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This study continues the development of a method, implicit calibration, for estimating kinetic parameters from on-line measurements of batch reactions. The basic idea of implicit calibration is to combine non-linear parameter estimation with the calibration of measured spectra with concentrations calculated by an assumed kinetic model. A new example is studied, an esterification reaction with a rather complicated kinetic mechanism, where activities, instead of concentrations, and NIR spectra are used as measurements. The emphasis in the study is on estimating the uncertainty of the kinetic parameters. Two approaches, linearization and bootstrap, are applied. In the case studied, the two approaches give closely similar estimates of the uncertainty. As well, a new way is introduced to control the rigidity of the implicit calibration, based on minimizing the lack of fit of the model. It is also shown that`mixed implicit calibration', i.e. implicit calibration combined with a few off-line calibrated concentrations, greatly enhances the identifiability of the kinetic model.

The mechanisms of formation and structure of precipitates hydrolyzed from aqueous solutions of titanium tetrachloride and titanium sulfate were studied by small-angle X-ray scattering (SAXS). SAXS was found a powerful method for that purpose. The small colloidal primary particles that were present in the solutions at room temperature started to aggregate when thermal precipitation started. The aggregated particles coalesced until their radius was approximately 1 nm depending of the precipitation conditions to some extent. After that, the aggregation continued producing either mass fractal or surface fractal structures. The structure was mass fractal when primary particle concentration was high enough and surface fractal when concentrations were closer to the equilibrium state. With a delay ionic titanium started to precipitate. Because of its rather slow precipitation rate in the conditions of this study, only surface fractal aggregates were formed. The mass fractal structure was found X-ray amorphous and the surface fractal aggregates nano crystalline. The mass and surface fractal dimensions of these aggregates were 2.2 (1 s ( 0.1) and 2.7 (1 s ( 0.2), respectively. The "titanic acids" were found to be aggregates of small titanium dioxide particles that have mass fractal structure in ortotitanic acid and surface fractal structure in metatitanic acid. The loose structure of the mass fractal aggregates causes the relatively easy solubility and the X-ray amorphous state found in ortotitanic acid. On the contrary, the more compact structure of metatitanic acid explains its nano crystallinity and insolubility. The changing of ortotitanic acid to metatitanic acid upon aging is obviously a consequence of the restructuring of the primary titanium dioxide particles toward the close-packed porous structure.