For the growth of any crystalline structure...basis are needed in sufficient number...that is concentration of atom/ ions...if solution is saturated and homogenious then the rate will remain constant until other parameters do not change...hence time for mixing process need to optimise...lets say 30min is sufficient then in 1hr it will not bring change...but with 10min, 20min it will show changes.
The sol-gel synthesis occurs in a colloidal system, so it is very sensible to changes in the viscosity, density, and polymerization of the isopropoxide with water.
I am wondering also why you apply 50 °C at your solution? I used to perform TiO2 sol-gel dip/spin-coating thin films, and the synthesis do not requires the use of a heat source.
So, taking this into account, of course during the mixing time the process of hydrolisis, polymerization and condensation of nanoparticles will change, especially because you are applying 50 °C on your system. You will expect nucleation of some crystals as the solvent evaporates.
Hello Fatima, most probably longer stirring time leads to formation of bigger crystallizaion sites which lead to bigger crystals and higher crystallinity of the final product.