Modeling the buildup of polyelectrolyte multilayer films having exponential growth

Two types of polyelectrolyte multilayer films have been reported in the literature. These are (i) films whose mass and thickness increase linearly as the number of deposited bilayers increases and (ii) films that grow exponentially. We present a model for the buildup of exponentially growing films that allows a discussion of the behavior of them in a unified manner. This model is based on the diffusion both in and out the whole film of part of the chains of at least one of the polyelectrolytes constituting the multilayer. In short, the film is brought into contact with the solution of polyelectrolytes that are able to diffuse into the film. Inside of the film, chains of this polyelectrolyte constitute the "free" chains. At the subsequent rinsing step, some of them diffuse outward from the film. The remaining chains leave the film as it is brought into contact further with the polyelectrolyte solution of opposite charge. As the "free" chains reach the film/solution interface, they are complexed by the polyelectrolytes of opposite charge. These complexes, which are composed of both types of polyelectrolytes, contribute to the formation of the additional mass of the multilayer. The model relies on the evaluation of the electrostatic potential in the film within the framework of the Debye-Huckel approximation and takes into consideration the Donnan effect, which is due to noncompensated fixed charges in the film. It also includes the situation where none of the polyelectrolytes diffuse within the multilayer, in which case the film grows linearly. The model predicts the existence of a free-energy barrier that prevents total diffusion of any "free" polyelectrolyte outward from the film during a rinsing step, following contact with a polyelectrolyte solution. It also predicts that usually only one of the two polyelectrolytes that comprise the film diffuses readily into it. Both polyelectrolytes that comprise the film can diffuse "into" and "out of" the multilayer only when the concentration of noncompensated fixed charges within the film is very small. Several predictions of the model are discussed in the light of experimental results that have already been published or are new.