3.3.2. Model-Fitting Technique

Table 7 shows the values of *Eθ*, R2, and A at different heating rates derived from the CR model for the GG samples. These were deduced from the slope of linear plots of ln *<sup>g</sup>*(*θ*) *T*2 against the reciprocal of temperature. The reaction order, *n*, may be taken as a positive or negative integer. However, it is more practicable to define it as Equation (9) [58].

$$0 \le n \le 3\tag{16}$$

There is a postulation that compares the average value of *E<sup>θ</sup>* obtained from the CR method with that of an iso-conversional technique such as FWO. This provides a means to choose an appropriate decomposition mechanism [8,59]. The closest *E<sup>θ</sup>* among the given integral models is believed to represent a probable reaction mechanism. In this investigation, this postulation was employed. Some non-realistic values were obtained for some models and stages of decomposition; therefore, the values of *E<sup>θ</sup>* that had the same order of magnitude as the model-free kinetic data were the only ones considered. Only the data from stage II decomposition satisfy this criterion and therefore are presented for discussion in Table 7. A strong correlation (R<sup>2</sup> > 0.9) was demonstrated for all the heating rates in both conditions—implying that the models fairly approximate the decomposition process. Of all the models, as listed in Table 2, it was demonstrated that only two of them, namely chemical reaction and diffusional, represent the probable mechanism that predominates the thermal process. This validates the assertion from the iso-conversional approximation regarding the multi-step reaction pathways and the associated complexities of GG thermal decomposition. The activation energy and the pre-frequency exponential factor, for the integral model, increase with the heating rates. For the chemical reaction model, they increase with an increase in reaction order.

For β 5, 10, 20, and ◦C/min under N2, the values of *E<sup>θ</sup>* for the second-order reaction model were 88.3, 102, and 103 kJ/mol, respectively, while the third-order reactions were, respectively, 109, 126, and 127 kJ/mol. In both (N2 and air) conditions, the diffusional model presents the highest average value of 216 kJ/mol (air) and 137 kJ/mol (N2). For the second stage of decomposition, the closest average value of *E<sup>θ</sup>* for the FWO (129 kJ/mol) and CR (130 kJ/mol) models in the N2 atmosphere represents the diffusional model. This suggests the critical role of diffusion in this stage of decomposition for the tropical grass being investigated. It has been reported in the literature that where the mobility of the reactant constituents depends on the lattice defects, the solid-state reactions mostly occur between either the molecules penetrating the lattices or the crystal lattices [59].


*Sustainability* **2022**, *14*, 112
