Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006     

Catalysis in aprotic solvents. Effect of the polarity of the catalyst.

The catalytic constants for the $\text{n}$-butylaminolysis of sultones in aprotic-apolar solvents are linearly correlated with a combination of the hydrogen-bonding parameter and the polarity parameter of the catalyst.     

Preliminary results on the use of Tenax for the extraction of pesticides and polynuclear aromatic hydrocarbons from surface and drinking waters for analytical purposes.

The use of Tenax GC for the extraction of organic micro-pollutants such as pesticides and polynuclear aromatic hydrocarbons from water has been studied. In the absence of other contaminants and under conditions standardized at the time as optimal, the recovery of such substances is, on average, over 90%, both for the organochlorine and organophosphorus pesticides and for polynuclear aromatic hydrocarbons. Research into the effectiveness of extraction with Tenax from natural waters and water artificially contaminated with surfactants, fats and oils etc., in the laboratory is now being carried out.     

Solid-solid phase transitions: interface controlled reactivity and formation of intermediate structures

Finding new pathways to novel materials is an open challenge in modern solid-state chemistry. Among the reasons that still prevent a rational planning of synthetic routes is the lack of an atomistic understanding at the moment of phase formation. Metastable phases are, in this respect, powerful points of access to new materials. For the synthetic efforts to fully take advantage of such peculiar intermediates, a precise atomistic understanding of critical processes in the solid state in its many facets, that is, nucleation patterns, formation and propagation of interfaces, intermediate structures, and phase growth, is mandatory. Recently we have started a systematic theoretical study of phase transitions, especially of processes with first-order thermodynamics, to reach a firm understanding of the atomistic mechanisms governing polymorphism in the solid state. A clear picture is emerging of the interplay between nucleation patterns, the evolution of domain interfaces and final material morphology. Therein intermediate metastable structural motifs with distinct atomic patterns are identified, which become exciting targets for chemical synthesis. Accordingly, a new way of implementing simulation strategies as a powerful support to the chemical intuition is emerging. Simulations of real materials under conditions corresponding to the experiments are shedding light onto yet elusive aspects of solid-solid transformations. Particularly, sharp insights into local nucleation and growth events allow the formulation of new concepts for rationalizing interfaces formed during phase nucleation and growth. Structurally different and confined in space, metastable interfaces occurring during polymorph transformations bring about distinct diffusion behavior of the chemical species involved. More generally, stable structures emerge as a result of the concurrence of the transformation mechanism and of chemical reactions within the phase-growth fronts.     

Zn3(C6H14N2)3[B6P12O39(OH)12] · (C6H14N2)[HPO4]: A Chiral Borophosphate – Triethylenediammonium Hydrogenphosphate Composite

A novel borophosphate, Zn₃(C₆H₁₄N₂)₃[B₆P₁₂O₃₉(OH)₁₂] · (C₆H₁₄N₂)[HPO₄] has been synthesised under mild hydrothermal conditions at T = 165 °C. The chiral crystal structure was determined by single crystal X‐ray diffraction data (trigonal, R3 (no. 146), Z = 3, a = 2089.55(4) pm, c = 1237.03(4) pm, V = 4677.5(2) · 10⁶ pm³, R₁ = 0.066, wR₂ = 0.164 for 5100 observed reflections). The title compound can be considered as an ordered composite of the two different and neutral structures which fit into each other: An open framework of composition Zn₃(C₆H₁₄N₂)₃[B₆P₁₂O₃₉(OH)₁₂] and columns of composition (C₆H₁₄N₂)[HPO₄]. The framework structure is formed by mixed octahedral‐tetrahedral secondary building units, in a three‐dimensional arrangement reflecting a hierarchical derivative of the NbO structure type. The underlying NbO topology is illustrated with the help of Periodic Nodal Surfaces. The composite nature of the compound is resolved in the spatial segregation of two frameworks with a separating surface.     

Site selectivity in the reactions of the hexanuclear platinum cluster [Pt6(mu-PtBu2)4(CO)6][CF3SO3]2

The previously reported hexanuclear cluster [Pt(6)(mu-PtBu(2))(4)(CO)(6)](2+)[Y](2) (1-Y(2): Y=CF(3)SO(3) (-)) contains a central Pt(4) tetrahedron bridged at each of the opposite edges by another platinum atom; in turn, four phosphido ligands bridge the four Pt-Pt bonds not involved in the tetrahedron, and, finally, one carbonyl ligand is terminally bonded to each metal centre. Interestingly, the two outer carbonyls are more easily substituted or attacked by nucleophiles than the inner four, which are bonded to the tetrahedron vertices. In fact, the reaction of 1-Y(2) with 1 equiv of [nBu(4)N]Cl or with an excess of halide salts gives the monochloride [Pt(6)(mu-PtBu(2))(4)(CO)(5)Cl](+)[Y], 2-Y, or the neutral dihalide derivatives [Pt(6)(mu-PtBu(2))(4)(CO)(4)X(2)] (3: X=Cl; 4: X=Br; 5: X=I). Moreover, the useful unsymmetrically substituted [Pt(6)(mu-PtBu(2))(4)(CO)(4)ICl] (6) was obtained by reacting equimolar amounts of 2 and [nBu(4)N]I, and the dicationic derivatives [Pt(6)(mu-PtBu(2))(4)(CO)(4)L(2)](2+)[Y](2) (7-Y(2): L=(13)CO; 8-Y(2): L=CNtBu; 9-Y(2): L=PMe(3)) were obtained by reaction of an excess of the ligand L with 1-Y(2). Weaker nitrogen ligands were introduced by dissolving the dichloride 3 in acetonitrile or pyridyne in the presence of TlPF(6) to afford [Pt(6)(mu-PtBu(2))(4) (CO)(4)L(2)](2+)[Z](2) (Z=PF(6) (-), 10-Z(2): L=MeCN; 11-Z(2): L=Py). The "apical" carbonyls in 1-Y(2) are also prone to nucleophilic addition (Nu(-): H(-), MeO(-)) affording the acyl derivatives [Pt(6)(mu-PtBu(2))(4)(CO)(4)(CONu)(2)] (12: Nu=H; 13: Nu=OMe). Complex 12 is slowly converted into the dihydride [Pt(6)(mu-PtBu(2))(4)(CO)(4)H(2)] (14), which was more cleanly prepared by reacting 3 with NaBH(4). In a unique case we observed a reaction involving also the inner carbonyls of complex 1, that is, in the reaction with a large excess of the isocyanides R-NC, which form the corresponding persubstituted derivatives [Pt(6)(mu-tPBu(2))(4)(CN-R)(6)](2+)[Y](2), (15-Y(2): R=tBu; 16-Y(2) (2-): R=-C(6)H(4)-4-C triple bond CH). All complexes were characterized by microanalysis, IR and multinuclear NMR spectroscopy. The crystal and molecular structures of complexes 3, 5, 6 and 9-Y(2) are also reported. From the redox viewpoint, all complexes display two reversible one-electron reduction steps, the location of which depends both upon the electronic effects of the substituents, and the overall charge of the original complex.