Poly(phenylene oxide) copolymer anion exchange membranes

Poly(phenylene oxide) block and random copolymers are synthesized by oxidative polymerization of 2,6-dimethylphenol and 2,6-diphenylphenol for potential alkaline exchange membrane application. The copolymers are functionalized on the methyl substituted repeat units through a two-step process to produce pendent quaternary ammonium cationic groups. The amount of quaternary ammonium cations and the ion exchange capacity are quantified through titration measurements. Ionic conductivity of the copolymer membranes is measured by electrochemical impedance spectroscopy. Block copolymers show increased bromide conductivity at higher ion exchange capacities compared with the random copolymer analogs. The bromide conductivity for a block copolymer film with an ion exchange capacity of 1.27 mequiv/g reaches 26 mS/cm at 90 °C and 95% relative humidity. The hydroxide conductivity for the same film was measured to be 84 mS/cm at 80 °C and 95% relative humidity. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1770–1778, 2013     

Nanoassemblies with light‐responsive size and density from linear flexible polyelectrolytes

This study presents electrostatically self‐assembled nanoparticles from linear flexible polyelectrolytes (poly(diallyldimethylammonium chloride or quarternized poly(4‐vinylpyridine)) and an ionic photo‐isomerizable azo dye (Acid Yellow 38) that can change their size upon UV‐light irradiation. Assemblies with narrow size distribution are stable in aqueous solution. For samples with under‐stoichiometric dye load, UV‐light exposure triggers a size decrease, e.g. from a hydrodynamic radius of R_h = 94 nm to R_h = 62 nm for an Ay38‐PDADMAC sample with a charge ratio of l_charge = 0.7. Size changes are caused by trans‐cis isomerization of the dye, accompanied by a change in hydrophilicity, binding enthalpy and entropy. Assemblies are characterized by static and dynamic light scattering, atomic force microscopy, UV–vis spectroscopy and isothermal titration calorimetry. Zeta potential measurements give insight into the electrostatic stabilization and size‐control of the ionic nano‐assemblies, revealing a master curve of effective surface charge density versus hydrodynamic radius. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys., 2013     

Comment on “Density functional theory study of 1,2‐dioxetanone decomposition in condensed phase”

In the preceding paper results are presented, which are in serious conflict with state‐of‐the‐art ab initio method. Based on these new results the authors propose a new explanation of the reason for the preferential production of a phosphorescent state. Here we show that these controversial results are flawed, since the model use exclude biradical electron structures. © 2012 Wiley Periodicals, Inc.     

DFT study of the effect of substituents on the absorption and emission spectra of Indigo

ABSTRACT: BACKGROUND: Theoretical analyses of the indigo dye molecule and its derivatives with Chlorine (Cl), Sulfur (S), Selenium (Se) and Bromine (Br) substituents, as well as an analysis of the Hemi-Indigo molecule, were performed using the Gaussian 03 software package. RESULTS: Calculations were performed based on the framework of density functional theory (DFT) with the Becke 3- parameter-Lee-Yang-Parr (B3LYP) functional, where the 6-31 G(d,p) basis set was employed. The configuration interaction singles (CIS) method with the same basis set was employed for the analysis of excited states and for the acquisition of the emission spectra. CONCLUSIONS: The presented absorption and emission spectra were affected by the substitution position. When a hydrogen atom of the molecule was substituted by Cl or Br, practically no change in the absorbed and emitted energies relative to those of the indigo molecule were observed; however, when N was substituted by S or Se, the absorbed and emitted energies increased.     

Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.