Thermo-Kinetic Framework for TGA Curve Modeling and Evaporation Enthalpy Determination in Composite Materials: The Case of Bone-Derived Hydroxyapatite.

A thermo-kinetic model based on nonequilibrium thermodynamics is presented to describe the sequential thermal degradation of multicomponent composite materials under nonisothermal conditions. The formulation is derived from the Gibbs free energy balance and the entropy-production principles, leading to a system of coupled differential equations in which mass-loss kinetics are governed by their conjugate thermodynamic forces and the externally imposed heating rate. Within this framework, the linear relations between fluxes and forces are characterized by generalized phenomenological coefficients defined in the Gibbs free energy representation, which are appropriate for experimentally controlled intensive variables. The model was applied to a biogenic hydroxyapatite composite obtained from bovine bone powder and validated by thermogravimetric analysis (TGA) at heating rates of 3, 5, 7, 25, 50, 75, and 100 °C/min. The model successfully reproduces the characteristic thermal degradation stages of the composite in inert conditions, enabling the determination of the apparent evaporation enthalpies of each constituent and revealing their dependence on the applied heating rate. Analysis of these trends identifies a quasi-static regime at low heating rates. For the specific case of the biohydroxyapatite system studied here, a heating rate of 5 °C/min lies within the quasi-stationary low-ramp regime and is therefore suitable for obtaining reliable apparent enthalpies. Owing to its general formulation, the model is applicable to composite systems with an arbitrary number of components, providing a physically grounded framework that extends the interpretation of TGA measurements beyond empirical curve fitting toward a consistent thermodynamic and physicochemical description of thermal degradation processes.