Phase behavior of polymer/nanoparticle blends near a substrate

We use the recent fluids density functional theory of Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005); J. Chem. Phys. 122, 094506 (2005)] to investigate the phase behavior of athermal polymer/nanoparticle blends near a substrate. The blends are modeled as a mixture of hard spheres and freely jointed hard chains, near a hard wall. There is a first order phase transition present in these blends in which the nanoparticles expel the polymer from the surface to form a monolayer at a certain nanoparticle concentration. The nanoparticle transition density depends on the length of the polymer, the nanoparticle diameter, and the overall bulk density of the system. The phase transition is due to both packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy, justifying the so-called "entropic push" observed in experiments. In addition, a layered state is found at higher densities which resembles that in colloidal crystals, in which the polymer and nanoparticles form alternating discrete layers. We show that this laminar state has nearly the same free energy as the homogeneously mixed fluid in the bulk and is nucleated by the surface.