## 2 Results and Discussion
### Investigating the Effect of Operational Parameters on Modified Fenton Reaction Efficiency  
As noted in Section 1, a key goal of the oxidation process was to determine the optimal ranges of parameters for Fenton oxidation of FFs. The efficiency of the treatment process was demonstrated based on fiber diameter reduction. As shown in Figure 2, the average diameter of raw fibers (fitted with the Gaussian model) was estimated as 12.3 \(\pm\) 0.5 \(\upmu\)m.  
In the Fenton reaction, hydrogen peroxide and iron species can play significant roles that affect chemical consumption costs and reaction efficiency. To amplify reaction efficiency, it is important to find the optimal ranges of external parameters such as hydrogen peroxide, Fe (II), pH, and time, according to the reduction of fiber diameter (cf. Figure 2). Figure 2 reveals the effect of the evaluated parameters on fiber diameter reduction. As shown in Figure 2a, for 10 wt.% H2O2, the average diameter was 10.7 \(\pm\) 0.67 \(\upmu\)m. Compared to raw FFs, the reduction in average fiber diameter can be related to the washing step, which may remove some impurities and non-cellulosic components from the fiber surface. The results reveal that incremental concentrations of hydrogen peroxide resulted in a greater reduction of fiber diameter. At a 10 wt.% H2O2 concentration, a slight reduction in the average diameter was observed, while the maximum H2O2 concentration that yielded the greatest reduction in flax fiber diameter was found to be 15 wt.%. According to the results, \begin{table}
\begin{tabular}{c c} \hline
**Iron Concentration (wt.\%)** & **Iron Content (wt.\%)** \\ \hline
0.1\% & Not detected \\
1.0\% & Not detected \\
2.5\% & 1.64\% \\
5.0\% & 4.50\% \\ \hline \end{tabular}
\end{table} 
Table 1: Atomic content weight (%)of iron adsorbed according to a binding energy of 710 eV on the surface of the flax fibers, as obtained by XPS analysis. Figure 2: Effect of the reaction parameters on the average flax fiber diameter upon treatment with the modified Fenton reaction: (**a**) effect of hydrogen peroxide on the fiber diameter, (**b**) effect of iron sulfate on the fiber diameter, (**c**) effect of pH on the fiber diameter, and (**d**) effect of reaction time on the fiber diameter. it can be concluded that there was no significant change in the average fiber diameter induced by increasing the H2O2 concentration from 10 to 15 wt.%. In Figure 2b, the role of iron concentration on the diameter of FFs in the Fenton process is evidenced by augmentation of the iron dosage onto the surface of FFs, where the efficiency of the reaction increased. On the other hand, with a further increment of iron content of 2 wt.%, there was negligible decrease in the average diameter of the treated fibers. According to the operational costs and the efficiency of the process, the desired iron salt concentration was 2 wt.%, in agreement with the XPS results in Figure 1[26]. The pH of the reaction medium is also an important operational parameter in the Fenton oxidation process, since it controls the generation of hydroxyl radicals, as noted in Figure 2c[27]. The results reveal that maximum Fenton reaction efficiency occurred at neutral pH, whereas reduced Fenton efficiency occurred in acidic media. This trend relates to the competition of H+ and Fe2+ ions for adsorption sites onto the surface of FFs. In addition to the above-mentioned parameters, reaction time is another significant parameter that influences the efficiency of the Fenton reaction. It is obvious that, by increasing the time, greater efficiency of the Fenton oxidation process occurred. To determine the desirable reaction time for modified Fenton treatment of flax fibers, the reaction was monitored for various periods up to 24 h. Thereafter, there was a minor change in the average diameter of the fibers.