The approach of numerical simulation of orthosilicic acid OSA polymerization and SiO₂ nanoparticle formation in hydrothermal solution have been developed based on the model of the homogeneous stage of nucleation and the subsequent growth of particles. The influence of surface tension on the interface of SiO₂–water, the rate of molecular deposition, and Zeldovich factor Z were evaluated. Temperature dependence on time, pH, initial OSA concentration, and ionic strength are the main parameters that determine the kinetics of colloid phase formation, the final average size of SiO₂ nanoparticles, and the particle size distribution and its polydispersity index. The results of the numerical simulation were verified with experimental data on OSA polymerization and measurement of nanoparticles sizes using the method of dynamic light scattering in a wide range of temperatures of 20–180 °C, pH = 3–9, SiO₂ content C_t of 300–1400 mg/kg, and ionic strength I_s of 0.0001–0.42 mol/kg. The results obtained can be used in the technology of hydrothermal synthesis of sols, gels, and nanopowders to regulate the kinetics of OSA polymerization and SiO₂ nanoparticle growth, particle size distribution, morphology, and structure of products.

The polycondensation kinetics of orthosilicic acid in hydrothermal solutions was studied experimentally at different temperatures, pH, and ionic strengths. As a result of the mathematical processing of experimental data, equations approximating the time dependence of the polycondensation process and the dependence of the polycondensation rate constant on the solution ionic strength were obtained. Experimental data on the kinetics of the reverse process of dissolving colloidal silica were obtained at different temperatures and pH.

Numerical simulation of the process of polycondensation of orthosilicic acid and colloid silica particles growth under different physical and chemical conditions was done: temperature, pH, ionic strength and other. Calculated dependences of orthosilicic acid concentration and mean radius of silica particles versus time, graphs of particles dimensions distributions were received. Results of calculations were compared with experimental data. Research is important for to make clear role of colloid silica on hydrothermal mineral formation and for industrial extraction and utilization of silica, and also for mineral synthesis.