Calculation of active fractions sizes in supported nanocrystals

Background: The paper is devoted to the determination of active nanoparticles sizes. Other particles that deviate from the calculated size limits do not demonstrate the special activity. that is the catalytic elimination of environmental pollutants, namely, carbon monoxide, under ambient conditions - low temperature, high humidity and the presence of anthropotoxins. This paper discusses the basic principles of catalysts used in environmental pollution abatement, in particular, the effect of nanocatalyst size on catalytic activity. It remains unclear why large palladium containing objects, as well as true solutions are not effective as catalysts for low-temperature carbon monoxide oxidation. Additionally It is know that only palladium containing nano systems over a narrow size range are effective catalysts. The submitted work is the first step in quantifying this range. Hopefully this will assist in the determination of the causes of unusually high nanocatalysts efficiency.
Methods: All calculations were made by using MS Office Professional 2013. A series of palladium nanocatalysts on activated carbon fibers «Busofit Carbopon-Activ» with active surface of 1300 m$^2$/g was prepared; sizes of nanoparticles varied by choosing modes of drying after application solutions with ions Pd$^{2+}$. The initial reaction rate was measured by decreasing of CO concentrations on air.
Results: Mathematical model was proposed which has allowed to determine limits of nanoparticles dimensions in borders of which their have displayed some special properties inherited to only nanostructures. The model has allowed to obtain decisions, that is to find values of maximum and minimum radiuses of particles in particular for catalytically active nanocomposites and also can be expended for exposure of others special properties inherited only to nano-systems. Described method allows to find the answer to one of two questions that's consist the main scope of investigations of the nanocrystalline state: is there some critical grain (particle) size below which the characteristic properties of nanocrystals become observable, and above which the material behaves as a bulk one.
Conclusion: The proposed calculation method for the first time opens easy way to calculate the sizes of the nanoparticles within which they are active. This establishes new opportunities to increase the efficiency of nanosystems by selecting the synthesis conditions with a maximum contents of required fractions.