Polynorbornene with pentafluorophenyl imide side chain groups: Synthesis and sulfonation

The mixtures of exo‐endo‐monomers and isomerically pure endo‐monomers of N‐pentafluorophenyl‐norbornene‐5,6‐dicarboximide ( 2a ) and N‐phenyl‐norbornene‐5,6‐dicarboximide ( 2b ) were synthesized and polymerized via ring opening metathesis polymerization using bis(tricyclohexylphosphine) benzylidene ruthenium ( IV ) dichloride ( I ) and tricyclohexylphosphine [1,3‐bis(2,4,6‐trimethylphenyl)‐4,5‐dihydroimidazol‐2‐ylidene][benzylidene] ruthenium dichloride ( II ). Ring opening metathesis polymerization of mixtures of exo‐endo‐monomers ( 2a ) and ( 2b ) and pure endo‐ 2b gave the corresponding high molecular weights poly(N‐pentafluorophenyl‐norbornene‐5,6‐dicarboximide) ( 3a ) and poly(N‐phenyl‐norbornene‐5,6‐dicarboximide) ( 3b ). The isomerically pure endo‐ 2a did not polymerize by I in these conditions, since I is the least active catalyst and endo‐ 2a is the least active monomer because of the intramolecular complex formation between the Ru active center and the fluorine atom of ring‐opened endo‐ 2a on the one hand and steric hindrances caused by the pentafluorinated ring on the other. The quantitative hydrogenation of the polymer 3a , at room temperature and 115 bar, was achieved by a Wilkinson's catalyst. The new polynorbornene bearing highly fluorinated sulfonic acid groups (5) was obtained by the reaction of the hydrogenated poly(N‐pentafluorophenyl‐norbornene‐5,6‐dicarboximide) (4) with sodium 4‐hydroxybenzenesulfonate dihydrate. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2925–2933, 2010     

On recurrence and transience of self-interacting random walks

Let µ₁,...,µ _k be d-dimensional probabilitymeasures in ? ^d with mean 0. At each time we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.     

On the point spectrum of periodic Jacobi matrices with matrix entries: elementary approach

This work consists of two parts. The first one contains a characterization (localization) of the point spectrum of one sided, infinite and periodic Jacobi matrices with scalar entries. The second one deals with the same questions about one sided, infinite periodic Jacobi matrices with matrix entries. In particular, an example illustrating the difference between the above localization property in scalar and matrix entries cases is given.     

Two-photon excitation of substituted enediynes

Electronic spectroscopy of nine benzannelated enediynes and a related fulvene was studied under one-photon and two-photon excitation conditions. We utilize measured absorbance and emission spectra and time-resolved fluorescence decays of these molecules to calculate their radiative lifetimes and fluorescence quantum yields. The fluorescence quantum yields for the other compounds were referenced to the fluorescence quantum yield of compound 3 and used to determine relative two-photon absorption cross-sections. Further insight into experimental studies has been achieved using time-dependent density functional (TD-DFT) computations. The probability of two-photon absorption (TPA) increases noticeably for excitation to the higher excited states. The photophysical properties of benzannelated enediynes are sensitive to substitutions at both the core and the periphery of the enediyne chromophore. Considerably enhanced two-photon absorption is observed in an enediyne with donor substitution in the middle and acceptor substitution at the termini. Excited states with B symmetry are not active in TPA spectra. From a practical point of view, this study extends the range of wavelengths applicable for activation of the enediyne moiety from 350 to 600 nm and provides a rational basis for future studies in this field. Our theoretical computations confirmed that lowest energy TPA in benzannelated enediynes involves different orbitals than lowest energy one-photon absorbance and provided further support to the notion that introduction of donor and acceptor substituents at different ends of a molecule increases TPA.     

Ab initio investigation of potential energy curves of the 23 electronic states of IBr correlating to neutral (2)P atoms

Potential energy surfaces for all Born-Oppenheimer electronic states of IBr molecule correlating to the neutral (2)P ((2)P(3/2) and (2)P(1/2)) iodine and bromine are calculated for the first time. Electric dipole and polarizability curves (static and transition) are also determined. Calculations include scalar and spin-orbit relativistic effects within all-electron Douglas-Kroll two-component Hamiltonian. Electron correlation is treated with quasi-degenerate multi-reference second-order perturbation theory. Seven adiabatic electronic states (X (1)Sigma(+), A'(3)Pi(2), A (3)Pi(1), 1 (3)Pi(0-), B (3)Pi(0+), B'(3)Sigma, and 2 (3)Pi(0+)) exhibit significant covalent bonding, and can support vibrational states. Calculated spectroscopic parameters agree with experiment to better than 1000 cm(-1) (T(e)), 10 cm(-1) (omega(e)), and 0.05 Angstrom (r(e)). A new 1 (3)Pi(0-) state correlating to ground-state atoms is predicted at T(e) approximately 14 000 cm(-1), omega(e) approximately 80 cm(-1), and r(e) approximately 3.0 Angstrom. The second new state (2 (3)Pi(0+)) correlates to excited iodine atom, with T(e) approximately 20 000 cm(-1), omega(e) approximately 115 cm(-1), and r(e) approximately 3.3 Angstrom. Non-adiabatic coupling parameters are calculated for the four avoided crossings, which arise due to electronic spin-orbit interaction. Estimated parameters of the B (3)Pi(0+)/B'(3)Sigma crossing (R(c) approximately 3.32 Angstrom; V approximately 120 cm(-1)) agree with experimental values. The previously unsuspected 2 (3)Pi(0-)/1 (1)Sigma(-) crossing of two repulsive surfaces provides a new collisional deactivation channel for Br* atoms at relative velocities above 1000 m s(-1). Several repulsive states (including 1 (1)Pi(1) and 2 (3)Pi(1)) intersect the B/B' system near the avoided crossing point, and may affect dynamics of IBr in strong laser fields.     

Singular Spectrum Near a Singular Point of Friedrichs Model Operators of Absolute Type

In we consider a family of selfadjoint operators of the Friedrichs model: . Here is the operator of multiplication by the corresponding function of the independent variable , and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel satisfying some smoothness condition. These absolute type operators have one singular point of order . Conditions on the kernel are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity . The sharpness of these conditions is confirmed by counterexamples.     

Moment analysis for localization in random Schrödinger operators

We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonance-diffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. The difficulty is avoided here through the use of a weak-L ¹ estimate concerning the boundary-value distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theory.     

(3,8,9,14‐Tetraethyl‐2,4,13,15‐tetramethyltripyrrinato)(trifluoroacetato)­palladium(II)

In the crystal structure, the title compound {systematic name: [2,5‐bis­(4‐ethyl‐3,5‐dimethyl‐2H‐pyrrol‐2‐ylidene­meth­yl)‐1H‐pyrrolato](trifluoroacetato)palladium(II)}, [Pd(C₂F₃O₂)(C₂₇H₃₄N₃)], forms chiral mol­ecules with a helical distortion of the tripyrrinate ligand backbone and an essentially planar PdN₃O core, with Pd—N distances ranging from 1.977 (3) to 2.045 (3) Å and a Pd—O distance of 2.051 (2) Å. This distortion of the organic ligand is considered as the conformational answer to the steric inter­action of the terminal methyl groups of the tripyrrinate ligand with the donor O atom of the trifluoro­acetate group.     

Lyotropic liquid crystal guest–host material and anisotropic thin films for optical applications

We propose a new approach for the production of thin film optical functional materials. The method is based on molecular design whereby two different types of lyotropic liquid crystals (LC), lyotropic LC based on columnar supramolecules and water-soluble rod-like polymer molecules are mixed. The resulting lyotropic guest–host system allows production of optical retardation films with tunable optical anisotropy controlled by composition of the guest–host system. Coatable retarders can be used in modern liquid crystal displays and TVs for optical compensation and enhancement of the LCD's performance.     

Complete Nevanlinna-Pick Property of Dirichlet-Type Spaces

We prove that all Dirichlet-type spaces of functions analytic in the unit disk whose derivatives are square area integrable with superharmonic weights have complete Nevanlinna-Pick reproducing kernels. As a corollary, we obtain a commutant lifting theorem for cyclic analytic two-isometries.