A universal model for describing responsive performances of both positively and negatively responsive smart gating membranes

In this study, a universal model is developed for describing the responsive performances of both positively and negatively responsive smart gating membranes with structural and responsive parameters. The model is derived by assigning the membrane pore size change ratio before and after immobilizing responsive gates and the volume change coefficient as well as the stacking effect coefficient of responsive gates as independent dimensionless variables. The reliability and fitting precision of the proposed model have been validated by the experimental results of positively thermo-responsive and negatively Pb2+-responsive gating performances of smart gating membranes, which are prepared by immobilizing poly(N-isopropylmethacrylamide-co-4-acrylamidobenzo-18-crown-6) (PNMB) microgels in porous poly(ether sulfone) (PES) membranes as functional gates that exhibit both thermo-induced shrinking and Pb2+-induced swelling responsive characteristics. All the experimental data of both positively and negatively responsive gating performances of smart gating membranes fit well with the developed model. The proposed model provides new insights for describing and explaining the responsive gating performances of both positively and negatively responsive smart gating membranes, and offers rational guidelines for designing and fabricating smart gating membranes with desired responsive gating performances by predetermining the structural and responsive parameters of smart gates for various applications.