## 3 Results and Discussion
### Initial Experiments to Define Lignin Isolation Variables and Further Optimization by RSM
As far as the molecular weight and the polydispersity are concerned, these values were also in a narrow margin but the improved polydispersity (1.90) was achieved with the highest DFRC value. Therefore, keeping in view the high efficiency of the synergism of dioxane: acetic acid under HCl catalyzed conditions we chose this combination and named this initial lignin as dioxane: acetic acid lignin (DA lignin) to further optimize in terms of high yield and with high DFRC values. To this end, we chose Design Expert software to sort out the optimum combination via a statistical way using response surface methodology. We selected three variables: time from 24 to 72 h, solids loading from 5% to 15%, and HCl dose from 5 to 15 mL. All these variables with their values along with their different experimental combinations were performed accordingly and the response was tabulated and reported in Table 2.  
For these performed experiments, the equation representing the adjusted quadratic model (model fitness with its significance suggested by software) in terms of coded factors is described in the following equation. Y= +8.33 +2.742X1 + 0.45X2 +1.69X3 +0.60 X1X2 + 0.88 X1 X3 + 0.000 X2 X3 - 1.78 X12 - 0.40X2 - 0.93 X32  
where the lignin yield is denoted by Y and the isolation variables are represented as X1 time, X2 as solids loading, and X3 as catalyst dose. In order to study the model adequacy, the ANOVA table is presented in Table 3. For this model the adjusted R-squared value and R-squared values were 0.9857 and 0.9994, respectively. As it can be seen in the Table 2, the lignin yield varied quite considerably with the variation of the extraction conditions. It became fairly prominent with the catalyst dose and the time of the extraction process adapted. This evidence was also found from the ANOVA table. It is evidenced there that the model is quite significant having a \(p\) value less than 0.0001. Moreover, the adjusted R squared value as well as the R squared value 0.9857 and 0.9994, respectively, are noticeably high showing thus the model adequacy. In our model, the independent variables of both the time and catalyst dose have a quite significant \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scheme 1**} & **Time** & **Solids Loading** & **Catalyst Dose** & \multirow{2}{*}{**Lignin Yield (\%)**} \\  & **(\(\chi_{1}\))** & **(\(\chi_{2}\))** & **(\(\chi_{3}\))** & \\ \hline
1 & 24 & 10 & 15 & 4.0 \\
2 & 24 & 10 & 5 & 2.0 \\
3 & 24 & 15 & 10 & 3.1 \\
4 & 24 & 5 & 10 & 3.5 \\
5 & 48 & 10 & 10 & 8.1 \\
6 & 48 & 15 & 15 & 9.0 \\
7 & 48 & 15 & 5 & 6.0 \\
8 & 48 & 5 & 15 & 8.0 \\
9 & 48 & 5 & 5 & 5.0 \\
10 & 48 & 10 & 10 & 8.3 \\
11 & 48 & 10 & 10 & 8.6 \\
12 & 72 & 15 & 10 & 10.0 \\
13 & 72 & 10 & 5 & 5.5 \\
14 & 72 & 10 & 15 & 11.0 \\
15 & 72 & 5 & 10 & 8.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Actual values of the experimental combinations. impact on the lignin yield. For the time the \(p\) value is <0.0001 showing a prominent effect on the yield. This phenomenon is mainly regarded as time prolongation that can help to loosen the native biomass web to dissolve out the lignin portion of the biomass under such conditions [42]. In the case of the catalyst dose, the \(p\) value also exhibited a value lower than 0.0001. This prominent effect is highly likely due to the strong protonation effect of the catalyst HCl [40]. This acid catalyst, regarding lignin isolation, offers a better selective extraction retaining a good quality [43]. However, in the case of solids loading it was not found to be that significant with a comparatively higher value of 0.0113. For this variable, under our conditions it is anticipated that the catalyst was not penetrated enough to open up the recalcitrant structure to dissolve out the lignin portion.