Potential of Mean Force between Bare or Grafted Silica/Polystyrene Surfaces from Self-Consistent Field Theory

We investigate single and opposing silica plates, either bare of grafted, in contact with vacuum or melt phases, using self-consistent field theory. Solid-polymer and solid-solid nonbonded interactions are described by means of a Hamaker potential, in conjunction with a ramp potential. The cohesive nonbonded interactions are described by the Sanchez-Lacombe or the Helfand free energy densities. We first build our thermodynamic reference by examining single surfaces, either bare or grafted, under various wetting conditions in terms of the corresponding contact angles, the macroscopic wetting functions (i.e., the work of cohesion, adhesion, spreading and immersion), the interfacial free energies and brush thickness. Subsequently, we derive the potential of mean force (PMF) of two approaching bare plates with melt between them, each time varying the wetting conditions. We then determine the PMF between two grafted silica plates separated by a molten polystyrene film. Allowing the grafting density and the molecular weight of grafted chains to vary between the two plates, we test how asymmetries existing in a real system could affect steric stabilization induced by the grafted chains. Additionally, we derive the PMF between two grafted surfaces in vacuum and determine how the equilibrium distance between the two grafted plates is influenced by their grafting density and the molecular weight of grafted chains. Finally, we provide design rules for the steric stabilization of opposing grafted surfaces (or fine nanoparticles) by taking account of the grafting density, the chain length of the grafted and matrix chains, and the asymmetry among the opposing surfaces.