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

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 ( E a ) 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 E a 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 E a,1 of approximately 68 kJ mol −1 ; (2) a reaction accompanied by liquefaction controlled by an autocatalytic rate behavior with E a,2 of approximately 123 kJ mol −1 ; (3) a diffusion-controlled dehydration of gel powder with E a,3 of approximately 82 kJ mol −1 .