Liquid state theory of the structure and phase behaviour of polymer-tethered nanoparticles in dense suspensions, melts and nanocomposites

We have studied the structure and phase behaviour of spherical nanoparticles grafted with a modest number of polymer tethers in the dense suspension and pure melt states, and dissolved in a homopolymer matrix, using the polymer reference interaction site model integral equation theory. In the absence of a polymer matrix, fluids of tethered nanoparticles exhibit strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation as the total packing fraction and/or nanoparticle attraction strength increase. For nanoparticles of core diameter twice that of the monomer, carrying one, two and four tethers, the microphase spinodal temperature grows roughly as a power-law function of packing fraction. As the number of polymer tethers increases, the microphase spinodal curve shifts to lower temperatures due to steric shielding of the nanoparticle core. In the presence of a homopolymer matrix, the microphase spinodal curve of single-tethered particles exhibits both dilution-like and depletion-like features and a non-monotonic dependence of the spinodal temperature on matrix chain length. As the number of tethers is increased, the microphase curves become more dilution-like and the effect of matrix degree of polymerisation, particle size and tether length on the apparent spinodal temperature diminishes.