Simulation of Interaction Forces between Nanoparticles:  End-Grafted Polymer Modifiers.

The interaction forces between nanoscale colloidal particles coated with end-grafted Lennard-Jones homopolymers are calculated using off-lattice Monte Carlo simulations in the NVT ensemble. The focus of this work is on grafted polymers that are of approximately the same size as the nanoparticle, a regime intermediate to the star-polymer and Derjaguin limits. The effects of chain length (N), nanoparticle diameter (σc), grafting density (ρa), and colloid-polymer and polymer-polymer interaction energies (εcp and εpp) on the polymer-induced force between the nanoparticles are explored. The inclusion of attractive dispersion interactions between the particle and polymeric modifier results in either long-ranged attraction and short-ranged repulsion or pure repulsion, depending on the molecular parameters. The polymer-induced attraction occurs even under good solvent conditions below a threshold grafting density (ρa) and chain length (N) and could be attributed to both bridging (colloid-polymer) and intersegmental (polymer-polymer) attraction. Above the threshold ρa and N values, chain entropy and excluded volume effects begin to dominate and lead eventually to polymer-induced repulsion and, consequently, nanoparticle stabilization. These results point to the importance of considering dispersion attractions between grafted segments and the nanoparticle surface in modeling these high-curvature colloid interactions.