## 3 Results and Discussions
### Optimization of Dispersive Solid-Phase Extraction Procedure
#### 3.2.4 Full Factorial Experimental Design for the Optimization of the d-SPE Method  
The 2-Level factorial design (2\({}^{\text{k}}\)-FD, k is the factor's amount) is the most commonly used factorial design. Herein, the selected factors were investigated at two levels, i.e., a high and a low level which are coded as \"+\" or \"+1\" and \"-\" or \"-1\", respectively. In this work, the following factors were optimized: mass of NaGO (m), time of adsorption (t\({}_{\text{ads}}\)), time of desorption (t\({}_{\text{des}}\)) and concentration of the acid used as eluent (C\({}_{\text{acid}}\)). Therefore, 16 experiments were required, which were conductedin duplicates and two center points were added, resulting in a total sum of 34 experiments. Table S2 shows the examined levels and the matrix that was obtained. The run order of the experiments was randomized in order to eliminate systematic errors.  
The regression models for all metals were found to be statistically significant. Criteria for rejecting an outlier, coming from the errors' normal distribution, require that the standardized residuals must exhibit mean zero and unit variance [31]. Therefore, the standardized residuals must have values up to \(\pm\)3. If higher standardized residuals were observed, they were considered as outliers and they were discarded from further statistical analysis. For the construction of the mathematical model, ANOVA was used to evaluate the statistical significance of each variable.  
For the examined metals, their linear term, their quadratic and interactions were studied for a confidence level 95%. Thus, p values lower than 0.05 mean that the factor or the interaction of factors has a statistically significant effect. Table S3 shows the regression analysis for the six elements. Bold letters indicate the significant factors and/or their interactions. The pareto charts for Ba, Cd, Ni, Cu, Zn and Pb are presented on Figure S1. As can be observed, different experimental factors (i.e., acid concentration for Cd, Ba, Cu and Zn, as well as sorbent mass for Zn, Cu and Ni, \(\rm{t_{des}}\) for Ba and Ni and \(\rm{t_{ads}}\) for Ni) and interactions of factors (e.g., interaction of sorbent mass and desorption time for Ni) were found to be significant. In principle, the quantity of the sorbent has to be sufficient to provide adsorption of the target analytes, the adsorption and desorption time have to be sufficient to achieve adsorption and desorption of the analytes, respectively, while the concentration of the acid has to be sufficient to provide desorption of the adsorbed metal ions.  
From the experimental data, it is clear that there is a different behavior under the specific experimental conditions between the examined analytes. Thus, in order to obtain the optimum conditions, a compromise was conducted using Derringer's Desirability Function. Therefore, the experimental conditions that resulted in the optimum extraction recovery for the examined metals are: mass = 25 mg, \(\rm{t_{ads}}\) and \(\rm{t_{des}}\): 5 min, nitric acid concentration: 1.5 M. It is important to mention that hydrochloric acid (HCl) and acetic acid (CH\({}_{3}\)COOH) were also tested at the concentration of 1.5 M. Differentiation of the % extraction recoveries was \(\pm\)10% for the examined metals. Therefore, similar behavior of the three examined eluents was observed and nitric acid was finally chosen.