Synthesis, electrochemical behavior and magnetic properties of polyradicals of the TTM series

Condensation reactions between (4-amino-2,6-dichlorophenyl)bis(2,4,6-trichlorophenyl)methyl radical and a new hexafunctionalized radical of the TTM series, tris(3,5-dichloroformil-2,4,6-trichlorophenyl)methyl radical or its corresponding diamagnetic precursor 6 yield macromolecular heptaradical 3 and hexaradical 4, respectively, with high magnetic purity. Both solid polyradicals show stability in nitrogen at temperatures up to 300 °C and in solution their electronic absorptivities do not decrease appreciably for weeks. EPR studies of both polyradicals in solution suggest that unpaired electrons are exchange coupled, and at low temperatures they show weak dipolar spin-spin couplings. Their electrochemical behavior was analyzed by cyclic voltammetry and differential pulse voltammetry. Heptaradical 3 is reduced in seven-electron two-stage processes, and oxidized in seven-electron one-stage process.     

Reunion Probabilities of N One-Dimensional Random Walkers with Mixed Boundary Conditions

In this work we extend the results of the reunion probability of \(N\) one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter \(c\) , which can be varied from \(c=0\) (independent walkers) to \(c\rightarrow \infty \) (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of \(N\) one-dimensional particles. We use Bethe ansatz and Gaudin’s conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory. Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than \(L\) takes the form \(F_N(L)=A_N\sum _{\varvec{k}\in \Omega _{\text {B}}} \mathrm{e}^{-\sum _{j=1}^Nk_j^2}\mathcal {V}_N(\varvec{k})\) , where \(A_N\) is a normalization constant, \(\mathcal {V}_N(\varvec{k})\) contains a deformed and weighted Vandermonde determinant, and \(\Omega _{\text {B}}\) is the solution set of quasi-momenta \(\varvec{k}\) obeying the Bethe equations for that particular boundary condition.     

Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables

Dynamical heterogeneities--strong fluctuations near the glass transition--are believed to be crucial to explain much of the glass transition phenomenology. One hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data to construct coarse grained observables and decompose their fluctuations into two transverse components associated with the postulated soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and time scales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with those of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.     

Wavefront sensing with an axicon

The use of a large apex-angle axicon for common-path interferometric wavefront sensing is proposed. The approach is a variant of point-diffraction interferometry bearing similarities to pyramidal wavefront sensing. A theoretical basis for wavefront sensing with an axicon is developed, and the outcomes of numerical simulations are compared to experimental results obtained with spherical and cylindrical ophthalmic trial lenses. It is confirmed that the axicon can be used for wavefront sensing, although its refraction may ultimately complicate and limit its operational range.     

Solution of boundary and eigenvalue problems for second‐order elliptic operators in the plane using pseudoanalytic formal powers

We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = div p grad + qin the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

An evaluation method for determination of non-polar pesticide residues in animal fat samples by using dispersive solid-phase extraction clean-up and GC-MS

A rapid and easy method has been proposed, optimized and evaluated for quantitative determination at trace level of a representative group of non-polar pesticides in fat samples. The method includes n-hexane-saturated acetonitrile extraction, fat precipitation by cooling pre clean-up followed by dispersive solid-phase extraction (d-SPE) based on QuEChERS procedure clean-up. Determination was performed by gas chromatography?Cmass spectrometry (GC-MS) in selected ion monitoring (SIM) mode. Efficiency of the d-SPE clean-up step was evaluated by comparison with fat oxidation treatment and gel permeation chromatography. Different combinations of d-SPE extraction reagents and sample amounts were tested in order to minimize matrix co-extractives and interferences. Best recoveries were obtained with 1200?mg of MgSO₄, 400?mg of end-capped C₁₈, 400?mg of PSA and 1?g of sample amount. SIM method, matrix effect, precision, and accuracy were evaluated with spiked pork fat samples for 38 representative pesticides. Results of this study showed that this technique is applicable in routine analysis for its application into monitoring programs. It simplifies time-consuming clean-up steps and allows a satisfactory long-term chromatographic performance.     

Synthesis and characterization of covalent diphenylalanine nanotube-folic acid conjugates

Traditionally, organosilica nanoparticles have been prepared inside micelles with an external silica shell for mechanical support. Here, we compare these hybrid core–shell particles with organosilica particles that are robust enough to be produced both inside micelles and alone in a sol–gel process. These particles form from octadecyltrimethoxy silane as silica source either in microemulsions, resulting in water-dispersible particles with a hydrophobic core, or precipitate from an aqueous mixture to form particles with both hydrophobic core and surface. We examine size and morphology of the particles by dynamic light scattering and transmission electron microscopy and show that the particles consist of Si–O–Si networks pervaded by alkyl chains using nuclear magnetic resonance, infrared spectroscopy, and thermogravimetric analysis.     

Bloch,Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions

In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of these spaces is well known, and thus their study in the framework of slice hyperholomorphic functions is relevant, especially in view of the fact that this class of functions has recently found several applications in operator theory and in Schur analysis. We also discuss the property of invariance of these function spaces with respect to Möbius maps by using a suitable notion of composition.     

Copper Versus Thioether‐Centered Oxidation: Mechanistic Insights into the Non‐Innocent Redox Behavior of Tripodal Benzimidazolylaminothioether Ligands

A series of Cu⁺ complexes with ligands that feature varying numbers of benzimidazole/thioether donors and methylene or ethylene linkers between the central nitrogen atom and the thioether sulfur atoms have been spectroscopically and electrochemically characterized. Cyclic voltammetry measurements indicated that the highest Cu²⁺/Cu⁺ redox potentials correspond to sulfur‐rich coordination environments, with values decreasing as the thioether donors are replaced by nitrogen‐donating benzimidazoles. Both Cu²⁺ and Cu⁺ complexes were studied by DFT. Their electronic properties were determined by analyzing their frontier orbitals, relative energies, and the contributions to the orbitals involved in redox processes, which revealed that the HOMOs of the more sulfur‐rich copper complexes, particularly those with methylene linkers (? N? CH₂? S? ), show significant aromatic thioether character. Thus, the theoretically predicted initial oxidation at the sulfur atom of the methylene‐bridged ligands agrees with the experimentally determined oxidation waves in the voltammograms of the NS₃‐ and N₂S₂‐type ligands as being ligand‐based, as opposed to the copper‐based processes of the ethylene‐bridged Cu⁺ complexes. The electrochemical and theoretical results are consistent with our previously reported mechanistic proposal for Cu²⁺‐promoted oxidative C? S bond cleavage, which in this work resulted in the isolation and complete characterization (including by X‐ray crystallography) of the decomposition products of two ligands employed, further supporting the novel reactivity pathway invoked. The combined results raise the possibility that the reactions of copper–thioether complexes in chemical and biochemical systems occur with redox participation of the sulfur atom.