Mathematical Model of Graphene Yield in Ultrasonic Preparation

Based on the Box–Behnken design (BBD) methodology, an experimental study of the preparation of graphene using ultrasonication was conducted. The yield of graphene served as the response variable, with ultrasonication process time, ultrasonic power, the graphite initial weight, and their interactive effects acting as the independent variables influencing the yield. A multivariate nonlinear regression model was established to describe the ultrasonic production of graphene. Verification of the experiments suggests that the developed multivariate nonlinear regression model is highly significant and provides a good fit, enabling an effective prediction of the graphene yield. The yield of graphene was found to increase with higher ultrasonic power but decrease with longer ultrasonication times and the initial weight of the graphite. The optimal process parameters according to the regression model were determined to be 30 min of ultrasonication time, an ultrasonic power of 1500 W, and a graphite initial weight of 0.5 g. Under these conditions, the yield of graphene reached 31.6%, with a prediction error of 2.8% relative to the actual value. Furthermore, the results were corroborated with the aid of scanning electron microscopy (SEM), Raman spectroscopy, and transmission electron microscopy (TEM). It was observed that under constant ultrasonic power and graphite initial weight, a reduction in the ultrasonication processing time led to an increase in the thickness of the graphene. Continuing to increase the ultrasonication time beyond 30 min did not decrease the thickness of the graphene but rather reduced its lateral size. Decreasing the ultrasonic power resulted in thicker graphene, and even with an extended ultrasonication time, the quality of the graphene was inferior compared to that produced under the optimal processing parameters.