In this research, the solid–liquid adsorption systems for MSAC (PbFe₂O₄ spinel-activated carbon)-phenol and pristine activated carbon-phenol were scrutinized from the thermodynamics and statistical physics (sta-phy) viewpoints. Experimental results indicated that MSAC composite outperformed pristine AC for the uptake of phenol from waste streams. By increasing the process temperature, the amount of phenol adsorbed onto both adsorbents, MSAC composite and pristine AC, decreased. Thermodynamic evaluations for MSAC demonstrated the spontaneous and exothermic characteristics of the adsorption process, while positive values of ΔG for pristine AC indicated a non-spontaneous process of phenol adsorption in all temperatures. In a mechanistic investigation, statistical physics modeling was applied to explore the responsible mechanism for phenol adsorption onto the MSAC composite and pristine AC. The single-layer model with one energy was the best model to describe the experimental data for both adsorbents. The adsorption energies of phenol onto both adsorbents were relatively smaller than 20 kJ/mol, indicating physical interactions. By increasing temperature from 298 to 358 K, the value of the absorbed amount of phenol onto the MSAC composite and pristine AC at saturation (Q_sat) decreased from 158.94 and 138.91 to 115.23 and 112.34 mg/g, respectively. Mechanistic studies confirm the significant role of metallic hydroxides in MSAC to facilitate the removal of phenol through a strong interaction with phenol molecules, as compared with pristine activated carbon.

A novel lead ferrite-magnetic activated carbon (lead ferrite-MAC) composite was developed using the chemical co-precipitation method. Instrumental analyses such as X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FTIR), and Brunauer–Emmett–Teller (BET) analysis were performed to characterize adsorbent. The uptake of phenol from aqueous solutions using the developed adsorbent was compared to that of pristine activated carbon. The maximum adsorption capacity of lead ferrite-MAC composite (145.708 mg/g) was more than that of pristine activated carbon (116.606 mg/g) due to the metal hydroxides coated on activated carbon since they improve the retention of phenol on the available active sites of adsorbent and create an additional electrostatic interaction with the phenol adsorbate. Regarding the high value of the coefficient of determination (R²) and adjusted determination coefficient (R²_adj), coupled with the lower values of average relative error (ARE) and minimum squared error (MSE), it can be found that the isothermal data for the lead ferrite-MAC adsorbent were in agreement with the isotherm models of Redlich-Peterson and Langmuir. From the kinetic viewpoint, pseudo-second-order and linear driving force models explained the phenol adsorption data for both adsorbents. The reusability tests for lead ferrite-MAC composite revealed that after six cycles, 85% of the initial adsorption capacity was maintained. The developed adsorbent can be successfully applied to uptake phenol from aqueous solutions.