# Oxidative Thermolysis of Sulfobutyl-Ether-Beta-Cyclodextrin Sodium Salt: A Kinetic Study
## 3 Results and Discussion
As a result, the calculated activation energy (E\({}_{\text{a}}\)) may not be accurate for reactions that exhibit multi-step or overlapping mechanisms [22; 46]. The good correlation of the data sets suggested by the ASTM E698 method (Figure 5) may suggest a single-step degradation of SBECD, but this must be further analyzed by employing multi-point model free methods, like the Friedman and Flynn-Wall-Ozawa methods, since one-point model free methods, like ASTM E698, have clear limitations [21; 45]. Isoconversional kinetic analysis is a robust tool used to study the degradation behavior of materials, providing a non-mechanistic method for estimating the kinetic parameters of a reaction [28; 29; 41]. In contrast to model-fitting methods, which rely on predefined reaction mechanisms, isoconversional models determine kinetic parameters solely from the experimental data obtained across various heating rates [29; 47]. The investigated process corresponds to the first degradation step of anhydrous SBECD, occurring within the following temperature ranges: 221-289 \({}^{\circ}\)C (at \(\beta\) = 2 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)), 228-298 \({}^{\circ}\)C (at \(\beta\) = 4 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)), 235-303 \({}^{\circ}\)C (at \(\beta\) = 6 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)), 238-309 \({}^{\circ}\)C (at \(\beta\) = 8 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)), and 239-313 \({}^{\circ}\)C (at \(\beta\) = 10 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)). As expected, the process shifts to higher temperatures, and the reaction rate increases with higher heating rates, as shown in the plots of the reaction progress vs. temperature (Figure 6a) and reaction rate vs. temperature (Figure 6b). This behavior is attributed to the thermal inertia of the samples during heat transfer at elevated heating rates. The analysis of the reaction rate curves from Figure 6b reveal two separate processes that concur at the decomposition of anhydrous SBECD, when the thermal treatment is carried out at low heating rates (\(\leq\)4 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\)). At higher heating rates, due to thermal inertia, the processes are no longer separated or a change in the decomposition mechanism takes place. To get a clear view of the influence of the heating rate over the decomposition of SBECD, three well-established isoconversional methods were employed, namely Flynn-Wall-Ozawa (FWO), Friedman (FR), and non-parametric kinetics (NPK). The linear plottings obtained by using the FWO and FR methods are presented in Figure 7a,b, while the corresponding apparent E\({}_{\text{a}}\) values vs. \(\alpha\) (with a variation step for \(\alpha\) of 0.05) are shown in Table 1, along with corresponding errors. Figure 5: ASTM E698 plot for SBECD degradation in dynamic air flow at selected five heating rates. By analyzing the data presented in Table 1 and Figure 8, it can be observed that the data processing by the integral and differential protocols reveals a similar trend regarding the variation of \(\mathrm{E_{a}}\) with the advance of the reaction, namely at low conversion degrees (\(\alpha\leq 0.2\) for FR and \(\alpha\leq 0.5\) for FWO), and the decrease in \(\mathrm{E_{a}}\) was observed, followed by an increasing trend as the conversion increases (\(\alpha>0.2\) for FR and \(\alpha>0.5\) for FWO).