Electroreduction of some pyridine carboxamides on carbon electrodes in aqueous solutions

The electroreductions of the NAD⁺ model compounds nicotinamide (I), N₁-methyl nicotinamide (II), N′-methyl nicotinamide (III) and isonicotinamide (IV) on carbon electrodes have been studied in aqueous media in the pH range 0–12 by linear-sweep cyclic voltammetry (Scheme 1, I-IV). Logarithmic analyses of the reduction peaks were performed by computing the convolution of the current with time as a function of the potential. On the basis of the experimental results it was concluded that the irreversibility of the electron transfers increased when a glassy carbon electrode was used, and this irreversibility being more marked when a plastic formed carbon electrode was employed. The reduction processes occurred with more difficulty on carbon electrodes than on mercury electrodes. Both the reduction and the reoxidation (when occurred) processes changed with respect to those observed on mercury electrodes, being irreversible electron transfers the rate-determining steps in most cases. Thus, for compounds I, II and III at pH < 2 the reductions occurred by the uptake of two electrons and two H⁺ ions, and the rate determining step was found to be the first one-electron transfer, for I and III, and the irreversible second electron transfer, preceded by the uptake of an H+ ion, for II. At pH>3 the processes consisted of electrodimerization reactions, preceded by the protonation of the heterocyclic nitrogen in cases I and III. The second electron transfer of the electroreduction of IV always appeared irreversible, in contrast with that found for mercury electrodes.     

γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < ω〉?}\text{J}{}^{\mathrm{\omega }}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

Characterizing polymer macrostructures by identifying and locating microstructures along their chains with the kerr effect

In this brief report, we demonstrate that Kerr effect measurements, which determine the excess birefringence contributed by polymer solutes in dilute solutions observed under a strong electric field, are highly sensitive to and capable of determining their microstructures, as well as their locations along the macromolecular backbone. Specifically, using atactic triblock copolymers with the same overall composition of styrene (S) and p-bromostyrene (pBrS) units, but with two different block arrangements, that is, pBrS₉₀-b-S₁₂₀-b-pBrS₉₀ (I) and S₆₀-b-pBrS₁₈₀-b-S₆₀ (II), which are indistinguishable by NMR, we detected a dramatic difference in their molar Kerr constants (_mK), in agreement with those previously estimated. Although similar in magnitude, their Kerr constants differ in sign, with _mK(II) positive and _mK(I) negative. In addition, S/pBrS random and gradient copolymers synthesized by reversible addition-fragmentation chain-transfer (RAFT) polymerization exhibit a heretofore unexpected enhanced enchainment of racemic (r) pBrS-pBrS diads. Comparison of their observed and calculated _mKs suggests that the gradient S/pBrS copolymers possess an unanticipated additional gradient in stereosequence that parallels their comonomer gradient, that is, as the concentration of pBrs units decreases from one end of the copolymer chain to the other, so does the content of r diads. This conclusion could only be reached by comparison of observed and calculated Kerr effects, which access the global properties of macromolecules, and not NMR, which is only sensitive to local polymer structural environments, but not to their locations on the copolymer chains. Molar Kerr constants are characteristic of entire polymer chains and are highly sensitive to their constituent microstructures and their distribution along the chain. They may be used to both identify constituent microstructures and locate them along the polymer chain, thereby enabling, for the first time, characterization of their complete macrostructures. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Effect of bandpass filtering on melodic contour identification by cochlear implant users

Melodic contour identification was measured in cochlear implant (CI) and normal-hearing (NH) subjects for piano samples processed by four bandpass filters: low (310-620 Hz), middle (620-2480 Hz), high (2480-4960 Hz), and full (310-4960 Hz). NH performance was near-perfect for all filter ranges and much higher than CI performance. The best mean CI performance was with the middle frequency range; performance was much better for some CI subjects with the middle rather than the full filter. These results suggest that acoustic filtering may reduce potential mismatches between fundamental frequencies and harmonic components thereby improving CI users' melodic pitch perception.     

Experience in making rheological measurements at high pressures

Summary We review the difficulties encountered in the design and operation of apparatus for rheological studies on liquids at pressures up to 900 MN m^–2 and temperatures from –30 to 120°C. Such rheological information is required in connection with elastohydrodynamic lubrication in which high pressures and shear rates are encountered.With 3 figures     

Beyond microstructures: Using the Kerr Effect to characterize the macrostructures of synthetic polymers

The macrostructures of synthetic polymers are essentially the complete molecular chain architectures, including the types and amounts of constituent short‐range microstructures, such as the regio‐ and stereosequences of the inserted monomers, the amounts and sequences of monomers found in co‐, ter‐, and tetra‐polymers, branching, inadvertent, and otherwise, etc. Currently, the best method for characterizing polymer microstructures uses high field, high resolution ¹³C‐nuclear magnetic resonance (NMR) spectroscopy observed in solution. However, even ¹³C‐NMR is incapable of determining the locations or positions of resident polymer microstructures, which are required to elucidate their complete macrostructures. The sequences of amino acid residues in proteins, or their primary structures, cannot be characterized by NMR or other short‐range spectroscopic methods, but only by decoding the DNA used in their syntheses or, if available, X‐ray analysis of their single crystals. Similarly, there are currently no experimental means to determine the sequences or locations of constituent microstructures along the chains of synthetic macromolecules. Thus, we are presently unable to determine their macrostructures. As protein tertiary and quaternary structures and their resulting ultimate functions are determined by their primary sequence of amino acids, so too are the behaviors and properties of synthetic polymers critically dependent on their macrostructures. We seek to raise the consciousness of both synthetic and physical polymer scientists and engineers to the importance of characterizing polymer macrostructures when attempting to develop structure–property relations. To help achieve this task, we suggest using the electrical birefringence or Kerr effects observed in their dilute solutions. The molar Kerr constants of polymer solutes contributing to the birefringence of their solutions, under the application of a strong electric field, are highly sensitive to both the types and locations of their constituent microstructures. As a consequence, we may begin to characterize the macrostructures of synthetic polymers by means of the Kerr effect. To simplify implementation of the Kerr effect to characterize polymer macrostructures, we suggest that NMR first be used to determine the types and amounts of constituent microstructures present. Subsequent comparison of observed Kerr effects with those predicted for different microstructural locations along the polymer chains can then be used to identify the most likely macrostructures. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 155–166     

Matchings and independent sets of a fixed size in regular graphs

We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size ℓ in a d-regular graph on N vertices. For bounded away from 0 and 1, the logarithm of the bound we obtain agrees in its leading term with the logarithm of the number of matchings of size ℓ in the graph consisting of disjoint copies of K_d,d. This provides asymptotic evidence for a conjecture of S. Friedland et al. We also obtain an analogous result for independent sets of a fixed size in regular graphs, giving asymptotic evidence for a conjecture of J. Kahn. Our bounds on the number of matchings and independent sets of a fixed size are derived from bounds on the partition function (or generating polynomial) for matchings and independent sets.     

Investigation of the effects of silicate modification on polymer‐layered silicate nanocomposite morphology

The morphological behavior of a series of polymer‐layered silicate nanocomposites (PLSNs) has been investigated. The goal was to probe the effect of “textured” silicate surfaces on PLSN morphology. The nanocomposites were fabricated by mixing montmorillonite clay that was carefully modified with tailor‐made polystyrene (PS) surfactants into a PS homopolymer matrix, where the chemical similarity of the matrix polymer and surfactants assures complete miscibility of surfactant and homopolymer. To examine the effect of silicate surface “texture,” clay was modified with combinations of long and short surfactants. The samples were then direct melt annealed to allow the equilibrium morphology to develop, and characterized by small‐angle X‐ray scattering. Based on the implications of the Balazs model and other work on the wetting behavior of polymer melts with longer surfactants and textured surfaces we expected that the intercalation of the homopolymer matrix material into the modified clay would be promoted. Extensive characterization of both the modified clays as well as the resultant nanocomposites clearly show that the modified clays exhibit a high degree of order, but also that only phase‐separated morphologies are formed in the corresponding nanocomposites. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4075–4083, 2004     

Slow mixing of Glauber dynamics for the hard‐core model on regular bipartite graphs

Let ∑ = (V,E) be a finite, d‐regular bipartite graph. For any λ > 0 let π_λ be the probability measure on the independent sets of ∑ in which the set I is chosen with probability proportional to λ^|I| (π_λ is the hard‐core measure with activity λ on ∑). We study the Glauber dynamics, or single‐site update Markov chain, whose stationary distribution is π_λ. We show that when λ is large enough (as a function of d and the expansion of subsets of single‐parity of V) then the convergence to stationarity is exponentially slow in |V(∑)|. In particular, if ∑ is the d‐dimensional hypercube {0,1}^d we show that for values of λ tending to 0 as d grows, the convergence to stationarity is exponentially slow in the volume of the cube. The proof combines a conductance argument with combinatorial enumeration methods. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006