Application of the full factorial design to improving the properties of CoFe2O4 nanoparticles by simultaneously adding apple cider vinegar and agarose

•The full factorial design of experiment was used to optimize the properties of CoFe2O4 nanoparticles.•The effect of simultaneous presence of agarose and apple cider vinegar was investigated.•The optimal amounts of agarose and apple cider vinegar were determined to achieve the best properties.•The structural properties of the synthesized CoFe2O4 nanoparticles were determined by the Rietveld refinement method and TEM. In this paper, the full factorial design of the experiment was used to optimize the structural, microstructural, and magnetic properties of the cobalt ferrite nanoparticles, which were synthesized using sol–gel method in the simultaneous presence of agarose and apple cider vinegar. The analysis of variance showed that both agarose and apple cider vinegar are statistical significance but there was no significant interaction between these two factors. The X-ray diffraction confirmed the formation of high purity CoFe2O4 nanoparticles after calcination at 800 ℃. Also, the Rietveld refinement results showed a decrease in average crystallite size from 36.8 to 17.4 nm by adding these additives. The results obtained from the main effect plot revealed that simultaneous adding 1.5 g of agarose and 5 ml of apple cider vinegar leads to the optimal conditions, so that its coercivity and magnetization saturation were equal to 1110.3 Oe and 71.8 emu/g, respectively.