Model for reversible nanoparticle assembly in a polymer matrix.

The clustering of nanoparticles (NPs) in solutions and polymer melts depends sensitively on the strength and directionality of the NP interactions involved, as well as the molecular geometry and interactions of the dispersing fluids. Since clustering can strongly influence the properties of polymer-NP materials, we aim to better elucidate the mechanism of reversible self-assembly of highly symmetric NPs into clusters under equilibrium conditions. Our results are based on molecular dynamics simulations of icosahedral NP with a long-ranged interaction intended to mimic the polymer-mediated interactions of a polymer-melt matrix. To distinguish effects of polymer-mediated interactions from bare NP interactions, we compare the NP assembly in our coarse-grained model to the case where the NP interactions are purely short ranged. For the "control" case of NPs with short-ranged interactions and no polymer matrix, we find that the particles exhibit ordinary phase separation. By incorporating physically plausible long-ranged interactions, we suppress phase separation and qualitatively reproduce the thermally reversible cluster formation found previously in computations for NPs with short-ranged interactions in an explicit polymer-melt matrix. We further characterize the assembly process by evaluating the cluster properties and the location of the self-assembly transition. Our findings are consistent with a theoretical model for equilibrium clustering when the particle association is subject to a constraint. In particular, the density dependence of the average cluster mass exhibits a linear concentration dependence, in contrast to the square root dependence found in freely associating systems. The coarse-grained model we use to simulate NP in a polymer matrix shares many features of potentials used to model colloidal systems. The model should be practically valuable for exploring factors that control the dispersion of NP in polymer matrices where explicit simulation of the polymer matrix is too time consuming.