A kinetic study of the electron-transfer reaction of the phthalimide-N-oxyl radical (PINO) with ferrocenes

A kinetic study of the one-electron oxidation of a series of ferrocenes (FcX: X = H, CO2Et, CONH2, CH2CN, CH2OH, Et, and Me2) by PINO generated in CH3CN by reaction of N-hydroxyphthalimide (NHPI) with the cumyloxyl radical produced by 355 nm laser flash photolysis of dicumyl peroxide has been carried out. Ferrocenium cations were formed, and the reaction rate was determined by following the decay of PINO radical at 380 nm as a function of the FcX concentration. Rate constants were very sensitive to the oxidation potential of the substrates and exhibited a good fit with the Marcus equation, from which a lambda value of 38.3 kcal mol(-1) was calculated for the reorganization energy required in the PINO/ferrocenes electron-transfer process. Knowing the ferrocene/ferrocenium self-exchange reorganization energy it was possible to calculate a value of 49.1 kcal mol(-1) for the PINO/PINO- self-exchange reaction in CH3CN. Moreover, from the Marcus cross relation and the self-exchange rates of ferrocene and dimethylferrocene, the intrinsic reactivity of PINO in electron-transfer reactions has been calculated as 7.6 x 10(2) M(-1) s(-1). The implications of these values and the comparison with the electron-transfer self-exchange reorganization energies of peroxyl radicals are briefly discussed.     

New algorithms to look for the most stable conformations of a molecule

Summary Some new algorithms useful for the study of the ≪low-energy conformational space≫ of a molecule are described, and in particular an algorithm which detects the most stable conformations through a random sampling of the energy hypersurface. An application of this algorithm to ethylmethylphosphate (a model molecule of the chain segment of nucleic acids between two furanose rings) is also shown. Presented in part at the Fourth Annual Montedison Chemistry Meeting (Milan, March 4, 1986).     

Ethylene polymerization catalyzed by metallocene/methylaluminoxane systems: quantum-mechanical study on the role of olefin separated ion pairs (OSIP) in the polymerization mechanism

DFT (density-functional theory) calculations were performed to investigate the thermodynamics of formation of Olefin Separated Ion Pairs (OSIP) Cp₂MtCH₃⁺/C₂H₄/Cl₂Al[O(AlMe₃)AlHMe] (Cp = η₅-C₅H₅, Mt = Ti, Zr, Me = CH₃) from ethylene and Cp₂MtMe · Cl₂Al[O(AlMe₃)AlHMe]₂, a model of adduct produced by metallocence/methylaluminoxane (MAO) systems for olefin polymerization. The results account for the high cocatalytic activity of MAO and show that titanium complexes are potentially more active than zirconium homologues, as confirmed by low temperature polymerization tests.     

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.     

Ethene/propene copolymerisations with rac-EBTHIZrR2/alumoxane: σ-ligands effect

We report here about the role played by the σ-ligands of a metallocene in ethene/propene (E/P) copolymerisations promoted by rac-[ethylenebis(4,5,6,7-tetrahydro-1-indenyl)]zirconium dichloride 1, and its corresponding dimethyl derivative rac-EBTHIZrMe₂ 2 and binaphtholate rac-EBTHIZr(BNP) 3 derivative, in the presence of several alumoxanes.

Alumoxanes alternative to the traditional polymethylalumoxane (MAO) were synthesised and characterised. They are based on Al(2,4,4-trimethylpentyl)₃ (TIOA) 4 and were prepared by reaction of 4 with water to give either tetraisooctylalumoxane (TIOAO) 5 or polyisooctylalumoxane (TAO) 6 depending on the stoichiometry of the reaction. ¹H NMR spectra of these products are characterised by the presence of broad bands and of resolved multiplets. Their relative amount in the region between 1.9 and 2.5 ppm was identified as the “fingerprint” of the polymerisation activity. A comparison of the results obtained in polymerisation with metallocenes having different σ-ligands allowed us to shed more light on the role played by those species.

In conclusion, the nature of the σ-ligands of a metallocene affects its catalytic activity in polymerisation, as a function of the alumoxane employed and of the relative ratio with the metallocene, and this effect is enhanced in “critical conditions,” i.e. with a weakly activating cocatalyst or at a low Al/Zr ratio.     

Formation of Symmetric Structures in the Dynamics of Repelling Particles

We consider Hamiltonian systems corresponding to the motions of a system of N repelling particles evolving in space under the action deriving from a very long range potential energy; the asymptotic behavior of the system is analysed for the cases U=− ln r and . Only special “asymptotic?shapes” are reached, which may present quite interesting symmetries and correspond to the critical points of a gradient system. The relationships between the original Hamiltonian and the asymptotic gradient system are discussed. Accepted: May 25, 1999     

Quadratic nonlinear optical and preliminary piezoelectric investigation of crosslinked samples obtained from a liquid chromophore

A push–pull chromophore has been synthesized, which is liquid at room temperature and can be crosslinked owing to the presence of two methacrylate moieties. Thin films of the chromophore have been prepared by spin coating, and they have been simultaneously crosslinked and poled under strong electric field. On the poled crosslinked films, the quadratic nonlinear optical (NLO) characterization was performed through nonresonant second harmonic generation measurements at 1368 nm as the fundamental wavelength, yielding a fairly good d₃₃ value of 46 pm/V, with retention of 80% of that value after 2 months at 85 °C. Following the theoretical issue that the quadratic NLO and piezoelectric tensors of a material have the same symmetry properties, and exploiting the easy processing of the chromophore in the liquid phase, we have prepared poled crosslinked samples of the chromophore suitable for piezoelectric tests that were performed using a commercial piezoceramic sample as the reference. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

An exact description of nonlinear wave interaction processes ruled by 2 × 2 hyperbolic systems

By means of a reduction approach to 2 × 2 quasilinear hyperbolic homogeneous systems of first-order PDEs, a full and exhaustive analysis of nonlinear wave interactions is achieved. The alteration in the profile as well as in the wave time distortion of the emerging pulses caused by the interaction process is illustrated in detail through exact solutions of initial value problems. Canonical forms of 2 × 2 systems which allow for special (soliton-like) hyperbolic wave interactions and of interest in applications are also determined.