Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

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     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Synthesis and characterization of alt‐bipyridinylene‐phenylene copolymers containing ruthenium(II) complexes

Poly{bis(4,4′‐tert‐butyl‐2,2′‐bipyridine)–(2,2′‐bipyridine‐5,5′‐diyl‐[1,4‐phenylene])–ruthenium(II)bishexafluorophosphate} ( 3a ), poly{bis(4,4′‐tert‐butyl‐2,2′‐bipyridine)–(2,2′‐bipyridine‐4,4′‐diyl‐[1,4‐phenylene])–ruthenium(II)bishexafluorophosphate} ( 3b ), and poly{bis(2,2′‐bipyridine)–(2,2′‐bipyridine‐5,5′‐diyl‐[1,4‐phenylene])–ruthenium(II)bishexafluorophosphate} ( 3c ) were synthesized by the Suzuki coupling reaction. The alternating structure of the copolymers was confirmed by ¹H and ¹³C NMR and elemental analysis. The polymers showed, by ultraviolet–visible, the π–π* absorption of the polymer backbone (320–380 nm) and at a lower energy attributed to the d–π* metal‐to‐ligand charge‐transfer absorption (450 nm for linear 3a and 480 nm for angular 3b ). The polymers were characterized by a monomodal molecular weight distribution. The degree of polymerization was approximately 8 for polymer 3b and 28 for polymer 3d . © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2911–2919, 2004     

Design and synthesis of Ru(II-bipyridyl-containing conjugated polymers

A series of novel π-conjugated polymers containing ruthenium bipyridine complexes was synthesized by a cross-coupling reaction and characterized. These polymers exhibit absorption maxima around 330–350 nm (π-π*) and 460–500 nm metal-to-ligand charge transfer (MLCT), respectively. They are soluble in common organic solvents, and all polymers can be converted into transparent films. We investigated the influence of different donating and acceptor diethynylarenes of the ultraviolet-visible spectra. The oxidation potential, which was measured by cyclic- and square-wave voltametry, showed a typical Ru^2+/3+ exhibited at 1.25 V versus the saturated calomel electrode. The polymers were further characterized with photoluminescence measurements. When excited at 442 nm ( 11a ), the polymer exhibited an emission peak at 690 nm. This peak was attributed to the MLCT states. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 722–732, 2004     

Metallo‐supramolecular block copolymer micelles: Improved preparation and characterization

Micelles prepared from amphiphilic block copolymers in which a poly(styrene) segment is connected to a poly(ethylene oxide) block via a bis‐(2,2′:6′,2″‐terpyridine‐ruthenium) complex have been intensely studied. In most cases, the micelle populations were found to be strongly heterogeneous in size because of massive micelle/micelle aggregation. In the study reported in this article we tried to improve the homogeneity of the micelle population. The variant preparation procedure developed, which is described here, was used to prepare two “protomer”‐type micelles: PS₂₀‐[Ru]‐PEO₇₀ and PS₂₀‐[Ru]‐PEO₃₇₅. The dropwise addition of water to a solution of the compounds in dimethylformamide was replaced by the controlled addition of water by a syringe pump. The resulting micelles were characterized by sedimentation velocity and sedimentation equilibrium analyses in an analytical ultracentrifuge and by transmission electron microscopy of negatively stained samples. Sedimentation analysis showed virtually unimodal size distributions, in contrast to the findings on micelles prepared previously. PS₂₀‐[Ru]‐PEO₇₀ micelles were found to have an average molar mass of 318,000 g/mol (corresponding to 53 protomers per micelle, which is distinctly less than after micelle preparation by the standard method) and an average hydrodynamic diameter (d_h) of 18 nm. For PS₂₀‐[Ru]‐PEO₃₇₅ micelles, the corresponding values were M = 603,000 g/mol (31 protomers per micelle) and d_h = 34 nm. The latter particles were found to be identical to the “equilibrium” micelles prepared in pure water. Both micelle types had a very narrow molar mass distribution but a much broader distribution of s values and thus of hydrodynamic diameters. This indicates a conformational heterogeneity that is stable on the time scale of sedimentation velocity analysis. The findings from electron microscopy were in disagreement with those from the sedimentation analysis both in average micelle diameter and in the width of the distributions, apparently because of imperfections in the staining procedure. The preparation procedure described also may be useful in micelle formation from other types of protomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4458–4465, 2004     

Thermal behavior of metallodendrimers possessing bis(terpyridinyl)Ru(II) connectivity and different surface functionality

A series of metallodendrimers, assembled by means of bis(terpyridinyl)Ru^(II) connectivity on poly(propylene imine) dendrimer scaffolds, with homogeneous or heterogeneous surfaces, were prepared. Differential scanning calorimetry and thermogravimetric analysis were used to determine their thermal behavior, glass‐transition temperatures, and the decomposition kinetics and temperatures; no synergy effects for these properties were observed for the heterogeneously surfaced constructs in contrast to the corresponding homogeneously coated materials, which exhibited different values depending on their surface functionalities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1487–1495, 2004     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

Synthesis,dynamic light scattering,and luminescence properties of copolymers containing iridium(III) bisterpyridine in the side chain

Supramolecular block‐random copolymers containing [Ir(terpy)₂]³⁺ in the side chain were synthesized via postfunctionalization of a P(S‐b‐AC_terpy) block copolymer. Absorbance and emission spectra compared to a model compound show that the polymer backbone has a minor effect on the polymer absorbance but produces a larger shift for the phosphorescence signals to higher wavelength. Dynamic light scattering of the metal complex containing copolymer studied in various solvents showed monomodal aggregation with decreasing aggregate size as the solvent dielectric constant increased. The copolymer precursor P(S‐b‐AC_terpy) shows multimodal aggregation in different solvents with the major population consisting of single chains. This difference in behavior between the two polymers is attributed to the electrolytic nature of the complex and the amphiphilicity induced by the charged metal complex. Supramolecular copolymers like these will continue to have interesting self‐organizational properties and may find applications in multicomponent systems for photoinduced charge separation processes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1109–1121, 2007