Polyaniline/montmorillonite nanocomposite thin layers deposited on different substrates

Preparation method of polyaniline/montmorillonite (PANI/MMT) nanocomposite in the form of thin layer deposited on various substrates is optimized in this work to obtain high electrical conductivity. Simple method (i.e. polymerization of anilinium sulfate in the presence of MMT) has been used for the preparation and following four conditions were varied: preparation temperature (T = 10 or 20 °C), preparation time (t = 4 or 6 h), size fraction of MMT (p < 1 or 5 µm), and type of substrate (microscope glass slides, silica glass slides, polyester foils). Therefore, 24 samples were prepared, characterized and their electrical conductivity was compared. Raman spectroscopy and scanning electron microscopy were used for the characterization of the structure of samples. Thickness of layers was measured using atomic force microscopy. Based on the comparison of samples and with respect to the aim of obtaining high electrical conductivity, it was found that the most suitable substrate is polyester foil and preparation conditions are T = 20 °C, t = 6 h, p < 5 µm. To obtain highly conductive layers on glass substrates (although less conductive than layers on foil), preparation time have to be shortened to 4 h.     

Raman study of PANI thin film during long time period in dependence on storage conditions

Conducting polymer polyaniline which is nowadays in forefront of the interest was in our study prepared in a form of thin films from anilinium sulfate by its chemical oxidation using ammonium peroxydisulfate. During the oxidation process, the polyaniline was deposited on glass slides and immersed into reaction mixture. Two sets of polyaniline thin films were prepared with different oxidation times (10, 20, 30, and 40 min). The first set was kept dry in desiccator and the second one was freely exposed to air moisture. Raman spectroscopy, nondestructive technique which is very sensitive to changes in structure of polymers, was used for the characterization of the protonation state of prepared polyaniline thin films. It was found that storage conditions affect the protonation state which in case of samples kept in desiccator is maintained without significant changes for longer time. Raman spectroscopy also revealed the dependence of protonation state on the oxidation time and 10 min proved as not sufficient for the creation of the protonation form of polyaniline.     

The isolation of new norcycloartene triterpenoids from the tropical marine alga Tydemaniaexpeditionitis (chlorophyta)

Three new Δ³-norcycloartene triterpenoids, with differing side chain functionalities, have been isolated from the tropical green alga $\text{Tydemania}$$\text{expeditionitis}$ collected in Guam. The structures of these new compounds were secured by x-ray crystallography and by chemical interconversion.     

The synthesis and structure of bis(acetonitrile)nitrosyl tris(3,5-dimethylpyrazolyl)borato molybdenum hexafluorophosphate

Summary Treatment of [Mo{HB(3,5-Me₂C₃HN₂)₃}(NO)I₂] with one or two moles of AgPF₆ in acetonitrile afforded the paramagnetic (one unpaired electron) complex [Mo{HB(3,5-Me₂C₃NH₂)₃}(NO)(NCMe)₂][PF₆]. The structure of this complex was determined crystallographically, and the six-coordinate geometry of the complex cation confirmed.     

Geometry optimization in Cartesian coordinates: Constrained optimization

An efficient algorithm for constrained geometry optimization in Cartesian coordinates is presented. It incorporates mode-following techniques within both the classical method of Lagrange multipliers and the penalty function method. Both constrained minima and transition states can be located and, unlike the standard Z-matrix using internal coordinates, the desired constraints do not have to be satisfied in the initial structure. The algorithm is as efficient as a Z-matrix optimization while presenting several additional advantages.     

On the trace problem for Lizorkin–Triebel spaces with mixed norms

The subject is traces of Sobolev spaces with mixed Lebesgue norms on Euclidean space. Specifically, restrictions to the hyperplanes given by x₁ = 0 and x_n = 0 are applied to functions belonging to quasi‐homogeneous, mixed norm Lizorkin–Triebel spaces ; Sobolev spaces are obtained from these as special cases. Spaces admitting traces in the distribution sense are characterised up to the borderline cases; these are also covered in case x₁ = 0. For x₁ the trace spaces are proved to be mixed‐norm Lizorkin–Triebel spaces with a specific sum exponent; for x_n they are similarly defined Besov spaces. The treatment includes continuous right‐inverses and higher order traces. The results rely on a sequence version of Nikol'skij's inequality, Marschall's inequality for pseudodifferential operators (and Fourier multiplier assertions), as well as dyadic ball criteria. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coincidences of projections and linear n-valued maps of tori

We prove that the Nielsen fixed point number N(φ) of an n-valued map φ:X?X of a compact connected triangulated orientable q-manifold without boundary is equal to the Nielsen coincidence number of the projections of the graph of φ, a subset of X×X, to the two factors. For certain q×q integer matrices A, there exist “linear” n-valued maps Φn,A,σ:Tq?Tq of q-tori that generalize the single-valued maps fA:Tq→Tq induced by the linear transformations TA:Rq→Rq defined by TA(v)=Av. By calculating the Nielsen coincidence number of the projections of its graph, we calculate N(Φn,A,σ) for a large class of linear n-valued maps.     

Computation of Time-Periodic Solutions of the Benjamin–Ono Equation

We present a spectrally accurate numerical method for finding nontrivial time-periodic solutions of nonlinear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which in the case of the Benjamin–Ono equation, are the mean, a spatial phase, a temporal phase, and the real part of one of the Fourier modes at t=0.     

Accuracy of staircase approximations in finite-difference methods for wave propagation

While a number of increasingly sophisticated numerical methods have been developed for time-dependent problems in electromagnetics, the Yee scheme is still widely used in the applied fields, mainly due to its simplicity and computational efficiency. A fundamental drawback of the method is the use of staircase boundary approximations, giving inconsistent results. Usually experience of numerical experiments provides guidance of the impact of these errors on the final simulation result. In this paper, we derive exact discrete solutions to the Yee scheme close to the staircase approximated boundary, enabling a detailed theoretical study of the amplitude, phase and frequency errors created. Furthermore, we show how evanescent waves of amplitude \(O(1)\) occur along the boundary. These characterize the inconsistencies observed in electromagnetic simulations and the locality of the waves explain why, in practice, the Yee scheme works as well as it does. The analysis is supported by detailed proofs and numerical examples.