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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]

Abstract: The isothermal kinetics of the titanium-oxo-alkoxy clusters (TOAC) growth obtained in the controlled hydrolysis–condensation reaction of Ti(OPr i )4 with H2O in n-propanol solution was investigated. Kinetic curves of the TOAC growth were measured at five different temperatures: 298K, 303K, 308K, 313K and 318K. It was established that the kinetic curves of the TOAC growth could be mathematically modelled by the cumulative two-parameter Weibull probability distribution function of the growth time (t). The forms of functional dependencies on temperature for the shape (β) and the scale (η) parameters were determined. It was shown that the isothermal TOAC growth is a complex kinetic reaction and the activation energy of growth (E a,α) for different degrees of growth (α), was calculated. Based on knowing E a,α(α) dependence, the procedure for calculating isothermal dependence of activation energy (E a) on growth time, was described. The isothermal probability distribution density functions of E a for TOAC growth process, were calculated. It was established that the isothermal kinetics of the TOAC growth can be modelled by an infinite number of parallel first-order growth reactions with time-varying value of the pre-exponential factor (ln A) and activation energies which are distributed in accordance with a specific function of E a. [Copyright &y& Elsevier]

The isothermal kinetics of the exchange of absorbed water in calcium alginate hydrogels with ethanol was investigated. The isothermal kinetic curves were measured within the temperature range from 297 to 316 K. By the application of differential isoconversional methods, it was found that the process of exchange of water absorbed in calcium alginate hydrogel with ethanol has a unique rate determining step (a single step process). Using the model fitting method, it was determined that the kinetics of the exchange can be mathematically described with the kinetic model of the first-order chemical reaction. The values of the kinetic parameters of water exchange: the rate constants (km), energy of activation (Ea = 18.0 kJ.mol-1), and the pre-exponential factor (ln[A/min-1] = 4.0) were calculated. By using Eyring's equation, the values of thermodynamics parameters: standard enthalpy of activation (ΔH*), standard entropy of activation (ΔS*), and Gibbs energy of activation (ΔG*) were calculated. It was found that the rate of rearrangements of the bound water around hydrophilic groups of a polymeric network has a dominant effect on the kinetics of the exchange of the absorbed water with ethanol. The mechanism of the exchange of adsorbed water with ethanol was suggested. [ABSTRACT FROM AUTHOR]