A model of an evolutionary route for the preparation of functional materials

A mesokinetic model of the formation of a solid substance and the change in its properties under the action of factors that transform a substance into a functional material is proposed. Equations are introduced that represent the conditions of preservation of the number of molecules and particles of the substance during their nucleation, growth, and aggregation in supersaturated environments as well as during the ordering of the particles after the imposition of a temperature field and the introduction of additives. The equations describe the rate of change in the state distribution function of particles and can be reduced to the Liouville equation and the Fokker-Planck equation. The model contains unknown frequency functions subject to experimental determination. After these functions are determined, the model makes it possible to construct a methodological scheme for seeking the optimum route for the preparation of a new nanomaterial with desired properties.