Study on the grain size control of metatitanic acid in a mixture acid system based on Arrhenius and Boltzmann fitting

Herein, to control the particle size of metatitanic acid produced via titanium thermal hydrolysis in sulfuric-chloric mixture acid (SCMA) solutions, the relationship between its grain size and hydrolysis parameters is discussed, and the corresponding mathematical model was established using the experimental data. Firstly, Ti(OH)(SO₄)(Cl)(H₂O)₃ was selected as the most likely initial structure in the SCMA solution by comparing the experimental and corresponding simulated Raman spectra by density functional theory (DFT). Secondly, according to the predicted initial structure of TiO²⁺ and the experimental data for the hydrolysis process, with an increase in the concentration of TiO²⁺ and reaction temperature, the hydrolysis rate and grain size increased, while the agglomerate particle size decreased. Finally, a mathematic model was established and fitted by the Arrhenius equation and the Boltzmann distribution to describe the relationship between the grain size and hydrolysis parameters, as follows.