In this study, a minimum-run resolution IV and central composite design have been developed to optimize tetracycline removal efficiency over mesoporous carbon derived from the metal-organic framework MIL-53 (Fe) as a self-sacrificial template. Firstly, minimum-run resolution IV, powered by the Design-Expert program, was used as an efficient and reliable screening study for investigating a set of seven factors, these were: tetracycline concentration (A: 5-15 mg/g), dose of mesoporous carbons (MPC) (B: 0.05-0.15 g/L), initial pH level (C: 2-10), contact time (D: 1-3 h), temperature (E: 20-40 °C), shaking speed (F: 150-250 rpm), and Na+ ionic strength (G: 10-90 mM) at both low (-1) and high (+1) levels, for investigation of the data ranges. The 20-trial model was analyzed and assessed by Analysis of Variance (ANOVA) data, and diagnostic plots (e.g., the Pareto chart, and half-normal and normal probability plots). Based on minimum-run resolution IV, three factors, including tetracycline concentration (A), dose of MPC (B), and initial pH (C), were selected to carry out the optimization study using a central composite design. The proposed quadratic model was found to be statistically significant at the 95% confidence level due to a low P-value (<0.05), high R2 (0.9078), and the AP ratio (11.4), along with an abundance of diagnostic plots (3D response surfaces, Cook's distance, Box-Cox, DFFITS, Leverage versus run, residuals versus runs, and actual versus predicted). Under response surface methodology-optimized conditions (e.g., tetracycline concentration of 1.9 mg/g, MPC dose of 0.15 g/L, and pH level of 3.9), the highest tetracycline removal efficiency via confirmation tests reached up to 98.0%-99.7%. Also, kinetic intraparticle diffusion and isotherm models were systematically studied to interpret how tetracycline molecules were absorbed on an MPC structure. In particular, the adsorption mechanisms including "electrostatic attraction" and "π-π interaction" were proposed.
Keywords: adsorption mechanisms; central composite design; mesoporous carbon; metal-organic framework; minimum-run resolution IV; response surface methodology.