Effective interactions and self-Assembly of hybrid polymer grafted nanoparticles in a homopolymer matrix

We apply the microscopic polymer reference interaction site model integral equation theory to study the structure and phase behavior of spherical nanoparticles with six symmetrically grafted chains in a homopolymer matrix that is chemically identical to the grafted polymer. Calculations of the particle-particle potential of mean force (PMF), pair correlation functions, and collective structure factors under athermal conditions and in the presence interfiller attractions are presented. Polymer grafted nanoparticles disperse or aggregate in the homopolymer matrix depending on how much of the filler surface is effectively covered by the tethered chains which sterically shield direct intercore attractions. If the nanoparticle volume is less than its total tether analogue, the filler surface is well shielded and nanoparticles tend to disperse. For smaller filler cores (~2 nm) the grafting density is more brush-like, and the PMF becomes more attractive at contact with increasing matrix chain length due to decreasing wettability of the tether layer. For larger particles with much lower grafting density, the effect of matrix chain length on the PMF is different, and for all matrix lengths, the PMF at contact can be switched from attractive to repulsive by increasing the grafted chain length. At nonzero filler concentrations, nanoparticles with tether volume matching the filler core volume exhibit a critical attraction strength below which repulsive forces dominate resulting in good dispersion. Above the critical attraction strength, enthalpic effects dominate and the PMF becomes increasing attractive at contact and favors nanoparticle aggregation. When the tether and matrix chain lengths are equal, as the nanoparticle size increases less of its surface is shielded and modest clustering occurs due to direct core-core attraction and matrix-induced depletion attraction. The microphase spinodal temperature of nanoparticles with six grafted chains monotonically decreases upon homopolymer addition ("dilution" behavior), while nanoparticles with only one or two grafted chains exhibit subtle competition between dilution and matrix-mediated depletion attraction that increases their microphase separation temperature.