Structure of solvent-free nanoparticle-organic hybrid materials

We derive the radial distribution function and the static structure factor for the particles in model nanoparticle-organic hybrid materials composed of nanoparticles and attached oligomeric chains in the absence of an intervening solvent. The assumption that the oligomers form an incompressible fluid of bead-chains attached to the particles that is at equilibrium for a given particle configuration allows us to apply a density functional theory for determining the equilibrium configuration of oligomers as well as the distribution function of the particles. A quasi-analytic solution is facilitated by a regular perturbation analysis valid when the oligomer radius of gyration R(g) is much greater than the particle radius a. The results show that the constraint that each particle carries its own share of the fluid attached to itself yields a static structure factor that approaches zero as the wavenumber approaches zero. This result indicates that each particle excludes exactly one other particle from its neighborhood.