A Generalized Model for Describing Particle Formation in the Synthesis of Monodisperse Oxide Particles Based on the Hydrolysis and Condensation of Tetraethyl Orthosilicate

A generalized model considering reaction and diffusion processes as rate determining steps is proposed for the formation of particles from hydrolysis and condensation of tetraethyl orthosilicate (TEOS). Reaction rate constant is assumed to be proportional to contact-surface area of two particles. Diffusion rate constant is given by Fuchs' stability theory with interparticle potential containing van der Waals attraction and electrostatic repulsion. To examine the validity of the model, ammonia-catalyzed reactions of TEOS were carried out in an ethanol–water solution at a water concentration of 11 mol/dm3, an ammonia concentration of 1.0 mol/dm3, and TEOS concentrations of 0.2 and 0.4 mol/dm3 in the presence and in the absence of electrolytes. The experiments included competitive particle growth and seeded and nonseeded reactions. The model quantitatively expressed the results of the competitive growth experiments in which particles with different sizes grew at the same rate. The model gave the expected trend for the effect of ionic strength on particle sizes in the nonseeded reaction and the suppression of secondary particles in the seeded reaction by the addition of an electrolyte KCl. Good estimation was also obtained for transient particle size distributions in the nonseeded reaction and the seeded reaction in which secondary particles were generated.