Eigenvalues of propagation through liquid crystals

Abstract

Analytical expressions are given for the propagation constant through an homogeneous liquid crystal, following the 4 × 4 matrix formulation of Berreman. Also propagation through polarizers can be calculated analytically; it is a special case of a situation described by Teitler and Henvis.     

Chronocoulometric and rotating disc electrode determination of the charge propagation current through poly-4-vinylpyridine films containing hexachloroiridate anions

Charge propagation currents through polymer films coated on electrodes which contain redox active sites are usually determined by potential step methods. The aim of this study was to compare the charge propagation current obtained from chronocoulometric measurements with charge transport through a poly-4-vinylpyridine/IrCl₆²⁻ film during the mediated oxidation of Fe²⁺ at a rotating disc electrode. The two methods gave identical results for the model system chosen.     

Axial propagation in a magnetic-dielectric cholesteric medium

The existence of an exact solution for axial propagation in a dielectric cholesteric medium has been often remarked upon. Here, we obtain the exact solution for axial propagation in a magnetic-dielectric cholesteric medium, using the 4 × 4 matrix method of optics. Our solution procedure also enables us to identify the specific features that make axial propagation in cholesteric media remarkable in having an analytical solution.     

Influence of Phase Miscibility on the Crack Propagation Kinetics of Nanostructured Binary S‐(S/B)‐S Triblock Copolymer Blends

Summary: The crack propagation kinetics of binary styrene‐(styrene/butadiene)‐styrene triblock copolymer blends based on one with symmetrical (LN4) and another with asymmetrical (LN3) molecular architecture is discussed with respect to post‐yield crack‐tip blunting and stable crack propagation behavior while highlighting the dynamic mechanical properties of the blends. The crack‐tip opening displacement (CTOD) rate is revealed to be sensitive to phase behavior, which is in agreement with a transition in phase miscibility in a critical composition range of 40–60 wt.‐% of LN3. Analyses of R‐curves from CTOD‐values reveal that kinetics of crack propagation is controlled by phase behavior, whereas the resistance to stable crack initiation is largely dependent on the composition. Our investigation offers new possibilities to tailor and optimize the crack resistance (crack propagation stability) of block copolymer blends through the control of phase miscibility and hence, fundamentally, adds a new dimension to the development of novel materials based on toughened nanostructured polymers.

Crack resistance curves for LN3 blends having different compositions.     

Cationic polymerization of styrene with electrochemically generated perchloric acid—I

The electroinitiated polymerization of styrene in LiClO₄-propylene carbonate solutions leads to polystyrene at the anode through the formation of HClO₄. The influences on this polymerization of factors such as temperature, current, monomer and electrolyte concentrations, and dielectric constant of the medium, have been examined. The trends of the yields as functions of these factors show some anomalies. In particular, there is a maximum in the yield vs current curve. The molecular weights are relatively low, due to transfer processes, both spontaneous and involving monomer. The propagation proceeds by a cationic mechanism, in which free ions are in equilibrium with ion pairs.     

Synthesis of aromatic polyethers by Scholl reaction. VII. Oxidative polymerization of 2,2-bis[4-(1-naphthoxy)phenyl]propane and 2,2-bis [4-(1-naphthyl)phenyl]propane

The synthesis and the mechanism of oxidative polymerization of 2,2-bis[4-(1-naphthoxy)phenyl]propane ( 4 ) and 2,2-bis[4-(1-naphthyl)phenyl]propane ( 9 ) are presented. Both monomers polymerize by two different propagation steps. The first one represents a cation-radical dimerization of the naphthyl groups to dinaphthyl structure. H⁺[FeCl₄]^? generated from the first propagation step initiates a transalkylation reaction which provides structural units containing isopropylidenic groups inserted between phenyl and naphthyl, and between two naphthyl groups, respectively. Since the phenyl groups resulted from the second propagation reaction are unreactive in both the oxidative coupling and the transalkylation steps this polymerization reaction leads to polymers with low molecular weights containing phenyl chain ends.     

Pulse radiolysis study of initiation and propagation in radiation induced polymerisation of cyclohexyl methacrylate

Initiation and individual propagation rate constants for the first few steps are determined for e^-_aq, OH radical and H atom reactions with cyclohexyl methacrylate as the monomer using the technique of pulse radiolysis. Though the rate constants for initiation are higher, the propagation rate constants for the transient species formed by reaction of OH radical and H atom are lower compared to that by reaction of e^-_aq with the monomer. It is also observed that in the case of e^-_aq reaction the first propagation step is about an order of magnitude faster than the second propagation step and propagation through radical-anionic form is much faster than its radical counterpart.     

Photographic measurements of propagation speeds of the conducting zone in polyaniline films during electrochemical switching

In order to observe the propagation of a conducting zone of a polyaniline film in response to anodic switching, propagation perpendicular to the film surface was simulated by propagation along the film by mounting the film on an insulated plate. A polyaniline film electrochemically deposited on an indium tin oxide (ITO) electrode was reinforced by casting polymethylmethacrylate solution on the film. It was peeled off the ITO, chemically reduced and then potentiostatically oxidized at one end in 1 mol dm⁻³ H₂SO₄ solution. Dynamic growth of the conducting zone was observed through an optical microscope. A well-defined boundary between the conducting zone and the insulating zone was seen. The contrast of the boundary did not vary with the electrolysis time, the growth length or the applied potential. The growth rate decreased slightly with the electrolysis time as a result of IR drop across the film. A differential equation for growth rate involving the effect of the IR drop was presented and solved to give more accurate values of the rate. The logarithmic growth ratio exhibited a linear relation with the applied potential, indicating a charge-transfer rate of the Tafel type. The anodic transfer coefficient was 0.2 and the rate constant was 5 × 10⁻⁵ m s⁻¹. The propagation on a molecular scale was discussed on the basis of the experimental results.     

Polymérisation anionique des diènes. III. Etude thermodynamique de la propagation du butadiène et de i'isoprène par les organo-alcalins

The present work is concerned with the influence of the polymerization temperature on the propagation mechanisms of polyisoprenyl- and polybutadienyl-alkali metals. The thermodynamic parameters of the contact ion pairs and free ions propagations have been calculated. With Li⁺ in dioxane solvent, the vinyl propagation is stereospecific (for isoprene, the propagation is mainly 4–3). In comparison with benzene, the vinyl propagation of the polydienyl-Li contact ions pairs should be due to complexation of Li⁺ by dioxane, an electron donor having a weak dielectric constant. In general, the stereospecificity of the propagation of contact ion pairs decreases with increasing counterion size; little difference has been observed with K⁺ and Cs⁺ ion pairs in dioxane and benzene media. For isoprene, the methyl substituant should have chiefly a steric effect in the propagation of free ions, whereas it should confer a polar character to the isoprene molecule in the presence of ions pairs.     

Measurement of rapid crack propagation in pressure pipes: A static S4 approach

A method for creating rapid crack propagation in pressurized pipes under slow static loading using modified S4 apparatus is described. In the development of the method a complexity involved with dynamic loading in the S4 test (ISO 13477) is eliminated by the use of a displacement controlled static loading machine. The experimental system consisted of an universal testing machine, a low compliance wedge loading device, notch tip quenching apparatus and a pipe specimen where a through thickness hole is drilled to accommodate the wedge loading device. The pipe specimen is made in such a way that a section containing a hole is free from the internal pressure, while the rest of the specimen is made to carry the internal pressure which would eventually drive the unstable crack along the pipe axis. The idea of such rapid crack initiation under static loading was derived from the concept of time-temperature equivalence, where impact loading may in part be simulated by lowering the temperature at the site of rapid crack initiation. The details of the method for rapid crack propagation under static loading are described and the correlation of the results to rapid crack propagation obtained by ISO 13477 is illustrated. The two methods were shown to compare quite well in terms of critical pressure determination and the details regarding normalized rapid crack length versus the internal pressure curve as well as the crack propagation pattern.     

Direct measurements of the addition and recombination of acrylate radicals: Access to propagation and termination rate constants?

Acrylate radicals produced by the addition of an aminoalkyl radical to five acrylate monomers were directly observed by transient absorption spectroscopy, which allowed us to easily follow their chemical reactivity. It was possible (1) to characterize their absorption in the visible part of the spectrum, (2) to calculate their absorption properties, (3) to determine the energy barriers of the addition through quantum mechanical calculations, (4) to monitor the kinetics of the subsequent addition to another monomer unit, and (5) to follow the recombination of two acrylate radicals. These two latter points could mimic the propagation and termination reactions of polymerization‐propagating acrylate radicals. Methacrylate and acrylonitrile radicals were also studied. The obtained results were in good agreement with the propagation rate constants determined by the well‐established pulsed laser polymerization techniques. Our method could likely provide rapid access to both the propagation and termination rate constants in suitable systems and appears to be powerful and promising for studying and comparing the reactivities of different acrylate monomer structures. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3577–3587, 2006     

Polymerization of butadiene by polybutadienyllithium in the presence of tetrahydrofuran

Polymerization of butadiene by polybutadienyllithium (PBLi) has been studied in THF for concentrations of PBLi between 10^?4 and 10^?2 mol/I in the range 20–70°, and also in a non-polar medium using THF as an added electron donor at various THF/PBLi ratios. The kinetic order with respect to PBLi in THF was 0.5 and the activation energies of the overall process and the propagation on free carbanions were 7.5 and 6.7 kcal/mol respectively. Rate constants for propagation on the free carbanions were calculated at three temperatures and rate constants for propagation on contact ion pairs were determined at two THF/PBLi ratios. Data on the kinetics of polymerization and the microstructure of the polymers suggest that contact ion pairs and free carbanions participate in propagation reactions.     

Polymerization of N,N′-methylenebisacrylamide initiated by two new redox systems involving acidic permanganate

Two new redox systems, viz. KMnO₄ with ethyleneglycol and KMnO₄ with thioglycollic acid, have been used as initiators for the polymerization of the divinyl monomer, N,N′-methylenebisacrylamide. The initiating radical is formed when a monomer-Mn³⁺ complex interacts with the redox complex. An intramolecular cyclization prior to propagation is involved in the mechanism suggested to explain the kinetics. The higher rate of polymerization for this monomer, when compared with acrylamide and methacrylamide, gives added evidence for this new type of propagation.     

Control of Ice Propagation by Using Polyelectrolyte Multilayer Coatings

Ice propagation is of great importance to the accumulation of ice/frost on solid surfaces. However, no investigation has been reported on the tuning of ice propagation through a simple coating process. Herein, we study the ice propagation behavior on polyelectrolyte multilayer (PEM) surfaces coated with the layer‐by‐layer (LBL) deposition approach. We discover that ice propagation is strongly dependent on the amount of water in the outermost layer of PEMs, that is, the ice propagation rate increases with the amount of water in the outermost layer. The ice propagation rate can be tuned by up to three orders of magnitude by changing the polyelectrolyte pairs, counterions of the outermost polymer layer, or the salt concentration during the preparation of PEMs. Because the simple, versatile, and inexpensive LBL deposition approach is generally applicable to almost all available surfaces, the PEM coatings can tune ice propagation on a wide range of substrates.     

A WAVE-OPTICS EFFECT WHICH ENHANCES LIGHT ABSORPTION BY CHLOROPHYLL IN VIVO

Abstract Light is widely thought to move through cells and tissues as rays. Actually light is inherently wave-like; ray motion is a special simple case of wave motion. To determine how well rays simulate light propagation and gradients within cells, absorption and scattering by particles were calculated with two sets of equations: one based on wave propagation within the particle and the other based on ray propagation. The ray model is found to substantially describe absorption at all particle size levels; however, it does not correctly describe scattering. Furthermore, for biological cells and structures larger than λ, the wave equations predict absorption cross sections which are 8–10% larger than expected on the basis of ray optics and extraction data: i.e. absorption is increased by a peculiar wave optics effect. This effect must enhance the efficiency with which the plants collect light energy for photosynthesis. The effect should be accounted for in corrections for the sieve effect.     

Interaction of laser radiation with doppler-broadened media in coherent population trapping regime: law of light propagation

The influence of thermal motion of atoms on laser light propagation through a coherent optically dense medium is investigated theoretically. If the laser light intensity does not exceed a certain threshold value (intensity of coherent population trapping switching on multiplied by square of ratio of Doppler broadening to natural linewidth), the propagation law is strongly influenced by atomic motion: the laser intensity decreases neither exponentially, nor linearily, but as second-order polynomial of the optical depth. Above this threshold the propagation law is linear.     

ESTIMATION OF THE OPTICAL PARAMETERS AND LIGHT GRADIENTS IN LEAVES: MULTI-FLUX versus TWO-FLUX TREATMENT

Abstract— Parameters of light propagation in plant leaves—absorption and scattering coefficients, asymmetry of scattering—have been estimated on the basis of measured transmission and remission as well as internal fluxes. This estimation has been carried through by solving the inverse problem of the 4-flux radiative transfer—a theory considering forward and backward diffuse as well as directed components of the overall radiation in a multiply scattering sample. Using the gained parameters, light flux gradients in a two-layered model leaf have been calculated at different wavelengths. Monte Carlo simulation of absorption spectra performed with the parameters obtained with this treatment is in a good agreement with experimental spectra, thus substantiating the theory. Parallel calculations with the two-flux (Kubelka-Munk) theory provide an estimation of the accuracy and applicability of this more simple treatment. Calculations have been performed for two different plants.     

Spherical symmetric diffusion problem

We introduce a general and versatile MS Windows application for solving the spherically symmetric diffusion problem, involving up to two coupled spherically symmetric Smoluchowski equations. The application is based on a modular, configurable, user-friendly graphical interface, in which input parameters are introduced through a graphical representation of the system of partial differential equations and output attributes can be obtained graphically during propagation. The numerical algorithm consists of finite differencing in space and Chebyshev propagation in time; it includes an implementation of virtual gridding, which enhances the accuracy of calculating boundary conditions and steep potentials. The program has b een checked against a wide collection of analytical solutions and applied to an experimentally open problem in excited-state proton-transfer to solvent. © 1996 by John Wiley & Sons, Inc.     

THE ROLE OF SUPEROXIDE AND SINGLET OXYGEN IN LIPID PEROXIDATION

Abstract— An investigation into the mechanism of lipid peroxidation catalyzed by xanthine oxidase showed a dependence upon superoxide, singlet oxygen and adenosine 5'-diphosphate chelated iron (ADP-Fe³⁺). In the absence of ADP-Fe³⁺ or in the presence of superoxide dismutase there is complete inhibition of enzymatic peroxidation. Initiation of peroxidation likely occurs through an ADP-perferryl ion complex formed by ADP-Fe³⁺ and superoxide. Use of the singlet oxygen trapping agent 2,5-diphenylfuran showed that singlet oxygen does not participate in the initiation of peroxidation but rather in the propagation of peroxidation. The mechanisms of NADPH-cytochrome P450 reductase-catalyzed and ADP-Fe²⁺ catalyzed lipid peroxidation parallel that of xanthine oxidase in that initiation occurs through a superoxide dismutase-sensitive reaction and that singlet oxygen is present during propagation of lipid peroxidation.     

Initiation and propagation in γ-radiation-induced polymerization of ethylene

The initiation and propagation reaction in γ-ray-induced polymerization of ethylene was studied by the two-stage irradiation method, i.e., a first stage in which initiation and propagation occur at a high dose rate, and a second stage where only the growth of polymer radical occurs. The rate of initiation is calculated from the amount of polymerized monomer and the degree of polymerization as the rate of increase in the number of polymer chains. The initiation rate is shown to be proportional to the ethylene density in the reactor and dose rate. G_R of radical formation is found to be about 1.6 at 30°C. at a dose rate of 2.5 × 10⁴ rad/hr. and is almost independent of ethylene density but decreases slightly with increasing irradiation dose rate. The lifetime of the growing polymer chain radical is shown to be long at normal temperature. The absolute propagation rate is proportional to the square of ethylene fugacity and depends on dose rate to some extent. For chain growth, irradiation of low dose rate is necessary. The apparent activation energy for the propagation reaction is ?9 kcal./mole.