Response surface optimization for producing microcellular polymethyl methacrylate foam using supercritical CO₂

A regression model constructed by response surface methodology was employed to optimize the relationships between the cell density of microcellular polymethyl methacrylate foam and three independent variables: foaming pressure, temperature, and time. A Box–Behnken Design statistical approach was employed to fit the available response data to a second-order polynomial response surface model. The analysis of variance of the model indicated that the interactions between the foaming pressure and temperature, and that between the foaming temperature and the saturation time, both positively affect the cell density. Experimental verification of the predicted optimum conditions of foaming pressure = 21 MPa, foaming temperature = 313 K, and saturation time = 6.9 h gave an actual maximum cell density of 20.86 × 10 9 cells/cm 3 , which is close to the data predicted by the regression model.