(732c) Depletion, Bridging, and Ordering in Bare and Grafted Nanorod-Polymer Mixtures

We present a detailed study of polymer-nanorod composites.  Using integral equation theory  we have determined the structure and phase behavior non-interacting, attractive, and grafted nanorods in polymer melt.  Depletion-induced phase separation is predicted between polymer and rods of nearly all aspect ratios.  Miscibility is achieved by introducing a small amount of attractive interaction between polymer and nanoparticles.  At large polymer-nanoparticle attraction strengths a few polymer molecules bridge several nanoparticles giving rise to another phase separated regime.  Large diameter nanorods tend to be bridged my more than a single polymer layer (telebridging).  This creates a finite miscibility window below the depletion temperature and above the bridging temperature.

Small changes in nanorod aspect ratio induce a drastic narrowing of the miscibility window, particularly for thin nanorods.  However, as the rod radius of gyration approaches the radius of gyration of the polymer, the phase boundaries are nearly independent of aspect ratio.  Our work confirms previous experimental findings that depletion-driven phase separation is enhanced with increasing size of nanospheres.  However, we predict that nanorods display a subtle, and non-montonic dependence of the depletion line on the rod thickness.  In the bridging regime, larger nanospheres show enhanced bridging while nanorods display a non-monotonic behavior.  The width of the miscibility window is, therefore, a non-monotonic function of the nanorod thickness.  Close to both bridging-driven, and depletion-driven phase separation, the attractive force between rods increases with rod thickness, while remaining independent of rod length.  However, this attractive force operates at different inter-particle separations in the two regimes.  Our work with grafted nanorods (with various graft lengths) illustrates that even short polymer grafts at moderate grafting densities can prevent the entropic depletion-driven phase separation.  On the other hand, grafted nanoparticles are likely to form ordered, microphase separated structures within the polymer melt.