Free energy model for layer-by-layer processing of polyelectrolyte multilayer films

A free energy model for the processing of polyelectrolyte multilayer (PEM) films via layer-by-layer assembly is developed for polyelectrolyte components of pH-tunable charge density, allowing for the prediction of cumulative thickness as a function of number of deposited layers, as well as the hydrated layer thickness and concentration of each adsorbed layer within the PEM. Using a "sharp interface" approximation in which the deposition of each layer is controlled by the effective charge density at the surface of the previously adsorbed layer, PEM build-up on a SiO2 substrate is predicted to be linear with number of layers deposited after an initial nonlinear "ramp up" regime extending three to four bilayers in thickness. For a system of weak polyelectrolytes deposited at the same pH, layer thickness of both film components is predicted to be a strong function of bath pH, transitioning from very thick layers when one species is fully charged and the second is of intermediate charge density to molecularly thin layers when both species are fully charged, qualitatively capturing the behavior observed for poly(acrylic acid) and poly(allylamine hydrochloride) under conditions of low ionic strength (Macromolecules 2000, 33, 4213).