Thresholds and Lines of Percolation Research Papers (original) (raw)

The basis for a theory of porous electrodes is the percolation problem. Its solution would make it possible to answer the question of how effectively the structure of a porous electrode is used for ensuring the occurrence of electrochemical processes on its inner surface, for bringing together all its participants (reagents, ions, electrons, catalyst particles), and for removing the formed products. For the solution of this problem, it is necessary that both the elements of the structure of a porous electrode and the substances filling it should be connected. In the case of hydrophobized electrodes, these are exemplified by a mixture of agglomerated grains of polytetrafluoroethylene and catalyst, the gaseous reagent entering the electrons, and the electrolyte. In this publication, we describe a general method intended for the calculation of thresholds and lines of percolation and present particular estimates for an important class of lattices modeling porous media – rectangular: plane, square lattice, three-dimensional cubic, and their analogues in space of any number of measurements.

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- Percolation, Lattices, Square Lattice, Thresholds and Lines of Percolation

The charge percolation mechanism (CPM) of olefin polymerization in the presence of transition metal compounds has been applied to explain the polymerization of ethylene by silica-supported chromium oxide. In the previous work of this series, the fundamental issues and mechanism of this polymerization were presented. In this work, the compatibility of the CPM with the empirical findings is confirmed. The CPM has been applied to explain: the appearance of an induction period; the deactivation of active centers and the formation of oligomers; the effects of chromium concentration on the silica surface, the silica surface discontinuity and the pore size of silica on polymerization and the formation of the structure of polyethylene. A mathematical model has been derived to explain the effects of the CrOx/SiO2 ratio on the productivity of Phil-lips catalysts in the polymerization of ethylene. The empirical findings have also been confirmed by computer simulations.