Mathematical model of charge and density distributions in interfacial polymerization of thin films

Abstract

A general model for interfacial polymerization is proposed and solved numerically. The model takes into account diffusion and reaction of monomers, presence of unreacted functional groups on the growing polymer, and solubility effects. The formation of a polyamide film in composite separation membranes is taken as an example. The evolution of the concentrations of the polymer and unreacted moieties are followed explicitly, thus enabling the calculations of the limiting thickness and the asymmetric distribution of density and charge in the resulting film. Such knowledge is important for the prediction of rejection and transport properties of the film. The effects of reaction kinetics, monomer concentrations, and hydrodynamic conditions on the properties of the film are analyzed, and a number of analytical correlations are developed.

Pressure Retarded Osmosis and Forward Osmosis Membranes: Materials and Methods

“…Freger et al presented a mathematical model for IP and investigated TEM-cross sections of membranes. They concluded that the PA-layer is heterogeneous and cannot be characterized by a single value of parameters such as charge or local polymer density [90,91]. Furthermore, they proposed that IP proceeds in three markedly different kinetic regimes.…”

An experimental study of polyurea membrane formation by interfacial polycondensation

“…Some recent theoretical and simulation studies [11,12] propose an alternative mechanistic picture in which the reaction intermediates (the oligomers) diffuse away from the site of reaction, reacting with other oligomers and the monomers as they diffuse. There is no explicit phase separation leading to film formation in such mechanisms, and what can be called the 'film' is the region occupied by the oligomeric species.…”

Interfacial polycondensation—Modeling of kinetics and film properties

“…In the second, the reaction is assumed to occur in a reaction zone which lies on the organic side of the interface mentioned above, and the polymer formed is excluded from the reaction zone as it forms; the reaction zone gets pushed into the organic phase as the film grows [12,13,15,17]. In the third, the reaction is assumed to occur in a steady reaction zone having a finite thickness, in which the polymer forms and accumulates (the viscosity in the zone increasing as a result), ultimately taking on a gel-like form [16]. In the first two approaches, the film thickness is explicitly calculated, increases with time and increases the diffusion resistance with time.…”

“…Experimental evidence [3,5,6,11,[18][19][20][21] points to a strong influence of the conditions employed in the preparation on the nature and properties of the film that forms. However, most of the models [7][8][9][10][11][14][15][16][17] focus on the kinetics and the variation of film thickness with time, and do not attempt to predict quantitatively the polymer properties as a function of process parameters. Properties such as molecular weight, polydispersity and crystallinity affect important characteristics of the polymer [20][21][22] such as mechanical properties, viscosity, ease of processing, permeability.…”