Self-aggregation of dendritic poly(benzyl ether)–poly(acrylic acid), an amphiphilic block copolymer, studied by 1H NMR

The dynamic properties of the micelles of a novel synthesized amphiphilic block copolymer, dendritic poly(benzyl ether)–poly(acrylic acid) (Dendr.PBE-PAA), formed in aqueous solutions were studied by the ¹H self-diffusion coefficient, relaxation measurements and 2D nuclear Overhauser enhancement spectroscopy. The experimental results show that Dendr.PBE-PAA molecules self-aggregate in aqueous solution. The dynamic properties of the Dendr.PBE-PAA micelles vary with their total concentration in the solution. The motion of the molecules in the micelles of a concentrated solution is more restricted than that in a less concentrated one. The main chains of PAA are densely packed in the surface layer of the hydrophobic core with the carboxyl side chain pointing to the aqueous medium and the hydrophobic phenoxy rings stay in the interior. The self-aggregate becomes larger as the degree of polymerization of PAA increases. However the phenoxy rings situated in the interior of the hydrophobic core become more loosely packed. n-Hexadecane is solubilized in the micelles. The optimal position of n-hexadecane is between the phenoxy rings next to the PAA chains. Received: 25 January 2001 Accepted: 18 July 2001     

Synthesis of new fluorinated allyl ethers for the surface modification of thiol–ene ultraviolet‐curable formulations

Thiol–ene photocurable systems based on a trifunctional thiol [trimethylolpropane tris‐(3‐mercaptopropanoate)] and two different multifunctional allyl ethers (trimethylolpropane triallyl ether and Boltorn U2, an allyl functional dendritic polyester) were examined. To these systems, small amounts (<1 wt %) of fluorinated allyl ethers were added for the modification of their surface properties. Two new fluorinated allyl ethers, 1H,1H‐perfluoro‐1‐heptylallyl ether and 1H,1H‐perfluoro‐1‐decylallyl ether, were synthesized for this purpose by allylation of the corresponding 1H,1H‐perfluoro alcohols. The fluorinated monomers, despite their very low concentrations, caused sharp changes in the surface properties of the films and in the solvent resistance without any changes in the curing conditions and bulk properties. Completely hydrophobic surfaces were obtained (as a result of the selective enrichment of the fluorinated monomers on the film surfaces) that depended on the monomer structure and its concentration. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2583–2590, 2002     

Theoretical consideration of the molecular mass distribution of starlike polymers formed by attachment of linear polymers to dendritic cores

Star‐shaped polymers can be synthesized by condensation of linear polymers to dendritic cores. The distribution of molecular masses of such hybrid star polymers and the factors influencing it have been investigated by calculations based on population balance equations and Laplace transformations. Moreover, the expressions for numerical calculations of molecular mass distributions have been derived for both Poisson and Schultz–Zimm types of initial molecular mass distributions. According to the calculation results, the molecular mass distribution of the star polymers is strongly dependent on the distribution of the length of linear polymers. Beyond this, the molecular mass development is affected by several parameters that describe the reaction degree of dendritic cores, thus, by the fraction of all functional groups of dendritic cores involved in grafting, denoted by p; the average branching degree of one starlike molecule, represented by ρ; or the fraction of dendritic molecules becoming the cores of star polymers, expressed by p/ρ, provided the star molecule contains only one core. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2751–2758, 2001     

Concerning the shape of a geometric lattice

A well-known conjecture states that the Whitney numbers of the second kind of a geometric lattice (simple matroid) are logarithmically concave. We show this conjecture to be equivalent to proving an upper bound on the number of new copoints in the free erection of the associated simple matroid M. A bound on the number of these new copoints is given in terms of the copoints and colines of M. Also, the points-lines-planes conjecture is shown to be equivalent to a problem concerning the number of subgraphs of a certain bipartite graph whose vertices are the points and lines of a geometric lattice.     

Photophysical and self‐assembly behavior of poly(amidoamine) dendrons with chromophore as scaffold: The effect of dendritic architecture

Two series of amphiphiles composed of hydrophilic poly(amidoamine) dendrons (from the first to the third generation) as the shell and hydrophobic aromatic chromophores (3,6‐di(maleimidyl)‐9‐phenyl carbazole and 9‐(4′‐maleimidyl phenyl)‐3‐maleimidyl carbazole) as the central scaffold were synthesized. The effect of dendritic architecture on the photophysical properties and the self‐assembly behavior of these amphiphiles were studied by UV–vis absorption spectroscopy, fluorescence spectroscopy, and transmission electron microscopy (TEM) measurements. Both the generation of dendritic shell and the location of dendrons at the chromophoric scaffold had great effect on the photophysical properties of these amphiphiles. In addition, different spherical aggregates were formed from these amphiphiles in the aqueous solution at different concentrations. Because of the combined effects of steric hindrance and architecture of dendritic shells, the amphiphiles from G2 dendron with central chromophore self‐organized into ordered aggregates more readily than that from G1 and G3. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4584–4593, 2008     

Discrete strip-concave functions, Gelfand-Tsetlin patterns, and related polyhedra

Discrete strip-concave functions considered in this paper are, in fact, equivalent to an extension of Gelfand-Tsetlin patterns to the case when the pattern has a not necessarily triangular but convex configuration. They arise by releasing one of the three types of rhombus inequalities for discrete concave functions (or “hives”) on a “convex part” of a triangular grid. The paper is devoted to a combinatorial study of certain polyhedra related to such functions or patterns, and results on faces, integer points and volumes of these polyhedra are presented. Also some relationships and applications are discussed.In particular, we characterize, in terms of valid inequalities, the polyhedral cone formed by the boundary values of discrete strip-concave functions on a grid having trapezoidal configuration. As a consequence of this result, necessary and sufficient conditions on a pair of vectors to be the shape and content of a semi-standard skew Young tableau are obtained.     

Synthesis of dendritic silver nanostructures by means of ultrasonic irradiation

In this paper, a simple and effective route for the synthesis of silver dendritic nanostructures by means of ultrasonic irradiation has been developed. Well-defined silver dendritic nanostructures were obtained by sonicating the aqueous solution of 0.04 mol/L silver nitrate with 4.0 mol/L isopropanol as reducing agent and 0.01 mol/L PEG400 as disperser for 2 h. The effects of the irradiation time, the concentration of Ag⁺ and the molar ratio of PEG to AgNO₃ on the morphology of silver nanostructures were discussed. The structures of the obtained samples were characterized by transmission electron microscopy (TEM), selected area electron diffraction (SAED) and X-ray powder diffraction (XRD), and the chemical composition of the dendrites was examined by energy-dispersive X-ray spectrum (EDS).     

一种新型的树枝状负磁导率材料微带天线

基于树枝状金属结构单元模型的电磁特性,设计了一种双面刻有树枝状金属结构单元阵列的负磁导率介质材料,并将这种介质材料作为微带天线的基板,制备了中心工作频率为2.64GHz的树枝状负磁导率材料微带天线.仿真和测量结果都表明：相比普通微带天线,树枝状负磁导率材料微带天线的性能得到了明显改善,定向性得到了提高,E面和H面的3dB角分别收缩了18°和13°,增益提高了2.19dB,相当于有效辐射功率提高了65%.说明利用负磁导率材料作为微带天线的基板,可以明显改善微带天线的性能. 关键词： 树枝状结构 微带天线 负磁导率 增益     

三维枝晶生长的相场法数值模拟研究

基于薄界面限制、耦合界面能各向异性的相场模型,采用动态计算区域的加速算法,对纯物质的三维枝晶生长进行了定量模拟,真实再现了枝晶的生长过程.对枝晶尖端进行了剖切分析,表明主枝截面上各向异性没有主枝方向各向异性明显;对枝晶尖端生长速度、尖端半径、Peclet数及临界稳定性参数σ^*进行模拟计算,并与同条件下报道值进行了对比分析,两者符合良好,并得到了与结晶理论相一致的枝晶生长规律,证实了相场方法模拟三维空间枝晶生长可行有效. 关键词： 相场方法 枝晶生长 微观组织 三维数值模拟