Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds

Abstract

A mathematical description of the thermal degradation of spongin-based scaffolds is given. The Arrhenius integral was evaluated using the inverse problem approach, in which the unknown values were the activation energy EA, the pre-exponential factor A, and the model function f(α) characterizing the physical process. The form of f(α) was determined and the values of the parameters EA, A and TS were evaluated in detail. Moreover, the function f(α) assessed in this study was compared with classical solid-state model functions. Finally, the mean square minimization approach was used to solve the inverse problem with unknown function f(α) and pre-exponential constant A. Likewise, the approximation of f(α) with 6th- and 7th-degree polynomials was used to obtain numerical values of EA and A. This study evaluated the inverse problem approach for the Arrhenius equation. These investigations provide new insight into the description of the thermal degradation of spongin-based scaffolds.