The Effect of Graft Density on the Ordering of Block Copolymer Grafted Nanoparticles

The effect of graft density and length on the ordering of spherical nanoparticles with block copolymer (BCP) grafts was investigated using a dissipative particle dynamics model with a hard nanoparticle potential and protracted colored noise dynamics (PCND). The blocks in the BCP grafts were of equal volume fraction and thus formed lamellae with the nanoparticles within the core block domain. It was found that decreased graft density increases the energy barrier when graft length was kept constant, but when the total amount of polymer per particle is constant, the energy barrier appeared constant until very low graft density. Lower graft density sharply increased the energy barrier to forming lamellae significantly, rendering sampling over that barrier, even with PCND, exceedingly slow. This is caused by a combination of congestion of nanoparticles in the center of the nanoparticle rich domains and the formation of small aggregates at low graft densities.