An innovative approach to preparation of particles with optimal size distribution: an example of SiO2

An innovative method to determine experimental parameters for a desired particle size with the narrowest possible particle-size distribution was presented. The optimal experimental parameters were calculated from the regression equations with the help of the Lagrange multiplier method. To show the validity of the methodology, silica nanoparticles were prepared, and the results showed considerable agreement with the predictions of the present analysis. The methodology in this study can be used to predict optimal experimental parameters if regression equations are appropriate.