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

Abstract

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 E A , 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 E A , A and T S 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 E A 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.