Cationic polyelectrolytes. I. Soluble polymers prepared from reaction of chloromethylated polystyrene with tris(2-hydroxythyl)amine

The reaction of chloromethylated polystyrene with tris(2-hydroxyethyl)amine in N,N-dimethylformamide is described for the conditions to prepare soluble reaction products. The groups of the quaternary ammonium salt, which appear in the first stage of the reaction, transpose to the amino-ether groups. The reaction was followed by elementary analysis, IR and ¹H-NMR spectra, and viscosimetric measurements for nondialyzed and dialyzed samples. The presence of the tertiary amine groups on obtained polymers was also shown by titration. The polymers from the reaction of chloromethylated polystyrene with tris(2-hydroxyethyl)amine reacted easily with benzyl chloride.     

Hydrothermal Synthesis and Crystal Structure of AgVMO5 (M = Se,Te)

Single crystals of AgVSeO₅ and AgVTeO₅ were obtained under hydrothermal conditions at 190 °C by reacting stoichiometric amounts of AgNO₃, NaVO₃, TeO₂ and SeO₂, respectively. AgVSeO₅ crystallizes in Pbcm with a = 418.14(3) pm, b = 2007.70(6) pm, c = 521.17(2) pm, V = 437.52(2) × 10⁶ pm³ and Z = 4, as red needles. The structure consists of VO₅ square pyramids, trigonal SeO₃ pyramids and AgO₈ polyhedra, as primary building units. The VO₅ square pyramids are linked to chains running along the c‐axis, by sharing oxygen atoms in the basal plane in cis‐position. The remaining basal O atoms of the VO₅ moieties are shared with two oxygen atoms of the SeO₃ units. The resulting polyanionic strands of composition [VSeO₅]^? are interconnected by silver atoms to form a three dimensional network. AgVTeO₅ crystallizes as yellow needles in P2₁/c with a = 586.59(1) pm, b = 1137.98(2) pm, c = 680.78(1) pm, β = 102.733(1)°, V = 443.26(1) × 10⁶ pm³ and Z = 4. The structure consists of VO₄ tetrahedra, Ψ‐trigonal‐bipyramidal TeO₄ units and AgO₈ polyhedra as primary building units. The TeO₄ groups form dimers by edge sharing, which are linked through vertices to the VO₄ tetrahedra. The resulting one dimensional polyanion is extending along [101]. The structural motifs and charge distribution according to Se⁴⁺/V⁵⁺, and Te⁴⁺/V⁵⁺ respectively, seem to allow for a reshuffling of the charge distribution, thus inducing interesting physical phenomena, at elevated temperatures or pressures.     

Side chain thermotropic liquid crystalline polysulfone obtained from polysulfone udel by chemical modification

Polysulfone udel was chemically functionalized with chloromethylene functional groups via the chloromethylation reaction. A new azomethine dimesogen containing one phenolic hydroxyl functional group was recently synthesized and proved to exhibit a large nematic mesophase range in the liquid state. Further reaction of the dimesogen with the functionalized polysulfone using a transquaternization reaction led to new polysulfones bearing pendant rigid dimesogenic units--no spacer being involved in the chemical design of the polymer. The polymers were characterized by IR, ¹H NMR spectroscopy techniques, and their thermotropic liquid crystallinity behaviour was studied by optical polarizing microscopy (PLM) and DSC measurements. Enantiotropic nematic mesophases were observed under the PLM. A dependence of the melting temperature on the degree of substitution was noticed.     

Remarks on Q-integral complete multipartite graphs

A graph is Q-integral if the spectrum of its signless Laplacian matrix consists entirely of integers. In their study of Q-integral complete multipartite graphs, [Zhao et al., Q-integral complete r-partite graphs, Linear Algebra Appl. 438 (2013) 1067–1077] posed two questions on the existence of such graphs. We resolve these questions and present some further results characterizing particular classes of Q-integral complete multipartite graphs.     

Individual and joint influence of second- and third-order dispersion on the transmission quality in the presence of coherent interference

The shape of a resulting pulse (coherent interference superimposed to Gaussian pulse) along the linear optical fiber is determined by using attained analytical expressions. These analytical expressions enable the investigation of the influence of arbitrary dispersion order on pulse propagation. Individual and joint influence of second- and third-order dispersion on the transmission quality is examined in this paper. Pulse shape, eye diagram and bit error rate (BER) are used to represent in the best manner the above-mentioned influences.     

Research problems from the Aveiro Workshop on Graph Spectra

This is a collection of open problems presented at the Aveiro Workshop on Graph Spectra held at the University of Aveiro, Portugal from April 10-12, 2006.