Kinetics of film formation by interfacial polycondensation.

An approximate analytical model of film formation by interfacial polycondensation is presented. The analysis requires knowledge of a minimal set of certain kinetic parameters (monomer diffusivities and reaction rate constants) and reaction conditions (monomer concentrations and thickness of the unstirred layer). The process proceeds as a succession of two or three markedly different kinetic regimes. Each regime (insipient film formation, slowdown, and diffusion-limited growth) sets a different pattern of local polymer accumulation, with important implications for the structure of the emerging film. At the incipient stage, a loose polymer film begins to emerge in a fixed narrow region inside the boundary layer, followed by gradual densification of the middle part of the film. A condition for film formation is thus formulated on the basis of our analysis. The model predicts that two different scenarios are possible, which depend on the permeability of the polymer: films with a low permeability to both monomers pass through an abrupt slowdown of film growth, whereas permeable films undergo a smooth transition between the incipient film formation and diffusion-limited regimes. The model incorporates the highly important effects of the accumulation of reactive end groups and the decrease of monomer diffusion with the polymer concentration on the kinetics of the process and film characteristics. In addition, the validity of the utilized mean-field approach is analyzed, and the analysis suggests a direct correlation between the roughness and the thickness of the film. The results are in good agreement with an earlier numerical study and the direct structural studies of polyamide membrane films.