Mechanism and kinetics of mechanochemical processes in comminuting devices: 2. Applications of the theory. Experiment
Introduction
In the previous communication [1], we have reported the calculations of t–P–T conditions in local regions (in some vicinity x of an impact–friction contact) of the particles under treatment and deduced the generalized equations to describe the kinetics and to calculate the rate constants of mechanochemical processes in comminuting devices. In the present paper, we consider the application of results obtained earlier and confirmed experimentally 2, 3, 4, both to describe some general mechanisms of activation and chemical transformations of substances (these mechanisms being based on numerical evaluations and deduced from the local character Δx∼10−6 cm and short-time scale τ∼10−8 s of the existence of pressure σ∼1010–1011 dyn/cm2 and temperature ΔT∼103 K impulses), and to calculate numerically the rate constants of activation and mechanochemical reactions in ball planetary mills in the impact regime of their operation.
Section snippets
Mechanism of mechanochemical processes
The general questions concerning the effect of local character and short time scale (kinetic factors) on the mechanism of mechanochemical processes and specific character of their course had been discussed qualitatively earlier 5, 6. The quantitative aspect of this problem includes numerical estimates of heat and mass transfer in the local regions of the particles under some given t–P–T conditions aimed at the description of the possibilities and mechanisms of different physicochemical
The use of kinetic equations
In the previous communication [1], we obtained the generalized kinetic equations to describe the transformation degree of mechanochemical processes. The equation for the degree of mechanical activation, without taking account of the changes in particle size, is:Here, the geometric probability of the impact treatment of particles for unlined balls (see also below) isand the product of dimensionless functions ζη is
Conclusions
On the basis of the obtained theoretical results, it can be stated that the effect of short-time contact fusion of particles treated in various comminuting devices can play the key role in the mechanism of activation and chemical reactions for wide range of mechanochemical processes. This role involves several aspects, i.e., the very fact of contact fusion transforms the solid-phase process into another qualitative level, judging from the mass transfer coefficients. Spatial and time
List of symbols2
m′ and ms′ The rate and stationary rate of melting h and f(y,h) Dimensionless parameters of melting Hm Latent heat of melting μ Viscosity of the melting zone τc and A Time and constant of the crystallization process rcr and σs Linear dimension of the new phase formed and the crystal–melt surface tension ∇ Diffusion coefficient (diffusivity) k, χ and Kr0 The Boltzmann, structural and pre-exponential factors n, n0, n* The current, total, reacted number of molecules (atoms) Kr The reaction rate constant in the
Urakaev Farit Khisamutdynovich is a Doctor of Chemistry, the Chief of the Mass Crystallization Laboratory of the United Institute of Geology, Geophysics and Mineralogy of the Siberian Branch of the Russian Academy of Sciences, Acad. Koptyug Prosp. 3, Novosibirsk 630090, Russia.Boldyrev Vladimir Vyacheslavovich is a member of the Russian Academy of Sciences, he is also a Doctor of Sciences in Chemistry, Professor of Chemistry, and past Director of the Institute of Solid State Chemistry of the
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Urakaev Farit Khisamutdynovich is a Doctor of Chemistry, the Chief of the Mass Crystallization Laboratory of the United Institute of Geology, Geophysics and Mineralogy of the Siberian Branch of the Russian Academy of Sciences, Acad. Koptyug Prosp. 3, Novosibirsk 630090, Russia.Boldyrev Vladimir Vyacheslavovich is a member of the Russian Academy of Sciences, he is also a Doctor of Sciences in Chemistry, Professor of Chemistry, and past Director of the Institute of Solid State Chemistry of the Siberian Branch of the Russian Academy of Sciences, Kutateladze 18, Novosibirsk 630128, Russia.
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