A kinetic and spectroscopic study on the copper catalyzed oxidative coupling polymerization of 2,6-dimethylphenol. X-ray structure of the catalyst precursor tetrakis (N-methylimidazole) bis(nitrato) copper(II)

The complex of copper(II) nitrate with N-methylimidazole (Nmiz) ligand has been studied as a catalyst for the oxidative coupling of 2,6-dimethylphenol by means of kinetic and spectroscopic measurements. The order of the reaction in copper is fractional and depends on the N/Cu ratio and the base/Cu ratio, indicating that there are at least two possible rate-determining steps, i.e. the formation of a dinuclear copper species and the phenol oxidation. EPR spectroscopy performed on frozen solutions with varying ligand to copper ratios shows that all Cu(II) is converted into the precursor complex at a ratio of 4 to 1, whereas in kinetic experiments, maximum activity and selectivity are reached only at a ratio of at least 30 to 1. Base is needed as a co-catalyst, and the maximum reaction rate is reached at a base to copper ratio of 1.8 to 1. The solid-state X-ray structure of the catalyst precursor complex has been determined to be [Cu(Nmiz)₄(NO₃)₂], monoclinic, space group P2₁/n, a = 8.452(1) Å, b = 10.376(2)Å, c = 12.821(2)Å, β = 94.88(2) °, Z = 1, R = 0.049 for 3525 reflections. This structure consists of an axially elongated octahedral CuN₄O₂ chromophore, which is in agreement with frozen-solution EPR spectra. Investigations under conditions where water and dioxygen were carefully excluded, have shown that for the phenol oxidation step the presence of dioxygen is not required. However, the reaction does require a trace of water (or hydroxide) to form the reactive intermediate. A modified reaction mechanism for the oxidative coupling is presented with special attention to the first steps of the reaction and the equilibrium species present in solution. The role of dioxygen appears to be only to reoxidize the formed Cu(I) species and to regenerate base.     

On 1-convexity and nucleolus of co-insurance games

The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.     

Semi-marginalistic Values for Set Games

Concerning the solution theory for set games, the paper focuses on a family of values, each of which allocates to any player some type of marginalistic contribution with respect to any coalition containing the player. For any value of the relevant family, an axiomatization is given by means of three properties, namely one type of an efficiency property, the equal treatment property and one type of a monotonicity property. We present one proof technique which is based on the decomposition of any arbitrary set game into a union of simple set games, the value of which are much easier to determine. A simple set game is associated with an arbitrary, but fixed item of the universe.     

A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid

The breakup of an axisymmetric viscous jet is considered in the lubrication approximation. The discretised equations are solved on a fixed equidistant one-dimensional Eulerian grid. The governing equations are implemented in a conservative second order accurate total variation diminishing (TVD) scheme, preventing the numerical diffusivity. Singularities that occur at pinchoff and coalescence are regularised by a small modification on the surface tension. The modification is of the order of the spatial step Δx. This regularisation ensures that the solution of the presented numerical model converges to the exact solution of the breakup of a jet in the lubrication approximation. The results of the presented numerical model agree quantitatively with the analytical solution of the Rayleigh–Plateau instability, and with experimental results on the final stage of the Rayleigh–Plateau instability.