In this work the effect of mixing on a sol-gel process is quantitatively investigated. Titanium dioxide synthesis from titanium tetra-isopropoxide is used as a test reaction. Solutions of titanium alkoxide in isopropyl alcohol and water in isopropyl alcohol are mixed in a special mixing device (i.e., vortex reactor) at different mixing rates, and the effect of mixing is quantified and compared with the effect of the other relevant operating parameters, namely the water to alkoxide, acid to alkoxide ratios, and alkoxide initial concentration. Dynamic light scattering, specific surface area measurement through nitrogen adsorption, X-ray diffraction, and field emission scanning electron microscopy are employed to determine particle size distribution, morphology, and crystallite size of the different particulate products (i.e., sols, gels, powders) obtained before and after thermal treatments under different synthesis conditions. A factorial design is used to plan the experimental campaign and results show that the role of mixing cannot be neglected. Moreover results show that mixing can be actively used to control the final product characteristics and must be taken into account when a process is transferred from the laboratory to the industrial scale. Eventually a scale-up criterion based on our previous work will be discussed.
Classical sensitivity testing addresses mainly problems where the level of one stimulus only governs an abrupt transition in output, or response. Both parametric and nonparametric methods developed, and successfully applied over last century to tackle such problems, provide estimates of critical levels beyond which an item will either respond, or not, to a single stimulus, and of related statistics. However classical methods sometimes may not readily provide an answer, namely when more than one stimulus may reach critical level, and either singularly or jointly trigger transition. Factorial and response surface designs, adequate when dealing with continuous responses, may not perform as well for transition threshold estimation. A practical case at hand in chemical engineering concerns the production, through hydrolysis of a specific precursor, of titania sols and gels that find industrial use as additive for paints, concrete and other building materials due to its optical, photo-catalytic and super-hydrophilic properties. Particles formation and aggregation — controlled by varying the primary process parameters, namely initial alkoxide concentration, water to alkoxide and acid to alkoxide ratios, mixing conditions — may yield either stable, transparent nanometric sols, or monolithic gels, where aggregation of nanometric particles produces a final ceramic object. Depending on the application, one of the two products may be desirable, and therefore it is crucial to control the final product properties. Aggregation kinetics and physical properties of sols, and sol to gel transition, were found to depend strongly upon several factors, that is water to alkoxide initial concentration ratio, acid to alkoxide initial concentration ratio, and their interaction. The approach developed in order to estimate parameters pertaining to transition, and related uncertainty, is presented in the paper, and discussed in the light of experimental results.
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