Mathematical Model for the Formation of Thin-Film Composite Membranes by Interfacial Polymerization: Porous and Dense Films

A general model for the formation of thin-film composite membranes, that considers both diffusion- and reaction-controlled interfacial polymerization, under non-steady-state conditions, has been developed. Special models for either diffusion-controlled or reaction-controlled interfacial polymerization with steady- and non-steady-state conditions have been obtained by simplification; these agree with similar models, where available, in the literature. The porosity of the thin film is dependent on the amount of water that diffuses with the aqueous monomer into the formed film. The analytical solution for the model is consistent with the effect of diamine concentration and successfully predicts it for a polysulfonamide composite membrane fabricated from 1,2-ethanediamine and a disulfonyl chloride. The model allows simulation of various factors that affect thin-film formation, particularly for those factors that are difficult to measure experimentally. This work significantly extends existing theories and provides an important guide for effective control of the thickness of the surface barrier layer of thin-film composite membranes prepared by interfacial polymerization.