Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Loosely packed hydroxyl-terminated SAMs on gold

We report the preparation of loosely packed hydroxyl-terminated self-assembled monolayers (SAMs) on gold by the adsorption of bis(11,11'-dithioundecyl)perfluoroheptanoate and base-mediated cleavage of the fluorocarbon terminal group. As shown through complementary characterization methods, the partially fluorinated SAM exhibits a structure in which the outer surface contains mostly -CF(3) groups, the fluorocarbon groups are slightly canted on average, and the hydrocarbon chains underneath are in a fluidlike state. Upon cleavage of the fluorocarbon group, the hydroxyl-terminated alkyl chains relax into an increasingly canted, fluidlike state. The resulting monolayer packing exposes both methylene and hydroxyl functionalities, yielding an intermediate surface energy (theta(a)(H(2)O) approximately 68 degrees ). As compared to a densely packed hydroxyl-terminated SAM prepared from bis(11-hydroxyundecyl)disulfide, the cleaved films are thinner because of the greater average chain cant and exhibit a approximately 50% higher capacitance and a factor of 5 lower charge-transfer resistance. The addition of THF to the electrolyte solution as a cosolvent intercalates into the loosely packed SAM to double the charge-transfer resistance and increase the capacitance by approximately 20% but does not affect the capacitance of the densely packed SAM. The loosely packed SAM is also more easily exchanged upon exposure to a solution of n-docosanethiol.     

Growth and structure of surface-initiated poly(n-alkylnorbornene) films

We report the surface-initiated growth of poly(alkylnorbornene) films via ring-opening metathesis polymerization (ROMP). The films are grown by exposure of a vinyl-terminated self-assembled monolayer (SAM) on gold to Grubbs first-generation catalyst and the subsequent exposure to an alkylnorbornene monomer. We investigate the influence of alkyl side chains on the structure, barrier, surface properties, and the growth kinetics of surface-initiated ROMP-type poly(norbornene) films. Rate constants for film growth are estimated for the comparison of monomer reactivity. The rate constant for film growth decreases by 3 orders of magnitude from norbornene to decylnorbornene, indicating a strong effect of chain length on initiation and/or propagation rates. Reflectance-absorption infrared spectroscopy is used to show the molecular level packing within the poly(alkylnorbornene) films is disrupted by the alkyl side chains. Tapping-mode atomic force microscopy is used to show that norbornene, butylnorbornene, and hexylnorbornene polymerize from the surface to form dense coatings, whereas decylnorbornene polymerizes to form isolated polymer clusters. The methyl terminus of the alkyl side chains increases the hydrophobicity of the poly(alkylnorbornene) films (thetaA(H2O) = 109-114 degrees) beyond that of a typical poly(norbornene) film (thetaA(H2O) approximately 106 degrees). The additional hydrophobicity throughout the film correlates with superior resistances against redox probes (Rf approximately 105 Omega.cm2) for poly(hexylnorbornene) when compared to polynorbornene (Rf approximately 104 Omega.cm2). The resistance of the poly(decylnorbornene) film (Rf approximately 102 Omega.cm2) is consistent with its nonuniform, cluster-like morphology.     

Bi2223带材临界电流沿长度方向的统计分布

本文采用四引线法测量了Bi2223带材临界电流沿长度方向的分布,采用正态分布、对数正态分布、威布尔分布和最小极值分布对临界电流分布进行了拟合检验,确定了临界电流的最优统计分布模型.