The problem of optimal technologies for functional materials

Abstract

The work analyzes the possibility of treating the production of a functional material as the realization of the stage of separation of the substance forming the material from a supersaturated medium and the stages of physical and chemical modification of the separated substance. The key kinetic equation of variation of the distribution function of states of the particles of the substance at each stage is formulated, considering the discrete nature of the nucleation, growth, and aggregation of particles. Solutions to continuous versions of the kinetic equation with regard to each stage are given. The conception of the path \( \vec Z(\vec g) \) of obtaining the material is introduced in the form of the coupling function of the target properties \( \vec Z \) of the compound with characteristics \( \vec g \)} of the reactors where the material is produced. The conditions are considered under which the path can be regarded as optimal at each stage, and the optimality criteria of the routes are introduced.