## 3 Results and Discussion
### Optimisation of the Chromatographic Conditions
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Run**} & \multicolumn{2}{c}{**Levels**} & \multicolumn{2}{c}{**Factors**} & \multicolumn{2}{c}{**Responses**} \\ \cline{2-7}  & \(T\) & \(F_{R}\) & \(T\) (\({}^{\circ}\)C) & \(F_{R}\) **(mL/min)** & \(ST\) **(min)** & \(R_{s}\) & \(D\) \\ \hline
1 & +1 & +1 & 27.0 & 0.50 & 4.583 & 1.29 & 0.000 \\
2 & +1 & \(-1\) & 27.0 & 0.30 & 7.591 & 1.49 & 0.228 \\
3 & \(-1\) & +1 & 17.0 & 0.50 & 5.561 & 1.42 & 0.442 \\
4 & \(-1\) & \(-1\) & 17.0 & 0.30 & 9.265 & 1.71 & 0.000 \\
5 & \(-1.41\) & 0 & 15.0 & 0.40 & 7.244 & 1.59 & 0.382 \\
6 & +1.41 & 0 & 29.1 & 0.40 & 5.501 & 1.36 & 0.316 \\
7 & 0 & \(-1.41\) & 22.0 & 0.26 & 9.620 & 1.66 & 0.000 \\
8 & 0 & +1.41 & 22.0 & 0.54 & 4.660 & 1.31 & 0.141 \\
9 & 0 & 0 & 22.0 & 0.40 & 6.282 & 1.50 & 0.479 \\
10 & 0 & 0 & 22.0 & 0.40 & 6.289 & 1.49 & 0.466 \\
11 & 0 & 0 & 22.0 & 0.40 & 6.283 & 1.49 & 0.466 \\
12 & 0 & 0 & 22.0 & 0.40 & 6.286 & 1.49 & 0.466 \\
13 & 0 & 0 & 22.0 & 0.40 & 6.289 & 1.49 & 0.466 \\ \hline \hline \end{tabular}  
* \(T\): temperature; \(F_{R}\): flow rate; \(ST\): separation time (retention time of the last peak; \(R_{s}\): resolution OA/UA acc. to Equation (5); \(D\): Total response acc. to Equation (2).  
\end{table} 
Table 1: Experimental variables, levels, design matrix and responses for the central composite design 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Response 1**} & \multicolumn{2}{c}{**Reduced Response**} & \multirow{2}{*}{\(R^{2}\)} & \multicolumn{2}{c}{**Adjusted**} & \multirow{2}{*}{\(F\)**-Value 3**} & \multirow{2}{*}{\(p\)**-Value 4**} & \multirow{2}{*}{\(CV\) (\%) 5**} & **Adequate** \\  & & **Model** & & & \(R^{2}\)2 ** & **Adequate** \\  & & & & & & & & **Precision** \\ \hline \multirow{2}{*}{\(ST\)} & \(6.31-0.64T-1.72F_{R}\) & \multirow{2}{*}{0.9993} & \multirow{2}{*}{0.9989} & \multirow{2}{*}{1960.31} & \multirow{2}{*}{\(<\)0.0001} & \multirow{2}{*}{0.91\%} & \multirow{2}{*}{135.50} \\  & \(+0.42F_{R}+0.177F_{R}\) & \multirow{2}{*}{0.9984} & \multirow{2}{*}{0.9976} & \multirow{2}{*}{1268.19} & \multirow{2}{*}{\(<\)0.0001} & \multirow{2}{*}{0.40\%} & \multirow{2}{*}{113.43} \\ \multirow{2}{*}{\(R_{s}\)} & \(1.49-0.08T-0.01T^{2}\) & \multirow{2}{*}{0.9887} & \multirow{2}{*}{0.9806} & \multirow{2}{*}{122.57} & \multirow{2}{*}{\(<\)0.0001} & \multirow{2}{*}{9.29\%} & \multirow{2}{*}{25.61} \\  & \(-0.12F_{R}+0.02T_{R}\) & \multirow{2}{*}{0.9887} & \multirow{2}{*}{0.9806} & \multirow{2}{*}{122.57} & \multirow{2}{*}{\(<\)0.0001} & \multirow{2}{*}{9.29\%} & \multirow{2}{*}{25.61} \\ \multirow{2}{*}{\(D\)} & \(0.47-0.04T+0.05F_{R}\) & \multirow{2}{*}{0.9887} & \multirow{2}{*}{0.9806} & \multirow{2}{*}{122.57} & \multirow{2}{*}{\(<\)0.0001} & \multirow{2}{*}{9.29\%} & \multirow{2}{*}{25.61} \\ \multirow{2}{*}{\(D\)} & \(-0.07T^{2}-0.02F_{R}\)\({}^{2}-\) & \multirow{2}{*}{0.9887} & \multirow{2}{*}{0.9806} & \multirow{2}{*}{122.57} & \multirow{2}{*}{\(<\)0.0001} & \multirow{2}{*}{9.29\%} & \multirow{2}{*}{25.61} \\ \multirow{2}{*}{\(D\)} & \(0.17T_{R}\) & \multicolumn{2}{c}{} & & & & & \\ \hline \hline \end{tabular}  
* \(T\): temperature; \(F_{R}\): flow rate; \(ST\): separation time (retention time of the last peak; \(R_{s}\): resolution OA/UA acc. to Equation (5); \(D\): overall desirability function acc. to Equation (2). \({}^{2}\)\(R^{2}\) adjusted for number of terms in the model. 3 Test for comparing model variance with residual (error) variance. 4 Probability of seeing the observed \(F\)-value if the null hypothesis is true. 5 Coefficient of variance.  
\end{table} 
Table 2: Response models and statistical parameters obtained from ANOVA. After reaching the optimal values for \(T\) and \(F_{R}\), the separation was conducted in the optimised conditions. The close consistency between the calculated and experimental responses (Table 3) shows the usefulness of the models in predicting the chromatographic behaviour of the analytes. The experimental resolution of 1.497 was considered sufficient for quantitative analysis.