3.3.1. Model-Free Technique

Figure 4a,b, respectively, show the plots of the linear curves derived from the application of Equations (6)–(8) under N2 and air conditions. The DFM, FWO, and STK models have proven suitable in predicting the kinetic parameters because of the high correlation (R2 > 0.9) shown in both atmospheres. The plot was limited to a conversion degree, *θ*, (0.15 ≤ *θ* ≤ 0.8) as this region is where the chemical reactions are predominant, and the kinetic models are more likely to produce realistic results. For the conversion range of 0.2 to 0.6, particularly for the integral methods (FWO and STK), the lines of best fit were approximately parallel. This may be an indication of a similar kinetic behavior in which the same reaction mechanism is exhibited for the specified range. In some cases, the nonparallel nature of the lines was largely restricted to either the earlier or the later part of the conversion. Perhaps, it is a pointer to a dissimilarity in the reaction mechanism that characterizes these decomposition stages. It has been suggested that the non-parallel nature of the linear fits could be an indication of a change in the reaction mechanism at a higher decomposition temperature [54,55]. Wang et al. [56] attributed it to the heterogeneity of the solid produced at the latter stages of degradation. The reaction mechanism at this stage is considered to involve a complex intertwine of diffusion, secondary reactions, and in situ catalysis of metals. It is also important to note that the non-parallel trend demonstrated by the DFM technique affirms the complexity of biomass decomposition, which arises from its intrinsically heterogenous character [55].

The dependence of activation energy, *Eθ*, on conversion ratio, *θ*, for the three isoconversional methods is displayed in Figure 5a,b for the N2 and the air atmosphere, respectively. Table 6 also presents the *Eθ*, *θ*, and the coefficient of determination, R2, data for both scenarios. These values were determined at an increment of 0.05 for *θ*, from 0.15 to 0.8. The *E<sup>θ</sup>* had a significant positive correlation with *θ* (r = 0.27; *p* < 0.05). It has been noted that a significant variation in the apparent activation energy with conversion underscores the complexity associated with the kinetic process [57]. The effects of the decomposition atmospheres were also statistical analyzed, and it was shown that the *E<sup>θ</sup>* was negatively correlated for air (r = −0.25; *p* < 0.05), while it was positively correlated for N2 (r = 0.84; *p* < 0.05). The trend in the inert environment is different from that in the oxidative. In the inert scenario, the trajectories of the curves were similar, especially for the FWO and STK that are modeled according to the temperature integral approximation. The DFM is a differential technique that is not based on the integral approximation of the temperature function, and thus, it is relatively more accurate [36]. The *E<sup>θ</sup>* versus *θ* plots show three distinct stages (Figure 5a). The first decomposition stage, *θ* = 0.15–0.2 for DFM, FWO, and STK presents average values of *E<sup>θ</sup>* as 105, 101, and 98 kJ/mol, respectively. The degradation of the hemicellulose fractions is the predominant process at this stage due to its high reactivity relative to the other polymeric fractions. This may have accounted for the relatively low *E<sup>θ</sup>* values [22]. Following a similar sequence, the average values of *E<sup>θ</sup>* were evaluated as 137, 129, and 127 kJ/mol for *θ* = 0.25–0.6. At this stage, the combined contribution of the three polymeric constituents is more likely, albeit in different proportions. However, cellulose may be expected to play a significant role given its highly ordered crystalline nature that makes it stable thermally [22,51]. Again, this is corroborated by the earlier observation that cellulose degradation occurs within this period. In the

last reaction stage (*θ* = 0.65–0.8), the *E<sup>θ</sup>* surges to much higher levels, recording average values of 189, 165, and 164 kJ/mol with the widest variability. Other researchers have reported similar trends for other lignocellulosic biomass [36,53]. The final decomposition stage for the pyrolytic processes is typically characterized by lignin and secondary product decomposition as well as char formation [22,51].

**Figure 4.** Plots of linear curves for DFM, FWO, STK models in (**a**) N2 and (**b**) air environments.

**Figure 5.** Plots of apparent activation energy, *E*θ, against conversion ratio, *θ*, (**a**) N2 and (**b**) air environments.

**Table 6.** Values of *E<sup>θ</sup>* (kJ/mol), and R<sup>2</sup> for DFM, FWO, and STK models under N2 and air environments.


For the oxidative scenario, the three methods initially show a positive slope, and then plunge into a deep valley mid-way into the conversion (Figure 5b). A similar pattern has been reported in the literature [51]. At *θ* = 0.15–0.2, a gentle slope with a very high correlation of R<sup>2</sup> > 0.99 and comparable values of *E<sup>θ</sup>* (148, 158, 157 kJ/mol) was observed for the three methods. These values compare well with the published data for the *E<sup>θ</sup>* of *Lentinula edodes* pileus in a similar decomposition range [50]. Wu et al. [51] suggested the reactions here involve the oxidative breakdown of hemicellulose, pectin, and N-containing compounds. Although the activation energies for FWO and STK are about 160 kJ/mol, DFM displays a sharp rise in slope from 164 to 279 kJ/mol. It is noteworthy that the average value of *E<sup>θ</sup>* in stage II for DFM was much higher than the other stages as well as the other methods. This may be another attestation to the complexity involved in the thermal degradation processes as this stage involves the simultaneous oxidative decomposition of hemicellulose, cellulose, and lignin [51]. Just above *θ* = 0.5, *E<sup>θ</sup>* decreases to a minimum of around 0.68, then increases. This trend highlights the fact that this is a complex thermal process and the activation energy values obtained are simply "apparent". Therefore, it is not uncommon for the values of *E<sup>θ</sup>* to exhibit a marked variation from the intrinsic kinetic

parameters of an individual step [58]. Unlike the pyrolytic process, the last stage of the oxidative decomposition process involves the combustion of char [51].

Generally, the average values of *E<sup>θ</sup>* for air, for the first and second stages of decomposition, are much higher than for N2. For instance, the Friedman model at the second stage had *E<sup>θ</sup>* = 202 and 137 kJ/mol for air and N2, respectively. This observation has been previously observed [1]. The implication of this lower energy barrier is required for the reaction to proceed in an inert environment. Significantly, the average values of E<sup>θ</sup> in the final decomposition stage for N2 were higher than in air. For instance, *E<sup>θ</sup>* for the FWO method in air and N2 gave 125 and 165 kJ/mol, respectively. This may be due to the distinct phenomenon in an inert environment resulting in char formation, while in air it is combusted [51,53]. These results show that both the pyrolytic and the oxidative processes involve complicated, multi-step reaction mechanisms.
