As discussed earlier, the proposed mixed micellar system based on C
16MeImCl and Triton-X114 was used for the cloud point extraction and preconcentration of cobalt ions. To transfer the analyte ions into the micellar phase, we would convert the analyte ions to a complex hydrophobic molecule. Thus, APDC as a suitable ligand was used for the complexation of cobalt ions. Considering the absorption spectrum of the cobalt-APDC complex (
Figure 1), it was possible to measure the concentration of this ion at about 650 nm (wavelength of maximum absorption of the complex).
For quantitative extraction of cobalt ions by the mixed micellar system, the influences of various parameters affecting the extraction efficiency were primarily investigated using univariate optimization. In addition, a Box-Behnken design (BBD), which is a common response surface methodology (RSM) for experimental design, was used to investigate the effects of the mentioned variables and the probable interaction between them. The BBD always considers three coded levels (-1, 0, +1) for each variable. The number of experiments (N) required for the development of BBD is defined as N = 2k (k - 1) + C
0, where k is the number of variables to be tested, and C
0 is the number of repetitions at the central point (
37). Thus, five factors, including sample pH, amount of C
16MeImCl, the concentration of the chelating agent, amount of salt, and volume of Triton X-114 that could affect the extraction efficiency, were chosen according to the preliminary experiments (
Table 1). Other parameters such as temperature and extraction time, centrifuging rate, and time were kept constant. According to the above-mentioned equation, for five factors and three center points, 46 experimental runs were planned. Based on the matrix design (Appendix 1), 46 experiments were performed. The procedure used for the tests was the same as explained in section 2.3, using a standard solution of 1 mg L
-1 Co ions. The absorbance of the Co-APDC complex at 657 nm was used as the response. The experimental data were processed using Minitab 17 statistical software.
3.2. Optimization Using RSM Based on Box-Behnken Design
Applying the Box–Behnken design, a quadratic model was obtained to relate the analytical signal to the effective factors and their interactions. According to Appendix 2, all factors such as pH, ionic liquid, APDC, NaCl, and Triton X-114, except for their interactions [(pH × SAIL), (pH × APDC), (pH × Triton X-114), (pH × NaCl), (SAIL × APDC), (SAIL × TritonX-114), (SAIL × NaCl), (APDC × TritonX-114), (APDC × NaCl), and (Triton X-114 × NaCl)] were effective on the extraction efficiency. By ignoring the interactions from the suggested model, the following model was obtained, which is more consistent with the experimental data.
A = -2.5655 + 0.072075 pH + 0. 78696 SAIL + 4.440 APDC + 3.776 Triton X-114 + 1.3162 NaCl - 0.006097 pH × pH - 1.3502 SAIL × SAIL - 37.02 APDC × APDC - 1.9847 Triton X-114 × Triton X-144 - 0.8623 NaCl × NaCl
The model adequacy was evaluated by various statistical analysis tests such as the analysis of variance, residual analysis, and coefficient of determination. According to the ANOVA results in Appendices 2 and 3, all of the main effects, except for their interactions, were significant (P < 0.05), and the lack of fit of the model was not significant (P > 0.719) confirming the validity of the model. The validation was also done using the coefficient of determination (R
2) and the analysis of residuals. The R
2 (0.9983), R
2 adj. (0.9978), and R
2 pred. (0.9971) were much close to one, showing the adequacy of the proposed model. The analyses of residuals confirmed a normal distribution, which is the other evidence of the model's validity (
Figure 6). The response surface plots (Appendix 4) represent the effects of experimental variables and their mutual interactions on the analytical signal. These results were obtained by varying two important factors, while the third factor (in the middle point) was kept constant. These surfaces also showed the main five factors' effects (pH, SAIL, APDC, NaCl, and Triton X-114) on the analytical signal. Derringer's desirability function (D) was used to find the optimal conditions to maximize the analytical signal. The overall desirability is a geometric mean of the individual desirability values (di) that should be close to one (
39,
40). The optimum conditions were as follows: pH = 5.8939, SAIL concentration (mM): 0.2899, APDC volume (mL): 0.0599, NaCl concentration (%): 0.7641, and Triton X-114 volume (mL): 0.9515, which are required for the maximum analytical signal with overall desirability of D = 1. These results are in good agreement with those obtained without implementing the experimental design.
Normal probability plot of residuals for extraction efficiency of cobalt ions