Analysis of models for the ziegler-natta stereospecific polymerization on the basis of non-bonded interactions at the catalytic site—II: Edges,steps and reliefs on the surface of layered modifications of TiCl3

The computations performed in a previous paper for hypothetical structures of the site active in the polymerization of olefins at the (110) surfaces of TiCl₃-α are extended to edges, steps and reliefs on (111) surfaces of all the layered modifications of TiCl₃. Our computations suggest that edges, steps and reliefs of all the layered modifications of TiCl₃ should behave similarly in providing active sites; polymerization should occur on these more exposed sites because of the much lower activation energies than for plain surfaces. A unique general model emerges: lower steric repulsions appear to be implied for a coordination of the polymeric chain on the more hindered octahedral position at a titanium atom and this, in turn, causes a chiral orientation of the first carbon-carbon bond of the chain. This orientation may be the main factor in determining the stereospecificity.     

Activation energy and nonequilibrium effects in thermal reactions

Calculations of the nonequilibrium rate constant for the model system H₂O₂ + M → 2 OH + M over the temperature range of 300–1900°K, assuming that only vibrational, or that both vibrational and rotational, energy is transferred in a collision, show that (1) inefficient energy transfer leads to a distinctly non-Arrhenius temperature dependence, the nonlinearity being in principle different for different M, and (2) despite different activation energies for different M, the order of M efficiencies is preserved throughout the temperature range. A reversal of M efficiencies can occur only if there is a change of mechanism of the reaction over the temperature range investigated.     

Global regular and singular solutions for a model of gravitating particles

The existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of (generalized) pseudomeasures. This approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem.Mathematics Subject Classification (2000):35B40, 35K15, 82C21     

Regioselective cyclization of alpha,omega-alkynoic acids catalysed by TpRu complexes: synthesis of endocyclic enol lactones [Tp = hydrotris(pyrazolyl)borate

The sigma-enynyl complex [TpRu(C(Ph)=C(Ph)C identical to CPh)(P-MeiPr2)] efficiently catalyses the regioselective cyclization of alpha,omega-alkynoic acids to yield endocyclic enol lactones having ring size up to 12 atoms.     

On Logarithmic Smoothing of the Maximum Function

We consider the maximum function f resulting from a finite number of smooth functions. The logarithmic barrier function of the epigraph of f gives rise to a smooth approximation g of f itself, where >0 denotes the approximation parameter. The one-parametric family g converges – relative to a compact subset – uniformly to the function f as tends to zero. Under nondegeneracy assumptions we show that the stationary points of g and f correspond to each other, and that their respective Morse indices coincide. The latter correspondence is obtained by establishing smooth curves x() of stationary points for g , where each x() converges to the corresponding stationary point of f as tends to zero. In case of a strongly unique local minimizer, we show that the nondegeneracy assumption may be relaxed in order to obtain a smooth curve x().     

First Alexandroff Decomposition Theorem for Topological Lattice Group Valued Measures

Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2 ^X generated by F, let G be a Hausdorff commutative topological lattice group and let rba_F(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rba_F(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff.     

Comment on: “From classical to modern ether-drift experiments: the narrow window for a preferred frame” [Phys. Lett. A 333 (2004) 355]

In a recent article [M. Consoli, E. Costanzo, Phys. Lett. A 333 (2004) 355], M. Consoli and E. Costanzo have investigated classical and modern aether drift experiments and explored the narrow window for detection of a preferred reference frame. This Letter proposes an easy to perform variant of Fizeau's experiment, which may confirm or deny Consoli–Costanzo's claims.     

Nonlinear mobility of a driven system: Temperature and disorder effects

We consider the dissipative nonlinear dynamics of a model of interacting atoms driven over a substrate potential. The substrate parameters can be suitably tuned in order to introduce disorder effects starting from two geometrically opposed ideal cases: commensurate and incommensurate interfaces. The role of temperature is also investigated through the inclusion of a stochastic force via a Langevin molecular dynamics approach. Here, we focus on the most interesting tribological case of underdamped sliding dynamics. For different values of the chain stiffness, we evaluate the static friction threshold and consider the depinning transition mechanisms as a function of the applied driving force. As experimentally observed in QCM frictional measurements of adsorbed layers, we find that disorder operates differently depending on the starting geometrical configuration. For commensurate interfaces, randomness lowers considerably the chain depinning threshold. On the contrary, for incommensurate mating contacts, disorder favors static pinning destroying the possible frictionless (superlubric) sliding states. Interestingly, thermal and disorder effects strongly influence also the occurrence of parametric resonances inside the chain, capable of converting the kinetic energy of the center-of-mass motion into internal vibrational excitations. We comment on the nature of the different dynamical states and hysteresis (due to system bi-stability) observed at different increasing and decreasing strengths of the external force.     

Sulphonylium ions in the gas phase

Electron impact mass spectrometry was used to investigate the fragmentation of a series of arenesulphonyl chlorides. Sequential losses of a chlorine atom and sulphur dioxide from the molecular ions occurred and the reverse of these reactions had small critical energies that were generally unaffected by the ring substituent. However, an interesting intramolecular cyclization reaction occurring on the ortho-nitro derivative is discussed with the aid of kinetic energy release measurements on this derivative and on a model compound. Appearance energy measure ments combined with multiple scattering Xα calculations led to an estimate of the sulphur-chlorine bond strength in benzenesulphonyl chloride.