Multistep kinetics in self-induced sol–gel process of amorphous anhydride formation during thermal dehydration of potassium tetraborate tetrahydrate

Abstract

The physico-geometrical mechanism and kinetics of the multistep thermal dehydration of potassium tetraborate tetrahydrate was investigated as a model reaction to produce amorphous anhydrate via the self-induced sol–gel process. The thermal dehydration is composed of three consecutive dehydration steps: (1) a surface reaction in the solid-state accompanied by crack formation; (2) a rapid mass loss process accompanied by liquefaction to form the aggregate of the gel powders; and (3) the dehydration of gel powder aggregate to form a glassy anhydride. The changes in the contribution of the individual dehydration steps to the overall process according to the sample particle size and the heating rate (β) were identified as specific features of the multistep dehydration, which was characterized quantitatively using mathematical deconvolution analysis with log-normal four-parameter functions. The difficulty in determining the apparent activation energy (Ea) of the individual dehydration steps using isoconversional analysis due to the changes in the contribution depending on β values was addressed using modulated temperature thermogravimetry. Using the contributions and the apparent Ea of the individual dehydration steps as initial values, the kinetic description of the multistep thermal dehydration was refined through a kinetic deconvolution analysis using the cumulative kinetic equation. As a result, the individual dehydration steps were kinetically characterized as: (1) a surface reaction described by the first-order rate law with Ea,1 of approximately 68 kJ mol−1; (2) a reaction accompanied by liquefaction controlled by an autocatalytic rate behavior with Ea,2 of approximately 123 kJ mol−1; (3) a diffusion-controlled dehydration of gel powder with Ea,3 of approximately 82 kJ mol−1.