Response Surface Methodology for Modelling and Optimization of Chromium Adsorption onto Magnetic Carbon Nanocomposites

Magnetic carbon nanocomposites are promising adsorbents for toxic metal removal owing to their adsorption capacity and facile magnetic separation. In this study, Response Surface Methodology (RSM) using a Box–Behnken design was applied to investigate and optimize chromium removal from initially Cr(VI)-containing solutions using magnetic activated carbon (MAC) and magnetic biochar (MBC). The effects of pH, initial Cr(VI) concentration, adsorbent dose, and contact time were evaluated using quadratic regression models and analysis of variance (ANOVA). The RSM models were statistically significant for both adsorbents, with a stronger goodness-of-fit for MAC (R2 = 0.929, adjusted R2 = 0.835) than for MBC (R2 = 0.846, adjusted R2 = 0.640). For MAC, the largest fitted contributions were associated with initial Cr(VI) concentration and adsorbent dose, whereas the MBC response was more strongly associated with initial Cr(VI) concentration and contact time, including a significant pH × contact time interaction. Numerical optimization identified a model-predicted high-removal region for MAC at pH 5.33, an initial Cr(VI) concentration of 0.10 mg L−1, an adsorbent dose of 2.00 g L−1, and a contact time of 120.3 min, whereas the model-predicted maximum for MBC occurred at the boundary of the experimental domain. Random Forest and Support Vector Regression were additionally evaluated using leave-one-out cross-validation. For MAC, Random Forest yielded the numerically highest cross-validated performance (R2 = 0.613), although bootstrap uncertainty analysis did not support a definitive model ranking based on R2 and RMSE. Cross-validated predictive performance was substantially lower for the MBC dataset. Overall, RSM and machine learning provided complementary information on fitted response patterns, model-based optimization, and cross-validated predictive performance.