Bimolecular decomposition distanc

Assuming a random distribution of the catalyst in a matrix, the bimolecular decomposition distance was estimated to be almost contact distance between molecules. 

The bimolecular decomposition distance is nearly the contact distance between the molecules. 

When two catalyst molecules are needed for the 4-electron water oxidation, the catalytic activity shows an optimum catalyst concentration in the matrix since bimolecular decomposition still takes place, and cooperative distance between catalyst can be determined also by assuming a random distribution. 

When Ru-red was used as a catalyst in the presence of a large excess of Ce(IV) oxidant (Scheme 19.1), the rate of 02 evolution was first order with respect to the catalyst concentration, showing that Ru-red is capable of 4-electron oxidation of water. By the decomposition of the Ru-red, N2 was formed its formation rate was second order with respect to the catalyst concentration, showing that the decomposition is bimolecular. The decomposition distance in a polymer (Nafion) matrix was estimated by assuming the random distribution of the catalyst molecule in the matrix. The probability density P(r) of the distance between the nearest neighbor molecules (r nm) is represented by Eq. (19.5) according to the Poisson statistics... 

The development of molecular cavities based on a more inert framework that does not contain heteroatoms is desired for the kinetic stabilization of reactive species without perturbation of their intrinsic properties. For prevention of bimolecular decomposition of reactive species such as dimerization and self-condensation, it is considered essential to surround the functional group from all sides and from a distance in any conformation of the molecule. A simpler acyclic molecule with larger conformational flexibility could work as a molecular cavity for the stabilization of reactive species if it meets these criteria. 

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