## 3 Results and Discussion
### Optimisation of the Chromatographic Conditions
According to the basics of chromatography, elevation of temperatures reduces eluent viscosity and the observed backpressures, improves the sorption kinetics, increases the mass transfer and longitudinal diffusion, which result in shorter analysis times, but the resolution could suffer, especially for small molecules [43]. A similar effect (shorter time, but worse resolution) could be achieved by increasing the flow rate. The efficient combination of the two factors is a key to successful separation. The thorough examination of all combinations, even with only two factors to consider, can be time consuming and might not necessarily provide an optimal solution. Therefore, to facilitate the optimisation process, an experimental design was used. The central composite design (CCD) is generally accepted in chromatographic studies on various analytical stages from extraction to chromatographic separation [30]. It combines two-level full factorial design with axial or star points and at least one point at the centre of the experimental region being investigated. The design used in the present study comprised of four factorial and four axial runs, as well as five duplicates of the central point. After preliminary experiments setting the central point (flow rate, \(F_{R}\): 0.40 mL/min; temperature, \(T\) = 22 \({}^{\circ}\)C), the independent variables (\(F_{R}\), \(T\)) were tested on five different levels in the ranges of 15.0-29.1 \({}^{\circ}\)C for \(T\) and 0.26-0.54 mL/min for \(F_{R}\) (Table 1). Two responses were selected as a measure of efficiency of the method: resolution (\(R_{s}\)) and separation time (\(ST\), understood as the retention time of the last peak). As the two responses chosen have distinct targets, i.e., improving resolution usually means elongating analysis time, and the other way around, in order to establish optimal conditions a compromise is required. Therefore, a third response (\(D\)) was calculated using Derringer's desirability function (Equation (2)), which is defined as a geometric mean of the individual desirability functions (Equations (3) and (4)) [31; 32]. As the primary aim of the optimization was to minimize the analysis time while retaining the resolution still allowing reliable quantification of both analytes, the desirability function for \(R_{s}\) (Equation (4)) was centred at 1.5 (with the ranges of 1.3-1.7), which value is commonly accepted as a precondition for precise analysis. The ranges of the desirability function for \(ST\) (Equation (3)) were set between 5 and 8 min based on the experimental data with 5 min being the most and 8 min the least desirable result. The results were fitted with a second-order polynomial model (Equation (1)) and the insignificant coefficients (\(p>0.05\)) were eliminated using a backwards elimination process. The reduced equations calculated that way and statistical parameters obtained from ANOVA are presented in Table 2, and the corresponding response surfaces for the separation process are shown in Figures 3 and 4. The adjusted \(R^{2}\) (\(R^{2}\) adjusted for the number of terms in the model) values for all models (0.981-0.999) were well within the agreeable bounds of \(R^{2}>0.88\), which indicates good fitting of the experimental data with the calculated equations [44]. All models were found to be significant in the \(F\)-test with \(p\) value \(<0.0001\). The adequate precision, that is the measure of the response to deviation ratio, was in the range of 25.61-135.50, well above the desirable value of 4 [45]. The coefficient of variation (\(CV\)) for all models was calculated to be less than 10%, which demonstrated their good reproducibility. All ANOVA parameters show suitability of the established models for final optimisation calculations.