Photoreactive Langmuir–Blodgett–Kuhn multilayer assemblies from functionalized liquid-crystalline side chain polymers,I. Homopolymers containing azobenzene chromophores

Stable monomolecular layers of a liquid-crystalline homopolymer bearing azobenzene chromophores in the mesogenic side groups could be prepared at the water–air interface by slow compression at room temperature. From the area per monomer unit of A₀≈0.25 nm² a structural model with tightly packed azobenzene groups oriented nearly parallel to the surface normal was deduced. After transfer to a solid support in a Y-type mode the obtained Langmuir–Blodgett–Kuhn (LBK) multilayer assemblies of varying thicknesses (from a double layer to a thick film of d = 238 nm, capable of guiding optical modes) were prepared and analyzed by X-ray reflection and optical evanescent wave techniques. A monolayer thickness of d₀ = 2.52 nm, as well as the anisotropic index of refraction of these layers, could thus be evaluated. Photo-isomerization by UV-irradiation (at λ = (360±30)nm) was examined by UV-VIS absorption spectroscopy. X-ray reflectivity data of samples illuminated for 30 min showed a complete loss of the layered structure of the LBK samples. As a result strongly light-scattering films were obtained. Surface plasmon microscopy was used to demonstrate the usefulness of this photo-induced order–disorder transition for optical information storage.     

Spectral line shapes modeling in turbulent plasmas

In this work we investigate the influence of low frequency turbulence on Doppler spectral line shapes in magnetized plasmas. Low frequency refers here to fluctuations whose typical time scale is much larger than those characterizing the atomic processes, such as radiative decay, collisions and charge exchange. This ordering is in particular relevant for drift wave turbulence, ubiquitous in edge plasmas of fusion devices. Turbulent fluctuations are found to affect line shapes through both the spatial and time averages introduced by the measurement process. The profile is expressed in terms of the fluid fields describing the plasma. Assuming the spectrometer acquisition time to be much larger than the turbulent time scale, an ordering generally fulfilled in experiments, allows to develop a statistical formalism. We proceed by successively investigating the effects of density, fluid velocity and temperature fluctuations on the Doppler profile of a spectral line emitted by a charge exchange population of neutrals. Line shapes, and especially line wings are found to be affected by ion temperature or fluid velocity fluctuations, and can in some cases exhibit a power-law behavior. These effects are shown to be measurable with existing techniques, and their interpretation in each particular case would rely on already existing tools. From a fundamental point of view, this study gives some insights in the appearance of non-Boltzmann statistics, such as Lévy statistics, when dealing with averaged experimental data.     

Cubic spline functions and initial value problems

A numerical process is presented which provides a cubic spline function approximation for the solution of initial value problems in ordinary differential equations. With interpolate cubic spline functions we can achieveO(h ⁴) convergence.     

A primal-dual interior-point algorithm for nonlinear least squares constrained problems

This paper extends prior work by the authors on solving nonlinear least squares unconstrained problems using a factorized quasi-Newton technique. With this aim we use a primal-dual interior-point algorithm for nonconvex nonlinear programming. The factorized quasi-Newton technique is now applied to the Hessian of the Lagrangian function for the transformed problem which is based on a logarithmic barrier formulation. We emphasize the importance of establishing and maintaining symmetric quasi-definiteness of the reduced KKT system. The algorithm then tries to choose a step size that reduces a merit function, and to select a penalty parameter that ensures descent directions along the iterative process. Computational results are included for a variety of least squares constrained problems and preliminary numerical testing indicates that the algorithm is robust and efficient in practice.     

An estimation of the number of tie molecules in semicrystalline polymers by means of neutron scattering

A new method for the evalution of neutron scattering data from semicrystalline polymers is proposed for small and intermiediate q [q = (4π/λ)sinθ/2]. It is based on the assumption that, in general, a molecule cryustallizes in various lamellae. Within one lamella the crystalline stems connected by loop or folds from intramolecular “clusters,” which are connected by tie molecules. Without further assumptions the method yields in a straightforward manner the following quantities: (i) the average number of clusters per molecule, from which the number of tie molecules can be estimated; (ii) the radius of gyration <R> of the centers of the stems belonging to one cluster; and (iii) the radius of gyration <R> of the cluster centers with respect to the center of the molecule the method was successfully tested using experimental data obtained from poly(ethylene oxide), polyethylene, and isotactic polypropylene.