Study of Mathematical Models Describing the Thermal Decomposition of Polymers Using Numerical Methods

This research presents the results of a combined numerical and experimental study of the thermal decomposition behavior of copolymers based on polypropylene glycol fumarate phthalate. The thermal decomposition of polymers plays a key role in various fields, such as waste recycling and energy recovery, and in the development of new materials. The objective of this study is to model the degradation kinetics using thermogravimetric data, matrix-based numerical methods, and quantum chemical calculations. To solve the resulting systems of linear algebraic equations (SLAEs), matrix decomposition algorithms (QR, SVD, and Cholesky) were employed, which enabled the determination of activation energy values for the process. Comparison of the activation energy (<i>E_a</i>) results obtained using the decomposition method of Cholesky (207.21 kJ/mol), normal equations (205.22 kJ/mol), singular value decomposition (206.23 kJ/mol), and QR decomposition (206.23 kJ/mol) showed minor changes that were associated with the features of each method. Quantum chemical calculations based on density functional theory (DFT) at the B3LYP/6-31G(<i>d</i>) level were performed to analyze the molecular structure and interpret the IR spectra. This study establishes that the content of functional groups (ether and ester) and the type of chemical bonds exert critical influences on the decomposition mechanism and associated thermal parameters. The results confirm that the polymer's structural architecture governs its thermal stability. The scientific novelty of this work lies in the integration of numerical approximation methods and quantum chemical analysis for investigating the thermal behavior of polymers. This approach is applied for the first time to copolymers of this composition and may be employed in the design of heat-resistant materials for agricultural and environmental applications.