Self-consistent field modeling of adsorption from polymer/surfactant mixtures

We report on the development of a self-consistent field model that describes the competitive adsorption of nonionic alkyl-(ethylene oxide) surfactants and nonionic polymer poly(ethylene oxide) (PEO) from aqueous solutions onto silica. The model explicitly describes the response to the pH and the ionic strength. On an inorganic oxide surface such as silica, the dissociation of the surface depends on the pH. However, salt ions can screen charges on the surface, and hence, the number of dissociated groups also depends on the ionic strength. Furthermore, the solvent quality for the EO groups is a function of the ionic strength. Using our model, we can compute bulk parameters such as the average size of the polymer coil and the surfactant CMC. We can make predictions on the adsorption behavior of either polymers or surfactants, and we have made adsorption isotherms, i.e., calculated the relationship between the surface excess and its corresponding bulk concentration. When we add both polymer and surfactant to our mixture, we can find a surfactant concentration (or, more precisely, a surfactant chemical potential) below which only the polymer will adsorb and above which only the surfactant will adsorb. The corresponding surfactant concentration is called the CSAC. In a first-order approximation, the surfactant chemical potential has the CMC as its upper bound. We can find conditions for which CMC <CSAC . This implies that the chemical potential that the surfactant needs to adsorb is higher than its maximum chemical potential, and hence, the surfactant will not adsorb. One of the main goals of our model is to understand the experimental data from one of our previous articles. We managed to explain most, but unfortunately not all, of the experimental trends. At the end of the article we discuss the possibilities for improving the model.