Structure and Assembly of Dense Solutions and Melts of Polymer Tethered Nanoparticles

We generalize the microscopic Polymer Reference Interaction Site Model theory to study intermolecular pair correlation functions and collective structure factors of dense solutions and melts of polymer-tethered spherical nanoparticles. The complex interplay of entropy (translational, conformational and packing) and enthalpy (particle-particle attraction) leads to different structural arrangements with distinctive scattering signatures. Strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation occur as the total packing fraction and/or particle-particle attraction strength increase. A microphase spinodal curve is estimated by extrapolation of the inverse of the amplitude of the small angle scattering peak. For nanoparticles, twice the diameter of monomers, carrying a single tether the microphase spinodal temperature grows roughly as a power law function of packing fraction with an exponent much less than unity. Increasing the nanoparticle diameter lowers the microphase spinodal temperature and results in a qualitative change of its packing fraction dependence. The effect of nanoparticle size, number and length of tethers, position of the grafting sites, total packing fraction, and particle-particle attraction strength on the structure, scattering patterns and tendency for microphase ordering has been studied in detail.