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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. 相似文献
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Keizer SP Mack J Bench BA Gorun SM Stillman MJ 《Journal of the American Chemical Society》2003,125(23):7067-7085
The effect of introduction of perfluoro alkyl groups into phthalocyanines, as evidenced by the spectroscopic properties of 1,4,8,11,15,18,22,25-octa-fluoro-2,3,9,10,16,17,23,24-octa-perfluoro isopropyl zinc phthalocyanine, ZnF(64)Pc(-2) and its ring-reduced radical anion species, [ZnF(64)Pc(-3)](-), are reported. A combination of UV-visible absorption and magnetic circular dichroism (MCD) spectroscopy, ESI and MALDI-TOF mass spectrometry, cyclic and differential pulse voltammetry, and complete theoretical calculations using INDO/S and DFT techniques reveals that the substitution of all sixteen hydrogen atoms in protio ZnPc(-2) by eight F and eight i-C(3)F(7) groups red shifts the Q and pi --> pi transitions and narrows the HOMO-LUMO gap while simultaneously preventing ring photooxidation and stabilizing the radical anion. The [ZnF(64)Pc(-3)](-) species, which is in equilibrium in solution with the neutral complex when a reducing agent is present, is unusually stable. The above effects are attributed to the strong electron withdrawing properties of the peripheral substituents, which render ZnF(64)Pc extremely electron deficient. 相似文献
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