# Oxidative Thermolysis of Sulfobutyl-Ether-Beta-Cyclodextrin Sodium Salt: A Kinetic Study
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{\(\mathrm{E_{a}}\)/ \(\mathrm{kJ\cdot mol^{-1}}\)} & \multicolumn{6}{c}{**Conversion degree \(\alpha\)**} \\ \cline{2-9}  & **0.05** & **0.1** & **0.15** & **0.2** & **0.25** & **0.3** & **0.35** \\ \hline FWO & \(156.6\pm 0.2\) & \(154.6\pm 0.1\) & \(152\pm 0.1\) & \(149.7\pm 0.1\) & \(147.8\pm 0.1\) & \(146.3\pm 0.1\) & \(145.2\pm 0.1\) \\ \hline
**Friedman** & \(156.7\pm 0.9\) & \(130.7\pm 0.1\) & \(125.1\pm 0.4\) & \(123\pm 1.0\) & \(124.1\pm 1.6\) & \(127.2\pm 2.0\) & \(131.5\pm 2.5\) \\ \hline  & \multicolumn{6}{c}{**Conversion degree \(\alpha\)**} \\ \cline{2-9}  & **0.4** & **0.45** & **0.5** & **0.55** & **0.6** & **0.65** & **0.7** \\ \hline FWO & \(144.5\pm 0.2\) & \(144.3\pm 0.2\) & \(144.5\pm 0.2\) & \(145\pm 0.3\) & \(146\pm 0.4\) & \(147.4\pm 0.6\) & \(149.3\pm 0.8\) \\ \hline
**Friedman** & \(136.7\pm 2.7\) & \(143.2\pm 3.0\) & \(149.6\pm 3.3\) & \(155.5\pm 3.6\) & \(161.7\pm 3.8\) & \(166.8\pm 4.2\) & \(172\pm 4.9\) \\ \hline  & \multicolumn{6}{c}{**Conversion degree \(\alpha\)**} \\ \cline{2-9}  & **0.75** & **0.8** & **0.85** & **0.9** & **0.95** & \\ \hline FWO & \(151.6\pm 1.1\) & \(154.6\pm 1.6\) & \(158.1\pm 2.3\) & \(162.7\pm 3.9\) & \(169.7\pm 8.0\) & & **151.0 \(\pm\) 9.5** \\ \hline
**Friedman** & \(177.4\pm 6.2\) & \(181.5\pm 7.9\) & \(186.3\pm 10.7\) & \(191.2\pm 16.5\) & \(207.6\pm 28.7\) & & **155.2 \(\pm\) 37.7** \\ \hline \end{tabular}
\end{table} 
Table 1: Variation in \(\mathrm{E_{a}}\) vs. \(\alpha\) for SBED degradation using the FWO and FR isoconversional methods. Figure 6: The reaction progress expressed as conversion (**a**) and the reaction rate (**b**) vs. temperature for the first process of decomposition of SBED. Figure 7: Linear plotting of the FWO integral isoconversional method (**a**) and FR differential isoconversional method (**b**) at indicated conversion degrees \(\alpha\) for first process of decomposition of SBED. \(\overline{\text{E}_{\text{a}}}\) Regarding the uncertainty of each \(\text{E}_{\text{a}}\) value vs. conversion degree, it can be observed that the integral processing of the data reveals that the modification of the decomposition mechanism takes place only when \(\alpha\) is higher than 0.9, and when all the other values are placed in the confidence interval of \(\overline{\text{E}_{\text{a}}}\pm 0.1\cdot\overline{\text{E}_{\text{a}}}\) (or between \(0.9\overline{\text{E}_{\text{a}}}\) and \(1.1\overline{\text{E}_{\text{a}}}\)), with namely a 10% accepted variation around the mean value (Figure 8). However, the differential processing of the data reveals a complex pathway of decomposition, since the dependence of activation energy values with the conversion degree falls outside the above-mentioned confidence interval of 10% accepted variation around the mean value at low conversion degrees (\(\alpha\) between 0.1 and 0.4, and \(\alpha>0.75\)). The variation of \(\text{E}_{\text{a}}\) vs. \(\alpha\) may be explained by the modification of activation parameters during the decomposition process, by the complexity of the heterogenous process, or by the heat and mass transfer influence over the reaction rate [30,31,48]. [PERSON] et al. [49-51] associated the aspect of the \(\text{E}_{\text{a}}\) vs. conversion dependencies in the mechanism of the complex processes, suggesting that an increase in \(\text{E}_{\text{a}}\) with \(\alpha\) takes place when the process involves parallel or successive reactions, and a decrease in \(\text{E}_{\text{a}}\) with \(\alpha\) takes place when the process involves a reversible step or the process involves a diffusion transition. If the variation of \(\text{E}_{\text{a}}\) is non-monotonous, like in this case, the process is complex and the data cannot be processed solely by classic isoconversional methods, like FWO and FR.