Weibull Cumulative DistributionFunction for Modelingthe Isothermal Kinetics of the Titanium-oxo-alkoxy Cluster Growth.

The isothermal kinetics of the titanium-oxo-alkoxy cluster(TOAC)growth obtained in the controlled hydrolysis–condensation reactionof Ti(OPri)4with H2O in n-propanol solution was investigated. Kineticcurves of the TOAC growth were measured at five different temperatures:298, 303, 308, 313, and 318 K. It was established that the kineticcurves of the TOAC growth could be mathematically modeled by the cumulativetwo-parameter Weibull probability distribution function of the growthtime (t) in a wide range of the degree of growth(0.05 ≤ DG ≤ 0.95). It was found that the dependenciesof the shape parameter (β) and scale parameter (η) ontemperature (T) can be described by polynomial functions.The activation energy of TOAC growth (Ea,DG), as well as the pre-exponential factor (ln ADG) for different degrees of growth, were calculated usingFriedman’s isoconversional method. On the basis of knowing Ea,DG(DG) dependence, the procedure for calculatingisothermal dependence of Eavs growthtime was described. The isothermal probability distribution densityfunctions of Eafor the TOAC growth processwere calculated. It was established that the conversion kinetic curvesof the TOAC growth process could be fully described by a model ofthe infinite number of parallel first-order growth reactions withtime-varying value of the pre-exponential factor and activation energieswhich are distributed in accordance with a specific function of Ea. [ABSTRACT FROM AUTHOR]