Modeling the buildup of exponentially growing polyelectrolyte multilayer films

We develop a simplified one-dimensional model to describe the build-up of exponentially growing polyelectrolyte multilayer films. The model accounts for the migration of polycations in and out of the film, the existence of an energetic barrier at the film surface, and film dissolution. All the electrostatic interactions are modeled using a screened Coulombic potential. For appropriately chosen model parameters, the model predictions are in quantitative agreement with experimental results. The model predicts that the exponential-to-linear growth transition is set kinetically, and this transition occurs when the dipping time is not long enough for unbound polycations to uniformly distribute inside the film. Additionally, for a film to exhibit exponential growth, it is essential that very few unbound polycations move out of the film during the rinsing step that follows after dipping in a solution of polycations. The model predicts that this criterion is satisfied either when a sharply peaked energetic barrier is present at the film surface or when the film swells. Furthermore, the model predicts that when dipping time, t(d), is increased proportionally with H(2), where H is the film thickness, the film will grow exponentially as long as k(d)t(d) << 1, where k(d) is the dissolution rate. The results of this work shed light on the criteria that need to be satisfied for a film to grow exponentially, and could help in exercising better control over the thickness of polyelectrolyte multilayer films.