Final equation in terms of coded factors
9  Y = +  49.82 + 6.17 * A − 8.49 * B + 12.91 * C + 13.96 * D + 1.08 * A * B − 1.39 * A * C + 0.65 * A * D + 1.01 * B * C + 1.05 * B * D − 1.02 * C * D + 4.57 * A 2  + 2.12 * B 2  + 1  .05 * C 2  + 0.86 * D 2
The factors in the quadratic equation were coded to produce the response surface with limiting the responses into a range of −1 to +1. The ramp function graph for the maximum TC degradation rate is shown in Fig. 4. The optimization of experimental conditions was conducted for maximize the TC degradation at defined criteria of the variable. The developed quadratic model for the TC degradation (Eq. (8)) was applied as an objective function to the optimization of operating conditions. Consequently, the optimum parameters were achieved using the numerical technology based on the predicted model and the variable in their critical range. The maximum degradation of 95.01 % was achieved at pH = 9.9, TC concentration = 30.19 mg/L, PS concentration = 3.97 mM and reaction time = 119.98 min. in order to evaluation of the model validity, the experiments were carried out under the optimal operating conditions. 93.45 % TC degradation was obtained under the optimum operating conditions, which supported the results of the developed model.
Fig 4 Ramp function graph for the numerical optimization of TC degradation
The perturbation Plot of independent variables implies that reaction time (D) has the most significant effect (steepest slope) on the TC degradation rate, followed by S2O8−2 concentration (C) and TC concentration (B), whereas pH (A) has the lowest effect on the TC degradation. (Fig. 5).
Fig 5 The perturbation Plot of independent variables