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Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds
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 th...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9929043/ https://www.ncbi.nlm.nih.gov/pubmed/36788331 http://dx.doi.org/10.1038/s41598-023-29565-1 |
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author | Żółtowska, Sonia Ciałkowski, Michał Alejski, Krzysztof Jesionowski, Teofil |
author_facet | Żółtowska, Sonia Ciałkowski, Michał Alejski, Krzysztof Jesionowski, Teofil |
author_sort | Żółtowska, Sonia |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-9929043 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-99290432023-02-16 Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds Żółtowska, Sonia Ciałkowski, Michał Alejski, Krzysztof Jesionowski, Teofil Sci Rep Article 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. Nature Publishing Group UK 2023-02-14 /pmc/articles/PMC9929043/ /pubmed/36788331 http://dx.doi.org/10.1038/s41598-023-29565-1 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Żółtowska, Sonia Ciałkowski, Michał Alejski, Krzysztof Jesionowski, Teofil Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
title | Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
title_full | Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
title_fullStr | Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
title_full_unstemmed | Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
title_short | Investigation of the inverse problem for the Arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
title_sort | investigation of the inverse problem for the arrhenius equation using the example of thermal degradation of spongin-based scaffolds |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9929043/ https://www.ncbi.nlm.nih.gov/pubmed/36788331 http://dx.doi.org/10.1038/s41598-023-29565-1 |
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