## 3 Results and Discussion  
### Optimization of Chromatographic Conditions  
The preliminary experiments were conducted using standard solutions and direct injection through the SPME interface (60 \(\mu\)L volume) to determine the optimal chromatographic conditions for analyte separation. Table 1 summarizes the efficiency factor (N), retention factor (k\({}^{\prime}\)), and symmetry factor (S), measured as the peak width at 1/20 of its height above baseline (w\({}_{0.05\text{h}}\)), for both analytes using the optimized mobile phase: a water/methanol/ethanol mixture (56:40:6, \(v/v/v\)) with 1.2% acetic acid. Both the N and k\({}^{\prime}\) values were appropriate for the column type, and the Sw\({}_{0.05\text{h}}\) coefficient indicated excellent peak symmetry for both analytes. Solubility is a critical property of flavonoids, significantly influencing their behavior [4]. However, the literature on quercetin (Q) solubility is inconsistent [35]. Q can engage in intermolecular interactions with solvents, leading to variability in solubility and properties [36]. While Q is highly soluble in organic solvents and poorly soluble in water, its solubility increases with temperature [36]. However, in this study, higher temperatures negatively affected the stability of Q solutions. Aliquots of 1 mL of Q and R solutions (0.1 \(\mu\)g/mL) were incubated at 37 \({}^{\circ}\)C and 100 \({}^{\circ}\)C, and then kept at room temperature and analyzed at different time intervals (0, 30, 60, and 120 min). As shown in Table 2, the R peak areas remained constant, whereas the Q peak areas decreased significantly at higher temperatures. Calibration curves were constructed using a UV-DAD detector in the concentration range of 0.5 ng/mL to 5 \(\mu\)g/mL. The linear regression equations were y = 12839\(\cdot\)x \(-\) 199 for Q and y = 22998\(\cdot\)x + 126 for R, where x is the injected amount (ng) and y is the peak area. Both analytes exhibited good linearity (correlation coefficients \(>\) 0.999). The limits of detection (LOD, S/N = 3) and quantification (LOQ, S/N = 10) were 1.7 ng/mL (0.1 ng) and 5.0 ng/mL (0.3 ng) for Q and 0.8 ng/mL (0.05 ng) and 2.8 ng/mL (0.17 ng) for R, \begin{table}
\begin{tabular}{c c c c} \hline
**Analyte** & **N** & **k\({}^{\prime}\)** & **S\({}_{\text{W0.05h}}\)** \\ \hline R & 5642 & 1.260 & 0.58 \\ \hline Q & 6431 & 3.726 & 0.56 \\ \hline \end{tabular}
\end{table} 
Table 1: Efficiency factor (N), retention factor (k\({}^{\prime}\)), and symmetry factor (S) of the peak width at 1/20 of its height above baseline (w\({}_{0.05\text{h}}\)) obtained for R and Q.  
respectively. The precision (% RSD) was evaluated at 0.005, 0.05, and 0.5 \(\upmu\)g/mL, with intra-day (\(n\) = 3) and inter-day (\(n\) = 3 \(\times\) 5 days) precision values below 3.0% for Q and 1.8% for R, demonstrating excellent accuracy and repeatability. Fluorescence detection (FD) optimization was performed by evaluating excitation and emission wavelengths. For Q, the highest peak area was observed at 370 nm (excitation) and 540 nm (emission), while for R, optimal wavelengths were 310 nm (excitation) and 380 nm (emission). The calibration curves using FD in the range of 0.01-20 ng/mL showed linearity with correlation coefficients > 0.999. The LOD and LOQ values were 3.3 ng/mL and 11.1 ng/mL for Q, and 0.07 ng/mL and 0.22 ng/mL for R, respectively. The intra-day and inter-day precision values were below 3.3% for Q and 1.0% for R. Figure 1 shows typical LC-UV and LC-FD profiles for a 1 \(\upmu\)g/mL solution of both analytes under optimized conditions.