Modeling the particle size of nanomaterials synthesized in a planetary ball mill

Planetary ball milling (PBM) synthesis of nanoparticles involves conducting several trials to obtain the desired size. Mathematical modeling of the PBM process is a tool to tackle the issue of PBM synthesis. In this study, a conceptual model was proposed by integrating the kinematics of the PBM process along with the breakage mechanism of a material to determine particle size at different milling parameters and hence be able to select appropriate milling parameters for PBM synthesis. The conceptual model was tested for hydroxyapatite, zeolite and fly ash material. The conceptual model successfully simulated the size-reduction mechanism in PBM and predicted the particle size of the tested material with good accuracy. The most sensitive milling parameters were found to be the milling speed followed by the vial volume, milling time, and ball to powder ratio. The material properties input parameters were observed to be less sensitive than the milling parameters. The PBM model may be used as a prediction tool for determining the appropriate milling parameters needed in synthesizing any nanomaterial by knowing the material properties.