## 2 Materials and Methods
### Methods  
The _Salix psammophila_ was smashed and filtered with a 50-80 mesh sieve, then a certain mass of _Salix psammophila_ powder was weighed and put into the polytetrafluoroethylene (PTFE) reactor, and different volumes of concentrated sulfuric acid were added at different solid-liquid ratios. After standing for a certain period of time, the reactor body was put into the homogeneous reactor, a certain temperature was adjusted to react under rotation for a certain period of time, and the reactor was then taken out and put into ice water for sudden cooling. The cooled solid-liquid mixture was added into 300 mL distilled water, stirred, filtered, and washed repeatedly with hot distilled water until it had become neutral. Afterwards, the mixture was dried for 24 h in the oven at 100 \({}^{\circ}\)C, then ground, packaged into a seal bag, labeled, and stored in the dryer for use.  
A certain amount of oleic acid, methanol, and _Salix_ carboniferous solid acid catalyst were added into a 3-neck flask (the quality of catalyst: the quality of oleic acid = 7%, the amount of substance of methanol: the amount of substance of oleic acid = 10:1), which was then put into a water bath at a certain temperature (\(68\pm 1\)\({}^{\circ}\)C), and a reflux condenser was placed on the top of the 3-neck flask. After reaching the reaction temperature, the reaction time was counted when liquid reflux was observed in the reflux condensing tube above. After reaching the designated reaction time, the 3-neck flask was taken out and cooled rapidly. The solid acid catalyst was washed with ethanol, and the aqueous phase in the filtrate was evaporated using the rotatory evaporator to obtain the mixture of methyl oleate and oleic acid, which was then titrated.  
According to the determination of animal and plant fat acid value and acidity through the third method of hot ethanol method in GB 5009.229-2016, the mixture was dissolved into 50 mL of 95% ethanol, which was heated through a water bath and titrated using the 0.1 mol/L KOH standard solution, with phenolphthalein as the indicator. The titration end-point was reached when the solution became light red and did not fade within 1 min, and the oleic acid conversion rate, namely, the conversion level (\(X\)), was calculated.  
\[X=(A_{0}-A_{\mathrm{T}})/A_{0}\times 100\% \tag{1}\]  
where \(A_{0}\) is the initial acid value of the reaction(mmol/g), and \(A_{\mathrm{T}}\) is the instantaneous acid value of the reaction(mmol/g).  
The Box-Behnken four-factor three-level response surface method (RSM) design method was utilized, among which, reaction temperature, reaction time, solid-liquid ratio, and standing time were treated as the independent variables, while conversion level was considered as the response value. The factors and level coding are presented in Table 1. In total, 9 experiments (including 4 analytical experiments and 5 central experiments) were designed to estimate the experimental error. The response curve experimental design and results are displayed in Table 2. The Design-Expert software was used for analysis, and the following response surface model was constructed.  
\[\begin{array}{c}X=88.24+1.17A+0.49B-2.53C-1.01D-3.02\Delta B+4.60 AC+2.47 AD+2.28C-\\ 2.27B+4.41 CD-5.65A^{2}-2.92B^{2}-1.68C^{2}-1.47D^{2}\end{array} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Levels**} & **A: Reaction** & **B: Reaction** & **C: Solid-Liquid** & **D: Standing** \\  & **Temperature/\({}^{\circ}\)C** & **Time/min** & **Ratio** & **Time/min** \\ \hline \(-1\) & 120 & 60 & 1:4 & 30 \\ \(0\) & 135 & 90 & 1:5 & 60 \\ \(1\) & 150 & 120 & 1:6 & 90 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Factor levels for the experiments.