Untitled - Technische Universiteit Eindhoven

5.4. Conclusion 735.4 ConclusionThe cross-linking of silica monomers, which are gradually formed through the hydrolysisof a precursor, was described with a population balance model including a time-dependentsource term. This way, the effect of both the hydrolysis and the condensation rate onthe population balance evolution could be modeled. Like in common population balancecalculations, which usually involve a fixed initial amount of particles, the weight-averagemolecular weight of the aggregates grows critically and diverges at the gel transitionpoint. However, besides the condensation rate, the hydrolysis rate, which is included inthe source term, influences the gel transition time. The higher the hydrolysis and thecondensation rates, the shorter is the gel time. Furthermore, increasing the initial TMOSconcentration by a factor 2 results in a reduction of the gel time by a factor between1.3 and 2.1. Finally, a qualitative agreement between the predicted profiles for T 2 andthe experimental profiles was found using simple relations between the average aggregatemobility and the correlation time of the water molecules.