Coarse-Grained Model. To compute free energy of interaction between polymer-grafted NPs in a polymer matrix, we adopted a coarse-grained model similar to one we previously used. Polymer chains were treated as Kremer-Grest bead-chains, where beads, each of size 𝜎 and mass 𝑚, represent short segments of the chain. Chain lengths of 𝐿 = = 10 and 𝐿 > = 20 beads were used for modeling the grafts and the polymer matrix (Fig. ). The NP cores were modeled as rigid spheres of radius 𝑅 ?@ = 3𝜎 and mass 𝑚 ?@ = 216𝑚. The grafting points on the surface of the NP cores were uniformly distributed across the surface. We studied both bare NPs (with no grafts) as well as polymer-grafted NP cores of grafting densities in the range Γ = = 0.15-0.4 chains/𝜎 ! .