Novel coordination polymers with (Pyrazolato)-based tectons: catalytic activity in the peroxidative oxidation of alcohols and cyclohexane

Coupling five rigid or flexible bis(pyrazolato)based tectons with late transition metal ions allowed us to isolate 18 coordination polymers (CPs). As assessed by thermal analysis, all of them possess a remarkable thermal stability, their decomposition temperatures lying in the range of 340-500 degrees C. As demonstrated by N-2 adsorption measurements at 77 K, their Langmuir specific surface areas span the rather vast range of 135-1758 m(2)/g, in agreement with the porous or dense polymeric architectures retrieved by powder X-ray diffraction structure solution methods. Two representative families of CPs, built up with either rigid or flexible spacers, were tested as catalysts in (0 the microwave-assisted solvent-free peroxidative oxidation of alcohols by t-BuOOH, and (ii) the peroxidative oxidation of cydohexane to cydohexanol and cydohexanone by H2O2 in acetonitrile. Those CPs bearing the rigid spacer, concurrently possessing higher specific surface areas, are more active than the corresponding ones with the flexible spacer. Moreover, the two copper(I)-containing CPs investigated exhibit the highest efficiency in both reactions, leading selectively to a maximum product yield of 92% (and TON up to 1.5 x 10(3)) in the oxidation of 1-phenylethanol and of 11% in the oxidation of cydohexane, the latter value being higher than that granted by the current industrial process.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.