Magnetic sludge-derived biochar (MSDB) was synthesized using response surface methodology (RSM) optimization, with sludge as the raw material and sodium pyrophosphate as the modifier. The structure and surface properties of MSDB were characterized using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), vibrating sample magnetometer (VSM), and Brunauer-Emmett-Teller (BET) analysis. These analyses revealed that MSDB is rich in functional groups and exhibits magnetic properties, facilitating the adsorption of Cu(II) via complexation and easy separation of MSDB through magnetic means. Batch adsorption experiments showed that under conditions of 25 °C and pH 3.0, with an MSDB dosage of 0.75 g L−1, a Cu(II) removal efficiency of 95.67 % was achieved. Thermodynamic studies demonstrated maximum adsorption capacities of 173.69 mg g−1 at 25 °C, 183.26 mg g−1 at 35 °C, and 197.96 mg g−1 at 45 °C. Additionally, the BP neural network model showed a high coefficient of determination (R2 = 0.9396) and a low mean squared error (MSE = 0.0268) in simulating the MSDB-Cu(II) adsorption process, confirming the robustness of the model in both data simulation and predictive accuracy. This method offers a promising approach for kinetic modeling and predicting adsorption behavior in related fields of study.
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