In this work, we explore the effects of nanoparticle filling fraction, polymer chain length, and surfactant concentration on nanoparticle aggregation. We characterize the structure of the nano-composite using particle-particle radial distribution functions and the composite specific heat cV. With no surfactant added, the dependence of the specific heat on the filling fraction exhibits a maximum at a filling fraction of about 3.6 wt%, which we attribute to the nanoparticle agglomeration transition: at lower filling fractions the nanoparticles are in a dispersed state and for filling fractions exceeding 3.6 wt%, the nanoparticles show a tendency to agglomerate. The polymer-mediated particle-particle forces exhibit a more repulsive character in the case of longer chains than in the case of the shorter ones. We also show that the dispersed state of the nanocomposite becomes more stable as the molecular weight of polyethylene increases. This effect is most visible when the radius of gyration of the linear polymer exceeds the nanoparticle radius. The polymer gyration radius grows with nanoparticle filling fraction due to chain entanglement around the particles, which is typical in polymer reinforcement.
The addition of oleyl alcohol (a nonionic surfactant) reduces the effective attraction between the nanoparticles, further weakening the agglomeration, which was monitored via particle-particle contribution to the potential energy and the specific heat cV. Our results show that, for a surfactant concentration of greater or equal than 6.4 wt%, the particles remain in a homogeneously dispersed state, which is consistent with experimental findings.