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

Sonia Żółtowska; Michał Ciałkowski; Krzysztof Alejski; Teofil Jesionowski

doi:10.1038/s41598-023-29565-1

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

Sci Rep. 2023 Feb 14;13(1):2636. doi: 10.1038/s41598-023-29565-1.

Authors

Sonia Żółtowska¹, Michał Ciałkowski², Krzysztof Alejski¹, Teofil Jesionowski³

Affiliations

¹ Faculty of Chemical Technology, Institute of Chemical Technology and Engineering, Poznan University of Technology, Berdychowo 4, 60965, Poznan, Poland.
² Faculty of Environmental Engineering and Energy, Institute of Thermal Engineering, Poznan University of Technology, Piotrowo 3, 60965, Poznan, Poland.
³ Faculty of Chemical Technology, Institute of Chemical Technology and Engineering, Poznan University of Technology, Berdychowo 4, 60965, Poznan, Poland. Teofil.jesionowski@put.poznan.pl.

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.