MWCNTs were wrapped by poly(sodium 4-styrenesulfonate) (PSS), and different amounts of raw and polymer wrapped MWCNTs were implemented to fabricate PES mixed matrix membranes by phase inversion method. Success of wrapping was probed by FTIR spectroscopy, and prepared membranes were characterized by SEM, AFM, porosity, and water contact angle measurements. Response surface methodology (RSM) was employed to optimize the permeate flux and dye removal efficiency of membranes with three variables of concentration, pH of dye solution, and membrane composition. A response surface (RS) with a D-optimal design was defined to build the mathematical model, minimize the number of experiments, and investigate the effect of parameters on the response. Adequacy of the obtained model was confirmed by means of variance analysis and additional experiments. Based on observed and predicted results, wrapping CNTs by PSS improved permeation flux and dye removal efficiency of MMMs. Validity of model was verified according to the good agreement between predicted and experimental results. Membrane mixed with 0.1 wt.% polymer wrapped MWCNTs offered the highest permeation flux as well as dye removal efficiency. According to the model response, in order to achieve a higher dye removal, an acidic pH and a moderate dye solution concentration are recommended. Additionally, basic solution pH (9.0) and a dilute dye solution are suggested to reach a higher permeation flux.
