Direct synthesis of palladium porphyrins from acyldipyrromethanes

[reaction: see text] Palladium porphyrins are valuable photosensitizers and luminescent agents in biology and materials chemistry. New methodology is described wherein a 1-acyldipyrromethane is converted into the palladium chelate of a trans-A(2)B(2) porphyrin via a one-flask reaction. The reaction entails self-condensation of the 1-acyldipyrromethane in refluxing ethanol containing KOH (5-10 mol equiv) and Pd(CH(3)CN)(2)Cl(2) (0.6 mol equiv) exposed to air. This direct route to palladium porphyrins is more expedient than the four steps of the traditional synthesis: (1) reduction of the 1-acyldipyrromethane; (2) acid-catalyzed condensation; (3) oxidation of the porphyrinogen intermediate; and (4) metal insertion. The new synthesis requires neither acid nor DDQ and formally entails only a 2e(-) + 2H(+) oxidation overall versus the traditional multistep synthesis which requires a 2e(-) + 2H(+) reduction per each 1-acyldipyrromethane (4e(-) + 4H(+) overall) followed by a 6e(-) + 6H(+) oxidation. The analogous reaction of a 1,9-diacyldipyrromethane and a dipyrromethane also gives the palladium porphyrin. Seven palladium porphyrins have been prepared in yields of 25-57%. The direct route also can be used with Cu(OAc)(2).H(2)O to give the copper porphyrin albeit in low yield. In summary, this methodology readily affords palladium porphyrins directly from acyldipyrromethanes.     

Spectrophotometric determination of basicities of substituted acetylbiphenyls and biphenyl carboxylic acids

The basicities of several 2′-, 3′-, and 4′-substituted 4-acetylbiphenyls and biphenyl-4-carboxylic acids have been determined spectrophotometrically in sulphuric acid media at 30°C. The pK_BH ⁺ of 3′- and 4′-substituted compounds are correlated by the Hammett equation. The 4′-methoxy group deviates considerably in the Hammett plot. This is attributed to its conjugative interaction with the carbonyl or carboxyl group aided by protonation. Good correlation exists between pK_BH ⁺ and σ⁺. The basicities of 2′-substituted 4-acetylbiphenyls and biphenyl-4-carboxylic acids reaffirm the existence of π-electron steric effect of 2′substituents.     

Simple Markov‐chain algorithms for generating bipartite graphs and tournaments

We consider two problems: randomly generating labeled bipartite graphs with a given degree sequence and randomly generating labeled tournaments with a given score sequence. We analyze simple Markov chains for both problems. For the first problem, we cannot prove that our chain is rapidly mixing in general, but in the near‐regular case, i.e., when all the degrees are almost equal, we give a proof of rapid mixing. Our methods also apply to the corresponding problem for general (nonbipartite) regular graphs, which was studied earlier by several researchers. One significant difference in our approach is that our chain has one state for every graph (or bipartite graph) with the given degree sequence; in particular, there are no auxiliary states as in the chain used by Jerrum and Sinclair. For the problem of generating tournaments, we are able to prove that our Markov chain on tournaments is rapidly mixing, if the score sequence is near‐regular. The proof techniques we use for the two problems are similar. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14: 293–308, 1999     

Studies on the odd‐even effect of methylene spacers in poly(pyromellitimide‐ester)s

Three series of poly(pyromellitimide‐ester)s were synthesized from various N,N′‐bis(ω‐hydroxyalkyl)pyromellitimides (HAPMIs) by melt condensation with dicarboxylic acids, including terephthalic acid (TPA), 4,4′‐biphenyldicarboxylic acid (BPDA), and 4,4′‐azobenzenedicarboxylic acid (ABDA). Polymers were characterized by elemental analysis, solubility, inherent viscosity, spectra (IR, ¹H‐NMR, ¹³C‐NMR), and X‐ray diffraction (XRD). Thermal stability and phase transition behaviour were evaluated by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and hot‐stage optical polarized microscopy (HOPM). The d‐spacings, calculated from XRD data, showed an odd‐even effect with varying numbers of methylene spacers. Crystallinity of polymers decreased in the following order: azobenzene > biphenyl > phenyl polymers. Similarly, DSC‐obtained melting temperatures (T_m's) showed an odd‐even effect, and glass transition temperatures (T_g's) decreased with increasing numbers of methylene spacers. Thermal stability decreased as methylene chain length increased. Thermal stability of polymers occurred in the following order: phenyl > biphenyl > azobenzene polymers. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1755–1761, 1999     

Random walks and an O*(n5) volume algorithm for convex bodies

Given a high dimensional convex body K⊆ℝⁿ by a separation oracle, we can approximate its volume with relative error ε, using O*(n⁵) oracle calls. Our algorithm also brings the body into isotropic position. As all previous randomized volume algorithms, we use “rounding” followed by a multiphase Monte-Carlo (product estimator) technique. Both parts rely on sampling (generating random points in K), which is done by random walk. Our algorithm introduces three new ideas: the use of the isotropic position (or at least an approximation of it) for rounding; the separation of global obstructions (diameter) and local obstructions (boundary problems) for fast mixing; and a stepwise interlacing of rounding and sampling. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 1–50, 1997     

Polynomials hardly commuting with increasing bijections

Let I be an interval in the real line ℝ. Among the real polynomials that take I to I, we ask which ones do not commute with any increasing bijection of I other than identity. For this purely algebraic problem, the solution involves concepts in topological dynamics. Our main characterizations are in terms of full orbits of critical points and periodic points. Using these, we obtain simpler criterion, namely, that for no nontrivial subinterval K⊂I, the successive images {f ⁿ (K):n=0,1,2,…} form a pairwise disjoint collection. This problem is of interest in topological dynamics because it is about characterization of polynomials with unique self-topological-conjugacy.     

The median function on graphs with bounded profiles

The median of a profile π=(u₁,…,u_k) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of π. It is shown that for profiles π with diameter θ the median set can be computed within an isometric subgraph of G that contains a vertex x of π and the r-ball around x, where r>2θ−1−2θ/|π|. The median index of a graph and r-joins of graphs are introduced and it is shown that r-joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.     

Investigation on substituent effect in novel azo-naphthol dyes containing polymethacrylates for nonlinear optical studies

A novel structurally isomeric and free-radically polymerizable methacrylates bearing azo-naphthol group in the side chain spaced away from the backbone by a hexamethylene spacer and substituted in 4-position with electron-withdrawing and donating substituent were synthesized for NLO applications. These polymers were characterized by UV, IR, ¹H-NMR and ¹³C-NMR spectroscopy. The photoisomerization properties of all the polymers were studied. The glass transition temperature and thermal stability of the polymers were investigated by DSC and TGA, respectively. The third-order nonlinear optical properties of the polymer film were measured by the Z-scan technique using Ar-ion laser and exhibits negative optical nonlinearity. The results revealed that these polymers possess potential applications in nonlinear optics.     

Controlled crystalline structure and surface stability of cobalt nanocrystals

The synthesis of monodispersed 10 nm cobalt nanocrystals with controlled crystal morphology and investigation of the surface stability of these nanocrystals are described. Depending on the surfactants used, single crystalline or multiple grain nanocrystals can be reproducibly produced. The relative surface stability of these nanocrystals is analyzed using the temperature dependences of the dc magnetic susceptibility. The novel method, which allows sensitive monitoring of the surface stability, is based on the observation that, with particle oxidation, an anomalous peak appears at 8 K in zero-field-cooled magnetization measurements. It is found that the surfactant protective layer is more important for long-term stability at room temperature, while the high-temperature oxidation rate is controlled by the crystal morphology of the nanoparticles.