Rhodium-Catalyzed Intermolecular [4+2] Cycloaddition of Unactivated Substrates

No electron-withdrawing or electron-releasing substituents are necessary for the substrates in the rhodium-catalyzed [4+2] cycloaddition reaction between a vinylallene and an ordinary alkyne under mild conditions [Eq. (1)]. The use of the strongly electron-accepting P[OCH(CF₃)₂]₃ ligand affords the optimal rhodium catalyst. cod = 1,5-cyclooctadiene.     

Path integral Monte Carlo method for ab initio calculation

The Feynman path integral method is applied to the many-electron problem. We first give new closure relations in terms of ordinary complex and real numbers, which could be derived from an arbitrary complete set of state vectors. Then, in the path integral form, the partition function of the system and the ensemble average of energy are explicitly expressed in terms of these closure relations. It is impossible to evaluate the path integral by direct numerical integrations because of its huge amount of integration variables. Therefore, we develop an algorithm by the Monte Carlo method with constraints corresponding to the normalization condition of states to calculate the required integral. Finally, the ensemble average of energy for the hydrogen molecule is explicitly evaluated by the quantum Monte Carlo method and results are compared with the result obtained by the ordinary full configuration interaction (CI) method. © 1996 John Wiley & Sons, Inc.     

Nematic and smectic liquid single crystal elastomers: Influence of external stress parallel and perpendicular to the director

The influence of uniaxial mechanical stress applied parallel or perpendicular to the director axis (optical axis) of nematic and smectic-A elastomers having a permanent macroscopically ordered monodomain structure is investigated. Due to the different phase structures applying an external mechanical stress leads to completely different responses with respect to the young moduli and reorientation processes of the director. Nematic elastomers exhibit a weak anisotropy of the moduli parallel (μ₁₁ and perpendicular (μ) to the optical axis with μ₁₁ / μ = 1.5. The moduli are mainly determined by the rubber elasticity of the poly(siloxane) network. Applying the mechanical stress perpendicular to the initial director axis causes a rotation of the director axis that is connected with a periodic pattern formation and a ‘soft elastic’ response. For smectic-A elastomers μ₁₁/μ is in the order of 10². While μ reflects a rubber elastic response similar to that of the nematic system, μ₁₁ indicates an enthalpy-elastic behaviour of the one-dimensional long range order of the smectic layers. In this direction reorientation of the phase structure with a deformation of the smectic layers occurs above a threshold elongation. In contrast to the nematic networks, a deformation perpendicular to the optical axis causes no director reorientation, displaying the liquid-like properties within the smectic layers.     

Synthesis of silsesquioxanes having photochromic diarylethene pendant groups

Silsesquioxanes having 1-(2-methylbenzo[b]thien-3-yl)-2-[5-(4-butylphenyl)-2,4-dimethylthien-3-yl]perfluorocyclopentenes as the pendant groups were synthesized. Photochemical conversion from the open-ring to the closed-ring form of diarylethenes chemically bonded to polymers was by 15–25% lower than the conversion of the chromophores dispersed in the same matrix. No appreciable difference in the photoconversion of the fixed chromophores was observed below and above the glass transition temperature (T_g) of the polymer films.     

Synthesis and properties of polyimides bearing acid groups on long pendant aliphatic chains

A series of novel polyimide electrolytes having long pendant sulfo‐ or phosphoalkoxy groups were synthesized for fuel‐cell applications. Sulfodecyloxy‐, phosphodecyloxy‐, and sulfophenoxydodecyloxy‐substituted benzidine monomers were synthesized from dihydroxybenzidine. These monomers were copolymerized with naphthalene tetracarboxylic dianhydride and fluorenylidene dianiline to give the corresponding polyimides. A flexible, ductile, and self‐standing membrane was obtained via casting from the polyimide solution. Because the acid groups were on long pendant side chains and away from the main chains, the polyimide membrane showed improved oxidative and hydrolytic stability in comparison with the polyimides with sulfonic acid groups on the main chains or on the short side chains. High thermal stability (no glass‐transition temperature and a decomposition temperature > 200 °C) was also obtained. The polyimide membrane displayed high proton conductivity of 10^?1 S cm^?1 at 120 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3995–4005, 2006     

Effects of d.c. potential patterns on the performance of ion‐exchange polymer based molecular actuators

The dynamic performance (i.e. displacement, current, velocity, and force) of ion‐exchange polymer based actuators (the Nafion?/platinum electrodes) have been examined by developing instrumentation. The CCD imaging technique was examined to evaluate the displacement under the various d.c. potential patterns. Two different d.c. potential patterns with or without a rest were applied to the electrodes at 0.1 Hz. It was better to take a rest at 0 V for the polarization back and forth between +2 and ?2 V to give lower current consumption and longer displacement. The actuator produced the force of ca. 0.95 g at 3.25 V in air. The result also demonstrated that higher overpotential has to be avoided to maintain the maximum force. The generative force is in inverse proportion to the length of the actuators. The dimension of the film strongly governs the force production and its performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Laser-active colour centres with functional periodic structures in LiF fabricated by two interfering femtosecond laser pulses

We report a new technique to fabricate both laser-active F₂ and F₃⁺ colour centres in lithium fluoride and permanent periodic gratings with fringe spacings as fine as sub-micron size simultaneously by two interfering infrared femtosecond (fs) laser pulses. In particular, the optical properties of such colour centres produced by a single fs laser pulse are compared with those created by damage from radiation such as X-rays. Moreover, the present technique is applied to the first production of three-dimensional active channel waveguide and a pulsed distributed-feedback (DFB) laser at around 700 nm in LiF containing F₂ colour centres with fine-pitched micro-grating structures.     

Arithmetically independent integers and values of rational functions

We prove the existence of arithmetically independent integers and their properties and apply them to values of rational functions on algebraic varieties.