Study of fabrication of Fe3O4 nanoparticles polyether sulfone membrane (PES\Fe3O4 NPs) for the removal of methylene blue dye from aqueous solutions: Optimization through response surface methodology (RSM)

A three factor, three-level Box–Behnken experimental design combining with response surface modeling (RSM) and quadratic programming (QP) by Design Expert Version 7.0.0 was employed for maximizing methylene blue removal from aqueous solution by Fe3O4 nanoparticles polyether sulfone membrane (PES\Fe3O4 NPs) based on 17 different experimental data obtained in a lab-scale batch study. Three independent variables (initial pH of solution (pH0) ranging from 5 to 9, initial concentration of methylene blue (Ci) ranging from 5 to 15 ppm, and weight percent of modifier (Mp) ranging from 3 to 7 percent) were consecutively coded as x1, x2 and x3 at three levels (−1, 0 and 1), and a second-order polynomial regression equation was then derived to predict responses. The significance of independent variables and their interactions were tested by means of the analysis of variance (ANOVA) with 95% confidence limits (α = 0.05). The optimum values of the selected variables were obtained by solving the quadratic regression model, as well as by analyzing the response surface contour plots. The experimental conditions were determined to be pH0 = 7.54, Ci = 11.16 ppm, and Mp = 4.20, and the methylene blue removal efficiency was found to be about 91.58 %. Therefore, it is apparent that the response surface methodology not only gives valuable information on interactions between the factors but also leads to identification of feasible optimum values of the studied factors.