New ligands for the Fe(III)‐mediated reverse atom transfer radical polymerization of methyl methacrylate

A series of (di)picolinic acids and their derivates are investigated as novel complexing tridentate or bidentate ligands in the iron‐mediated reverse atom transfer radical polymerization of methyl methacrylate in N,N‐dimethylformamide at 100 °C with 2,2′‐azobisisobutyrontrile as an initiator. The polymerization rates and polydispersity indices (1.32–1.8) of the resulting polymers are dependent on the structures of the ligands employed. Different iron complexes may be involved in iron‐mediated reverse atom transfer radical polymerization, depending on the type of acid used. ¹H NMR spectroscopy has been used to study the structure of the resulting polymers. Chain‐extension reactions have been performed to further confirm the living nature of this catalytic system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2912–2921, 2006     

Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder

In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the differential quadrature (DQ) method. The vorticity‐stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 104 to 106 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the flow and thermal patterns. Copyright © 2002 John Wiley & Sons, Ltd.     

Circular perfect graphs

For 1 ≤ d ≤ k, let K_k/d be the graph with vertices 0, 1, …, k ? 1, in which i ～j if d ≤ |i ? j| ≤ k ? d. The circular chromatic number χ_c(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to K_k/d. The circular clique number ω_c(G) of G is the maximum of those k/d for which K_k/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G, we have χ_c(H) = ω_c(H). In this paper, we prove that if G is circular perfect then for every vertex x of G, N_G[x] is a perfect graph. Conversely, we prove that if for every vertex x of G, N_G[x] is a perfect graph and G ? N[x] is a bipartite graph with no induced P₅ (the path with five vertices), then G is a circular perfect graph. In a companion paper, we apply the main result of this paper to prove an analog of Haj?os theorem for circular chromatic number for k/d ≥ 3. Namely, we shall design a few graph operations and prove that for any k/d ≥ 3, starting from the graph K_k/d, one can construct all graphs of circular chromatic number at least k/d by repeatedly applying these graph operations. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 186–209, 2005     

Roles of rhenium diimine complexes as metal‐ion probes and photosensitizers in functional polyurethanes

Polyurethanes incorporated with rhenium diimine complexes were synthesized. The polymers exhibited interesting morphologies and solution properties. Results from gel permeation chromatography suggested the formation of polymer aggregates in solutions. The polymers could act as probes for metal ions. The addition of metal ions to polymer solutions led to significant changes in the electronic absorption properties of the polymer solutions. This was attributed to the interactions between the polyether moieties and metal ions. The metal complexes could also act as efficient photosensitizers. After doping with charge‐transport viologens, the photoconductivity of the polymers was greatly enhanced. The experimental quantum efficiency was simulated with Onsager's theory. The thermalization distances and the primary yields were typically 12–14 Å and 10^?3, respectively. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1708–1715, 2003     

D. Liu and X. Zhu,Erratum to: “Fractional chromatic number and circular chromatic number for distance graphs with large clique size”. Journal of Graph Theory47(2) 2004, 129–146

The original article to which this Erratum refers was published in Journal of Graph Theory 47:129–146,2004 .     

Synthesis of a soluble pyrrole copolymer with phenetidine

A new series of copolymers was synthesized through the oxidative polymerization of pyrrole (PY) and o‐phenetidine (PHT) with inorganic oxidants in acidic media. The polymerization parameters including the mixing method of the oxidant with the comonomer, the comonomer ratio, the time, the temperature, the oxidant, the organic medium, and the acid were systematically optimized for the synthesis of copolymers with high yields, intrinsic viscosities, and solubility. The resultant copolymers were characterized by elemental analysis, infrared, ultraviolet–visible, solution high‐resolution ¹H NMR and solid‐state high‐resolution ¹³C NMR, circular dichroism spectroscopy, and cyclic voltammetry. The results showed that the PY observed content in the copolymers was much higher than the PY feed content. The regular variation of the polymerization yield, intrinsic viscosity, solubility, macromolecular structure, and electroactivity of the resulting polymers with the comonomer ratio, together with the complete solubility of a PY/PHT (10/90) polymer in highly polar solvents, indicated the formation of real random copolymers containing both PY and PHT units rather than a mixture of two homopolymers. However, the polymers containing more than 59 mol % PY were not homogeneous copolymers consisting of soluble and insoluble parts. A semiquantitative relationship between the polymerization yield or solubility of the copolymers and the polarity index of the organic solvents was examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2073–2092, 2004     

Distributions of major-to-ultratrace elements among the particulate and dissolved fractions in natural water as studied by ICP-AES and ICP-MS after sequential fractionation.

In order to elucidate the distributions of the elements among the particulate and dissolved fractions in pond water, major-to-ultratrace elements in different sizes of particles as well as in the filtrate passed through the 0.05 microm filter were determined by inductively coupled plasma atomic emission spectrometry (ICP-AES) and inductively coupled plasma mass spectrometry (ICP-MS). The different sizes of particle samples (ca. 100-300 microg each) were collected on the membrane filters with pore sizes of 10, 3.0, 1.2, 0.4, 0.2 and 0.05 microm, respectively, by sequential fractionation. As a result, about 40 elements in different sizes of particles could be determined by ICP-AES and ICP-MS, after acid digestion using HNO3/HF/HClO4. Then, the fractional distribution factors of major-to-ultratrace elements among the particulate and dissolved fractions were estimated from the analytical results. The total contents of Al, Fe, Ti, REEs (rare earth elements), Bi, Pb and Ag in the particulate fractions (larger than 0.05 microm) were more than 80-90%, while those of Ca, Sr, Cs, W, Ba, Mn and Co in the dissolved fraction, which corresponded to the filtrate passed through the 0.05 microm membrane filter, were more than 80%. It was further found that the fractional distributions of Cu and Zn in the dissolved fraction were ca. 50%. In addition, the enrichment factors (EFs) of the elements in the particulate fractions with particle sizes of 3.0-10 microm and 0.05-0.2 microm were estimated to elucidate their geochemical characteristics in natural water.     

A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

Computation of confined coflow jets with three turbulence models

A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-? model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-? model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reatachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite volume procedure. Numerical credibility of the solutions is ensured by using second-order-accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-? model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-? model in capturing the essential flow features, while the RNG-based K-? model does not seem to give improvements over the standard K-? model under the flow conditions considered.     

Effect of end groups on complexation kinetics between cyclodextrins and guest polymers

α‐Cyclodextrin (α‐CD) has been complexed with various poly(ethylene glycol) (PEG) derivatives in aqueous solution. It has been found that the end groups of PEG derivatives affect the complexation kinetics greatly, but have only a little influence on the thermodynamic behavior. By increasing the hydrophobicity of end groups, the complexation speeds up rapidly. On the other hand, the bulky end groups slow down the threading of polymeric guests into the cavity of CD. By changing the hydrophobicity and the size of end groups, the complexation rate can be adjusted in the range of several orders of magnitudes, which should be quite useful in the design of new supramolecular systems. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2050–2057, 2006