Calculation of entropie terms governing nanoparticle self-assembly in polymer films

The entropic contribution to nanoparticle self-assembly in athermal polymer/nanoparticle composite blends were calculated by fluid density functional theory (DFT). The blend was modeled at a concentrated solution-like density with a total packing fraction of 0.3665 and the excess free energy was found to depend on free energy in the presence and absence of a hard wall. The only contributions to the free energy in a neat polymer film with no nanoparticles are found to be the chain configurational entropy and the monomer packing entropy. The polymer density profile in the mixed state at the phase transition is found to be nearly the same as in the neat polymer film. The DFT estimate of the entropic contribution shows that there is no layering transition and the nanoparticles replace the polymer smoothly and in direct proportion to their concentration.