Magnetic cobalt–chromium ferrite and ferrite cobalt nanoparticles were synthesized via the hydrothermal method. The resulting materials were characterized using field emission scanning electron microscopy (FE-SEM), X-ray diffraction (XRD), Transmission electron microscope(TEM,HRTEM) vibrating sample magnetometry (VSM), and photoluminescence spectroscopy (PL). The adsorption capacity of methylene blue dye onto the synthesized Co〖Cr〗_0.6 〖Fe〗_1.4 O_4 , Co〖Fe〗_2 O_4nanoparticles was investigated as a function of dye concentration, temperature, adsorbent dosage, pH, and contact time. The maximum adsorption capacity was observed at a dye concentration of 0.03 g/L, temperature of 25 °C, adsorbent dosage of 0.2 g/L, pH =7, and a contact time of 45 minutes.
Several isotherm models were evaluated, including the single-parameter Henry model, two-parameter Freundlich and Temkin models, three-parameter Redlich–Peterson model, and four-parameter Baudu and Fritz–Schlunder models. The best-fitting models were selected based on the highest correlation coefficient (R²) and the lowest sum of squared errors (SSE). Furthermore, various kinetic models were analyzed, among which the modified pseudo-second-order model provided the best fit for describing the adsorption of methylene blue onto the nanoparticles. Finally, thermodynamic parameters such as Gibbs free energy, enthalpy, and entropy changes were calculated to evaluate the nature of the adsorption process.