Doping phosphoric acid in polybenzimidazole membranes for high temperature proton exchange membrane fuel cells

Polybenzimidazole (PBI) membranes were doped in phosphoric acid solutions of different concentrations at room temperature. The doping chemistry was studied using the Scatchard method. The energy distribution of the acid complexation in polymer membranes is heterogeneous, that is, there are two different types of sites in PBI for the acid doping. The protonation constants of PBI by phosphoric acid are found to be 12.7 L mol^?1 (K¹) for acid complexing sites with higher affinity, and 0.19 L mol^?1 (K²) for the sites with lower affinity. The dissociation constants for the complexing acid onto these two types of PBI sites are found to be 5.4 × 10^?4 and 3.6 × 10^?2, respectively, that is, about 10 times smaller than that of aqueous phosphoric acid in the first case but 5 times higher in the second. The proton conducting mechanism is also discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2989–2997, 2007     

Synthesis of pyrazole-3-carboxylates and pyrazole-1,5-dicarboxylates by one-pot cyclization of hydrazone dianions with diethyl oxalate

The one-pot cyclization of hydrazone dianions with diethyl oxalate allows a convenient synthesis of pyrazole-3-carboxylates and pyrazole-1,5-dicarboxylates.     

Mixed boundary value problems for nonlinear elliptic equations in multidimensional non-smooth domains

The nonlinear elliptic equation is investigated. It is supposed that u fulfils a mixed boundary value condition and that Ω ? IRⁿ (n ≥ 3) has a piecewise smooth boundary. W^s,2 — regularity (s < 3/2) of u and L^p — properties of the first and the second derivatives of u are proven.     

Schwarz reflection geometry I: Continuous iteration of reflection

Differential equations are derived for a continous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry. Mathematics Subject Classification (1991):53C35, 53A30, 30D05.