethyl) formed complexes LAlEt (1a, 2a and 3a). The solid structure of complexes la, 2a and 3a confirmed by X-ray single crystal analysis manifested that these complexes were all monomeric and five-coordinated with an aluminum atom in the center. The configurations of these complexes varied from trigonal bipyramidal geometry (tbp) to square pyramidal geometry (sqp) due to their different auxiliary ligand architectures. H-1 NMR spectra indicated that all these complexes retained their configuration in solution states. Their catalytic properties to polymerize racemic-lacticle (rac-LA) in the presence of 2-propanol were also studied. The diimine bridging parts as well as the diketone segment substituents had very close relationship with their performance upon the polymerization process. All these complexes gave moderately isotactic polylactides with controlled molecular weight and very narrow molecular weight distributions.

New titanium complexes with two beta-enaminoketonato chelate ligands: Syntheses, structures, and olefin polymerization activities

New titanium complexes with two nonsymmetric bidentate beta-enaminoketonato (N,O) ligands (4a-e), [(Ph)NC(R-2)C(H)C(R-1)O](2)TiCl2, have been synthesized. X-ray crystal structure reveals that complex 4a has a C-2-symmetric conformation with a distorted octahedral geometry around the titanium center. With modified methylaluminoxane (MMAO) as a cocatalyst, complexes 4a-e are active catalysts for ethylene polymerization at room temperature, producing high molecular weight polyethylenes bearing linear structures. The 4a,b/MMAO catalyst systems exhibit the characteristics of a quasi-living polymerization of ethylene, producing polyethylenes with narrow molecular weight distributions. Moreover, the 4a-d/MMAO catalyst systems are also capable of promoting the quasi-living copolymerization of ethylene with norbornene at room temperature, yielding high molecular weight alternating copolymers with narrow molecular weight distributions. The quasi-living nature of the catalysts allows the synthesis of new A-B polyethylene-block-poly(ethylene-conorbornene) diblock copolymer.

Polymerization of methyl methacrylate by iron(II) pyridinebisimine complexes

Fe(II) pyridinebisimine complexes activated with trialkylaluminium or modified methylaluminoxane (MMAO) as catalysts were employed for the polymerization of methyl methacrylate. Polymer yields, activities and polymer molecular weights as well as molecular weight distributions can be controlled over a wide range by the variation of the structures of the Fe(II) pyridinebisimine complexes and the reaction parameters such as Al/Fe molar ratio, monomer/catalyst molar ratio, monomer concentration, reaction temperature and time applied to the polymerization of methyl methacrylate. Under optimum condition, the catalytic activity of Fe(II) complex is of up to 74.5 kg(polym)/mol(Fe)h.

Synthesis, molecular structures, and norbornene addition polymerization activity of the neutral nickel catalysts supported by beta-diketiminato [N, N], ketiminato [N, O], and Schiff-Base [N, O] ligands

A series of neutral nickel complexes [Ni(Ph)(PPh3)(N, O)] with Schiff-base ligands (N, O) [N, O = 5-Me-3-tert-Bu-(Ar-N=CH)C6H2O (1, Ar = 2,6-Me2C6H3; 2, Ar = 2,6-i-Pr2C6H3)], [Ni(Ph)(PPh3)(N,O)1, with beta-ketiminato ligands (N, O) [N, O = CH3COCHC=(CH3)N-Ar (3, Ar = 2,6-Me2C6H3; 4, Ar = 2,6-i-Pr2C6H3)] and [Ni(N, N)(PPh3)], and with beta-diketiminato ligands (N, N) [5, N, N = [2,6-i-Pr-2(C6H3)N=C(CH3)](2)CH] have been synthesized and characterized. The molecular structures of complexes 1, 4, and 5 have been confirmed by X-ray single-crystal analyses. Although their ligands have similar structures, complex 4 possesses a structure similar to that of four-coordination nickel with complex 1, while complex 5 reveals a rare three-coordination nickel geometry. These compounds show high catalytic activities of up to 3.16 x 10(7) g PNB mol(-1) Ni h(-1) for the addition polymerization of norbornene in the presence of modified methylaluminoxane (MMAO) as cocatalyst. Catalytic activities, polymer yield, molecular weights, and molecular weight distributions of polyborbornene have been investigated under various reaction conditions.

Ethylene-propylene copolymerization with bis(beta-enaminoketonato) titanium complexes activated with modified methylaluminoxane

Ethylene-propylene copolymerization, using [(Ph)NC(R-2)CHC(R-1)O](2)TiCl2 (R-1 = CF3, Ph, or t-Bu; R-2 = CH3 or CF3) titanium complexes activated with modified methylaluminoxane as a cocatalyst, was investigated. High-molecular-weight ethylene-propylene copolymers with relatively narrow molecular weight distributions and a broad range of chemical compositions were obtained. Substituents R-1 and R-2 influenced the copolymerization behavior, including the copolymerization activity, methylene sequence distribution, molecular weight, and polydispersity. With small steric hindrance at R-1 and R-2, one complex (R-1 = CF3; R-2 = CH3) displayed high catalytic activity and produced copolymers with high propylene incorporation but low molecular weight. The microstructures of the copolymers were analyzed with C-13 NMR to determine the methylene sequence distribution and number-average sequence lengths of uninterrupted methylene carbons.

Synthesis and characterization of ABC ternary segregated H-shaped copolymers

The synthesis of a novel ABC ternary segregated H-shaped copolymer is described, of which a central poly(ethylene glycol) (PEG) chain is terminated on both sides by polystyrene (PS) and poly(tert-butylacrylate) (PtBA) chains. The synthetic procedure involves functionalization of PEG by 2-bromosuccinic anhydride followed by esterification of 1,6-hexanediol, which gives its ends the bifunctional nature that allows sequential growth of two PS, then two PtBA arms via atom transfer radical polymerization (ATRP). The resulting segregated H-shaped copolymers were characterization by NMR spectroscopy and gel permeation chromatography (GPC). All these copolymers were affirmed to have well-defined structures and narrow molecular weight distributions.

Syntheses of chromium(III) complexes with Schiff-base ligands and their catalytic behaviors for ethylene polymerization

A series of chromium(III) complexes LCrCl3 (4a-c) bearing chelating 2,2'-iminodiphenyisulfide ligands [L = (2-ArMeC=NAr)(2)S] was synthesized in good yields from the corresponding ligands and CrCl3.(THF). Using modified methylaluminoxane (MMAO) as a cocatalyst, these complexes display moderate activities towards ethylene polymerization, and produce highly linear polyethylenes with broad molecular weight distribution. Polymer yields, catalyst activities and the molecular weights, as well as the molecular weight distributions of the polymers can be controlled over a wide range by the variation of the structures of the chromium(III) complexes and the polymerization parameters, such as Al/Cr molar ratio, reaction temperature and ethylene pressure.

Ethylene polymerization with porous polystyrene spheres supported Cp2ZrCl2 catalyst

A catalyst with porous polystyrene beads supported Cp2ZrCl2 was prepared and tested for ethylene polymerization with methylaluminoxane as a cocatalyst. By comparison, the porous supported catalyst maintained higher activity and produced polyethylene with better morphology than its corresponding solid supported catalyst. The differences between activities of the catalysts and morphologies of the products were reasonably explained by the fragmentation processes of support as frequently observed with the inorganic supported Ziegler-Natta catalysts. Investigation into the distribution of polystyrene in the polyethylene revealed the fact that the porous polystyrene supported catalyst had undergone fragmentation during polymerization.

Laser light-scattering study of novel thermoplastics .1. Phenolphthalein poly(aryl ether ketone)

Five different molecular weight phenolphthalein poly(aryl ether ketone) (PEK-C) fractions in CHCl3 were studied by static and dynamic laser light scattering(LLS). The dynamic LLS revealed that the PEK-C samples contain some large polymer clusters. These large clusters can be removed by filtering the solution with a 0.1-mu m filter. We found that the persistence length of PEK-C in CHCl3 at 25 degrees C is similar to 2 nm and the Flory characteristic ratio, C-infinity is similar to 25. Our results showed that [R(g)(2)](1/2)(z) = (3.50+/-0.20) x 10(-2)M(w)(0.54+/-0.01) and [D] = (2.37+/-0.05) x 10(-4)M(w)(-0.55+/-0.01), with [R(g)(2)](1/2)(z), M(w), and [D] being the z-average radius of gyration, the weight-average molecular weight, and the z-average translational diffusion coefficient, respectively. A combination of static and dynamic LLS results enabled us to determine D = (2.20+/-0.10) x 10(-4)M(-0.555+/-0.015), where D and M correspond to monodisperse species. Using this calibration between D and M,we have determined molecular weight distributions of five PEK-C fractions from their corresponding translational diffusion coefficient distribution.

Laser light scattering studies of soluble high-performance polyimides: Solution properties and molar mass distributions

Two soluble high-performance polyimides, poly(BCPOBDA/DMMDA) and poly(ODPA/DMMDA), in CHCl3 at 25 degrees C have been studied using laser light scattering. We found that the z-average radius of gyration ([R(g)]) can be scaled to the weight-average molecular weight (M(w)) as [R(g)] (nm) = 4.95 x 10(-2)M(w)(0.52) and [R(g)] (nm) = 1.25 x 10(-2)M(w)(0.66) respectively for poly(BCPOBDA/DMMDA) and poly(ODPA/DMMDA), indicating that poly(ODPA/DMMDA) in CHCl3 at 25 degrees C has a more extended chain conformation than poly(BCPOBDA/DMMDA). Using the wormlike chain model approach, we found that the Flory characteristic ratios (C*) of poly(BCPOBDA/DMMDA) and poly(ODPA/DMMDA) are similar to 20 and similar to 31, respectively, indicating that both of them have a slightly extended chain conformation in comparison with typical flexible polymer chains, such as polystyrene, whose C-infinity is similar to 10. A combination of the weight-average molar mass (M(w)) with the translational diffusion coefficient distributions (G(D)) has led to D (cm(2)/s) = 3.53 x 10(-4)M(-0.579) and D (cm(2)/s) = 4.30 x 10(-4)M(-0.613) respectively for two soluble high-performance polyimides, poly(BCPOBDA/DMMDA) and poly(ODPA/DMMTA), in CHCl3 at 25 degrees C. Using these two calibrations, we have successfully characterized the molar mass distributions of the two polyimides from their corresponding G(D)s. The exponents of these two calibrations further confirm that both of the polyimides have a slightly extended coil chain conformation in CHCl3. The chain flexibility difference between these two polyimides has also been discussed.

The Stability of a Vertical Single-Walled Carbon Nanotube Under Its Own Weight

It has been reported recently that single carbon nanotubes were attached to AFM tips to act as nanotweezers. In order to investigate its stability, a vertical single-walled carbon nanotube (SWCNT) under its own weight is studied in this paper. The lower end of the carbon nanotube is clamped. Firstly the governing dimensionless numbers are derived by dimensional analysis. Then the theoretical analysis based on an elastic column model is carried out. Two ratios, I.e., the ratio of half wall thickness to radius (t=R) and the ratio of gravity to elastic resilience ($\rho$gR=E), and their influences on the ratio of critical length to radius are discussed. It is found that the relationship between the critical ratio of altitude to radius and ratio of half thickness to radius is approximately linear. As the dimensionless number $\rho$gR=E increases, the compressive force per unit length (weight) becomes larger, thus critical ratio of altitude to radius must become smaller to maintain stability. At last the critical length of SWCNT is calculated. The results of this paper will be helpful for the stability design of nanotweezers-like nanostructures.